Fundamentals of Music Theory

🧭 Overview

🧠 One-sentence thesis

This book teaches the fundamentals of music theory—primarily stave notation, scale, key, harmony, and metre—while acknowledging that this system represents a particular European-oriented way of knowing music, not a universal or scientific account of all musical practice.

📌 Key points (3–5)

• What "music theory" means here: not a scientific theory, but a particular academic discipline and way of talking/thinking about music using stave notation.
• What "fundamentals" means: not elementary or simple; it requires sophisticated thinking and a combination of practical and conceptual skills.
• Common confusion: "music theory" sounds universal, but the system taught here is oriented to white European discourse from the past 150 colonial and post-colonial years—human musical imagination goes far beyond these classroom conventions.
• Where concepts come from: musical concepts originate in physical, human, cultural contexts of performance and perception; notation is a technology that visualizes and shapes our thinking.
• Why this system dominates: stave notation has become a widespread, globalized, influential technology, especially institutionalized in the UK.

🎯 What this book teaches (and what it doesn't)

🎯 The scope: literacy in stave notation

• The focus is mainly on literacy—learning to write down a musical language.
• Core topics covered:
  • Building blocks of stave notation
  • Scale and key
  • Harmony and metre

❌ What "music theory" is NOT

Music theory in this context: not a scientific theory that can account for features of the natural world; rather, it is a particular way of knowing, connected to how you can talk and think about music.

• Don't confuse: "theory" here does not mean a testable scientific hypothesis.
• "Fundamentals" does not mean elementary—it requires sophisticated thinking.
• "Music" in "music theory" does not give the full picture of human musical creativity; it signifies an orientation to white European discourse about music.

🌍 The limits of this system

• The scope of human musical imagination and creativity goes way past the classroom conventions of music theory.
• This dominant knowledge system is profoundly oriented to European notions of music born of the past 150 colonial and post-colonial years.
• Example: Many musical traditions and practices exist outside stave notation and European harmonic concepts.

🧠 Where musical concepts come from

🧠 Concepts originate in human experience

• Musical concepts come from people in the world—they start in the physical, human, cultural context of performance and imagination.
• Bodies perceive the physical vibrations of materials and make sense and patterns out of these experiences.
• Musical concepts don't start as symbols on paper; they emerge from embodied, cultural practice.

🛠️ Notation as technology

Musical notation, in its long and varied history, is a technology.

• Through notation we:
  • Write down concepts
  • Visualize them
  • Learn them
  • Imagine and create with them
• Every successful human technology integrates with our lives and shapes our thinking and imagination.
• Stave notation, as a form of literacy, has become a widespread, globalized, influential technology.

🔄 How notation shapes thought

• Notation is not neutral—it is a tool that influences how we conceptualize music.
• Example: Learning stave notation trains you to think in terms of pitches on a staff, bar lines, and harmonic progressions; other musical traditions may conceptualize sound differently (e.g., timbre, gesture, oral transmission).

🏛️ The institutional context

🏛️ Stave notation in the UK

• In the UK, the five-line stave is a dominant and thoroughly institutionalized language.
• Learning music theory generally means learning to read and write music notation.
• Many learners take it for granted that "music theory" and "reading/writing notation" come together.
• This assumption is more likely if you are already embedded in this institutional context.

⚠️ Why this matters

• Recognizing the European, colonial origins of this system helps learners understand:
  • Why certain concepts are emphasized (e.g., major/minor scales, functional harmony)
  • Why other musical traditions may not fit neatly into this framework
  • That fluency in this language is valuable but not exhaustive of musical knowledge

📚 How to use this book

📚 Structure and navigation

• The book is organized into topics.
• Each topic includes:
  • Video lecture links
  • Explanatory content (text and figures)
  • Suggestions for further reading
  • Transcripts at the end of each section
• Topic 0 (this introduction) is delivered independently of other topics.
• You can go straight to Topic 1 (the rudiments of music theory and notation) and return to Topic 0 when ready.

🗺️ Cross-references

• Because the videos originated from an openly shared course, presenters may cross-refer to lectures, topics, chapters, or "weeks."
• When this happens, return to the layout and organization of this resource to navigate as you wish.

🧭 Overview

🧠 One-sentence thesis

Music theory as taught here is not a scientific theory but a culturally shaped system of literacy and concepts rooted in white European discourse, institutionalized through colonial-era exam systems, that legitimizes certain musical knowledge while excluding others.

📌 Key points (3–5)

• Not scientific: Music theory does not explain natural-world phenomena; it is a particular way of knowing, talking, and thinking about music.
• Cultural, not universal: The "music" in music theory signifies an orientation to white European discourse, born of 150 colonial and post-colonial years, not the full scope of human musical creativity.
• Literacy-focused: The course teaches stave notation as a technology for communicating musical ideas—concepts like scale, key, harmony, and metre—but these concepts originate from people and cultural contexts, not from nature.
• Common confusion: Learning music theory often means learning to read/write notation, especially common practice harmony (European tonal music spanning ~2.5 centuries), but this is cultural convention, not scientific fact.
• What gets excluded: Prescribing certain ways of expressing knowledge (literacy, notation) makes other types of musical knowledge appear illegitimate or get skipped over.

🎓 What music theory is (and isn't)

🔬 Not a scientific theory

Music theory is not a scientific theory that can account for features of the natural world.

• It does not explain physical phenomena the way acoustics (the science of sound) does.
• Sound is real and material, but music theory is largely cultural convention.
• Instead, music theory is "a particular way of knowing, connected to how you can talk and think about music."

📖 A form of literacy

• The focus is on literacy: a musical language you learn to write down.
• Stave notation is a technology designed to communicate musical ideas.
• Being fluent in any music language requires a combination of practical and conceptual skills—it is challenging and sophisticated.
• Don't confuse: "fundamentals" does not mean elementary; "theory" does not mean scientific.

🌍 Culturally specific, not universal

• The "music" in music theory signifies an orientation to white European discourse about music.
• This dominant knowledge system is oriented to European notions of music born of the past 150 colonial and post-colonial years.
• The scope of human musical imagination and creativity goes way past the classroom conventions of music theory.
• Example: Many musical traditions and practices exist outside stave notation and European harmonic concepts, but they are not centered in this system.

🧩 Where musical concepts come from

🧩 Origins in human culture

• Musical concepts come from people in the world—from the physical, human, cultural context of performance and imagination.
• Bodies perceive the physical vibrations of materials and make sense and patterns out of these experiences.
• Musical concepts don't start off as symbols on paper; they begin in lived experience.

🛠️ Notation as technology

• Musical notation has a long and varied history; it is a technology.
• Through notation, we write down, visualize, learn, imagine, and create with musical concepts.
• Every successful human technology integrates with our lives and shapes our thinking and imagination.
• Stave notation has become a widespread, globalized, influential technology.

🎼 What this course teaches

• The course teaches the building blocks of stave notation as a system.
• Focus concepts: scale and key, harmony and metre.
• The apparatus of music theory more generally includes various—potentially unlimited—languages and terminology that people can use to think about music.
• Beneath all languages, including music-theoretic languages, we find concepts and ideas.

🏛️ Institutionalization and colonial history

🏛️ The UK exam system

• In the UK, the five-line stave is a dominant and thoroughly institutionalized language.
• Learning music theory generally means learning to read and write music notation; many people take it for granted that these two things come together.
• This is especially true if you are familiar with taking formal music exams.

🎵 Common practice harmony

Common practice harmony: a harmonic language that roughly unites European tonal music for around 2.5 centuries up to the twentieth century.

• It spans an array of styles and so-called eras of European classical music: late Baroque, Classical, Romantic.
• At the heart of the majority of music exam systems is common practice harmony.

🌐 Colonial expansion of the exam system

• The graded music examination system started in London in 1877 (the later part of the common practice period).
• Within 25 years—by the start of the twentieth century—a very substantial portion of these music theory exams were taking place overseas.
• This exam system was "quite an industry" at a time when the British Empire held power over nearly a quarter of the world's population.
• The system has changed somewhat in recent years but is basically continuous now for nearly 150 years.

🚫 What gets legitimized—and what gets excluded

🚫 Literacy and legitimacy

• Education theory teaches us to think critically about literacy: what we take for granted when we prescribe certain ways of expressing knowledge in a curriculum.
• When we make some types of language-use legitimate, other types of knowledge, content, and facts get skipped over, denied, or appear illegitimate.

🚫 What this system explains (and doesn't)

• Broadly speaking, this music theory system explains and legitimizes some elements of musical compositions better than others.
• The basic principles of notation on a five-line stave do not actually tie you to any particular musical genre (the excerpt ends here, implying flexibility, but also exclusion of non-notated traditions).
• Don't confuse: just because something is not easily notated or explained by this system does not mean it is less musical or less sophisticated.

🚫 Cultural convention, not natural law

• A huge part of what you're studying in music theory is cultural convention, not objective scientific truth.
• Example: The choice to center common practice harmony and stave notation reflects historical and colonial power structures, not an inherent superiority of these systems.

🧭 Overview

🧠 One-sentence thesis

The five-line stave and common practice harmony dominate UK music education not because they are scientifically universal, but because they were institutionalized through a graded exam system that spread globally during the British Empire and continues to shape what counts as legitimate musical knowledge today.

📌 Key points (3–5)

• What "learning music theory" means in the UK: it generally means learning to read and write five-line stave notation, often taken for granted as the standard.
• Historical origin of the system: the graded music exam system started in London in 1877, during the common practice harmony period, and spread overseas rapidly during British colonial rule.
• What the system teaches: common practice harmony—a harmonic language uniting roughly 2.5 centuries of European tonal music (late Baroque, Classical, Romantic eras).
• Common confusion: music theory sounds scientific, but it is largely cultural convention, not a coherent scientific theory like acoustics.
• Why it matters: this system legitimizes certain musical knowledge while marginalizing others, reflecting historical power structures and shaping whose music is considered "proper" or "sophisticated."

🏛️ The dominant system in the UK

🏛️ Five-line stave as the default language

• In the UK, the five-line stave is a dominant and thoroughly institutionalized language.
• "Learning music theory generally means learning to read and write music notation"—the two are often assumed to be the same thing.
• This assumption is especially strong for those familiar with formal music exams.

🎼 Common practice harmony at the core

Common practice harmony: a harmonic language that roughly unites European tonal music for around 2.5 centuries up to the twentieth century.

• It spans styles and eras: late Baroque, Classical, Romantic.
• This harmonic language sits "at the heart of the majority of music exam systems."
• Example: if you take a graded music exam, the theory you learn is likely rooted in this European tradition.

📜 Historical roots of the exam system

📜 When and where it started

• The graded music examination system began in London in 1877, during the later part of the common practice period.
• Within 25 years (by the start of the twentieth century), a very substantial portion of these exams were taking place overseas.

🌍 Colonial expansion

• The exam system operated "at a time when the British Empire held power over nearly a quarter of the world's population."
• It was "quite an industry"—not just an educational tool, but a commercial and cultural export.
• The system has changed somewhat in recent years but has been "basically continuous now for nearly 150 years."

🧪 Theory vs. convention

🧪 Not a scientific theory

• The excerpt reminds us: "we're not describing a coherent scientific theory."
• Sound is real and material; acoustics is the science of sound.
• Music theory, by contrast, is "a huge part of what you're studying is cultural convention."

🔍 Don't confuse

• Acoustics (science of sound) vs. music theory (cultural conventions about how to organize and notate music).
• The five-line stave and common practice harmony are technologies and languages, not laws of nature.

🧩 What gets legitimized—and what gets left out

🧩 Literacy and legitimacy

• Education theory teaches us to think critically about literacy: what we take for granted when we prescribe certain ways of expressing knowledge in a curriculum.
• "When we make some types of language-use legitimate," other types of knowledge, content, and facts "are going to get skipped over. They are denied. They appear illegitimate."

🎵 Which music is explained well

• This music theory system "explains—it legitimizes—some elements of musical compositions better than others."
• The basic principles of stave notation "don't actually tie you at all to any particular musical genre or tradition."
• Example: Jazz and popular musicians since the early twentieth century have been "some of the strongest advocates for the artistic sophistication that music notation can enable."

🏛️ The dominant ideology

• The dominant musical ideology of the stave comes from its association with European classical music institutions as understood for the past 100–150 years (since around 1877).
• This association arose from "a desire to formalise, or rather, to classify, music education and its attainment."

🧭 Critical perspectives on the system

🧭 Postcolonial and critical scholarship

• Critical and postcolonial scholarship has given new ways to understand music education in the UK.
• What is taught in schools today is "light years away from the Victorian exam system."
• However, "very recent work suggests that the institutions of classical music seems still to be strongly shaped by the collective imagination of an idealized human form."

🧑 The idealized form

• The idealized human form in classical music institutions is described as:
  • White
  • Male
  • Able-bodied
• "The discourse of classical music education appears aspirational and beyond politics. But, of course, it intersects with social class and sex, and gender and disability."
• "This has consequences for the musical lives of, well, most people."

🧠 Music Theory with capital letters

• "Music theory sometimes comes with a capital M and capital T."
• The American music theorist Philip Ewell explains how the language and academic enterprise of music theory "isn't at all scientifically or politically neutral regarding race."
• Ewell uses critical race and feminist scholarship to detail how this is so; his blog posts are freely available.

📌 Summary: convention, not universal law

📌 The core ideas are not scientific universals

• The ideas taught in this course—scale, key, harmony, metre—and the five-line stave notation used to express them "don't map simply onto scientific universals."
• Taking a "big wide view of human music-making," we should expect "huge variety in the core principles and theories."
• The system taught here is one cultural tradition among many, shaped by historical power and institutional choices.

🧭 Overview

🧠 One-sentence thesis

The music theory system taught in graded exams is not a scientific universal but a cultural convention rooted in European classical institutions and British colonial expansion, which legitimizes certain musical knowledge while marginalizing others.

📌 Key points (3–5)

• Historical origin: The graded music exam system began in London in 1877 during the British Empire and spread overseas within 25 years, teaching "common practice harmony" from European tonal music (late Baroque through Romantic eras).
• Cultural, not scientific: Music theory is largely cultural convention, not coherent scientific theory like acoustics; it prescribes certain ways of expressing musical knowledge while denying others.
• Institutional bias: The system is shaped by an idealized human form (white, male, able-bodied) and intersects with social class, sex, gender, and disability, affecting most people's musical lives.
• Common confusion: "Music theory" sounds universal and scientific, but it actually explains some musical compositions better than others and is not politically neutral regarding race.
• Empowerment through awareness: Understanding this context equips learners to resist, transform, and create with the system rather than accept it uncritically.

🏛️ Historical roots and spread

📜 The exam system's colonial origins

• The graded music examination system started in London in 1877, during the later part of the common practice period.
• Within 25 years (by 1900), a substantial portion of these exams were taking place overseas.
• This expansion occurred when the British Empire controlled nearly a quarter of the world's population.
• The system has been basically continuous for nearly 150 years, with some recent changes.

🎵 What "common practice harmony" means

Common practice harmony: a harmonic language that roughly unites European tonal music for around 2.5 centuries up to the twentieth century, spanning late Baroque, Classical, and Romantic eras.

• This is the core content taught in the majority of music exam systems.
• It refers to a specific historical and geographical tradition, not all music everywhere.
• Example: The system teaches conventions from European classical music, not necessarily jazz, popular music, or non-European traditions.

🧩 Cultural convention vs. scientific theory

🔬 Why music theory is not science

• Sound is real and material; acoustics is the science of sound.
• Music theory, however, is largely cultural convention, not a coherent scientific theory.
• The excerpt emphasizes: "study music theory, and a huge part of what you're studying is cultural convention."
• Don't confuse: Acoustics (scientific study of sound waves) vs. music theory (culturally specific ways of organizing and explaining musical ideas).

📚 What gets legitimized and what gets denied

• When a curriculum prescribes certain ways of expressing knowledge, it makes some types of language-use legitimate.
• Logically, this means other types of knowledge, content, and facts get skipped over or denied—they appear illegitimate.
• The music theory system explains and legitimizes some elements of musical compositions better than others.
• Example: Five-line stave notation can be used for jazz and popular music, but its dominant ideology comes from association with European classical music institutions.

🎭 Institutional bias and social impact

🧑 The idealized human form

• Recent critical and postcolonial scholarship reveals that classical music institutions are strongly shaped by the collective imagination of an idealized human form: white, male, and able-bodied.
• The discourse of classical music education appears aspirational and beyond politics, but it actually intersects with social class, sex, gender, and disability.
• This has consequences for the musical lives of most people.

🌍 Race and neutrality

• The American music theorist Philip Ewell explains how the language and academic enterprise of "Music Theory" (capital M, capital T) is not scientifically or politically neutral regarding race.
• Ewell uses critical race and feminist scholarship to detail how this is so.
• The excerpt notes that readers can find more on Ewell's blog posts and other reading suggestions.

🏫 Changes in music education

• What's taught in UK schools today is "light years away from the Victorian exam system."
• However, the institutions of classical music still carry the legacy of that historical context.

🛠️ Using the system with awareness

💪 Empowerment through context

• The excerpt emphasizes: "Knowing some of its context, you are better equipped to resist it, transform it, create with it."
• The material covered is "a system, like any other language."
• Learners are in charge of their reasons for learning and are not obliged to make this their only way of thinking musically.

⚖️ Strengths and weaknesses

Aspect	What the excerpt says
Widespread use	Stave notation based on this system has become very widespread for communicating musical ideas
Strengths and weaknesses	The system has some of each
"Fundamentals"	Does NOT mean easy or elementary
"Theory"	Does NOT mean scientific
"Music"	Is partial—does not cover all music
Political neutrality	As a cultural system, it is NOT politically neutral

🌈 Variety in human music-making

• Taking a big wide view of human music-making, we should expect huge variety in core principles and theories underpinning different musical traditions.
• Variety arises from:
  • Geographical separation between groups
  • Differences between instrumental music and song
  • Technologies
  • Function and social organization
  • Genres and scenes
• Even within Western tonal music, different musical forms and performance contexts give rise to wildly different types of harmonic conventions and opportunities.
• Don't confuse: The system taught in this course is one tradition among many, not a universal framework for all music.

✅ The invitation to learn

• The excerpt concludes: "whoever you are, whatever your reasons, you are entitled—and you are welcome—to choose to learn this."
• The goal is informed choice and critical engagement, not uncritical acceptance.

🧭 Overview

🧠 One-sentence thesis

Stave notation and the music theory taught in this course—scale, key, harmony, and metre—are not scientific universals but a culturally shaped system that learners can choose to adopt, resist, or transform.

📌 Key points (3–5)

• What the course teaches: scale, key, harmony, metre, and five-line stave notation—these do not map onto scientific universals.
• Why variety exists: human music-making shows huge variety in core principles due to geography, instrumental vs vocal traditions, technology, function, social organization, genres, and eras.
• Common confusion: "fundamentals" does not mean easy; "theory" does not mean scientific; "music" is partial—this system is not politically neutral.
• How to approach it: stave notation is a widespread communication system with strengths and weaknesses; learners can resist, transform, or create with it.
• Who it's for: whatever your reasons, you are entitled and welcome to choose to learn this system—it need not be your only way of thinking musically.

🎼 What this course covers and what it is not

🎼 The core elements taught

The course focuses on:

• Scale
• Key
• Harmony
• Metre
• Five-line stave notation to express these ideas

These are presented as tools for communicating musical ideas, not as universal truths.

🚫 Three key clarifications

The excerpt emphasizes three important distinctions:

Term	What it does NOT mean	What it actually means
Fundamentals	Easy or elementary	Basic building blocks of this particular system
Theory	Scientific or universal	A framework within one cultural tradition
Music	All music everywhere	A partial view—one system among many

Don't confuse: calling something "music theory" does not make it scientifically neutral or universally applicable.

🌍 Why this system is partial

• Taking a wide view of human music-making, we should expect huge variety in core principles and theories across different musical traditions.
• Musical realities and conceptualizations vary due to:
  • Geographical separation between groups
  • Differences between instrumental music and song
  • Technologies
  • Function
  • Social organization
  • Genres and scenes
• Even within Western tonal music across different eras, different musical forms and performance contexts produce wildly different harmonic conventions and opportunities.

🧭 Understanding the system as cultural, not neutral

🧭 Stave notation as a widespread but not universal system

Stave notation based on elements of this music theory system: a very widespread system of communicating about musical ideas.

• It has become widespread, meaning many people use it.
• It has strengths and weaknesses (the excerpt does not detail them, but acknowledges both exist).
• Widespread does not mean universal or scientifically grounded.

🏛️ The system is not politically neutral

• The excerpt states clearly: "As a cultural system, it is not politically neutral."
• This follows from earlier discussion (referenced but not fully detailed in this excerpt) about how classical music institutions and music theory have been shaped by idealized forms (white, male, able-bodied) and intersect with social class, sex, gender, and disability.
• Don't confuse: a system being widely taught or used does not make it neutral or objective.

🛠️ How to approach learning this system

🛠️ The system as a language

The excerpt compares the material to "a system, like any other language."

• Languages are learned tools, not inherent truths.
• Knowing the context of this system equips you to:
  • Resist it
  • Transform it
  • Create with it

Example: just as learning a language lets you critique or play with its conventions, learning stave notation and this music theory lets you use it critically or creatively.

🎯 You are in charge of your reasons

• You are not obliged to learn this particular system of musical thinking.
• It really need not be your only way of thinking musically.
• Whatever your reasons for choosing to learn on this course, you are in charge of them.
• Whoever you are, whatever your reasons, you are entitled and welcome to choose to learn this.

Key message: the excerpt explicitly invites learners not to be put off by the system's cultural and political context; instead, approach it as a choice and a tool.

🧭 Overview

🧠 One-sentence thesis

The octave divides into twelve distinct pitch classes (semitones), and scales are pathways through an octave built on specific patterns of tones and semitones that give music its characteristic sound.

📌 Key points (3–5)

• The octave's real structure: although "octave" suggests eight, modern instruments divide it into 12 distinct pitch classes (semitones), not just seven note names.
• Intervals measure vertical distance: the distance between notes is named by counting (second, third, fourth, etc.), and the smallest working distance is the semitone.
• Tones vs semitones: a tone equals two semitones; the major scale uses a specific pattern (T-T-S-T-T-T-S) that defines its quality.
• Common confusion: all seconds are intervals of two note-names, but some span a tone (two semitones) while others span only a semitone—they have different qualities.
• Why scales matter: scales are pools of notes from which melodies are drawn; the pattern of intervals between notes gives the scale its characteristic flavor.

🎹 The structure of the octave

🎹 Twelve pitch classes, not eight

Octave: the interval spanning from one note to the same note name in the next register (e.g., A to A).

• The prefix "oct-" suggests eight, and there are seven distinct note names (A, B, C, D, E, F, G, then back to A).
• However, modern instruments (guitar, piano) divide the octave into 12 distinct pitch classes.
• On a guitar, counting frets from an open A string to the next A gives 12 steps before the pattern repeats.
• On a piano, counting all white and black keys from A to the next A also gives 12 steps.
• Don't confuse: the octave is a natural phenomenon, but the 12-division is a feature of the tuning system (equal temperament) dominant since the twentieth century.

🎸 Physical demonstration: halving the string

• The video shows that halving a guitar string produces the octave above.
• This relates to the harmonic series: a mathematical relationship (often attributed to Pythagoras) where halving a string repeatedly produces not just octaves but other intervals as well.
• The excerpt notes that others likely discovered this before Pythagoras.

📏 Intervals: measuring vertical distance

📏 What intervals are

Interval: the vertical distance between two notes, named by counting the note positions inclusively.

• Intervals quantify "high pitches or low pitches" on the vertical axis.
• They are not only counted from C; any two notes form an interval (e.g., G to A is a second, F to A is a third).
• Example: C to D is a second (count: one, two); C to E is a third (count: one, two, three); C to G is a fifth (count: one, two, three, four, five).

🎵 Semitones and tones

Semitone: the smallest working distance between two notes in this system (where "semi-" means half).

Tone: the distance equal to two semitones.

• On a keyboard, a semitone is the distance from one key to the very next key (white or black).
• A tone skips one key in between.
• Example: C to D is a tone (two semitones); B to C is a semitone (no black key between them on the keyboard).
• The excerpt identifies two pairs of natural semitones (using only white keys): B–C and E–F.

🔍 Same interval name, different quality

• The excerpt points out that B to C is a second (counting two note-names), but it spans only a semitone.
• F to G is also a second, but it spans a tone (two semitones).
• Both are correctly called "seconds," but they have different qualities.
• The video promises more detail on this distinction next week.

🎼 Scales: pathways through the octave

🎼 What a scale is

Scale: a pathway through an octave; a pool or set of notes from which melodies can be drawn.

• Scales are not just abstract patterns—they help make music.
• The excerpt emphasizes that each note on its own doesn't mean much; what matters is how notes sound next to each other and the relationships they build.
• Example: the C major scale can produce melodies like "Twinkle Twinkle Little Star" (which Mozart used for a set of variations).

🎹 The C major scale

• The C major scale uses all the white keys from C to C on a piano.
• The note names are: C, D, E, F, G, A, B, C.
• This is also the "Do, Re, Mi, Fa, Sol, La, Ti, Do" from Julie Andrews's song.
• The first note (C) is called the tonic note of the scale.

Tonic: the letter name that the scale is named after (e.g., C is the tonic of C major; F is the tonic of F major).

🔢 The tone-semitone pattern

The C major scale follows this pattern of intervals:

Step	Interval	Notes
C → D	Tone (T)
D → E	Tone (T)
E → F	Semitone (S)	no black key between
F → G	Tone (T)
G → A	Tone (T)
A → B	Tone (T)
B → C	Semitone (S)	no black key between

• The overall pattern is: T–T–S–T–T–T–S.
• This pattern of two tones, then a semitone, then three more tones, then a final semitone gives the major scale its characteristic sound.
• The excerpt stresses that this pattern of relationships—not the individual notes—gives the scale its quality (its overall flavor or sound).

🎶 Diatonic scales

Diatonic scale: a scale with seven notes and a pattern of five tones and two semitones between the tonic in one octave and the same tonic in the next octave.

• The prefix "dia-" means "between" (between two tonics).
• The C major scale is an example of a diatonic scale.
• All diatonic scales have seven distinct note names plus the octave repetition, and always contain five tones and two semitones in some arrangement.

🌍 Scope and context

🌍 Common Practice focus

• The course focuses on techniques from the Common Practice era: Western Europe from 1600 to 1900 (music of Bach, Haydn, Mozart, Beethoven, etc.).
• The excerpt acknowledges that other forms of music around the world use different techniques.
• The Common Practice system applies to much pop, rock, jazz, and folk music, so it serves as a good foundation.

🎵 Beyond semitones: microtones and tuning systems

• The semitone as a fixed-size interval comes from equal temperament, the dominant tuning system since the twentieth century.
• Other tuning systems exist (e.g., just intonation, well temperament) where some "semitones" are deliberately smaller than others.
• Intervals smaller than a semitone are called microtones.
• Examples of microtones: singers or guitarists "bending" notes in Blues, Rock, and Jazz; mid-twentieth-century classical music; and essential elements in much music from other cultures.
• Don't confuse: the 12-semitone octave is not universal or "natural"—it is a product of a specific tuning technology.

🧭 Overview

🧠 One-sentence thesis

Musical notation uses a systematic hierarchy of symbols—note-heads, stems, flags, and beams—to communicate duration, and these symbols work relationally to express not just individual sound lengths but also the larger rhythmic structure of a composition.

📌 Key points (3–5)

• Duration hierarchy: note symbols (semibreve, minim, crotchet, quaver, semiquaver) work in 2:1 relationships, where each level halves the duration of the one above it.
• Rests mirror notes: silence symbols correspond exactly to note durations, using the same naming and proportional relationships.
• Notation is contextual, not just code: the choice between flags and beams for the same duration (e.g., quavers) communicates information about the rhythmic grouping and structure of the piece, not just individual sound units.
• Common confusion: notation may look like a simple one-to-one code, but it's more like language—symbols vary in appearance and convey structural meaning beyond just mapping sounds.
• Pick-ups (anacrusis): a single note before a strong downbeat may be notated separately (not beamed) to show its structural role, even when surrounded by notes of the same duration.

🎵 The duration hierarchy

🎵 How note symbols work

Musical duration symbols: forms of note-heads, stems, flags, and beams that conventionally indicate how long a note should last.

• The system is relational: symbols work in relation to one another, not as absolute values.
• Each level in the hierarchy represents half the duration of the level above it.
• The crotchet serves as the reference point: it lasts for one count.

📊 The five main durations (UK English naming)

Symbol	Name	Duration (in counts)	Relationship
Semibreve	Whole note	4 counts	Top of hierarchy
Minim	Half note	2 counts	Half of semibreve
Crotchet	Quarter note	1 count	Half of minim
Quaver	Eighth note	0.5 count	Half of crotchet
Semiquaver	Sixteenth note	0.25 count	Half of quaver

• Example: In the same time span of four counts, you could have one semibreve, two minims, four crotchets, eight quavers, or sixteen semiquavers.
• Each row in the pyramid represents the same total amount of musical time.

🔇 Rest symbols

• Rests indicate gaps or silences where no sound is made.
• They correspond exactly to note durations: semibreve rest, minim rest, crotchet rest, quaver rest, semiquaver rest.
• The same 2:1 relationships apply: a semibreve rest is worth four counts, two minim rests, four crotchet rests, eight quaver rests, or sixteen semiquaver rests.

🧩 Notation as communication, not just code

🧩 Variation in appearance

• The excerpt emphasizes that there is no "one perfect form" of musical notation.
• Notation is about expressing and communicating human musical ideas, so symbols vary across different scores and contexts.
• The handwritten graphics in the source are intentionally uneven to reinforce this point.
• Don't confuse: notation with a rigid code—it's more like language, with variation in how symbols are formed.

🗣️ Notation communicates structure

• Notation is not just about representing individual sounds unit by unit; it's more subtle, like written language.
• Example from language: the letter 'Q' and 'q' are both Qs but look different depending on context.
• Musical notation works similarly to communicate how a composition hangs together, not just what individual notes to play.

🎯 Flags vs beams: structural meaning

🎯 Two ways to write quavers

• A quaver can be written with a flag (individual note) or a beam (joined to other notes).
• Both represent the same duration, but the choice between them is not arbitrary.

🎯 What the choice communicates

• The decision to use a flag or beam communicates something about the bigger picture of the composition.
• It expresses information about how the piece organizes time and rhythm.
• Example: In Mozart's Horn Concerto in E-flat, K.495 (Rondo, third movement), both types of quaver notation appear in the same melody line.

🎯 Pick-ups (anacrusis)

Anacrusis (pick-up): a note that comes in just before a strong downbeat in the music.

• The very first quaver in the Mozart example is notated with a flag, all on its own, even though the following notes are the same duration.
• This notational choice communicates that the first note is a pick-up, expressing a structural role.
• Don't confuse: the visual separation with a difference in duration—the quaver is still the same length, but its structural function is different.

🎧 Examples of pick-ups vs downbeats

• With pick-ups (anacrusis): Mozart Horn Concerto Rondo (1786); Dolly Parton's "Jolene" (1974).
• Without pick-ups (starting on downbeat): Dua Lipa's "Levitating" (2020); Edvard Grieg's "Morning Mood" from Peer Gynt suite (1875).
• Listening for pick-ups helps you notice how notation reflects rhythmic structure.

🧭 Overview

🧠 One-sentence thesis

By starting on different white keys and playing through an octave, we create seven distinct diatonic modes, each with a unique quality determined by the reordered pattern of five whole-tones and two semitones.

📌 Key points (3–5)

• What changes the scale quality: changing the order of the five tones and two semitones by choosing a different starting note (tonic).
• How to generate modes: start on any white key (A, B, C, D, E, F, or G), play only white keys through an octave until the starting note repeats—each produces a different mode.
• Seven diatonic modes: Ionian (C), Dorian (D), Phrygian (E), Lydian (F), Mixolydian (G), Aeolian (A), and Locrian (B)—each has a specific name and pattern.
• Common confusion: all seven modes use the same pool of notes (the white keys), but the different starting point reorders the tones and semitones, creating different qualities.
• Why it matters: modes are used across many musical traditions—ancient church music, jazz, rock, folk—and understanding them helps develop musicianship and tonality awareness.

🎹 How changing the tonic changes the scale

🎹 Same notes, different order

• The excerpt explains that using all white keys but starting on a different note produces a different quality or sound.
• The pattern of five whole-tones and two semitones remains, but their sequence changes.
• Example: Starting on C gives one pattern; starting on A gives tone–semitone–tone–tone–semitone–tone–tone (T S T T S T T).

🏠 The tonic as "home"

• The starting note is called the tonic.
• The tonic feels like "home"—melodies often return to it or finish on it.
• Example: In God Rest Ye Merry Gentlemen, the melody keeps coming back to A; in Scarborough Fair, D feels like home.

🎵 The A natural minor scale / Aeolian mode

🎵 What it is

The A natural minor scale (also called the Aeolian mode): the scale pattern obtained by starting on A and playing all white keys through an octave.

• The pattern is: T S T T S T T (tone, semitone, tone, tone, semitone, tone, tone).
• It is still a diatonic scale (seven notes with five tones and two semitones), but the sequence differs from the major scale.

🎶 Example: God Rest Ye Merry Gentlemen

• The excerpt uses this Christmas carol (probably from the seventeenth century) to illustrate the A natural minor quality.
• The melody is oriented around A as the tonic.
• The excerpt suggests circling all the As in the notation and noticing how the melody returns to A while listening.

🌍 The seven diatonic modes

🌍 How to discover them

• Stick to the white keys on a keyboard.
• Start on any note (A, B, C, D, E, F, or G) and play through an octave until the starting note repeats.
• Each starting note generates a different pattern of tones and semitones, identified as a particular mode with a specific name.

📜 The mode names and starting notes

Starting note	Mode name	Mnemonic
C	Ionian	I
D	Dorian	Don't
E	Phrygian	Punch
F	Lydian	Like
G	Mixolydian	Muhammad
A	Aeolian	A-
B	Locrian	Li

• The excerpt provides the mnemonic: "I Don't Punch Like Muhammad A-Li" to help memorize the order.
• These are the 20th-century names, often called the "church modes," and are used in ancient church music, jazz (from the late 1950s onward), rock, and popular music.

🎼 Examples of modes in songs

• Dorian mode (starting on D): Scarborough Fair (D feels like home) and What Shall We Do With a Drunken Sailor (starts on A, goes down to D on "ken," finishes on D).
• Aeolian mode (starting on A): God Rest Ye Merry Gentlemen (melody oriented around A).
• Mixolydian mode (starting on G): She Moved Through the Fair (the excerpt mentions a "slightly jazzy version" built on G Mixolydian; G is the tonic).

🔍 Don't confuse: same notes, different quality

• All seven modes use the same pool of notes (all white keys).
• The different starting point (tonic) reorders the tones and semitones, creating a different "flavour" or "quality."
• Example: C major (Ionian) and A natural minor (Aeolian) use the same notes, but sound different because the tonic and the pattern order differ.

🎓 How to learn and experience modes

🎓 Practical exercises

• Memorize the mode names and starting notes using the mnemonic.
• Play each mode yourself: start on each white key and play through an octave; notice the different sequence of tones and semitones.
• Play songs by ear: try Scarborough Fair (start on D, use only white keys) or What Shall We Do With a Drunken Sailor (start on A, go down to D); pay attention to how the tonic feels like "home."
• Improvise: play along with She Moved Through the Fair and try to "feel" G as the tonic by playing G repeatedly and noticing how it "fits."

🎯 Why this matters

• Playing around at the keyboard helps you experience tonality and develop general musicianship.
• The excerpt emphasizes playing "for fun" and for "discovery and satisfaction," not just as a formal exercise.
• Real knowledge about concepts and terminology comes from hands-on experience.

📚 Further topics mentioned

📚 Pentatonic scales

• The excerpt notes that pentatonic scales are "very common in all kinds of music" but have not been covered yet.
• The excerpt suggests using Wikipedia for more information on pentatonic scales.

📚 More on modes

• The excerpt mentions there is "much more to say about modes and other kinds of scales."
• For a detailed article on modes and their history, the excerpt recommends starting with Wikipedia.

🧭 Overview

🧠 One-sentence thesis

Triads—three-note chords built from scale degrees—have distinct internal structures (major, minor, or diminished) determined by the intervals between their notes, and understanding these structures prepares you to grasp how chords function in tonal music.

📌 Key points (3–5)

• What a triad is: a three-note chord derived by stacking the 1st, 3rd, and 5th notes of a scale.
• Internal structure matters: the interval between the bottom and middle note (major third = 4 semitones, minor third = 3 semitones) determines whether a triad sounds major or minor; both types share a perfect fifth (7 semitones) between bottom and top.
• Three chord types from one scale: building triads on each degree of the C major scale yields three major chords (C, F, G), three minor chords (D, E, A), and one diminished chord (B).
• Common confusion—scale degrees vs intervals: scale degrees (1st, 2nd, 3rd…) label positions in a scale; intervals (second, third, fourth…) measure the distance between two notes.
• Why it matters: these triads form the foundation of tonal harmony, and the three primary chords (I, IV, V) are the only major triads available from the major scale.

🎹 What is a triad and how to build one

🎹 Definition and construction

Triad: a three-note chord.

• To build a triad, take the 1st, 3rd, and 5th notes of a scale and stack them vertically (play them at the same time).
• Example: from the C major scale (C D E F G A B C), isolate C, E, and G → the C major triad.
• Example: from the A natural minor scale (A B C D E F G A), isolate A, C, and E → the A minor triad.

🏷️ Chord symbols (lead sheet notation)

Different styles use different shorthand:

Chord type	Notation examples
C major	C, Cmaj, CM
A minor	Amin, Am, A−
B diminished	B°, Bdim

• These symbols replace written-out notation in genres like rock and jazz.

🔍 Internal structure: what makes a triad major, minor, or diminished

🔍 The two key intervals

Every triad has two intervals to check:

1. Bottom to top note (the fifth)
2. Bottom to middle note (the third)

The excerpt emphasizes: "It is this difference in the 'size' of the interval of the third that makes all the difference (perceptually) between these two chords."

📏 Perfect fifth (bottom to top)

Perfect fifth: an interval spanning 7 semitones.

• Both C major (C to G) and A minor (A to E) have a perfect fifth.
• Count the semitones: tone + tone + semitone + tone = 7 semitones.
• The two notes "sound nice together."

📐 Major third vs minor third (bottom to middle)

Interval	Semitones	Example	Result
Major third	4	C to E (tone + tone)	Major triad
Minor third	3	A to C (tone + semitone)	Minor triad

• The minor third is "smaller by one semitone."
• Example: C major triad has C–E (major third, 4 semitones) + perfect fifth → sounds major.
• Example: A minor triad has A–C (minor third, 3 semitones) + perfect fifth → sounds minor.

⚠️ Diminished triad (the exception)

Diminished fifth: an interval spanning only 6 semitones, one semitone smaller than the perfect fifth.

• Building a triad on B in the C major scale gives B, D, F.
• B to F = 6 semitones (diminished fifth) + B to D = 3 semitones (minor third) → diminished triad.
• This triad "sounds different" and has a different structure from the rest.

🎼 All seven triads from the C major scale

🎼 The full set

Building a triad on each degree of the C major scale produces:

Scale degree	Triad notes	Fifth	Third	Type
1 (C)	C E G	Perfect (7)	Major (4)	Major
2 (D)	D F A	Perfect (7)	Minor (3)	Minor
3 (E)	E G B	Perfect (7)	Minor (3)	Minor
4 (F)	F A C	Perfect (7)	Major (4)	Major
5 (G)	G B D	Perfect (7)	Major (4)	Major
6 (A)	A C E	Perfect (7)	Minor (3)	Minor
7 (B)	B D F	Diminished (6)	Minor (3)	Diminished

• Three major chords: C, F, G
• Three minor chords: D, E, A
• One diminished chord: B
• All from "one set of white notes."

🎯 The three primary chords

The excerpt introduces three special triads:

Tonic triad (I): built on the 1st scale degree (the tonic).
Subdominant triad (IV): built on the 4th scale degree (the subdominant).
Dominant triad (V): built on the 5th scale degree (the dominant).

• In C major: I = C major, IV = F major, V = G major.
• These are the only major chords you can build from the C major scale by stacking triads on scale degrees.
• Roman numerals label these triads: I, IV, V.
• The excerpt emphasizes: "These are important terms: memorise them."

🗣️ Terminology: scale degrees vs intervals

🗣️ Don't confuse the two counting systems

The excerpt warns: "We need to use a lot of different systems of counting and labelling."

Concept	What it labels	Example
Scale degree	Position of a note in a scale	"The 1st degree of the scale, the 2nd degree, the 3rd degree…"
Interval	Distance between two notes	"An interval of a second, third, fourth…"

• Scale degrees: 1, 2, 3, 4, 5, 6, 7, back to 1.
• Special names: degree 1 = tonic, degree 4 = subdominant, degree 5 = dominant.
• When asked "Which scale degree is this?" answer "It's scale degree 5, the fifth note of the scale, the dominant."
• When asked "What's this interval?" answer "It's a second!" (or third, fourth, etc.).

🧠 Why this matters

• You are "learning to speak Music Theory now. This is the lingo."
• Mixing up scale degrees and intervals will cause confusion when analyzing chords and harmony.
• Example: "the third note of the scale" (scale degree 3) vs "an interval of a third" (distance from one note to another).

🧭 Overview

🧠 One-sentence thesis

The three primary chords—tonic, subdominant, and dominant—are the only major triads built from the major scale and form the foundation for harmonizing melodies in common practice music, jazz, pop, rock, and folk.

📌 Key points (3–5)

• The three primary chords: tonic (I), subdominant (IV), and dominant (V) are the major triads built on the first, fourth, and fifth degrees of the major scale.
• Why they matter: these three chords can harmonize every note of the major scale and are sometimes called the "Three Chord Trick."
• Harmonization principle: in common practice music, melody notes typically belong to the chord backing them.
• Common confusion: in C major, only these three primary chords are major; building triads on D, E, or A creates minor chords, and B creates a diminished triad.
• Practical application: countless songs have been written using just these three chords in various progressions.

🎹 The three primary chords

🎵 Tonic triad (I)

Tonic triad: the major chord built on the first degree (tonic) of the scale.

• In C major, this is the C major chord (C–E–G).
• It is the "home" chord and typically where pieces finish.
• Roman numeral: I

🎵 Subdominant triad (IV)

Subdominant triad: the major chord built on the fourth degree of the scale.

• In C major, this is the F major chord (F–A–C).
• The name means "one underneath the dominant."
• Roman numeral: IV

🎵 Dominant triad (V)

Dominant triad: the major chord built on the fifth degree of the scale.

• In C major, this is the G major chord (G–B–D).
• The name "dominant" refers to its importance in the key.
• Roman numeral: V

🎼 Why these three are special

🔑 Only major chords in the key

• When you build triads on all seven degrees of the C major scale, you get:
  • Three major chords: C (I), F (IV), G (V)
  • Three minor chords: D minor (ii), E minor (iii), A minor (vi)
  • One diminished chord: B diminished (vii°)
• The three primary chords are the only major triads available using just the notes of the major scale.

🎯 The "Three Chord Trick"

• These three chords have become important through time in:
  • Common practice classical music
  • Jazz, pop, rock, and folk music
• Many hit songs have been written using just these three chords.
• Example progressions mentioned in the excerpt demonstrate how versatile these three chords are in different musical contexts.

🎶 Harmonizing the major scale

🎵 The harmonization principle

In common practice music, it is normal to have the melodic note be a member of the chord that is backing it.

• This means: if your melody note is C, you would typically use a chord that contains C (either C major or F major).
• This principle is less strict in jazz, 20th-century classical music, or 1970s rock, but it holds for most traditional harmony.

🎵 How each scale degree is harmonized

Scale degree	Note (in C major)	Primary chord(s) that contain it	Chord choice
1	C	C major (I), F major (IV)	Usually C major
2	D	G major (V) only	G major
3	E	C major (I) only	C major
4	F	F major (IV) only	F major
5	G	G major (V), C major (I)	Either chord
6	A	F major (IV) only	F major
7	B	G major (V) only	G major
8	C	C major (I), F major (IV)	Usually C major to finish

• Every note of the major scale can be harmonized by at least one of the three primary chords.
• The most common ending progression is from B (with G major/dominant) to C (with C major/tonic).
• Don't confuse: some notes have two chord options (C, G), but most have only one primary chord that contains them.

🎵 Practical application

• Example: To harmonize a melody in C major, identify each melody note and choose the primary chord(s) that contain it.
• The excerpt emphasizes: "You have to sit down and play through for yourself" to hear how this works.
• With these three chords, "you could write a hit"—the excerpt notes that quite a few songs have been built this way.

🔍 Context and importance

📚 Relationship to other triads

• The excerpt builds on the previous section, which identified all seven triads in C major.
• The three primary chords are a subset of those seven, selected because they are major and functionally important.
• The other triads (three minor, one diminished) will be covered in later sections.

📚 Looking ahead

• These primary chords will become more important in later lectures, especially in series four and five.
• The excerpt concludes: confining ourselves to just the white notes of the piano and the C major scale, we found three different kinds of triads and "all sorts of internal relationships which already give us the possibility of making music."

🧭 Overview

🧠 One-sentence thesis

By applying the major scale pattern (tone–tone–semitone–tone–tone–tone–semitone) to any starting note, you will need sharps or flats to maintain the correct intervals, because the piano keyboard's layout creates semitones in uneven places.

📌 Key points (3–5)

• The major scale pattern is portable: start on any note and apply TTSTTTS to build a major scale, not just on C.
• Why sharps and flats are needed: the white keys alone don't always give the right intervals; black notes (and sometimes white notes) must be used to create the correct tone or semitone.
• Enharmonic naming: the same black key can be called sharp (one semitone higher than the note below) or flat (one semitone lower than the note above); context and the "one of each letter" rule determine which name to use.
• Common confusion: B–C and E–F are already semitones with no black key between them; don't assume every pair of white keys has a black key in between.
• Why the asymmetry helps: the uneven spread of note names across the keyboard gives landmarks for eyes and ears.

🎹 The major scale pattern on any note

🎹 Applying TTSTTTS to different starting notes

• The excerpt shows that the C major scale uses only white keys because the pattern happens to line up with them.
• When you start on G, you need F-sharp to maintain the pattern (specifically, to get a whole tone between the 6th and 7th scale degrees).
• When you start on D, you need F-sharp and C-sharp to widen intervals that would otherwise be semitones if you used only white keys.
• When you start on F, you need B-flat (not A-sharp) to keep one of each letter name and to create the correct semitone between the 3rd and 4th degrees.

🔤 The "one of each letter" rule

• Scales must use each letter name (A, B, C, D, E, F, G) exactly once.
• Example: in F major, the pattern requires a note between A and B; because you already have A, you call it B-flat (not A-sharp), so you have F–G–A–B♭–C–D–E–F.
• This rule determines whether you name a black key as a sharp or a flat.

🎼 Understanding sharps, flats, and semitones

🎼 What sharps and flats mean

Sharp: one semitone higher than the named note.
Flat: one semitone lower than the named note.

• A black key between, say, F and G can be called F-sharp (one semitone above F) or G-flat (one semitone below G).
• The choice depends on the scale context and the letter-name rule.

🎹 Where semitones naturally occur on the keyboard

• B to C and E to F are semitones with no black key in between.
• Example: on a guitar, the first fret on the E string is F (a semitone above the open E); the first fret on the B string is C (a semitone above the open B).
• Don't confuse: not every adjacent pair of white keys has a black key between them; the keyboard layout is asymmetric.

🗺️ Why the asymmetry is useful

• The uneven distribution of black and white keys creates landmarks for both visual recognition and aural orientation.
• The excerpt emphasizes that this unevenness helps musicians latch onto reference points when reading or hearing music.

🛠️ Practical application

🛠️ Building a major scale from any note

The excerpt walks through the process step by step:

Starting note	Pattern applied	Sharps or flats needed	Result
C	TTSTTTS	None	C major (all white keys)
G	TTSTTTS	F-sharp	G major
D	TTSTTTS	F-sharp, C-sharp	D major
F	TTSTTTS	B-flat	F major

• Example task from the video: start on D and apply the pattern yourself; you will discover that you need F-sharp (to make a tone between scale degrees 2 and 3) and C-sharp (to make a tone between scale degrees 6 and 7).

🎸 Visualizing on different instruments

• The excerpt acknowledges that "white notes and black notes" language is piano-centric.
• Guitar players can use the same logic: a semitone is one fret; a tone is two frets.
• The supporting material includes blank and annotated keyboard and fretboard diagrams for reference.

👂 Learning through multiple senses

• Eyes: study the keyboard or fretboard layout.
• Fingers: play the intervals on your instrument.
• Ears: practice hearing and distinguishing whole tones from semitones.
• The excerpt stresses that understanding comes from integrating visual, tactile, and aural practice—not just reading about it.

🧭 Overview

🧠 One-sentence thesis

Key signatures tell us which notes are consistently sharp or flat throughout a piece, helping us identify the key (the tonal "home" and the set of notes the music uses) and making written music easier to read.

📌 Key points (3–5)

• What a key is: not just a scale, but the relationship between notes where one note (the tonic) feels like "home" or a point of rest.
• What a key signature does: it announces sharps or flats at the start of the music so you don't have to write them every time, and it signals what key the music is in.
• The circle of fifths: a visual tool that shows the order of sharps (clockwise: F C G D A E B) and flats (anticlockwise: B E A D G C F) and helps you read or write any key signature.
• Common confusion: scale vs. key—a scale is an ordered string of notes; a key is the feeling of relationships and gravity toward the tonic.
• Accidentals: sharps, flats, or naturals that appear outside the key signature; they apply for the rest of the bar and can temporarily alter notes.

🎹 What is a key?

🎹 Key vs. scale

Key: the relationship and feeling that exists between notes, where one note (the tonic) has a sense of gravity and feels like "home" or rest.

• A scale is an ordered sequence of notes (e.g., C D E F G A B C).
• A key is the context in which those notes work together, with the tonic pulling you back and giving a sense of completeness.
• Example: music using the notes of the G major scale is "in the key of G major," and G feels like the home note.
• Don't confuse: the two terms are related but not identical—scale = the notes themselves; key = the relationships and the feeling of tonic.

🏠 The tonic

• The tonic is the note that feels most stable and complete.
• When you arrive back at the tonic, there's a feeling of rest or resolution.
• Example: in G major, G is the tonic; it has a kind of gravity that pulls the music home.

🔖 What is a key signature?

🔖 Purpose of a key signature

Key signature: a set of sharps or flats written at the very start of the music (right after the clef) to tell you which notes are altered throughout the piece.

• It does two things:
  1. Musical: signals where the tonic is and the relationships between notes in that key.
  2. Visual: tidies up the notation—you don't have to write a sharp or flat next to every single note; you see it once at the start and take it as read.
• Example: if a piece is in D major (which has F♯ and C♯), the key signature shows F♯ and C♯ at the start, so every F and C in the piece is automatically sharp unless otherwise marked.

📖 Reading a key signature

• The key signature tells you what key the music is in by showing which notes are sharp or flat.
• Example: if you see two sharps (F♯ and C♯) at the start, the music is in D major.
• The excerpt emphasizes that key signatures make it easier to follow the music, especially when sight-reading.

🔄 The circle of fifths

🔄 How the circle works

Circle of fifths: a diagram that shows all twelve keys arranged in a circle, moving by intervals of a fifth (clockwise) or a fourth (anticlockwise).

• Clockwise (sharps): each step adds one sharp; the keys move in fifths (C → G → D → A → E → B → F♯ → C♯).
• Anticlockwise (flats): each step adds one flat; the keys move in fourths (C → F → B♭ → E♭ → A♭ → D♭ → G♭ → C♭).
• C major (at 12 o'clock) has no sharps or flats.
• Example: G major (one step clockwise from C) has one sharp (F♯); D major (two steps clockwise) has two sharps (F♯ and C♯).

🔢 The order of sharps and flats

• Sharps always appear in this order: F C G D A E B (clockwise around the circle).
  • Mnemonic: "Father Christmas Gave Dad An Electric Blanket" or "Father Charles Goes Down And Ends Battle."
• Flats always appear in this order: B E A D G C F (anticlockwise around the circle).
  • Mnemonic: "Blanket Explodes And Dad Gets Cold Feet" or "Battle Ends And Down Goes Charles' Father."
• You will never have a key signature with both sharps and flats mixed together.

🔍 Reading key signatures with the circle

To identify a key from its signature:

1. Count the number of sharps or flats.
2. Start at C (12 o'clock).
3. If sharps, count clockwise; if flats, count anticlockwise.

Example	Sharps/Flats	Steps	Result
3 sharps	F♯, C♯, G♯	C → G (1), G → D (2), D → A (3)	A major
6 flats	B♭, E♭, A♭, D♭, G♭, C♭	C → F (1), F → B♭ (2), B♭ → E♭ (3), E♭ → A♭ (4), A♭ → D♭ (5), D♭ → G♭ (6)	G♭ major

✍️ Writing key signatures with the circle

To write a key signature for a given key:

1. Count steps from C to that key (clockwise for sharps, anticlockwise for flats).
2. The number of steps = the number of sharps or flats.
3. Use the order of sharps or flats to know which ones to write.

• Example: D major is 2 steps clockwise from C → 2 sharps → F♯ and C♯.
• Example: F major is 1 step anticlockwise from C → 1 flat → B♭.

🎵 Accidentals

🎵 What accidentals are

Accidental: a sharp, flat, or natural sign that appears in front of a note, altering it in a way that is not part of the key signature.

• It's absolutely fine to use notes outside the key signature; you just need to mark them with an accidental.
• Example: in G major (key signature: F♯), you can use a B♭ by writing a flat sign in front of the B.

🔀 Types of accidentals

• Sharp (♯): raises a note by a semitone.
• Flat (♭): lowers a note by a semitone.
• Natural (♮): cancels out a sharp or flat (either from the key signature or from an earlier accidental in the same bar).

⏱️ How long accidentals last

• An accidental applies for the rest of the bar (until the next vertical line across the staff).
• Example: if you see a B♭ in the middle of a bar, any other B in that bar is also flat—unless a natural sign cancels it out.
• A natural sign also lasts until the end of the bar.
• Don't confuse: the key signature applies to the whole piece; an accidental only applies within its bar.

📝 Example walkthrough

The excerpt gives an example in G major (one sharp: F♯):

• A sharp in front of a note makes it G♯ (not in the key).
• A flat in front of a B makes it B♭ (not in the key).
• A natural in front of the next B cancels the flat, so it's B-natural again.
• In the next bar, a natural in front of an F cancels the F♯ from the key signature, making it F-natural.

📐 Visual conventions

📐 Why key signatures must be written correctly

• When you get used to reading key signatures, you begin to see them as a complete visual symbol—like recognizing a whole word without sounding out each letter.
• Consistency helps with quick recognition, especially when sight-reading.

📐 Key signatures in different clefs

• Key signatures move around a bit depending on the clef (treble, bass, alto, tenor, etc.).
• The excerpt notes that all key signatures are presented in four different clefs in the supporting material, so you can see the correct placement for each.

🧭 Overview

🧠 One-sentence thesis

Minor keys share key signatures with their related major keys but create a different tonal quality by starting from a different tonic note, and composers use three types of minor scales—natural, harmonic, and melodic—to achieve different musical effects.

📌 Key points (3–5)

• Relative major/minor relationship: Major and minor keys that share the same key signature are called "relative" to each other; the relative minor starts on the 6th degree of the major scale.
• Three types of minor scales: Natural minor uses only the notes from the key signature; harmonic minor raises the 7th degree; melodic minor raises both 6th and 7th ascending but reverts to natural minor descending.
• Why different minor scales exist: The natural minor can feel ambiguous about which note is the tonic; the harmonic minor's raised 7th creates a stronger pull to the tonic; the melodic minor smooths out the awkward interval in the harmonic minor for easier singing.
• Common confusion: Parallel vs. relative relationships—parallel means same starting note (e.g., C major and C minor); relative means same key signature (e.g., A major and F-sharp minor).
• Accidentals last for the whole bar: An accidental applies to all occurrences of that note until the next vertical line (bar line); a natural sign cancels previous accidentals.

🎼 Accidentals and bar rules

🎼 How accidentals work within bars

• When an accidental appears, it affects the whole bar (until the next vertical line across the stave).
• Example: If a B-flat appears early in a bar, any other B in that same bar is also flat—you don't need to write the flat sign again.

♮ Natural signs cancel accidentals

• A natural sign cancels out a previous accidental (flat or sharp) in the same bar.
• Example: A B-flat appears, then later in the same bar a natural sign appears before another B → that second B is played as B-natural, not B-flat.
• The natural sign's effect also lasts until the end of the bar.
• A natural can also cancel a sharp from the key signature within a bar (e.g., F-natural instead of F-sharp).

🔗 Major and minor relationships

🔗 Parallel (tonic) vs. relative relationships

Relationship type	Definition	Example
Parallel (tonic)	Major and minor scales starting on the same note	C major and C minor; B-flat major and B-flat minor
Relative	Major and minor scales that share the same key signature	A major and F-sharp minor (both have three sharps)

• Don't confuse: Parallel means same starting note but different key signatures; relative means same key signature but different starting notes.

🔗 Finding the relative minor from a major key

• The relative minor is built from the 6th degree of the major scale.
• Method: Count up the major scale to find scale degree 6; that note is the tonic of the relative minor.
• Example: In A major, count 1=A, 2=B, 3=C-sharp, 4=D, 5=E, 6=F-sharp → F-sharp minor is the relative minor of A major.
• Both keys use the same notes (same key signature), but starting and ending on F-sharp creates a minor tonality instead of the major tonality you get starting and ending on A.

🔗 Finding the relative major from a minor key

• Reverse the process: the minor tonic becomes scale degree 6 in the major key.
• Alternative method: Find the note a minor 3rd above the minor tonic (3 semitones = 1½ whole tones).
• Example: From A minor, count up 3 semitones: A → B (1 semitone) → C (2 more semitones) → C is the relative major of A minor.

🎵 Why tonality emerges

• Although major and relative minor scales contain the same seven notes, not all notes occur with equal regularity in real music.
• You hear more of the tonic, fifth, fourth, and seventh notes.
• Tonality emerges from this hierarchy of note usage, plus other compositional features.
• This is why the natural minor can feel ambiguous—it can easily pull back to the relative major's tonic.

🎶 Three types of minor scales

🌿 Natural minor (Aeolian mode)

Natural minor: all notes taken directly from the key signature, starting and ending on the relative minor tonic.

• Easiest to understand: just play the major scale starting from the 6th degree.
• Example: A major has F-sharp, C-sharp, G-sharp; F-sharp minor natural uses exactly those notes, but starts and ends on F-sharp.
• Limitation: Because it uses only the major scale notes, it can feel like the music wants to resolve back to the major tonic (e.g., back to A instead of F-sharp).

🎺 Harmonic minor

Harmonic minor: the natural minor with the 7th degree raised (sharpened) by a semitone.

• Why raise the 7th: The raised 7th is called the leading note; it creates a strong pull upward to the tonic, making the minor tonic feel more stable.
• Example: F-sharp minor natural has E as the 7th degree; harmonic minor raises it to E-sharp → this E-sharp "leads" the ear strongly to F-sharp.
• Distinctive sound: The harmonic minor has a characteristic sound because of the large gap (three semitones = a tone and a half) between the 6th and raised 7th degrees.
• This scale is useful in composition and will be important when studying harmony and chord progressions (covered in later lectures).

🎤 Melodic minor

Melodic minor: ascending form raises both the 6th and 7th degrees; descending form reverts to the natural minor.

• Why it exists: The big interval (three semitones) between the 6th and raised 7th in the harmonic minor is awkward to sing.
• Ascending form: Raises both 6th and 7th degrees to smooth out the melodic shape.
  • Example: F-sharp minor melodic ascending: F-sharp, G-sharp, A, B, C-sharp, D-sharp (raised 6th), E-sharp (raised 7th), F-sharp.
• Descending form: The leading-note function is less important going down, so both the 6th and 7th revert to natural minor.
  • Example: F-sharp minor melodic descending: F-sharp, E (natural 7th), D (natural 6th), C-sharp, B, A, G-sharp, F-sharp.
• Don't confuse: This is the only scale type where ascending and descending forms differ.

🎧 Why you must listen

• The differences between the three minor scales "only make proper sense when you consider how they sound."
• You must play or sing these scales to understand how the variations create different musical patterns.
• The excerpt emphasizes that intervals and tonality are about heard experience, not just theory on paper.

📚 Practice and memorization

📚 Learn the pairs

• Spend time working out pairs of relative majors and minors.
• The excerpt stresses: "There's no shortcut: just do it, through practice and repetition."
• Use the circle of fifths to find relative minors quickly.
• Practice counting scale degrees and semitone intervals to reinforce the relationships.

🧭 Overview

🧠 One-sentence thesis

Intervals describe the audible quality between two pitched notes, and to fully name them you need both a numeric count (e.g., 3rd, 6th) and a quality descriptor (e.g., major, minor, perfect), which can be determined by comparing the interval to the major scale built on the lower note.

📌 Key points (3–5)

• What an interval is: the particular sounded (audible) quality generated between two tuneful notes—it's about heard experience, not just abstract theory.
• Two pieces of information needed: the numeric interval (count the steps from lower to higher note, inclusive) and the quality (major, minor, perfect, augmented, or diminished).
• How to find the quality: imagine the lower note is the tonic of a major key, then check whether the upper note belongs to that major scale; if yes, the interval is major (for 2nd, 3rd, 6th, 7th) or perfect (for unison, 4th, 5th, octave).
• Common confusion: the same numeric interval (e.g., two different 3rds or two different 7ths) can have different qualities—don't stop at counting steps; you must also determine the quality.
• How qualities change: making a major interval smaller by a semitone yields a minor interval; making a perfect interval larger by a semitone yields an augmented interval; making a perfect interval smaller yields a diminished interval.

🔢 Calculating the numeric interval

🔢 Counting steps inclusively

• Start on the lower note and count up to the higher note, including the starting note.
• Example: C to A → C=1, D=2, E=3, F=4, G=5, A=6 → the interval is a 6th.
• If you have a maths or science background, think of this as a bounded interval containing all endpoints.

🔢 Why the count matters

• The numeric interval tells you the "size" category (unison, 2nd, 3rd, 4th, etc.), but it does not tell you the exact sound quality.
• Two intervals with the same numeric count can sound different because of accidentals (sharps or flats).

🎵 Determining the quality

🎵 Using the major scale as reference

The major scale pattern is a useful starting point because it's constant (T T S T T T S) and doesn't have variations or alterations, compared to minor scales.

• Imagine the lower note is the tonic of a major key.
• Check whether the upper note belongs to that major scale.
• If yes, the interval is major (for 2nd, 3rd, 6th, 7th) or perfect (for unison, 4th, 5th, octave).
• Example: C to A → in C major, A is scale degree 6 → the interval is a major 6th.

🎵 Quality labels from the major scale

Interval from tonic	Quality
Unison	Perfect
2nd	Major
3rd	Major
4th	Perfect
5th	Perfect
6th	Major
7th	Major
Octave	Perfect

• Perfect intervals (unison, 4th, 5th, octave) are the same in both major and minor keys—hence "perfect."
• Major intervals (2nd, 3rd, 6th, 7th) are defined by the major scale.

🎵 When the upper note is not in the major scale

• If the upper note does not belong to the major scale of the lower note, the interval is not major.
• Example: C to A♭ → C major contains A♮, not A♭ → the interval is a semitone smaller than a major 6th → it becomes a minor 6th.
• Don't confuse: the numeric interval (6th) stays the same; only the quality changes.

🔄 How interval qualities change with semitones

🔄 From major intervals

• Major interval + 1 semitone (raise the upper note) → augmented interval.
• Major interval − 1 semitone (lower the upper note) → minor interval.
• Minor interval − 1 semitone (lower again) → diminished interval.

Example: a major 7th made smaller by a semitone becomes a minor 7th; a minor 7th made smaller by another semitone becomes a diminished 7th.

🔄 From perfect intervals

• Perfect interval + 1 semitone → augmented interval.
• Perfect interval − 1 semitone → diminished interval.

Example: a perfect 4th raised by a semitone becomes an augmented 4th; a perfect 5th lowered by a semitone becomes a diminished 5th.

🔄 Summary table

Starting quality	Change	Resulting quality
Major	+1 semitone	Augmented
Major	−1 semitone	Minor
Minor	−1 semitone	Diminished
Perfect	+1 semitone	Augmented
Perfect	−1 semitone	Diminished

🧩 Tricky examples and shortcuts

🧩 Canceling accidentals

• When both notes have the same type of accidental (e.g., both sharp or both flat), you can cancel them out to simplify the calculation.
• Example: D♯ to C♯ → cancel both sharps → D to C → count: D=1, E=2, F=3, G=4, A=5, B=6, C=7 → it's a 7th.
• Now check quality: D major has C♯ as scale degree 7 (a major 7th). But we canceled the sharps, so D to C♮ is a semitone smaller → minor 7th.
• Final step: D to C is a minor 7th, therefore D♯ to C♯ is also a minor 7th.

🧩 Why this works

• Raising or lowering both notes by the same amount does not change the interval size or quality.
• This trick helps you avoid imagining exotic keys like D♯ major (which is off the circle of fifths).

📏 Compound intervals

📏 What compound intervals are

A compound interval is a way of describing an interval that extends beyond an octave.

• If you count more than 8 steps (e.g., 9th, 10th, 11th), the interval spans more than one octave.
• Example: middle C up to F (an octave and a 4th higher) → count gives 11 → it's an 11th.

📏 Re-imagining compound intervals

• You can re-imagine the interval by moving one note up or down an octave.
• Example: middle C to F (11th) → move the top F down an octave, or move the middle C up an octave → you get a perfect 4th.
• So the 11th can be described as a compound perfect 4th.
• This approach is common in jazz and popular music, where extended intervals are frequently used.

🎯 Practice and application

🎯 Why intervals can be tricky

• Intervals require both counting (numeric) and quality judgment (major, minor, perfect, etc.).
• Forgetting that intervals are about heard experience can lead to confusion—always think about the sound, not just the theory.

🎯 How to practice

• The excerpt recommends musictheory.net for interval practice.
• You can customize the difficulty using controls on the site.
• The best way to master intervals is through repeated practice and application.

🧭 Overview

🧠 One-sentence thesis

Western musical notation expresses note durations as fractions or multiples of a beat rather than absolute time, using a hierarchical system of symbols that can be subdivided into halves or grouped into tuplets.

📌 Key points (3–5)

• Duration is beat-relative, not absolute: notes are written as fractions/multiples of beats, not seconds; beats relate to pulse and tempo (beats per minute).
• Hierarchical subdivision by halves: the whole note (semibreve) divides into halves, quarters, eighths, sixteenths, etc., with both British and American names.
• Rests mirror note durations: every note duration has an equivalent rest symbol to indicate silence.
• Common confusion—flags vs beams: individual short notes use flags; when grouped, flags turn into horizontal beams to show beat boundaries and make reading easier.
• Tuplets allow non-binary divisions: triplets, quintuplets, etc., divide beats into 3, 5, or other arbitrary numbers instead of the standard powers of two.

🎵 Core concept: beat-relative duration

🎵 Why fractions of beats, not seconds

Duration in Western musical notation is expressed as fractions or multiples of a beat, rather than as a duration in seconds.

• Beats are related to (or synonymous with) pulse.
• Beats connect to tempo, often expressed as beats per minute.
• Rhythm concerns multiples or subdivisions of beats.
• This system makes notation independent of absolute time—the same written rhythm can be played faster or slower by changing tempo.

🎼 Notation uses both notes and rests

• Rhythm is expressed symbolically in the form of both rests and notes.
• Rests indicate where a musician stops playing.
• Most music consists of notes surrounded by space; otherwise musicians would never get a chance to breathe or rest, and neither would the music.

🔢 The hierarchical subdivision system

🔢 The whole note (semibreve) as the reference

• All Western rhythmic notations are related to the whole note (American) or semibreve (British).
• In 4/4 meter (the most common meter), the semibreve represents the full duration of one bar.
• The semibreve can be subdivided, and these subdivisions have different names.

📊 British vs American nomenclature

Division	British name	American name	Relationship
1	Semibreve	Whole note	Full bar in 4/4 (4 beats)
1/2	Minim	Half note	Two per semibreve
1/4	Crotchet	Quarter note	Four per whole note
1/8	Quaver	Eighth note	Eight per whole note
1/16	Semiquaver	Sixteenth note	Sixteen per whole note

• American nomenclature advantage: derived from German; makes it easy to see how many of a particular rhythm fit in a whole note (all rhythms expressed in relation to the whole note).
• Example: "quarter note" immediately tells you there are four in a whole note; "eighth note" tells you there are eight.

🎶 Visual notation recap

• Whole note/semibreve: open round note symbol (4 beats long in 4/4 meter).
• Half note/minim, quarter note/crotchet, eighth note/quaver, sixteenth note/semiquaver: progressively shorter durations.
• Each subdivision is half the duration of the previous level.

🔇 Equivalent rest symbols

• Every note duration has a corresponding rest symbol.
• Listed in the excerpt:
  • Semibreve/whole note rest
  • Minim/half note rest
  • Crotchet/quarter note rest
  • Quaver/eighth note rest
  • Semiquaver/sixteenth note rest

🏴 Flags and beams for short notes

🏴 How flags work

• Quaver (eighth note) and semiquaver (sixteenth note) notes are essentially crotchets (quarter notes) with little flags on their stems.
• Each flag you add divides the rhythm by two.
• Example progression:
  • Crotchet (no flag) → quaver (1 flag) → semiquaver (2 flags) → demisemiquaver/32nd note (3 flags) → hemidemisemiquaver/64th note (4 flags), etc.

🔗 When flags become beams

Flags can turn into what we call beams.

• Beams are used to group notes into twos, fours, eights, etc.
• Purpose: to easily see a beat's worth (or sometimes more) of shorter notes.
• This makes it easier to orientate ourselves in the flow of the music—we can recognize where the beat boundaries are.
• The number of flags in individual notes is reflected in the number of horizontal beams.
• Adding one more beam is equivalent to adding one more flag (subdividing the rhythm into two).
• Don't confuse: flags are for individual notes; beams connect multiple notes to show grouping and beat structure.

🎲 Tuplets: non-binary divisions

🎲 What tuplets are

Tuplets: divisions of rhythms into subdivisions of three, five, seven, etc.—any arbitrary division of a note.

• Standard subdivision is always by two (half, quarter, eighth, etc.).
• Tuplets allow other divisions.
• The most common tuplet is the triplet.

🎵 Triplets explained

• Three triplet quavers (eighth notes) to a quarter note: three in the time of two.
• Three triplet quarter notes to a half note.
• Any basic rhythm can be subdivided in this manner.
• Example: if a beat goes at quarter-note speed, triplets would be "one two three, one two three, one two three…"

🎶 Other tuplet types

• Quintuplets: divide a note into five equal parts.
• Example from the excerpt: divide a minim (half note) into five quintuplet eighth notes.
• Counting: "1, 2, 3, 4, 5. 1, 2, 3, 4, 5…"
• Tuplets can be any arbitrary division, though triplets are most common.

🧭 Overview

🧠 One-sentence thesis

Tuplets allow musicians to divide rhythms into arbitrary subdivisions—most commonly three notes in the time of two—making it possible to create rhythmic patterns that don't fit regular binary divisions.

📌 Key points (3–5)

• What tuplets are: divisions of notes into arbitrary groupings (three, five, seven, etc.) rather than the standard binary subdivisions.
• Most common type: triplets—three notes played in the time of two (e.g., three triplet eighth notes fit into one quarter note).
• How they're notated: a number above a beam (implicit ratio) or a bracket with a number (explicit ratio like "4:3" when needed).
• Common confusion: the number above the beam means "this many notes in the time of the usual number"—three triplet eighth notes take the same time as two regular eighth notes, not three.
• Why they matter: tuplets enable rhythmic flexibility beyond simple binary divisions, making it easier to create varied musical flows.

🎵 What tuplets are and why we need them

🎵 Beyond binary subdivision

• Standard rhythm notation divides notes into two: one quarter note splits into two eighth notes, one eighth note splits into two sixteenth notes, etc.
• Tuplets break this pattern by allowing arbitrary divisions: three, five, seven, or any other number.
• This flexibility helps composers and performers create rhythms that don't fit neatly into binary subdivisions.

🎶 The triplet—most common tuplet

Triplet: three notes played in the time of two equivalent notes.

• Three triplet eighth notes fit into the duration of one quarter note (which normally holds two eighth notes).
• Three triplet quarter notes fit into the duration of one half note (which normally holds two quarter notes).
• Example: If a beat goes at quarter-note speed, triplets would be counted "one-two-three, one-two-three, one-two-three…"

🔢 Other tuplet types

• Quintuplets: five notes in the time of a standard duration.
  • Example: divide a half note into five quintuplet eighth notes, counted "1-2-3-4-5, 1-2-3-4-5…"
• Any basic rhythm can be subdivided this way, though triplets are by far the most common in practice.

✍️ How tuplets are notated

✍️ Number above a beam

• The simplest notation: place a number (e.g., "3") above the beam connecting the notes.
• The number implicitly means "this many notes in the time of the usual number."
  • A "3" above three eighth notes means "three in the time of two."
  • Normally, a quarter note divides into two eighth notes; the "3" tells you to fit three eighth notes into that same quarter-note duration.

🔖 Brackets and explicit ratios

• When notes don't have flags or beams (e.g., triplet quarter notes), use a bracket to group the notes with the number.
• If the ratio isn't obvious, you can write it explicitly, such as "4:3" (four notes in the time of three).
• This clarifies exactly how many shorter notes fit into how many longer notes.

🚫 Don't confuse: what the number means

• The number above the tuplet does not mean "play this many notes at normal speed."
• It means "squeeze this many notes into the space normally occupied by fewer notes."
• Example: Three triplet eighth notes take the same total time as two regular eighth notes, not three regular eighth notes.

🧩 Practical understanding

🧩 Recognizing tuplets in context

• Tuplets help you orientate yourself in the flow of music by creating rhythmic variety.
• They can sometimes be confusing at first because they break the usual binary pattern.
• The excerpt encourages learners to use forums and discussion to clarify concepts like tuplets.

🧩 Counting and performing tuplets

• Triplets: count evenly in groups of three within one beat or standard duration.
  • Example: "one-two-three, one-two-three…" fits three syllables into each beat.
• Quintuplets: count evenly in groups of five.
  • Example: "1-2-3-4-5, 1-2-3-4-5…" fits five syllables into the space of a standard duration.
• The key is to divide the time evenly among all the notes in the tuplet, not to rush or drag.

🧭 Overview

🧠 One-sentence thesis

Ties and dots are two notational tools that extend a note's duration beyond regular beat divisions, with dots adding half the original duration and ties connecting separate notes into one continuous sound.

📌 Key points (3–5)

• What ties do: connect two notes so they are played as one extended duration, not as two separate attacks.
• What dots do: a dot immediately to the right of a note extends its duration by half its original value (e.g., a dotted quarter note = 1.5 quarter notes).
• Common confusion: a dot to the right of a note affects rhythm/duration; a dot above or below a note indicates staccato articulation and has nothing to do with rhythm.
• Multiple dots: two dots extend by half + half of that half; triple and quadruple dots exist but are rare.
• Ties vs dots: when a note is tied to another note that is half its duration, you can replace the tie with a single dot (they mean the same thing).

🔗 Ties: connecting notes into one duration

🔗 What a tie does

A tie is a line connecting one note to another, meaning the note is played as one extended duration rather than two separate notes.

• You do not play the second note again; you hold the first note through the combined duration.
• Example: a quarter note tied to an eighth note = one note lasting 1.5 beats, not two separate attacks.

🔄 When ties and dots are equivalent

• The excerpt states: "In this simple case of a quarter note tied to an eight note we can use a dot to indicate exactly the same duration."
• The key is that the second tied note is half the duration of the first.
• Example: quarter tied to eighth = dotted quarter (both = 1.5 beats).

🔵 Dots: extending duration by half

🔵 What a dot means

A dot immediately to the right of a note extends the indicated duration by half its duration again.

• A dotted quarter note lasts 1.5 quarter notes (1 + 0.5).
• A dotted eighth note lasts 1.5 eighth notes, equivalent to tying an eighth to a sixteenth.

⚠️ Don't confuse: dot position matters

Dot position	Meaning	Related to rhythm?
Immediately to the right of the note	Extends duration by half	Yes
Immediately above or below the note	Staccato articulation (detached)	No

• The excerpt warns: "you've got to be careful here"—a dot above/below is "another matter altogether and nothing to do with rhythm."

🔵🔵 Multiple dots

• Two dots: extend by half + half of that half.
  • Example: a double-dotted quarter note = 1 + 0.5 + 0.25 = 1.75 quarter notes.
• Triple or quadruple dots: exist but are "a lot less common."

⏸️ Other rhythm symbols

⏸️ Pause or fermata

• Symbol placed over any note or rhythm.
• Indicates an out-of-time pause whose length is determined by the musician.
• General rule of thumb: about twice as long as the indicated duration.

✍️ Writing rhythms: spacing and alignment

✍️ Horizontal spacing

• It would be reasonable to assume a quarter note takes the horizontal space of two eighth notes.
• Some composers prefer this; most publishers "squash longer durations into less horizontal space."
• You can adopt either approach when writing.

✍️ Vertical alignment

• When writing more than one part, coincident notes must vertically align so you can see which notes sound together.
• This is the key constraint: alignment shows simultaneity.

🧭 Overview

🧠 One-sentence thesis

Metre organizes music into regular groupings of beats per bar, with time signatures indicating how many beats and what type, and simple versus compound metres determining how those beats subdivide.

📌 Key points (3–5)

• What metre does: groups music into bars with a fixed number of beats (most commonly 2, 3, or 4 beats per bar).
• How time signatures work: the top number shows how many beats per bar; the bottom number shows the beat type (e.g., 4/4 = four quarter notes per bar).
• Strong vs weak beats: Western classical music typically accents downbeats (odd beats like 1 and 3), while pop/jazz often emphasizes off-beats (even beats like 2 and 4).
• Common confusion—simple vs compound: simple metres divide beats into groups of two (e.g., 4/4 subdivides into eighth notes); compound metres use dotted notes as the basic beat and subdivide into three (e.g., 6/8 feels like two dotted quarter notes, each split into three eighth notes).
• Why it matters: metre creates the rhythmic framework and characteristic feel of different musical styles.

📏 What metre is and how it works

📏 Organizing music into bars

Metre: the rhythmic grouping of music into bars, each containing a fixed number of beats.

• Music is most often organized into groups of 2, 3, or 4 beats per bar.
• Bar lines mark the boundaries between bars to make reading easier.
• Less common groupings include 5, 7, 8, 10, or any number of beats, but 2, 3, and 4 are standard.

🏷️ Types of metre by beat count

Metre type	Beats per bar	Typical genre
Duple	2	Marches
Triple	3	Waltzes
Quadruple	4	Western classical, electronic dance music

• Quadruple metre (4 beats per bar) is so common in Western classical and electronic dance music that it is called "common time."
• The beat can be any basic rhythmic duration (quarter notes, eighth notes, half notes, etc.), though quarter notes (crotchets) are most typical.

🔢 Time signatures

🔢 How to read a time signature

Time signature: two numbers (like a fraction) that indicate metre—the numerator shows how many beats per bar, the denominator shows the beat type.

• Numerator (top number): how many beats are in each bar.
• Denominator (bottom number): what type of note gets one beat.
• Example: 4/4 means four quarter notes (crotchets) per bar.
• Example: 3/8 means three eighth notes (quavers) per bar.

🎵 Common time notation

• 4/4 is so common it is called "common time."
• Sometimes written as a C symbol instead of 4/4—they mean exactly the same thing.
• Cut-common time is 4/4 "cut" in two to make 2/2 time.

Don't confuse: the C symbol is not the letter C for "common"; it is an alternative time signature symbol for 4/4.

🎶 Strong and weak beats

🎶 Accent patterns in different styles

• Each bar tends to have strong (accented) beats and weak (unaccented) beats.
• Western classical music: typically favors downbeats (odd beats).
  • In 4/4, beats 1 and 3 are accented.
  • Example: Mozart's "Eine kleine Nachtmusik" clearly accents beats 1 and 3.
• Pop and jazz music: often favors off-beats (even beats).
  • In 4/4, beats 2 and 4 are accented.
  • This creates the characteristic rhythmic feel, often with a strong snare drum on those off-beats.

Don't confuse: downbeats vs off-beats—downbeats are the odd-numbered beats (1, 3); off-beats are the even-numbered beats (2, 4).

🔀 Simple vs compound metre

🔀 Simple metre

Simple metre: beats divide into groups of two, four, eight, etc. (powers of two).

• The basic beat subdivides into two equal parts.
• Example: in 4/4, each quarter note beat subdivides into two eighth notes, four sixteenth notes, etc.
• Simple metres use regular (undotted) notes as the basic beat.

🔀 Compound metre

Compound metre: uses dotted rhythms as the basic beat, making it easy to subdivide into three.

• The basic beat subdivides into three equal parts.
• The most common compound metre is 6/8.
  • 6/8 has six eighth notes (quavers) per bar.
  • But it is felt as two dotted quarter notes per bar, each subdivided into three eighth notes.
  • This avoids having to write triplets constantly.
• Example: 6/8 is equivalent to a 2/4 bar with triplet eighth notes, but the compound notation is cleaner.

🔀 How to distinguish simple from compound

Feature	Simple metre	Compound metre
Basic beat	Undotted note	Dotted note
Subdivision	Groups of 2, 4, 8	Groups of 3
Common example	4/4 (four quarter notes)	6/8 (two dotted quarter notes)
Feel	Even divisions	Lilting, triplet feel

Don't confuse: 6/8 is not six beats per bar—it is two beats per bar, each subdivided into three eighth notes.

🧭 Overview

🧠 One-sentence thesis

Common time is a widely used time signature in Western music that organizes four crotchet (quarter note) beats per bar, and it is so prevalent that it has its own alternative symbol (C) and serves as the foundation for understanding metre and time signatures.

📌 Key points (3–5)

• What common time is: another name for four-four time (4/4), meaning four crotchets (quarter notes) per bar.
• Why it's called "common": this time signature is extremely prevalent in Western classical music and electronic dance music.
• Alternative notation: the symbol C can be written instead of 4/4 to indicate common time.
• Related concept: Cut-Common Time is 4/4 "cut" in two to make 2/2 time.
• Common confusion: don't confuse the C symbol with something else—it stands for common time and is exactly the same as 4/4.

🎵 What common time means

🎵 Definition and structure

Common time: another name for four-four time (4/4), consisting of four crotchets (quarter notes) per bar.

• The name comes from how frequently this time signature appears in music.
• It represents quadruple meter: four beats per bar.
• The excerpt emphasizes that four-four is "most common in western classical music or electronic dance music."

🔤 The C symbol

• Instead of writing 4/4, composers sometimes write the symbol C.
• This is simply an alternative notation—the C stands for "common time."
• The excerpt advises: "If you see this time signature written in music, don't panic."
• Example: A piece marked with C has exactly the same rhythmic structure as one marked 4/4.

✂️ Cut-Common Time

• This is a related concept: 4/4 "cut" in two.
• It produces 2/2 time (two minim/half-note beats per bar).
• Don't confuse: Cut-Common Time is not the same as common time—it has a different number of beats per bar.

📏 Understanding metre and time signatures

📏 What metre organizes

• Music is organized into groups of beats per bar, most often two, three, or four.
• Bar lines indicate bar boundaries and make reading easier.
• The excerpt notes that "any grouping is possible," but two, three, and four are most common.

🔢 How time signatures work

Time signature: two numbers (numerator and denominator) that indicate metre; the numerator tells how many beats per bar, the denominator indicates the beat type.

Component	What it tells you	Example (4/4)
Numerator (top number)	How many beats per bar	4 beats
Denominator (bottom number)	Beat type (which note value)	Quarter notes (crotchets)

• Four-four means four quarter notes (crotchets) per bar.
• Three-eighth means three quaver (eighth notes) per bar.
• The beat can be any basic rhythmic duration (minims, quavers, etc.), though crotchets are most common.

🎼 Types of metre

Metre type	Beats per bar	Typical use	Example
Duple	2	Marches	2/4
Triple	3	Waltzes	3/4
Quadruple	4	Western classical, electronic dance	4/4 (common time)

• Less standard groupings include five, seven, eight, or ten beats.
• Quadruple meter (four beats per bar) is the most common, hence "common time."

🎯 Accents and beat emphasis

🎯 Strong and weak beats

• Each bar tends to have weak or strong beats.
• In Western classical music, downbeats (odd beats) are generally favoured.
• Example: In a four-four bar, the accent is generally on beats one and three, as heard in Mozart's 'Eine kleine Nachtmusik'.

🎶 Pop and jazz differences

• Some pop and jazz music favours the off-beats or even beats.
• In a four-four bar, this means beats two and four.
• This creates "the characteristic rhythmic feel we associate with this type of music, very often with a strong snare drum stroke on those off beats."
• Don't confuse: classical emphasis (beats 1 and 3) vs. pop/jazz emphasis (beats 2 and 4) give different rhythmic feels even in the same time signature.

🔀 Simple vs. compound metres

🔀 Simple metres

• Simple meters divide into beats of two, four, eight, etc. (powers of two).
• Example: A simple four-four bar subdivides into eighth notes, sixteenth notes, etc.
• The basic beat is not dotted.

🔀 Compound metres

• Compound meters use dotted rhythms as their basic beat, making it easy to subdivide into three.
• The most common compound meter is six-eight (6/8).
• Six-eight has six quavers (eighth notes) per bar, but is felt as two dotted crotchets (dotted quarter notes) per bar, each subdivided into three.
• This avoids having to write tuplets or triplets constantly.
• Example: The equivalent of compound metre subdivision would be a triplet eighth note in a two-four bar.

📚 Terminology notes

📚 UK vs. American terms

The excerpt references an external tutorial that uses American terminology and provides translations:

American term	UK term
Staff	Stave
Measure	Bar
Quarter notes	Crotchets
Eighth notes	Quavers
Half notes	Minims
Whole notes	Semibreves

• It is useful to be familiar with both sets of terms when reading music theory materials.

🧭 Overview

🧠 One-sentence thesis

Music is organized hierarchically from small rhythmic units up through beats, bars, phrases, and larger sections, with anacrusis (pickup notes) and motives serving as structural tools that shape how melodies begin and develop.

📌 Key points (3–5)

• Anacrusis (pickup notes): an under-full bar at the start of a piece, typically just the last beat before the first full downbeat.
• Phrase structure: phrases are melodic units of several bars (most often four) that feel more or less complete and are articulated by harmony and cadences.
• Hierarchy of structure: rhythms group into beats → beats into bars → bars into phrases → phrases into periods/sections → sections into movements or songs.
• Motives vs phrases: motives are short, easily recognizable musical statements (often repeated and varied), shorter than phrases but can form or contribute to complete phrases.
• Common confusion: phrase marks and slur lines look similar but are not equivalent—phrase marks show melodic units; slur lines indicate passages performed in one breath.

🎵 Anacrusis and pickup notes

🎵 What anacrusis is

Anacrusis: a partial bar before the first full bar, containing the note or group of notes that happens before the first downbeat.

• Also called "pickup" or "pickup notes."
• The piece or section begins with an under-full bar, most characteristically just the last beat.
• Example: "Happy Birthday to You" and the main theme of the final movement of Brahms's First Symphony both start with pickup notes.

⚖️ Balancing the final bar

• In written Western music, when a piece has an anacrusis, the same number of beats are typically absent from the final bar.
• This ensures the total number of bars in the music is a whole number.

🔁 Anacrusis in phrases

• When music uses anacrusis, each phrase in the music tends to start with the pickup note.
• The pickup note becomes a recurring structural feature throughout the piece.

📐 Phrases and their structure

📐 What a phrase is

Phrase: a part of a melody consisting of a group of several bars (most often four) that forms a melodic unit feeling more or less complete, depending on its harmonic context at the end.

• Phrases are generally articulated by harmony, particularly by cadences (covered in week five).
• Not coincidentally, a phrase is often the approximate length of a singer's or wind player's breath.
• There might be rests at the end of a phrase where performers can take a breath.

🎼 Notation of phrases

• Phrases may be indicated by a curved line above the stave.
• This looks similar to a wind player's slur line (which indicates a passage performed in one breath).
• Don't confuse: phrase marks and slur lines are related and look the same, but they are not equivalent.

🏛️ Hierarchy of musical structure

The excerpt describes a clear hierarchy from smallest to largest units:

Level	Unit	Groups into
Smallest	Rhythms	Beats
	Beats	Bars
	Bars	Phrases
	Phrases	Periods or phrase groups
	Periods/sections	Movements or songs
Largest	Movements	Symphonies, concertos, etc.; or songs into albums

🎭 Periods and phrase groups

• Phrases group into periods (when grouped into pairs) or phrase groups (when not paired).
• Example from "Greensleeves": the melody consists of four four-bar phrases grouped into two periods.
• Each period has an antecedent phrase (doesn't come home to the tonic) and a consequent phrase (does come home to the tonic).

🧩 Motives and melodies

🧩 What a motive is

Motive (or motif): a concise musical signpost, usually a short musical statement easily recognizable by its strong rhythmic or intervallic character.

• Motives are often repeated considerably and developed and varied both rhythmically and melodically during a piece.
• They are usually shorter than what we'd normally consider a phrase.
• A motive can by itself, or in combination with extensions of itself, form a complete phrase of music.

🎺 Famous motive example

• The most famous music motive in Western classical music is found at the very opening of Beethoven's Fifth Symphony.
• This is typical of motives: an isolated short statement with strong character.

🎶 Melodies and their scope

• Melodies sit somewhere between phrases and sections in the structural hierarchy.
• The confines of melodies are open-ended: they may or may not constitute a complete section, depending on stylistic context.
• It depends on how long the melody is (Wagner's melodies were famously never-ending).
• Melodies generally consist of several phrases.

🍃 "Greensleeves" example

The excerpt uses "Greensleeves" to illustrate multiple concepts:

• Meter: six-eight (compound duple with two dotted crotchet beats per bar).
• Anacrusis: pickup on the last eighth note (last quaver) of the six-eight bar.
• Phrase structure: four four-bar phrases.
• Period structure: two periods, each with two phrases (antecedent and consequent).
• Harmonic function: antecedent phrase doesn't return to the tonic of G; consequent phrase does come home.

🧭 Overview

🧠 One-sentence thesis

Musical form is the hierarchical organization of sections and their repetitions into movements, with basic patterns like Binary (A B), Ternary (A B A), and Rondo (A B A C A) providing structural frameworks for composition.

📌 Key points (3–5)

• Hierarchical structure: Form builds from bars → phrases → periods → sections → movements/songs.
• Binary Form: Two sections (A and B), usually with B in a different key; both sections are often repeated.
• Ternary Form: Three-part structure (A B A) with a return to the opening section after a contrasting middle section.
• Common confusion: The returning A section may be modified (notated A'), not always identical to the original.
• Other forms: Rondo (recurring section between contrasting sections) and 12 Bar Blues (repeating form) are also common.

🏗️ Building blocks of form

🏗️ Hierarchical relationships

• Form emerges from clear layers of organization:
  • Bars → phrases
  • Phrases → periods
  • Periods → sections
  • Sections → movements and songs
• The excerpt notes that once phrases are built into sections, these sections and their repetitions can be combined into movements.

🎵 Motives and phrases

Motives: short musical statements that are easily recognizable by their strong rhythmic or intervallic character.

• Motives are usually shorter than a phrase but can form a complete phrase by themselves or with extensions.
• They are often repeated and developed (varied rhythmically and melodically) throughout a piece.
• Example: Beethoven's Fifth Symphony opening is described as "the most famous music motive in Western classical music"—an isolated short statement.

🎶 Melodies

• Melodies sit "somewhere between phrases and sections."
• Their boundaries are open-ended and depend on stylistic context and length.
• Generally consist of several phrases.
• Example: The tune Greensleeves has four four-bar phrases grouped into two periods (each period has an antecedent phrase that doesn't resolve to the tonic and a consequent phrase that does).

📐 Basic formal structures

📐 Binary Form (A B)

• The simplest form: two sections, A and B.
• Section B is usually closely related in character to A but in a different key.
• Both sections are quite likely to be repeated.

Feature	Description
Structure	A B
Key relationship	B typically in a different key from A
Repetition	Both A and B are often repeated

🔄 Ternary Form (A B A)

• Three-part structure with a return to the opening section after a contrasting middle.
• Section B changes key; then the piece returns to A.
• The returning A may be modified, notated as A' (A prime), with the apostrophe signifying modification.

Feature	Description
Structure	A B A (or A B A')
Key relationship	B in a different key; A returns (possibly modified)
Modification	A' indicates a modified return

Don't confuse: The return of A is not always identical—it may be varied or developed.

🎼 Sonata Form

• Closely related to Ternary Form; common in Western classical period first movements (symphonies, sonatas, concertos).
• Basic structure: A B A' labeled as:
  • Exposition (A)
  • Development (B)
  • Recapitulation (A')
• The excerpt suggests reading more via a Wikipedia link for further detail.

🔁 Rondo Form

• Features a recurring section between contrasting sections.
• Example structure: A B A C A (or similar patterns).
• The A section returns multiple times, alternating with different contrasting material.

🎸 12 Bar Blues Form

• A very common repeating form.
• The excerpt mentions it as a "repeating 12 Bar Blues Form" but does not detail its internal structure.
• Further reading is suggested via a Wikipedia link.

🔁 Repeat marks and notation

🔁 How repeat marks work

Repeat marks: symbols used to indicate a section of music that should be repeated.

• Single repeat sign: means repeat from the beginning, then continue.
• Paired repeat signs (facing opposite directions): the second sign indicates where the repeated section begins.
• When repeated once, the player ignores the repeat mark to avoid an infinite loop.

🔢 First and second endings

• When a repeat calls for a different ending, number brackets above the bars indicate which to play:
  • 1 = first-time bar (play the first time through)
  • 2 = second-time bar (play the second time through)
• Also called "first and second endings."

Example: All music within the repeat marks should be repeated; numbered endings guide which bars to play on each pass.

🧭 Overview

🧠 One-sentence thesis

Triads are three-note chords identified by their root note and character (major, minor, augmented, or diminished), and they remain identifiable even when their notes are rearranged into different inversions.

📌 Key points (3–5)

• What a triad is: a 3-note chord containing a root, a third, and a fifth.
• Four triad types: major, minor, augmented, and diminished—distinguished by the intervals between root, third, and fifth.
• Inversions: triads can be rearranged (root position, first inversion, second inversion) without changing their identity, though the arrangement affects the sound.
• Common confusion: even when notes are reordered, the root note remains perceptually the most important and identifies the chord—don't confuse the lowest-sounding note with the root in inverted chords.
• Labeling system: Roman numerals with letters (a, b, c) indicate chord position and inversion.

🎵 What triads are and how they're built

🎵 Definition and structure

A triad is a 3-note chord containing a root, a third, and a fifth.

• Built by playing a note, skipping a note, playing a note, skipping a note.
• Example: starting on F, play F (root), skip G, play A (third), skip B, play C (fifth) → F-A-C triad.
• The bottom note (root) is the one that "sticks out to our ears" perceptually.

🎧 Perceptual importance of the root

• When a triad is played, the root note is the most important perceptually, even if multiple notes are sounded.
• Example: In a demonstration, after hearing a series of triads, a listener hummed the root note (the tonic key note) because it stood out most strongly.
• Even when notes repeat across octaves in different voices, the root remains the strongest and identifies the chord.

🎨 Four types of triads

🎨 Distinguishing triad types by intervals

All triads share a root and a fifth, but the third determines the character (major vs. minor vs. augmented vs. diminished).

Triad type	Root to third	Root to fifth	Notes (example on C)	Special feature
Major	Major third (4 semitones)	Perfect fifth (7 semitones)	C, E, G	—
Minor	Minor third (3 semitones)	Perfect fifth (7 semitones)	C, E♭, G	—
Augmented	Major third (4 semitones)	Augmented fifth (8 semitones)	C, E, G♯	Consecutive major thirds
Diminished	Minor third (3 semitones)	Diminished fifth (6 semitones)	C, E♭, G♭	Consecutive minor thirds

🔑 The third is the key

• The interval between the root and the third distinguishes major from minor.
• The interval from root to fifth is a perfect fifth (7 semitones) for both major and minor triads.
• Don't confuse: the fifth is the same for major and minor; the third is what changes the "flavor."

🔄 Inversions: rearranging triad notes

🔄 What inversion means

Inversion: re-ordering the notes of a triad so that a note other than the root is the lowest pitch.

• All triads shown initially are in root position: root is the lowest pitch (e.g., C-E-G).
• Notes can appear vertically in any order and still be identified as the same chord.
• Example: C-E-G, E-G-C, and G-C-E all contain C, E, and G, so all are C major triads.

🔄 Three positions

Position	Lowest note	Example (C major)	Label
Root position	Root	C, E, G	Va (or just V)
First inversion	Third	E, G, C	Vb
Second inversion	Fifth	G, C, E	Vc

• The position affects the sound and how the chord relates to other chords in a progression.
• Don't confuse: the root note is still the perceptual "identity" of the chord, even when it's not the lowest-sounding note.

🏷️ Labeling system

• Roman numerals indicate the chord (e.g., V = dominant chord, built on scale degree 5).
• Letters a, b, c indicate inversion:
  • a = root position (often implied, so "V" alone means Va).
  • b = first inversion.
  • c = second inversion.
• For chords with more than 3 notes (e.g., 7th chords with 4 notes), the system expands to include d for third inversion.

🎧 Perceptual stability of the root

• Even when notes are rearranged, the root note remains the one that identifies the chord.
• Example: In a demonstration, after hearing an A-minor chord with many repeated As, Cs, and Es in different voices, the listener sang the note A because the root was perceptually strongest.
• This is how we identify a chord as an "A triad" regardless of inversion.

📚 Additional context

📚 Why inversions matter

• Inversions affect the sound of the chord and its relationships in harmonic progressions.
• The excerpt notes that inversions will be addressed more fully in Topic 5 of the course.
• For now, the videos keep triads in root position to make it easier to talk about the first, third, and fifth.

🧭 Overview

🧠 One-sentence thesis

Cadences—harmonic progressions that create finality or pause—arise from the structural relationships between triads built on different scale degrees, especially the dominant and tonic, and these relationships establish the tonal identity of a key.

📌 Key points (3–5)

• What a cadence is: a melodic or harmonic progression that creates a sense of finality (finished) or pause (unfinished).
• Perfect vs imperfect cadence: V7→I sounds finished (perfect); I→V7 sounds unfinished (imperfect) because it ends on the unstable dominant.
• Why cadences work: the dominant triad (built on scale degree 5) contains scale degrees 5, 7, and 2; the tonic triad (built on degree 1) contains 1, 3, and 5—movement from dominant to tonic creates resolution.
• Common confusion: "imperfect" does not mean "wrong"—it means the music pauses on the dominant chord, which sounds unresolved and requires continuation.
• Key and harmony as building blocks: harmony describes the effect and relationships of triads within a key; together, key and harmonic structure are the two most important building blocks for tonal music.

🎵 What cadences are and how they sound

🎵 Definition of cadence

A cadence: a melodic or harmonic progression that creates a sense of finality or a pause in the music.

• Cadences mark structural points where music "comes to rest."
• Some cadences sound finished (closed); others sound unfinished (open).
• The excerpt emphasizes that cadences are created by specific chord progressions.

✅ Perfect cadence (finished sound)

• Chord progression: V7 → I (dominant seventh chord followed by tonic chord).
• Example in C major: G7 → C.
• Why it sounds finished: moving from the dominant (unstable) to the tonic (stable) creates a sense of resolution and "coming home."
• The excerpt calls this a perfect cadence because it provides full closure.

⏸️ Imperfect cadence (unfinished sound)

• Chord progression: I → V7 (tonic chord followed by dominant seventh chord).
• Example in C major: C → G7.
• Why it sounds unfinished: ending on the dominant seventh chord leaves the music hanging—the dominant is unstable and "sounds as if it requires a resolution."
• Don't confuse: "imperfect" does not mean defective; it means the cadence pauses without full closure, creating expectation for continuation.

🏗️ How triads and scale degrees create cadences

🏗️ Tonic and dominant triads

The excerpt identifies two triads with "particularly strong structural properties":

Triad	Scale degrees	Example in C major	Structural role
Tonic (I)	1, 3, 5	C, E, G	Stable; "home" chord
Dominant (V)	5, 7, 2	G, B, D	Unstable; creates tension

• The tonic triad is built on the first degree of the scale and contains the 1st, 3rd, and 5th scale degrees.
• The dominant triad is built on the fifth degree and contains the 5th, 7th, and 2nd scale degrees.
• These two triads are the most important for establishing harmonic structure in a key.

🎶 Melody and cadence in "Twinkle, Twinkle Little Star"

The excerpt uses a familiar tune to illustrate cadences by singing scale degree numbers:

• Unfinished phrase: "Up above the world so high, like a diamond in the sky"—ends on scale degrees that belong to the dominant chord (especially 5 and 2), creating an open, unfinished feeling (imperfect cadence).
• Finished phrase: "Twinkle, twinkle little star, how I wonder what you are"—ends by moving from dominant chord notes back to the tonic (ending on scale degree 1), creating closure (perfect cadence).
• Example: the melody "four, four, three, three, two, two, one" moves away from the dominant and returns to the tonic, producing a sense of completion.

🔑 Tonality and tonal identity

Tonality: the quality of the key; the overarching sense created by the relationships between and within triads in a key.

• The excerpt states that "key and harmonic structure, or key and harmony, are the two most important building blocks for music that sits in a tonal tradition."
• A strong tonal identity means the tonic (e.g., C in the key of C major) comes across very clearly as the "home" note.
• Harmony describes "the effect of those triads...and the relationships and the patterns between the triads when we use them in a key."

🔧 Keys, scales, and triads recap

🔧 Key signatures and scales

• The major scale has a distinctive pattern: tone, tone, semitone, tone, tone, tone, semitone.
• Key signatures signal which sharps or flats will be used in a piece, allowing any of the twelve pitch classes to serve as the tonic.
• The excerpt recommends memorizing key signatures and refers to mnemonic devices from earlier material.

🔧 Building triads on scale degrees

• The excerpt mentions that triads can be built on each degree of the major scale and the minor scale (using the harmonic minor).
• The pattern of triads is consistent within each scale type (major or minor), though the excerpt does not detail all seven triads here.
• Example: in C major, the tonic triad is C-E-G (I) and the dominant triad is G-B-D (V).

🔧 Perceptual effect of triads

• Within a triad, one note is "more important" and gives the triad its label (the root).
• The relationships between triads contribute to the overall sense of tonality in a key.
• Don't confuse: a triad's identity (its root) is distinct from its function (tonic, dominant, etc.) within a key.

🧭 Overview

🧠 One-sentence thesis

Building triads on every degree of the major and minor scales produces predictable patterns of chord qualities that serve as the structural foundation for harmonizing melodies.

📌 Key points (3–5)

• Predictable patterns emerge: in any major key, triads follow the pattern major–minor–minor–major–major–minor–diminished (I–II–III–IV–V–VI–VII); in harmonic minor, the pattern includes diminished, augmented, and major chords due to the raised seventh.
• Primary chords dominate: chords I (tonic), IV (subdominant), and V (dominant) are the most important structural building blocks and can harmonize any diatonic melody because every scale degree appears in at least one of them.
• Notation convention: scale degrees use normal numbers (1, 2, 3…), while chords built on those degrees use Roman numerals (I, II, III…).
• Common confusion: the harmonic minor scale's raised seventh creates an augmented triad on III and ensures V is major (not minor), distinguishing it from natural minor patterns.
• Practical application: understanding triad patterns allows you to harmonize melodies by choosing appropriate chords that contain the melody notes.

🎼 Triads in the major scale

🎵 The major-scale triad pattern

When you build a triad on each degree of a major scale, a fixed pattern of chord qualities emerges:

Scale degree	Roman numeral	Chord quality
1 (tonic)	I	Major
2	II	Minor
3	III	Minor
4 (subdominant)	IV	Major
5 (dominant)	V	Major
6	VI	Minor
7	VII	Diminished

• This pattern holds in any major key—chord V is always major, chord II is always minor, etc.
• The excerpt illustrates this in C major, but the principle applies universally.

🔺 The diminished VII chord

Diminished triad: a chord with a minor third and a diminished fifth (one semitone smaller than a perfect fifth).

• Chord VII is unique: it contains a diminished fifth (not a perfect fifth like the others).
• Example: in C major, the VII chord has a minor third from the root to the third and a diminished fifth from the root to the fifth.
• Don't confuse: a perfect fifth would be 7 semitones; a diminished fifth is 6 semitones.

🔢 Notation: scale degrees vs. chord numbers

• Scale degrees (the individual notes): written with normal numbers—1, 2, 3, 4, 5, 6, 7.
• Chords/triads built on those degrees: written with Roman numerals—I, II, III, IV, V, VI, VII.
• This distinction helps differentiate "the fifth note of the scale" from "the chord built on the fifth degree."

🎹 Triads in the harmonic minor scale

🎶 The harmonic-minor triad pattern

Building triads on each degree of the harmonic minor scale produces a different pattern because of the raised seventh:

Scale degree	Roman numeral	Chord quality
1 (tonic)	i	Minor
2	ii	Diminished
3	III	Augmented
4 (subdominant)	iv	Minor
5 (dominant)	V	Major
6	VI	Major
7	vii	Diminished

• The excerpt uses A minor for illustration, but the pattern is the same in any minor key.
• The raised (sharpened) seventh in the harmonic minor scale is the key difference from natural minor.

🔼 The augmented III chord

Augmented triad: a chord with a major third and an augmented fifth (one semitone larger than a perfect fifth, i.e., 8 semitones from root to fifth).

• Chord III in harmonic minor is augmented because it includes scale degrees 3, 5, and the raised 7.
• The raised seventh creates an augmented fifth above the root.
• This is a new chord type not found in the major-scale triad pattern.
• Don't confuse: an augmented fifth is 8 semitones; a perfect fifth is 7 semitones.

🎯 Why V is major in harmonic minor

• The raised seventh (the leading note) ensures that chord V is major, not minor.
• This gives harmonic minor the same strong dominant–tonic relationship as major keys.
• The excerpt emphasizes that this makes the dominant chord "really unambiguous" and structurally important.

🏗️ Primary chords and harmonization

🏛️ The three primary chords

The excerpt identifies chords I, IV, and V as the most important structural building blocks:

• I (tonic): the home chord.
• IV (subdominant): often appears before V, extending cadential structures.
• V (dominant): creates tension that resolves to I.

Why these three matter:

• Every single scale degree occurs in at least one of these three chords.
• This means any diatonic melody (a melody using only notes from the scale) can be harmonized using just I, IV, and V.

🎼 Harmonizing diatonic melodies

• The excerpt references the "3-chord trick" (from an earlier video): you can harmonize simple melodies with just the primary chords.
• Example: the melody Twinkle Twinkle Little Star uses primarily chords I and V (tonic and dominant).
• Now that you know all seven triad types in a key, you can choose from a wider palette of chords to harmonize melodies, not just the primary three.

🔄 Cadences and chord IV

• The subdominant (IV) often precedes the dominant (V), extending the cadential structure.
• Recap from earlier in the excerpt:
  • Imperfect cadence: ends on the dominant (V)—sounds unfinished.
  • Perfect cadence: moves from dominant (V) back to tonic (I)—sounds finished, "coming home."
• Adding IV before V creates a longer harmonic journey: IV → V → I.

🧩 Patterns and universality

🔁 Why patterns matter

• Just as the major scale always follows the interval pattern tone–tone–semitone–tone–tone–tone–semitone, the triad qualities follow a fixed pattern in any given key type.
• In major keys: I–ii–iii–IV–V–vi–vii° (major–minor–minor–major–major–minor–diminished).
• In harmonic minor keys: i–ii°–III+–iv–V–VI–vii° (minor–diminished–augmented–minor–major–major–diminished).
• These patterns are universal: they hold regardless of which note you start on.

🎓 Practical implication

• Once you learn the pattern for one key, you know it for all keys of that type.
• Example: if you know chord V is always major in a major key, you can instantly identify the dominant chord in any major key.
• This makes analysis and composition more systematic: you can predict chord qualities and plan harmonic progressions.

🧭 Overview

🧠 One-sentence thesis

Harmonising melodies involves choosing chords to accompany a melody, and while the primary chords (I, IV, V) suffice for diatonic melodies, adding other chord types—especially chord VI, chord II, and the dominant seventh—creates richer colour, stronger cadences, and more interesting progressions.

📌 Key points (3–5)

• Basic harmonisation: any diatonic melody can be harmonised using only the tonic (I), subdominant (IV), and dominant (V) chords (the "3-chord trick").
• Expanding the palette: chords built on other scale degrees (especially II and VI) add colour and new directions without losing coherence.
• Dominant seventh chord: adding the fourth scale degree to the dominant triad (creating a four-note chord) strengthens the pull back to the tonic through two semitone movements (leading note 7→1 and 4→3).
• Common confusion: a G major triad could theoretically be chord I in G major, but when it appears with F natural (not F♯) it signals the dominant seventh in C major, not G major—context determines function.
• Circle of fifths in progressions: root movement by fourths (or fifths in the opposite direction) produces flowing, logical harmonic progressions; the II–V–I pattern is a classic example.

🎸 Practical harmonisation with primary and secondary chords

🎸 The 3-chord trick revisited

• The excerpt recaps that chords I, IV, and V can harmonise any diatonic melody.
• Example: Twinkle Twinkle Little Star harmonised with only chords I and V, then with I, IV, and V.
• This provides the essential structural framework and cadential points.

🎨 Adding chord VI for colour

Chord VI: the triad built on the sixth degree of the scale (e.g., E minor in the key of G major).

• Using chord VI at the end of a phrase (instead of chord I) gives "a completely different sound" and "a new direction to go off in."
• Why it works: chord VI contains scale degrees 6, 1, and 3, which overlap significantly with the tonic chord (1, 3, 5).
• Example: in G major, replacing the final G major chord with E minor changes the feel and colour of the melody.
• Don't confuse: chord VI is not a substitute for the tonic in a final cadence, but it can delay or redirect the harmonic resolution.

🎨 Adding chord II to extend progressions

Chord II: the triad built on the second degree of the scale (e.g., A minor in the key of G major).

• Placing chord II just before chord V creates a II–V–I progression.
• This extends the feeling towards the end of the phrase and is "really important," especially in jazz.
• Example: in G major, the progression A minor (II) → D major (V) → G major (I) sounds smooth and logical.
• The excerpt emphasises that this is a recognisable sound even for those unfamiliar with the theory.

🔥 The dominant seventh chord

🔥 What it is and why it matters

Dominant seventh chord: a four-note chord built on the fifth degree of the scale, adding the fourth scale degree (a minor seventh interval above the root).

• In C major: G–B–D–F (scale degrees 5, 7, 2, 4).
• Adding the seventh note gives "a greater sense of pull towards the tonic" compared to the plain dominant triad.
• The progression V → V⁷ → I creates a "quite strong cadence."

🔥 Two harmonic pulls

The dominant seventh chord contains two semitone movements that resolve to the tonic:

1. Leading note (7 → 1): B → C in C major.
2. Fourth to third (4 → 3): F → E in C major.

• These are the two semitones in the major scale, and both want to resolve inward to the tonic chord.
• This dual pull makes the dominant seventh especially effective in cadences.

🔥 Distinguishing context: G major vs. dominant in C

• A G major triad (G–B–D) could theoretically be chord I in G major.
• But when you add F natural (not F♯), you get G–B–D–F, which is the dominant seventh in C major, not a seventh chord in G major.
• In G major, a seventh chord on G would be G–B–D–F♯ (a major seventh).
• The presence of F natural "really, really giving us quite emphatically our sense of 'key'"—it tells us we are in C major, not G major.
• Don't confuse: the same triad can have different functions depending on the key and added notes.

🔄 Root movement and the circle of fifths

🔄 II–V⁷–I progression

• Instead of V → V⁷ → I, the progression II → V⁷ → I is harmonically strong and "never static."
• It stays securely within the key, shows where the tonic is, and includes both major and minor chords.
• The bass moves in fourths: D (II) up to G (V), then G down to C (I).
• Up a fourth is equivalent to down a fifth (they reach the same note).

🔄 Circle of fifths and flowing progressions

• Moving anti-clockwise around the circle of fifths = moving in fourths.
• D → G is a fourth; G → C is a fourth.
• "Some harmonic progressions sound more logical and flowing than others and they tend to get used more than others."
• Root movement by fourths (or fifths) produces this flowing sound.
• Memorable progressions often combine circle-of-fifths movement with repeated patterns.

🔄 Bass vs. upper voices

• In the II–V⁷–I progression, the upper notes move smoothly in small jumps.
• The bass moves in large jumps (fourths), providing "really solid" foundations—like "really big, wide placed pillars."
• This contrast between smooth upper motion and strong bass motion contributes to the progression's coherence.

🎹 Extended chords and harmonic function

🎹 Why four-note chords?

• The excerpt has focused on triads (three-note chords) to illustrate how chords work within keys.
• But there is "absolutely no reason why you should have to" use only three notes.
• Some styles (especially jazz) almost always use extended chords: sevenths, ninths, elevenths, thirteenths, and alterations.

🎹 Function remains the same

• Even with extended chords, harmonic function (tonic, subdominant, dominant) does not change.
• Adding extra notes gives "a definite colour, definite flavour" and sometimes softens the movement from one chord to another.
• Example: the progression II → V⁷ → I has "a lot of strong things going on" but is less abrupt than V → V⁷ → I.

🎹 Practical advice

• The excerpt recommends taking a simple, well-known melody and creating your own harmonisation.
• This ties theoretical knowledge to aural skills and helps you understand concepts more thoroughly.
• It is "not only good fun" but also reinforces learning.

🎼 Building seventh chords on every scale degree

🎼 The pattern in major keys

• Build a four-note chord by stacking thirds: root, skip one note, third, skip one, fifth, skip one, seventh.
• In C major, the chord on the first degree (C–E–G–B) is a major triad plus a major seventh interval from root to seventh.
• The excerpt begins to describe the quality of chords that emerge on each degree but does not complete the full list in the provided text.

🎼 The pattern in minor keys

• The same stacking process applies to the harmonic minor scale.
• The excerpt mentions that graphics show seventh chords built on each degree of the harmonic minor scale (illustrated in A harmonic minor).
• The text does not provide the full analysis of each chord quality in the excerpt.

🎼 Why it matters

• Understanding the quality of seventh chords on each scale degree helps you choose appropriate chords when harmonising melodies.
• Different chord qualities (major seventh, minor seventh, dominant seventh, etc.) have different colours and functions.
• The excerpt emphasises that this knowledge expands your harmonic vocabulary beyond the primary triads.

🧭 Overview

🧠 One-sentence thesis

Building seventh chords (four-note chords) on each degree of the major and minor scales produces distinct chord qualities that reinforce tonal structure, with the dominant seventh chord playing an especially important role in pulling back to the tonic.

📌 Key points (3–5)

• What seventh chords are: four-note chords built by stacking notes in thirds (root, 3rd, 5th, 7th) on each scale degree.
• Different qualities emerge: major 7th, minor 7th, dominant 7th, half-diminished, diminished 7th, augmented major 7th, and minor major 7th—depending on the scale degree and whether the scale is major or harmonic minor.
• Dominant 7th is structurally crucial: it contains scale degrees 7→1 and 4→3 (where semitones fall), creating strong pull back to the tonic and reinforcing the sense of key.
• Common confusion: the same Roman numeral (e.g., chord V) can have different seventh-chord qualities in major vs. minor, but the dominant 7th (V7) has the same important function in both.
• Why it matters: seventh chords elaborate harmonic structure and strengthen the perception of tonal center, extending beyond simple triads.

🎹 Building seventh chords on the major scale

🎹 The construction method

• Start with a triad (root, 3rd, 5th).
• Add the 7th degree above the root: "miss out every other note but continue on."
• Example: in C major, chord I uses C–E–G–B (root, skip D, 3rd, skip F, 5th, skip A, 7th).

🎵 Chord qualities in major

The excerpt builds seventh chords on each degree of C major and identifies the resulting qualities:

Scale degree	Triad quality	Interval to 7th	Seventh chord name
I	Major	Major 7th	Major 7th
ii	Minor	Minor 7th	Minor 7th
iii	Minor	Minor 7th	Minor 7th
IV	Major	Major 7th	Major 7th
V	Major	Minor 7th	Dominant 7th
vi	Minor	Minor 7th	Minor 7th
vii°	Diminished	Minor 7th	Half-diminished

• Major 7th chord: major triad + major 7th interval (I, IV).
• Minor 7th chord: minor triad + minor 7th interval (ii, iii, vi).
• Dominant 7th chord: major triad + minor 7th interval (V).
• Half-diminished chord: diminished triad + minor 7th interval (vii°).

🔑 Why chord V (dominant 7th) is special

The dominant 7th chord is built on the 5th degree (the dominant) and contains scale degrees 7→1 and 4→3, where semitones fall, creating strong resolution pulls back to the tonic.

• It "wants to resolve" to chord I because of these semitone movements.
• Example: in C major, G–B–D–F (V7) contains B (scale degree 7) pulling to C (1) and F (4) pulling to E (3).
• This is what distinguishes the dominant 7th and gives it its important harmonic function.

🎼 Building seventh chords on the harmonic minor scale

🎼 The construction in A harmonic minor

The excerpt uses A harmonic minor to demonstrate seventh chords on each degree.

Scale degree	Triad quality	Interval to 7th	Seventh chord name
i	Minor	Major 7th	Minor major 7th
ii°	Diminished	Minor 7th	Half-diminished
III+	Augmented	Major 7th	Augmented major 7th
iv	Minor	Minor 7th	Minor 7th
V	Major	Minor 7th	Dominant 7th
VI	Major	Major 7th	Major 7th
vii°	Diminished	Diminished 7th	Diminished 7th

🎶 New chord qualities in minor

• Minor major 7th: minor triad + major 7th interval (i in harmonic minor).
• Augmented major 7th: augmented triad + major 7th interval (III in harmonic minor).
• Diminished 7th chord: diminished triad + diminished 7th interval (vii° in harmonic minor).
• Don't confuse: half-diminished (diminished triad + minor 7th) vs. diminished 7th (diminished triad + diminished 7th).

🔑 Dominant 7th in minor

• Chord V in harmonic minor is also a dominant 7th (major triad + minor 7th).
• It has the same structural function as in major: scale degree 7 pulls to 1, and scale degree 4 pulls to 3.
• Example: in A minor, E–G♯–B–D (V7) wants to resolve to A minor (i) because G♯ (7) pulls to A (1) and D (4) pulls to C (3).
• This reinforces the sense of key and tonal center in minor just as in major.

🧩 Summary and structural role

🧩 From triads to seventh chords

• Earlier in the course, triads were built on each scale degree, giving qualities like major, minor, augmented, diminished.
• Adding the 7th degree creates four-note chords with richer qualities.
• The excerpt emphasizes that these qualities arise naturally from "missing out every other note" in the scale.

🏛️ Harmonic structure and tonality

Putting together chords—especially tonic, dominant, and subdominant—creates strong structural effects that reinforce the sense of key and tonal center.

• The dominant 7th chord is "really important" because of its pull back to the tonic.
• Other seventh chords "elaborate and extend that harmonic structural experience."
• This builds on the earlier idea (from lecture 2) that a scale leads the ear to hear one note as the key note; now, chords do the same for groups of notes.

📚 Supplementary material

The excerpt mentions:

• Additional examples for practice.
• Chord symbols used in pop music and jazz (not detailed in the excerpt).
• A reference guide (Topic 5) for organizing knowledge about notation systems, Roman numeral analysis, chord voicing, voice leading, and spelling out chords.

🧭 Overview

🧠 One-sentence thesis

Music theory uses multiple interconnected notation and naming systems—Roman numerals, lead sheet symbols, figured bass, and scale-degree names—to describe chords, inversions, and harmonic progressions in different contexts.

📌 Key points (3–5)

• Multiple systems exist: Roman numeral analysis, lead sheet chord symbols, figured bass, and macro analysis all describe musical elements differently but may all use stave notation.
• Three key technical concepts: chord voicing (which inversion to use), voice leading (how individual lines interact to create harmony), and spelling out a chord (identifying the letter names).
• Scale degrees have names: each step of a scale has a formal name (tonic, supertonic, mediant, etc.) used to describe position and function.
• Common confusion: different conventions for indicating inversions—UK uses Latin letters (a, b, c, d) with Roman numerals; lead sheets use slash notation; figured bass uses numbers below the stave.
• Why it matters: understanding these systems helps you read, write, and communicate about chord progressions and harmonic structure across different musical contexts.

🎼 Core notation systems

🎼 Roman numeral analysis

Roman numerals (I, II, III, IV, V, VI, VII) indicate the triad built on a particular scale degree.

• Capitals = major triad (e.g., I, IV, V in a major key)
• Lower-case = minor triad (e.g., ii, iii, vi, vii in a major key)
• This system shows harmonic function within a key, not absolute pitch.

🎸 Lead sheet symbols

• Use letter names plus abbreviations to specify chord quality and extensions.
• Example: "Cm7" means a minor seventh chord built on C (C, E♭, G, B♭).
• Slash notation indicates bass note: "C7/G" means play a C dominant seventh with G in the bass (second inversion).

📜 Figured bass (thoroughbass)

Figured bass tells performers how and (roughly) when to voice the chords to accompany the melodic line.

• Arose to support basso continuo, an improvised accompaniment style.
• Shows the bass line on the stave plus numerical annotations below indicating which chord to play.
• Numbers align vertically to show the metrical position (which beat) of chord changes.
• Does not include complete pitch information—performers improvise the upper voices based on the figures.

🔢 Scale degrees and their names

🔢 The seven scale-degree names

Use these names to indicate a particular step of a scale:

Number	Name
1	Tonic
2	Supertonic
3	Mediant
4	Subdominant
5	Dominant
6	Submediant
7	Leading note

• These names describe function and position within the scale.
• Example: the dominant (5) is the fifth step of the scale; a chord built on it is called the dominant chord.

🎹 Chord voicing and inversion

🎹 What chord voicing means

Chord voicing: the inversion in which a chord should be written out or played.

• The same chord can be arranged with different notes in the bass.
• Example: a C major triad can be C-E-G (root position), E-G-C (first inversion), or G-C-E (second inversion).

🔤 UK convention: Latin letters (a, b, c, d)

Local (UK-wide) convention uses Latin letters alongside Roman numerals to indicate voicing:

Inversion	Label	Example (V chord)
Root position	a	Va
First inversion	b	Vb
Second inversion	c	Vc
Third inversion (for 7th chords)	d	Vd

• Don't confuse: this is a local convention; other systems (lead sheet slash notation, figured bass numbers) indicate inversions differently.

🎵 Root position for finality

• It's common to end a piece on a root position chord for stability and finality.
• Example: "Twinkle Twinkle Little Star" ends on the root position tonic triad.

🗣️ Key technical expressions

🗣️ Voice leading

Voice leading: how individual lines (parts) sound and the way that they interact together as harmony, creating harmonic (chord) progressions.

• Focuses on the movement of individual melodic lines, not just the vertical chords.
• Good voice leading creates smooth, logical progressions.

✍️ Spell out a chord

Spell out a chord: identify which notes—which letter names—are indicated by a particular chord, chord symbol, or notated figure.

• Example: "Spell out Cm7" → C, E♭, G, B♭.
• This is a fundamental skill for reading and writing music in any notation system.

📊 Lead sheet chord symbol reference

📊 Common chord types and spellings

The excerpt provides a quick reference table. Key examples:

Chord type	Symbol alternatives	Spelling (intervals)	Example label	Example spelling
Major	(none)	1, 3, 5	C	C E G
Minor	m	1, ♭3, 5	Cm	C E♭ G
Diminished	dim, °, m♭5	1, ♭3, ♭5	C°	C E♭ G♭
Dominant 7th	7	1, 3, 5, ♭7	C7	C E G B♭
Major 7th	maj7, M7	1, 3, 5, 7	CM7	C E G B
Suspended 4th	sus4	1, 4, 5	Csus4	C F G
Added 9th	add9	1, 3, 5, 9	Cadd9	C E G D

• Intervals are counted from the root (1 = root, 3 = third, 5 = fifth, etc.).
• Flat (♭) lowers a note by a half step; sharp (#) raises it.
• Example: "1, ♭3, 5" means root, minor third, perfect fifth.

🎶 Seventh chords and extensions

• Seventh chords contain four notes and can be in third inversion (labeled "d" in UK convention).
• Examples: diminished 7th (C°7 = C E♭ G♭ B𝄫), half-diminished (Cø7 = C E♭ G♭ B♭), minor 7th (Cm7 = C E♭ G B♭).
• Don't confuse: "dominant 7th" (C7 = C E G B♭) vs "major 7th" (CM7 = C E G B)—the former has a ♭7, the latter a natural 7.

🧭 Overview

🧠 One-sentence thesis

Lead sheet chord symbols provide a standardized shorthand for labeling chord types and voicings, enabling musicians to quickly identify which notes to play and in what bass position.

📌 Key points (3–5)

• What lead sheet symbols encode: chord type (major, minor, diminished, etc.) and spelling (which scale degrees or intervals to include).
• How to read the table: each chord type has alternative notations (e.g., "m" for minor, "dim" or "o" for diminished) and a formula using scale degrees (1, 3, 5, etc.) with accidentals (♭, #).
• Voicing indication with slash notation: a slash (/) tells you which note to put in the bass, e.g., C7/G means play a C dominant seventh chord with G in the bass (second inversion).
• Common confusion: the numbers in lead sheet symbols (e.g., "7" in C7) refer to chord type (which intervals to include), not inversion; inversion is shown separately by slash notation.
• Contrast with figured bass: lead sheet symbols label the chord itself, whereas figured bass (introduced briefly after) annotates a bass line with numbers to guide improvised harmonization.

🎵 The quick reference table

🎵 Chord type labels and alternative notations

The excerpt provides a table mapping chord types to their common symbols:

Chord Type	Also Written As	Chord Spelling	Example Label	Example Spelling
Major	(none)	1, 3, 5	C	C E G
Minor	m	1, ♭3, 5	Cm	C E♭ G
Diminished	dim, o, m♭5	1, ♭3, ♭5	C°	C E♭ G♭
Diminished 7th	dim7, o7, dim	1, ♭3, ♭5, ♭♭7	C°7	C E♭ G♭ B♭♭
Half Diminished	m7♭5, ø	1, ♭3, ♭5, ♭7	Cø7	C E♭ G♭ B♭
Augmented	aug, +	1, 3, #5	C+	C E G#
Dominant 7th	7	1, 3, 5, ♭7	C7	C E G B♭
Minor 7th	m7	1, ♭3, 5, ♭7	Cm7	C E♭ G B♭
Major 7th	maj7, M7	1, 3, 5, 7	CM7	C E G B
Suspended 4th	sus4	1, 4, 5	Csus4	C F G
Suspended 2nd	sus2	1, 2, 5	Csus2	C D G
7th Suspended 4th	7sus4	1, 4, 5, ♭7	C7sus4	C F G B♭
7th Suspended 2nd	7sus2	1, 2, 5, ♭7	C7sus2	C D G B♭
Added 9th	add9	1, 3, 5, 9	Cadd9	C E G D
6th	6	1, 3, 5, 6	C6	C E (G) A
Minor 6th	m6	1, ♭3, 5, 6	Cm6	C E♭ (G) A

• Alternative notations: many chord types have multiple symbols (e.g., diminished can be "dim," "o," or "m♭5").
• Chord spelling: uses scale degrees (1 = root, 3 = third, 5 = fifth, 7 = seventh, etc.) with flats (♭) or sharps (#) to show alterations.
• Example: a minor chord is spelled 1, ♭3, 5, meaning root, lowered third, and fifth.

🔢 What the numbers mean

• The numbers in the spelling column (1, 3, 5, 7, etc.) refer to scale degrees or intervals above the root.
• Accidentals (♭, #, ♭♭) modify those degrees:
  • ♭3 = lowered third (minor third)
  • ♭7 = lowered seventh (minor seventh)
  • ♭♭7 = double-flat seventh (diminished seventh)
  • #5 = raised fifth (augmented fifth)
• Example: C7 (dominant seventh) = 1, 3, 5, ♭7 → C, E, G, B♭.

🎹 Suspended and added chords

• Suspended chords (sus4, sus2): replace the third with a fourth or second.
  • Csus4 = 1, 4, 5 → C, F, G (no E).
  • Csus2 = 1, 2, 5 → C, D, G (no E).
• Added chords (add9): include an extra note without replacing the third.
  • Cadd9 = 1, 3, 5, 9 → C, E, G, D (the 9 is the same as the 2nd, an octave higher).
• 6th chords: add the sixth scale degree.
  • C6 = 1, 3, 5, 6 → C, E, (G), A.
  • The excerpt shows (G) in parentheses, suggesting it may be optional or implied.

🎚️ Indicating voicings with slash notation

🎚️ How slash notation works

If you see a chord label using a slash (/), this tells you which note to use in the bass.

• The format is: Chord / Bass note.
• Example from the excerpt: C7/G means "play the notes of a dominant seventh on C, with a G in the bass."
• This specifies inversion: which chord tone is in the lowest voice.

🔄 Slash notation and inversion

• The slash does not change the chord type; it only changes the bass note.
• Example: C7/G is still a C dominant seventh (C, E, G, B♭), but G is now the lowest note → this is second inversion.
• Don't confuse: the "7" in C7 tells you the chord type (dominant seventh); the "/G" tells you the voicing (which note is in the bass).

🎼 Why voicing matters

• The excerpt does not elaborate on musical reasons, but it implies that bass-note choice affects the sound and function of the chord.
• Example: a root-position chord (root in the bass) sounds more stable; an inverted chord (third or fifth in the bass) may sound less final or more transitional.

🎻 Brief mention of figured bass

🎻 What figured bass is

Figured bass – also known as thoroughbass – tells performers how and (roughly) when to voice the chords to accompany the melodic line.

• It arose to support basso continuo, an improvised accompaniment style.
• The system uses a single bass line (notated on a five-line staff) plus numerical annotations below the staff.
• The numbers indicate which intervals to play above the bass note, guiding the performer in harmonization.

🎻 How figured bass differs from lead sheet symbols

Feature	Lead sheet symbols	Figured bass
What it labels	The chord itself (type and root)	Intervals above a given bass note
Notation	Chord symbol (e.g., C7)	Bass note + numbers below the staff
Voicing detail	Minimal (slash for bass note)	Rough guidance; performer improvises
Historical context	Modern popular and jazz music	Baroque-era basso continuo

• Lead sheet symbols name the chord and optionally specify the bass note (via slash).
• Figured bass provides a bass line and tells you which intervals to add above it, leaving more freedom to the performer.
• Example: figured bass might show a bass note C with the number "6" below, meaning "play the sixth above C" (and other notes as appropriate), whereas a lead sheet would write "C6" to specify the chord type directly.

🎻 Alignment and timing

• The excerpt notes that figured bass numbers are "aligned vertically to show the metrical position of the chord changes (i.e. on which beat of the bar the harmony should change)."
• This means the numbers tell you when to change chords, not just what to play.
• Lead sheet symbols typically appear above the staff at the relevant measure or beat, serving a similar timing function.

🧭 Overview

🧠 One-sentence thesis

Figured bass is a notation system that tells performers which chords to play and roughly when to voice them, by combining a written bass line with numerical annotations that indicate the harmonies above it.

📌 Key points (3–5)

• What figured bass provides: a bass line (specific pitches) plus numerical figures that tell performers how to harmonize those notes.
• What it does NOT provide: complete, detailed voicing or exact pitch information for all parts—it leaves room for improvisation.
• When it arose: to support compositions featuring basso continuo, an improvised form of accompaniment.
• How to read the numbers: figures appear below the staff, aligned vertically to show the metrical position (which beat) of chord changes.
• Common confusion: figured bass is not a complete score; it gives the bass line and chord progression, but performers fill in the upper voicing.

🎼 What figured bass is and does

🎼 Definition and purpose

Figured bass—also known as thoroughbass—tells performers how and (roughly) when to voice the chords to accompany the melodic line.

• It arose to support musical compositions and performances featuring a basso continuo, an improvised form of accompaniment.
• Written or printed as part of a musical score, it shows:
  • How the bass line should sound (specific pitches on the staff).
  • What the chord progression should be (via numerical annotations).
• A figured bass would be provided in addition to the musical notation for the upper part(s) of a composition or song.

📝 What the notation includes

• The staff: uses the standard five-line staff.
• The bass line: single-line notation showing which pitch should be played.
• The numbers: numerical figures that indicate which chord should be played above the bass note.
• The numbers appear below the staff, aligned vertically to show the metrical position of the chord changes (i.e., on which beat of the bar the harmony should change).

🔍 What figured bass does NOT include

🔍 Incomplete information by design

• Figured bass does not include complete, detailed voicing or pitch information for all parts.
• It provides:
  • The specific notes/pitches for the bass line.
  • Numerical annotations that tell performers how to harmonize those notes.
• Don't confuse: figured bass is not a full score; it is a shorthand that leaves the upper voicing and exact realization to the performer's improvisation and judgment.

🎹 Improvisation and flexibility

• The system supports basso continuo, an improvised form of accompaniment.
• Performers use the bass line and figures as a guide, but they decide the exact voicing and rhythm of the chords above.
• Example: a figured bass might show a bass note and the number "6," telling the performer to play a chord in first inversion, but the performer chooses which octave and spacing to use.

📐 How to read figured bass

📐 The numbers and their meaning

• The numerical figures indicate which chord should be played.
• They are aligned vertically below the staff to show when (on which beat) the harmony should change.
• The excerpt refers to a separate resource ("Figured bass notation") for more detail about conventions for abbreviations and including accidentals.

🎵 Relationship to the bass line

• The single-line notation on the staff shows which pitch should be played in the bass.
• The numbers below tell performers how to harmonize that bass note.
• Together, the bass line and figures communicate the chord progression without writing out every note.

🧭 Overview

🧠 One-sentence thesis

Cadences—chord progressions that end phrases or pieces—create different degrees of finality, from the conclusive perfect cadence to the temporary pause of an imperfect cadence, and composers choose them to control whether music feels finished or must continue.

📌 Key points (3–5)

• Perfect/authentic cadence (V–I): sounds very final; used at the end of pieces.
• Imperfect/half cadence (ending on V): a temporary stopping point; the music must move on somewhere else.
• Interrupted/deceptive cadence (V–vi): changes the expected final chord to chord vi (submediant), creating surprise and demanding continuation.
• Plagal cadence (IV–I): subdominant to tonic; often heard in hymns ("Amen") and also in blues, rock, and pop.
• Common confusion: the actual cadence is only the final two chords of a phrase; earlier chords provide context but are not part of the cadence itself.

🎵 Perfect and imperfect cadences

🎵 Perfect/authentic cadence (V–I)

Perfect/authentic cadence: the progression from dominant (V) to tonic (I), sounding very final.

• This cadence is nearly always found at the end of a piece because it conveys a sense of finality and rest.
• Example: ending Twinkle Twinkle Little Star on root position of the tonic chord sounds complete and satisfying.
• The excerpt emphasizes that using the correct inversion (root position) is crucial for this finality.

🎵 Imperfect/half cadence (ending on V)

Imperfect/half cadence: a cadence that ends on the dominant (V), creating a temporary stopping point before the music continues.

• It does not sound final; the listener expects the music to move on.
• Example: in D major, a phrase might end on A major (the dominant), which is "obviously not the end of a piece."
• Don't confuse: the imperfect cadence is the movement to V (e.g., from D major to A major in the key of D major); the first chord provides context but the actual cadence is the final two chords.

🎭 Interrupted and plagal cadences

🎭 Interrupted/deceptive cadence (V–vi)

Interrupted/deceptive cadence: the progression from dominant (V) to submediant (vi) instead of the expected tonic (I).

• This cadence changes just one chord from the expected Ic–V–I progression: the final chord becomes chord vi (the submediant).
• The effect is surprising and "deceptive"—the music "obviously must continue."
• Example in D major: instead of resolving V to I, the progression moves V to vi (B minor), interrupting the expected resolution.
• Example in G minor: the same principle applies, moving to chord vi in a minor key.
• Why it works: both the terms "interrupted" and "deceptive" describe the effect well—the listener is led to expect finality but is denied it.

🎭 Plagal cadence (IV–I)

Plagal cadence: the progression from subdominant (IV) to tonic (I); sometimes called a hymn or church cadence.

• Often heard in the "Amen" at the end of a hymn.
• Used extensively in medieval and Renaissance church music, but also appears in blues, rock, and pop.
• Example: "With a Little Help from My Friends" by the Beatles ends with the last two chords forming a plagal cadence (IV–I).
• Extra flavor: the excerpt notes that in the Beatles example, the third-to-last chord is based on the flattened leading note, which gives a Mixolydian mode quality.

🎶 Mixolydian mode connection

• The plagal progression (IV–I) can be called a "Mixolydian cadence" when influenced by the flattened leading note.
• The Mixolydian mode: playing notes from G to G using only white keys produces a major-sounding scale with a flattened seventh.
• This progression is common in rock and funk.
• Example: the melody of a famous song follows the Mixolydian mode, and the plagal cadence fits naturally within this modal context.

🔧 Using inversions and second inversion cadences

🔧 Importance of correct inversion

• Each inversion of a chord has its own "feel," and using the right inversion is crucial for smooth and pleasing harmony.
• Root position conveys finality, so it is nearly always used at the end of a piece.
• Example: ending Twinkle Twinkle Little Star on a first inversion sounds "not quite right"; on a second inversion, it sounds "even more peculiar" and does not feel like arriving home.
• The correct way is to end on root position, which provides "a feeling of finality."

🔧 Ic–V–I cadence

• A very common progression found towards the end of a piece or section.
• Ic: second inversion of the tonic (I).
• V: dominant chord.
• I: root position of the tonic.
• Example in F major: the second inversion of F (Ic) moves to C (V), then to F root position (I).
• The second inversion "really wants to move on," helping the harmony progress strongly towards the final chord.

🔧 When to use second inversion

• Second inversion must be used very carefully; there are only two main situations:
  1. Cadences: as in the Ic–V–I progression just described.
  2. Passing second inversion: three chords move smoothly with the bass in conjunct (stepwise) motion, so the middle chord is a passing second inversion.
• Example of passing second inversion: the baseline moves by step, and the middle chord is "protected" by the chords on either side.
• Don't confuse: second inversion is not freely interchangeable with other inversions; it requires specific harmonic contexts to sound correct.

📋 Summary of cadence types

Cadence type	Progression	Effect	Typical use
Perfect/authentic	V–I	Very final, conclusive	End of a piece
Imperfect/half	Ends on V	Temporary pause, music must continue	End of a phrase, not the piece
Interrupted/deceptive	V–vi	Surprising, demands continuation	Mid-piece, to avoid expected resolution
Plagal	IV–I	Gentle finality, "Amen" feel	Hymns, also blues/rock/pop

Key reminder: the actual cadence is the movement between the final two chords; earlier chords provide harmonic context but are not part of the cadence itself.

🧭 Overview

🧠 One-sentence thesis

The interrupted (deceptive) cadence substitutes the expected tonic chord with chord vi (submediant), creating a sense that the music must continue rather than conclude.

📌 Key points (3–5)

• What it is: a cadence that moves V → vi instead of the expected V → I, sounding "interrupted" or "deceptive."
• How it differs from perfect cadence: the perfect cadence (V → I) sounds final; the interrupted cadence (V → vi) sounds like it demands continuation.
• Works in both major and minor: in major keys, V moves to vi (minor chord); in minor keys, V moves to VI (the submediant).
• Common confusion: don't confuse the entire phrase with the cadence itself—the cadence is only the final two-chord movement (V → vi), not the chords before it.
• Why it matters: this cadence creates expectation and forward momentum, signaling that the music is not yet finished.

🎵 What the interrupted/deceptive cadence is

🎵 The basic movement

Interrupted/deceptive cadence: a cadence that moves from chord V (dominant) to chord vi (submediant) instead of the expected V → I.

• The excerpt shows a D major example: a phrase finishes on chord vi, B minor.
• The cadence itself is the movement from V to vi, not the entire phrase.
• The first chord in the example is played "for context"—the actual cadence is only the final two chords.

🔄 Why "interrupted" and "deceptive"

• The excerpt states: "both the words 'interrupted' and 'deceptive' describe the effect here very well."
• The listener expects V → I (a perfect cadence), which sounds final.
• Instead, the music moves to vi, which "sounds very different" and "obviously must continue."
• Example: In D major, the expected Ic–V–I cadence is changed by substituting the final chord with chord six (the submediant).

🎹 Major and minor key examples

🎹 Major key (D major)

• The excerpt gives a D major example where the phrase ends on B minor (chord vi).
• Compared to the perfect/authentic cadence (V → I in D major), the interrupted cadence (V → vi) leaves the music unresolved.
• The movement is from the dominant (A major, chord V) to the submediant (B minor, chord vi).

🎹 Minor key (G minor)

• The excerpt also provides a G minor example.
• In minor keys, the interrupted cadence still moves V → VI (the submediant).
• Compared to the minor key perfect/authentic cadence (V → i in G minor), the interrupted cadence "demands that it continues."
• The movement is from the dominant to chord six, where "the music demands it, that it continues."

🔍 How to distinguish from other cadences

🔍 Perfect/authentic cadence vs interrupted cadence

Cadence type	Movement	Effect	Example (D major)
Perfect/authentic	V → I	Sounds final, conclusive	A major → D major
Interrupted/deceptive	V → vi	Sounds unfinished, must continue	A major → B minor

• Don't confuse: the first chord in the example is for context; the cadence is only the final two-chord movement.
• The interrupted cadence uses the same setup (often Ic–V) but substitutes the final tonic chord with the submediant.

🔍 Imperfect/half cadence vs interrupted cadence

• The imperfect cadence (discussed earlier in the excerpt) ends on chord V, creating a temporary stopping point.
• The interrupted cadence ends on chord vi, also creating a sense of continuation but with a different harmonic color.
• Example: In D major, an imperfect cadence moves to A major (V); an interrupted cadence moves from A major to B minor (V → vi).

🎼 Context: other cadences mentioned

🎼 Plagal cadence

• The excerpt briefly mentions the plagal cadence (IV → I), sometimes called a "hymn or church cadence."
• It is used in the "Amen" at the end of hymns and also appears in blues, rock, and pop music.
• Example: "With a Little Help from My Friends" and "Hey Jude" both use plagal cadences in their final chords.
• The plagal cadence is not the focus of this section but provides contrast to the interrupted cadence.

🎼 Mixolydian mode connection

• The excerpt notes that a plagal progression can be called a "mixolydian cadence" when influenced by a flattened leading note.
• The mixolydian mode is characterized as "sounding major in modality, but with a flattened seventh."
• This is mentioned in the context of the plagal cadence, not the interrupted cadence, but shows how modal thinking can enrich cadential understanding.

🧭 Overview

🧠 One-sentence thesis

Certain chord progressions recur frequently in music—especially at cadences—and the circle of fifths is a particularly important pattern that appears across centuries and genres, from Vivaldi to jazz.

📌 Key points (3–5)

• Most common cadential progression: Ic V7 I, which gives a strong sense of finality and appears in many familiar songs.
• Alternative cadential progression: iib V7 I (or ii7b V I), very common in jazz and popular music.
• Circle of fifths: a recurring sequence where bass notes descend by fifths; found in 18th-century classical music and 20th-century popular songs.
• Common confusion: circle of fifths can use all root-position chords or mix in first inversions—the latter smooths the bass line but keeps the same harmonic pattern.
• Modulation via circle of fifths: by introducing accidentals (chromatic notes) at key moments, the circle can pivot to a new key instead of returning to the original tonic.

🎵 Cadential progressions

🎵 The Ic V7 I progression

The most common cadence: Ic V7 I, where a seventh is added to the dominant chord to pull the music strongly towards the tonic.

• What it does: gives a pleasing finality to a phrase.
• How it works: the dominant seventh chord (V7) creates tension that resolves to the tonic (I).
• Example: "Hark the Herald Angels Sing" and "Happy Birthday" both end phrases with this progression.
• The excerpt calls this "possibly the commonest of the chord progressions and cadences."

🎷 The iib V7 I progression (ii7b V I)

• Alternative third-to-last chord: instead of Ic, use the supertonic (chord ii) with a seventh added, in first inversion.
• In G major: the supertonic is A minor; add a seventh → A minor 7; put it in first inversion → ii7b.
• The excerpt notes this is "very common in jazz also."
• Example: the progression ii7b V I appears frequently in jazz and Tin Pan Alley songs.

🔄 The circle of fifths

🔄 What the circle of fifths is

A recurring chord sequence in which bass notes descend by fifths.

• Pattern: in C major, the bass moves C → F → B → E → A → D → G → C (down a fifth each time).
• Chord structure: root-position triads built on each bass note.
• The excerpt emphasizes this is "a very important particular pattern."
• Example (in C major): I → IV → vii° → iii → vi → ii → V → I.

🎻 Historical and stylistic range

• 18th-century classical: Vivaldi used the circle of fifths in his Concerto Grosso, Opus 3.
  • The Vivaldi excerpt is in A minor; each bass note is played twice (repeated an octave lower).
  • Sequence of bass notes: D, G, C, F, B, E, A.
• 20th-century popular music: "Autumn Leaves" uses the same pattern in G minor, all chords in root position.
• The excerpt shows the circle appears "in 18th century music… but also in later music of all sorts."

🎹 Root position vs. inversions

Approach	Bass line	Effect
All root position	Descends strictly by fifths	Clear harmonic pattern
Mixed inversions (2nd, 4th, 6th chords in first inversion)	Smoother, stepwise motion	Same chords, but bass line is less angular

• Don't confuse: the circle of fifths is defined by the chord roots descending by fifths, not necessarily the bass notes.
• When some chords are inverted, "you don't see the pattern of fifths in the bass" but "it's the same chords."
• Example: in G major with inversions, the second, fourth, and sixth chords are in first inversion, making the bass line smoother.

🔀 Modulation using the circle of fifths

🔀 How the circle can change key

• Instead of completing the circle back to the original tonic, the progression can stop at a different chord and establish a new key.
• Key mechanism: introduce an accidental (chromatic note) to tilt the harmonic direction.
• The excerpt states: "depending on how you arrange things, you can actually use the circle of fifths to change key."

🎯 Modulating to the relative minor

• Example: C major → A minor.
• The circle stops at A (the relative minor of C).
• Crucial change: the fourth chord, normally iii (E minor), is changed to III (E major) by raising G natural to G-sharp.
• Why it works: E major is the dominant (chord V) of A minor; the G-sharp is the leading note of A minor, "which pulls our ear towards A minor."
• This "helps to give a sense of modulation, rather than just carrying on through the circle back to C."

🔑 Modulating to a different major key

• Example: C major → G major.
• Pivot chord: C major acts as tonic (I) in the old key and becomes subdominant (IV) in the new key of G major.

  Pivot chord: a chord that functions in both the old key and the new key, enabling smooth modulation.

• Next step: introduce F-sharp (foreign to C major, but the leading note in G major).
  • The excerpt notes: "that F-sharp chord is moving us into the tonality of G major… the note of F-sharp… has a very strong identity in G major, as the leading note which leads our ear to a new tonic."
• From there, the progression continues: iii7 vi7 ii V7 I (another very popular sequence in jazz).

🎶 Secondary dominant chords

• What they are: chords that create the effect of a perfect cadence (V → I) in a new key by introducing accidentals.
• Example: in the hymn "While Shepherds Watched Their Flocks by Night" (originally in F major):
  • One harmonization hints at modulation to C major.
  • Another moves towards A minor.
• Notation: V/V means "the dominant of the dominant"—a secondary dominant chord.
• The excerpt cites Bach's cantata "Wie schön leuchtet der Morgenstern" (BWV 1) as an example.
• Why modulation matters: "Music would be very boring and dull if pieces remained in the same key all the time."

🧭 Overview

🧠 One-sentence thesis

Modulation—moving from one key to another—keeps music interesting and dynamic, and composers use techniques like secondary dominant chords and hints at new keys to create variety and stronger cadences without always fully changing key.

📌 Key points (3–5)

• What modulation is: going from one key to another; pieces staying in one key would be boring and dull.
• Commonest modulation: to the dominant key, often quite near the beginning of a piece.
• Secondary dominant chords: create the experience of a perfect cadence (V to I) in a new key by introducing accidentals (chromatic notes), hinting at or moving toward that key.
• Common confusion: true modulation vs. hinting—sometimes a key is only suggested (e.g., secondary dominant) rather than firmly established, giving color and interest without a full key change.
• Subdominant hints: often occur later in a piece to emphasize the feeling of "coming home," using characteristic notes (e.g., B-flat in C major hints at F major).

🎵 What modulation is and why it matters

🎵 Definition and purpose

Modulation: going from one key to another.

• Music would be very boring and dull if pieces remained in the same key all the time.
• Modulations occur a lot in music, sometimes a great deal, to keep the music interesting and give a feeling that "we're moving on somewhere."

🔄 Types of key change

• Definite modulations: the new key is established quite firmly.
• Hints at keys: keys are simply suggested rather than a true modulation taking place; this still gives the music interest and a sense of movement.

🎹 Common modulation destinations

🎹 To the dominant

• The commonest modulation, often heard quite near the beginning of a piece.
• Example: a piece in F major might move to C major (the dominant) quite soon in its course.
• The excerpt mentions the Christmas carol "While shepherds watched their flocks by night" as an example: it starts in F major and moves to C major (the dominant).

🏠 To the subdominant (later in the piece)

• A move to the subdominant key often occurs later in the piece because it helps emphasize the feeling of "coming home."
• Sometimes composers actually modulate to the subdominant; other times they simply hint at it.
• Example: in C major, the subdominant chord is F; introducing B-flat (a note in the F major scale but not in C major) gives the flavor of the subdominant.
• Bach's "Prelude in C" from Book 1 of the 48 Preludes and Fugues introduces B-flat toward the end to hint at F major without actually going there, giving a "subdominant leaning."

🔀 Other modulations

• You can also modulate to the relative minor.
• Example: from C major to A minor, using the important G-sharp (the leading note of A minor) to pull toward A minor, with the circle of fifths in the bass.
• Or from C major to G major: the first fifth is not perfect (C to F-sharp instead of C to F), and the F-sharp pulls around to G.

🎶 Secondary dominant chords

🎶 What they are

Secondary dominant: a dominant 7th chord of the dominant (or of another scale degree), often notated as V/V.

• By introducing accidentals (chromatic notes) to harmonize a note, you can tilt the direction of harmonic travel toward a new key.
• This creates an effect such that you can have something of the experience of a perfect cadence (chord movement from V to I) in a new key.

🎶 How they work

• Instead of a straightforward progression, a secondary dominant suggests a new key and then resolves—either to that new key or back to the original.
• Example: in G major, the progression ii b7, V, I sounds like this: [normal progression]. If you change the bass from C natural to C-sharp, you create the dominant 7th in the key of D major. It doesn't go to D major; it just suggests D major and immediately goes to G, giving extra color.
• Don't confuse: a secondary dominant hints at a new key but doesn't necessarily modulate to it; it adds variety and can make the cadence sound more final and satisfying.

🎶 Examples in the excerpt

• "While shepherds watched their flocks by night": two harmonization options use secondary dominant chords.
  • The first hints at a modulation to C major from the original F major.
  • The second moves toward A minor instead.
• Bach's cantata "Wie schön leuchtet der Morgenstern" (BWV 1): Bach could have ended with a simple progression, but the added secondary dominant makes it just a bit more interesting by hinting at another key without actually modulating.
• "Blackbird": the tune ends in G major, and the third-last chord is the secondary dominant, which suggests D major but immediately comes back to G.

🧭 Using the circle of fifths for modulation

🧭 Arranging the circle

• Depending on how you arrange things, you can use the circle of fifths to change key.
• The circle in the bass helps pull toward the new key.

🧭 Examples

• C major to A minor: use the all-important G-sharp (the leading note of A minor) to pull toward A minor, with the circle in the bass (C major to A minor).
• C major to G major: the first fifth is not perfect—it goes C to F-sharp (not C to F)—and that F-sharp pulls around to G.