Music Theory and Harmony

Introduction

Music Theory and Harmony is the study of how musical sounds are organized and how notes work together. In this Grade 9–10 aiMOOC, you will connect written notation, scales, intervals, chords, chord progressions, cadences, and voice leading. You will not only learn terms: you will listen, analyze, perform, compose, and explain why a musical passage creates stability, motion, tension, or release.

Music theory is a set of tools for describing patterns that musicians use. It does not tell you that one style of music is “correct.” Different musical traditions organize pitch, rhythm, texture, and harmony in different ways. This course focuses mainly on tonal harmony as it is commonly taught in Western staff notation, while encouraging you to compare these ideas with the music you already know.

The image above shows several basic elements of staff notation. As you work through the course, use a keyboard, guitar, digital piano, notation app, or any instrument available to you. If you do not play an instrument, you can still sing, clap, use a virtual keyboard, or work with notation and listening examples.

Learning Goals

By the end of this aiMOOC, you should be able to explain and apply the main ideas of music theory and harmony. You should be able to read basic staff notation, recognize scale and chord patterns, build triads, label common chords with Roman numerals, identify harmonic functions, compare common cadences, follow individual voices through a chord progression, and create a short harmonic composition of your own.

You should also be able to justify your musical choices. For example, instead of saying “this chord sounds good,” you should be able to explain that a dominant chord creates expectation because of its position in the key, that a leading tone tends to move toward the tonic, or that smooth voice leading lets individual parts move by small intervals while the harmony changes.

Foundations: Pitch, Staff, Rhythm, and Meter

Pitch and Note Names

A pitch is the perceived highness or lowness of a sound. In the note-naming system used in this course, the letter names A, B, C, D, E, F, and G repeat in higher and lower octaves. On a piano keyboard, the repeating pattern of black keys helps you locate these notes.

An octave is the interval from one note to the next note with the same letter name, such as C to the next C. The higher note has twice the frequency of the lower note when both are tuned in the usual octave relationship. Musicians often treat notes separated by octaves as closely related, even though they are not identical in pitch.

The Staff and Clefs

The staff has five horizontal lines. Notes can be placed on lines, in spaces, or on short ledger lines above or below the staff. A clef tells you which pitches belong to the staff positions.

The treble clef is common for higher registers, including many melodies and the right hand of piano music. The bass clef is common for lower registers, including bass instruments and the left hand of piano music. Middle C sits between the two staves when they are combined as a grand staff.

Accidentals and Key Signatures

A sharp raises a written pitch by one semitone, and a flat lowers it by one semitone. A natural cancels a sharp or flat in the relevant notated context. Enharmonic notes, such as F-sharp and G-flat on an equal-tempered keyboard, can sound at the same pitch while having different spellings and harmonic meanings.

A key signature places sharps or flats near the clef to show which note spellings are normally altered in a key. Accidentals inside a measure can temporarily change notes outside that key signature.

Note Values, Rests, and Meter

Harmony unfolds through time, so rhythm matters. A note value indicates duration relative to the beat, while a rest represents measured silence. In common notation, whole, half, quarter, eighth, and sixteenth notes form a proportional system of duration.

A time signature organizes beats into measures. In 4/4, four quarter-note beats normally fill a measure. In 3/4, three quarter-note beats fill a measure. In 6/8, six eighth-note subdivisions are often felt as two larger beats, each divided into three. Meter affects how listeners hear strong and weak positions, which can influence harmonic rhythm and cadence placement.

Harmonic rhythm means the rate at which chords change. A song may keep one chord for a full measure, change twice per measure, or use an irregular pattern. The same chord progression can feel very different when its harmonic rhythm changes.

Scales, Keys, and Tonality

The Major Scale

A scale is an ordered collection of pitches. The major scale follows the step pattern whole, whole, half, whole, whole, whole, half. Starting on C and using only white piano keys gives C major: C, D, E, F, G, A, B, C.

The notes of a scale are called scale degrees. In a major key, scale degree 1 is the tonic, the tonal center. Scale degree 5 is the dominant. Scale degree 7 is the leading tone because it lies a semitone below the tonic and often moves upward to it.

Minor Scales

Minor keys use several related scale forms. The natural minor scale has the pattern whole, half, whole, whole, half, whole, whole. The harmonic minor raises scale degree 7 compared with natural minor, creating a stronger leading tone and usually a major dominant chord. The melodic minor form is treated differently in different traditions; in classical theory, scale degrees 6 and 7 are commonly raised when ascending and restored to the natural-minor form when descending.

For harmony, the raised seventh degree in harmonic minor is especially important because it strengthens the pull from dominant harmony to the tonic. For example, in A minor, G-sharp can lead upward to A.

Keys and the Circle of Fifths

A key gives a piece or passage a tonal center and a network of pitch relationships around that center. Major and minor keys can share the same key signature. These are called relative keys. C major and A minor are relative because neither key signature has sharps or flats.

The circle of fifths arranges keys so that neighboring major keys differ by one sharp or flat. Moving clockwise through major keys usually adds sharps; moving counterclockwise usually adds flats. Relative minor keys can be shown alongside their major relatives.

The circle is useful for predicting closely related keys, remembering key signatures, and seeing why certain chord roots often move effectively by fifths.

Intervals: Measuring the Distance Between Notes

An interval is the distance between two pitches. To name an interval, first count letter names inclusively to find the interval number. C to E spans C-D-E, so it is some kind of third. Then compare the number of semitones or the note spelling to determine its quality.

Common interval qualities include perfect, major, minor, augmented, and diminished. Unisons, fourths, fifths, and octaves use perfect as their basic quality. Seconds, thirds, sixths, and sevenths use major or minor.

Fehler beim Erstellen des Vorschaubildes:

Intervals matter because they are the building blocks of melodies and chords. A major third plus a minor third creates a major triad. A minor third plus a major third creates a minor triad. The perfect fifth appears in many stable-sounding chord structures.

Consonance and dissonance are context-dependent ways of describing relative stability and tension. They are influenced by musical style, tuning, register, timbre, spacing, and cultural expectations. Do not treat them as universal labels for “pleasant” and “unpleasant.”

Chords and Triads

Building Triads by Stacking Thirds

A chord is a group of notes understood as sounding together or functioning together. A triad contains three chord members arranged as a root, third, and fifth. You can build a triad by choosing a root and stacking two thirds above it.

Four common triad qualities are:

Major triad: A major third from root to third plus a perfect fifth from root to fifth.
Minor triad: A minor third from root to third plus a perfect fifth from root to fifth.
Diminished triad: A minor third from root to third plus a diminished fifth from root to fifth.
Augmented triad: A major third from root to third plus an augmented fifth from root to fifth.

Try this on C. C-E-G is a C major triad. C-E-flat-G is a C minor triad. C-E-flat-G-flat is a C diminished triad. C-E-G-sharp is a C augmented triad.

Root Position and Inversions

A chord is in root position when its root is the lowest note. In a triad, first inversion places the third in the bass, and second inversion places the fifth in the bass. The chord identity remains based on the root even when the bass note changes.

Inversions matter because they shape the bass line, spacing, and voice leading. A progression can sound smoother when the bass does not leap to every chord root.

Diatonic Triads in a Major Key

If you build a triad on every degree of a major scale using only notes from that key, the qualities follow a stable pattern:

I: major
ii: minor
iii: minor
IV: major
V: major
vi: minor
vii°: diminished

Uppercase Roman numerals usually indicate major triads, lowercase numerals indicate minor triads, and the degree symbol indicates diminished quality. Roman numerals are useful because they describe a chord's position and function in a key rather than only its letter name.

Diatonic Triads in Minor

Natural minor produces the basic triad pattern i, ii°, III, iv, v, VI, VII. In tonal harmony, however, the seventh scale degree is often raised. That change can turn v into a major V chord and create a diminished leading-tone chord vii°. These altered chords strengthen dominant-to-tonic motion.

Because minor-key harmony can draw from natural, harmonic, and melodic minor resources, you should expect more pitch variation than in a simple natural-minor scale.

Harmonic Function and Roman Numerals

Harmonic function describes the role a chord plays in creating stability, departure, preparation, tension, and return. A useful Grade 9–10 model groups many tonal chords into three broad functions.

The tonic function creates or confirms a sense of home. I is the clearest tonic chord in major, and i is the clearest tonic chord in minor. The vi chord can sometimes substitute for tonic-like stability in major, although it is not identical to I.

The predominant function prepares dominant harmony. IV and ii are common predominant chords in major. The term “subdominant function” is also used in some teaching traditions, especially for IV and related harmonies.

The dominant function creates strong expectation for the tonic. V and vii° contain scale-degree tendencies that point toward tonic harmony. The leading tone normally wants to resolve toward scale degree 1, and scale degree 4 often moves downward to 3 in a V–I resolution.

Fehler beim Erstellen des Vorschaubildes:

A common functional path is tonic → predominant → dominant → tonic. This is not a rule that every piece must follow, but it is a powerful model for understanding many tonal phrases.

Chord Progressions

A chord progression is an ordered series of chords. Chord progressions create larger harmonic motion and can support melodies, bass lines, grooves, and formal sections.

In C major, the progression I–IV–V–I is C major–F major–G major–C major. It begins at the tonic, moves away, builds dominant tension, and returns home. Another widely used progression is I–V–vi–IV. Its loop does not always create a strong final cadence, so it can keep musical motion going for many repetitions.

Root motion by descending fifth or ascending fourth is common in tonal harmony. For example, D minor to G major to C major forms ii–V–I in C major. This motion is especially important in classical, jazz, gospel, and many popular styles, though each style uses it differently.

How to Analyze a Progression

Use this process when you analyze harmony:

Find the key: Look at the key signature, important ending notes, repeated tonal centers, and cadences.
Spell each chord: Identify the notes sounding at the same time or implied by the texture.
Find the root: Rearrange the chord mentally into stacked thirds if necessary.
Label the Roman numeral: Compare the chord root and quality with the scale degrees of the key.
Describe the function: Decide whether the chord acts mainly as tonic, predominant, dominant, or another color.
Explain the motion: Track the bass, melody, tendency tones, common tones, and cadence.

If one chord does not fit the key, do not assume your analysis is wrong. The music may use a borrowed chord, secondary dominant, chromatic passing harmony, modal mixture, or a temporary change of key.

Cadences: Musical Punctuation

A cadence is a harmonic and melodic pattern that closes or pauses a phrase. Cadences can function like punctuation: some sound final, some unfinished, and some surprising.

An authentic cadence moves from dominant harmony to tonic harmony, usually V–I in major or V–i in minor. In some school systems, V–I is called a perfect cadence. In U.S. theory, the more specific term perfect authentic cadence describes a strong V–I ending with both chords in root position and the tonic in the highest voice at the end.

A half cadence ends on V and therefore sounds open or unfinished. In some British teaching traditions, this general idea is often called an imperfect cadence.

A plagal cadence moves IV–I and is often associated with a gentler closing effect. A deceptive cadence usually moves V to vi in major, avoiding the expected tonic. In some traditions this is called an interrupted cadence.

When identifying a cadence, listen to the melody as well as the chord roots. A strong sense of closure depends on rhythm, phrase position, bass motion, melody, voicing, and musical style.

Voice Leading and Part Writing

Voice leading is the way individual musical lines move from one harmony to the next. Imagine a four-part texture as four singers. Even when the chord label changes, each singer still needs a singable line.

Useful voice-leading strategies include keeping common tones in the same voice when practical, moving other voices by step or small interval, resolving tendency tones clearly, and avoiding unnecessary leaps. Contrary motion between outer voices can create independence.

In common-practice four-part writing, parallel perfect fifths and parallel octaves are usually avoided because they reduce the independence of voices in that style. This is a style convention, not a universal law. Parallel fifths, octaves, and doubled lines are used deliberately in many other musical traditions and genres.

When V moves to I in C major, the leading tone B often resolves up to C. The note F in a G7 chord often resolves down to E. These semitone movements are important parts of the dominant-to-tonic sound.

Melody, Non-Chord Tones, and Harmonic Context

A melody does not have to use only chord tones. Non-chord tones can create motion, decoration, and controlled tension.

A passing tone fills the space between two stable notes by step. A neighbor tone moves away by step and returns to the same note. A suspension holds a note from the previous harmony so that it briefly creates dissonance before resolving, often downward by step.

When you harmonize a melody, look for strong-beat notes, repeated notes, phrase endings, and longer durations. These tones often help define the harmony, while shorter notes between them may function as passing or neighbor tones.

A useful test is to ask: Which notes belong to the chord, and which notes are moving through or decorating it? This prevents you from changing chords every time the melody contains a non-chord tone.

Consonance, Dissonance, and the Harmonic Series

Musical sounds usually contain a fundamental frequency plus partials. In an idealized harmonic series, partial frequencies occur at whole-number multiples of the fundamental. Some simple frequency relationships help explain why octaves and perfect fifths can fuse strongly in many acoustic contexts.

Datei:Harmonic Series.png

However, harmony is not explained by acoustics alone. Musical training, style, tuning system, instrumentation, register, rhythm, and cultural expectation all shape what listeners hear as stable, tense, rough, smooth, familiar, or surprising. A dissonance can be expressive and desirable; its role matters more than a simple “good versus bad” label.

Ear Training and Listening

Theory becomes useful when you can connect symbols to sound. You can train your ear without perfect pitch. Relative pitch means hearing relationships between notes, such as recognizing that one note is a perfect fifth above another or that a chord progression moves from dominant to tonic.

Practice short listening cycles. First, sing or play the tonic. Next, listen for the bass. Then decide whether the harmony feels stable, departing, preparing, tense, or resolved. Finally, test your guess on an instrument or with notation.

For intervals, compare a new sound with a reference you can sing accurately. For chords, learn the contrast among major, minor, diminished, and dominant-seventh qualities. For cadences, focus on the final two harmonies and the melody's last note.

Composition Lab: Build an Eight-Measure Harmonic Study

Create a short eight-measure piece in C major, G major, F major, A minor, or another key you understand. Begin by choosing a meter and a simple harmonic rhythm. Use at least four different chords and include a clear cadence at the end.

A possible planning method is to make the first phrase establish the tonic, let the middle measures move through predominant and dominant functions, and make the final phrase return clearly to the tonic. You may use a repeated chord loop if you can explain how it affects the sense of closure.

Write a melody that includes both chord tones and at least two controlled non-chord tones. Then revise the bass line or chord inversions so that at least some voices move by step or remain on common tones.

Your finished work can be notation, a MIDI sequence, a live recording, a DAW project, or a written chord-and-melody chart. Add a short explanation naming the key, Roman numerals, cadence, and one voice-leading choice.

Common Misunderstandings

“Every song has to stay in one key.” No. Music can tonicize other chords, borrow notes, use modes, modulate, or avoid functional tonality altogether.

“Minor always sounds sad and major always sounds happy.” No. Mode can affect color, but tempo, rhythm, register, timbre, melody, dynamics, lyrics, and cultural context strongly influence expression.

“A chord is defined by its bass note.” No. The bass can be the root, third, fifth, or another chord tone. Inversions change the bass while the chord root remains the same.

“Dissonance is a mistake.” No. Dissonance can create energy, direction, color, and expression. Many styles depend on carefully placed dissonance.

“Roman numerals tell you the exact voicing.” No. They identify scale position and chord quality, but a single Roman numeral can be realized in many registers, inversions, spacings, and instrumental textures.

Summary

Music theory gives you a vocabulary for describing patterns. Harmony explains how simultaneous or implied pitches interact and how chords move through time. Scales organize pitch collections, intervals measure distance, triads build basic chord structures, Roman numerals show a chord's place in a key, functions explain harmonic roles, cadences shape phrase endings, and voice leading connects chords through individual lines.

The most useful habit is to connect symbol, sound, and musical purpose. Whenever you learn a theoretical idea, play or sing it, listen for its effect, find it in real music, and use it in a small composition of your own.

Interactive Tasks

Quiz: Test Your Knowledge

Which chord is the tonic triad in C major? (C major) (!D minor) (!F major) (!G major)

What is the interval from C up to G? (Perfect fifth) (!Major third) (!Minor sixth) (!Perfect fourth)

Which scale degree is called the dominant? (Fifth degree) (!Second degree) (!Third degree) (!Sixth degree)

Which sequence gives the whole-step and half-step pattern of a major scale? (Whole whole half whole whole whole half) (!Whole half whole whole half whole whole) (!Half whole whole half whole whole whole) (!Whole whole whole half whole half whole)

What quality is the triad built on the seventh degree of a major scale? (Diminished) (!Major) (!Minor) (!Augmented)

Which harmonic motion most directly creates an authentic cadence in a major key? (Dominant to tonic) (!Tonic to subdominant) (!Tonic to submediant) (!Subdominant to supertonic)

What does first inversion of a triad place in the bass? (The third) (!The root) (!The fifth) (!The seventh)

Which chord commonly has predominant function in a major key? (ii) (!I) (!V) (!vii diminished)

What is voice leading mainly concerned with? (How individual parts move between harmonies) (!How fast a piece is performed) (!How loudly each section is played) (!How instruments are tuned before rehearsal)

What usually happens in a deceptive cadence in a major key? (V moves to vi) (!IV moves to I) (!V moves to I) (!I moves to V)

Memory Game

Tonic	The tonal center and strongest sense of home
Dominant	A function that creates strong expectation for resolution
Predominant	A function that commonly prepares dominant harmony
Triad	A three-note chord built from a root third and fifth
Cadence	A phrase-ending harmonic and melodic pattern
Interval	The distance between two pitches
Inversion	A chord position in which a note other than the root may be in the bass
Voice leading	The motion of individual musical lines from one harmony to another

Drag and Drop

Match the correct terms.	Topic
Sense of home	Tonic function
Preparation for tension	Predominant function
Strong expectation of return	Dominant function
Phrase ending with surprise	Deceptive cadence
Small connected melodic movement	Smooth voice leading

Crossword Puzzle

Tonic	What is the tonal center of a key called
Dominant	Which function commonly creates strong tension before the tonic
Interval	What term names the distance between two pitches
Cadence	What is a phrase-ending harmonic pattern called
Triad	What three-note chord is built from root third and fifth
Consonance	What term often describes relative harmonic stability

LearningApps

Cloze Text

Open-Ended Tasks

Easy

Pitch Map: Draw or photograph a keyboard or instrument fingerboard and label one octave of note names, including at least two enharmonic spellings.
Rhythm Builder: Create four one-measure rhythm patterns in a chosen meter, perform them by clapping or tapping, and explain where the strong beats occur.
Interval Hunt: Find five intervals in a short melody you can read or play, name each interval, and test the names on an instrument.
Triad Workshop: Build and perform major, minor, and diminished triads on three different roots, then describe how changing one note changes the chord quality.

Standard

Roman Numeral Analysis: Choose an eight-measure tonal passage, identify its key, label at least six chords with Roman numerals, and explain two harmonic functions.
Cadence Recording: Record or sequence four short examples that demonstrate authentic, half, plagal, and deceptive cadences, then explain the different kinds of closure.
Harmony Interview: Interview a musician, teacher, producer, choir member, or songwriter about how they choose chords, and compare the interview answers with concepts from this course.
Chord Loop Remix: Write two different melodies over the same four-chord loop and explain how rhythm, non-chord tones, and phrase endings change the musical result.

Advanced

Voice Leading Study: Arrange one four-chord progression for four independent parts, revise it for smoother motion, and annotate the changes you made.
Minor Key Investigation: Compare natural and harmonic minor in a short composition by showing how the raised seventh degree changes dominant harmony and melodic direction.
Style Comparison: Analyze harmony in two contrasting musical styles and explain which course concepts transfer well, which conventions differ, and which ideas need different vocabulary.
Original Harmonic Composition: Compose and record or notate a sixteen-measure piece that includes functional harmony, at least one inversion, one non-chord tone, and a deliberate cadence, then write a short analytical commentary.

Learning Assessment

Functional Analysis: Given a short tonal score, identify the key, label the main chords, group them by function, and explain how the progression creates departure and return.
Harmonization Challenge: Harmonize an eight-measure melody with at least three chord functions, then justify two places where you chose an inversion or non-chord tone.
Listening Transfer: Listen to an unfamiliar tonal excerpt, propose a likely cadence and chord-function pattern, and explain the audible evidence for your answer before checking with an instrument.
Voice Leading Revision: Compare two versions of a four-part progression, identify which version creates smoother independent lines in common-practice style, and defend your judgment with specific note movements.
Creative Reharmonization: Take a simple four-chord progression and create a contrasting version by changing at least two chords while preserving the phrase shape, then explain how the emotional or directional effect changed.
Theory in Context: Choose a musical style that does not rely mainly on common-practice functional harmony and explain which ideas from this course still apply and which require adaptation.

Evidence of Learning

Knowledge: You can accurately explain pitch, meter, scales, intervals, triads, inversions, Roman numerals, harmonic function, cadences, non-chord tones, and basic voice-leading principles.

Skills: You can hear and identify basic harmonic relationships, build and label chords, analyze short tonal progressions, follow individual voices, and connect written symbols with performed sound.

Products: Your evidence may include annotated scores, chord charts, recordings, MIDI or DAW projects, ear-training logs, interval studies, harmonizations, interviews, and original compositions.

Transfer: You can apply theory to unfamiliar music, compare harmonic conventions across styles, revise a composition using analytical evidence, and explain when a theoretical rule is a style-specific convention rather than a universal law.