Music Theory: The Grammar of Sound
"Music is the shorthand of emotion." — Leo Tolstoy
Music theory is the study of the practices and possibilities of music — the grammar that underlies the language of sound. You don't need to read this to play music, just as you don't need to study linguistics to speak. But understanding it illuminates what's happening when music moves you.
Sound Basics
What Is a Note?
A note is a sound with a specific pitch — determined by the frequency of vibration (Hz). A440 (the A above middle C) vibrates 440 times per second. Double the frequency, and you get the next A (880 Hz). This doubling relationship is an octave.
The Twelve Notes
In Western music, the octave is divided into 12 equal half-steps (semitones):
C — C#/Db — D — D#/Eb — E — F — F#/Gb — G — G#/Ab — A — A#/Bb — B — (C)
Notes with two names (C#/Db) are enharmonic equivalents — the same pitch, spelled differently depending on context.
Half Steps and Whole Steps
- Half step (semitone): The smallest interval in Western music. C to C# is a half step.
- Whole step (tone): Two half steps. C to D is a whole step.
These are the building blocks of all scales, chords, and melody.
Scales
A scale is a set of pitches arranged in ascending or descending order. Scales give a piece its tonal "color."
The Major Scale
The major scale has a bright, happy quality. Its pattern of whole (W) and half (H) steps:
W-W-H-W-W-W-H
C Major (all white keys on piano): C — D — E — F — G — A — B — C
Scale degrees: | Degree | Name | C Major | |--------|------|---------| | 1 | Tonic | C | | 2 | Supertonic | D | | 3 | Mediant | E | | 4 | Subdominant | F | | 5 | Dominant | G | | 6 | Submediant | A | | 7 | Leading tone | B |
The Natural Minor Scale
Minor scales have a darker, more melancholic quality. Pattern:
W-H-W-W-H-W-W
A Natural Minor (also all white keys): A — B — C — D — E — F — G — A
A major scale's relative minor begins on the 6th degree. C major → A minor. G major → E minor.
Pentatonic Scales
Five-note scales — the backbone of folk, blues, and rock worldwide.
Major Pentatonic (C): C — D — E — G — A Minor Pentatonic (A): A — C — D — E — G
The minor pentatonic is perhaps the most important scale in popular music. Almost all blues, rock, and pop guitar solos draw from it.
Blues Scale
Minor pentatonic + one added "blue note" (flat 5): A — C — D — Eb — E — G
The Eb (between D and E) is the signature sound of the blues.
Keys
A key is the home base of a piece — the scale and tonal center around which the music revolves.
- A piece in C major uses the notes of the C major scale and resolves to C.
- A piece in A minor uses the A minor scale and resolves to A.
Key signature: Written at the beginning of sheet music, showing which notes are sharped or flatted throughout.
Key Signatures at a Glance
| Key (Major) | Sharps/Flats |
|---|---|
| C major | None |
| G major | 1 sharp (F#) |
| D major | 2 sharps (F#, C#) |
| A major | 3 sharps |
| E major | 4 sharps |
| F major | 1 flat (Bb) |
| Bb major | 2 flats |
| Eb major | 3 flats |
The Circle of Fifths
The circle of fifths is the single most useful visual tool in music theory. It organizes all 12 keys in a circle, arranged by perfect fifths:
C
F G
Bb D
Eb A
Ab E
Db B
Gb/F#
Moving clockwise: Each key adds one sharp. (C → G → D → A → E → B → F#) Moving counterclockwise: Each key adds one flat. (C → F → Bb → Eb → Ab → Db → Gb)
Adjacent keys are closely related. Songs that modulate (change key) usually move to adjacent keys. Chord progressions often move in circle-of-fifths patterns.
Finding relative minors: Each major key's relative minor is its 6th scale degree — and sits inside the circle (inner ring).
Intervals
An interval is the distance between two notes. Intervals are the vocabulary of melody and harmony.
| Interval | Half Steps | Example | Sound |
|---|---|---|---|
| Unison | 0 | C to C | Same note |
| Minor 2nd | 1 | C to C# | Half step, dissonant |
| Major 2nd | 2 | C to D | Whole step |
| Minor 3rd | 3 | C to Eb | Sad, minor quality |
| Major 3rd | 4 | C to E | Happy, major quality |
| Perfect 4th | 5 | C to F | Open, stable |
| Tritone | 6 | C to F# | Tense, unstable |
| Perfect 5th | 7 | C to G | Open, powerful |
| Minor 6th | 8 | C to Ab | |
| Major 6th | 9 | C to A | |
| Minor 7th | 10 | C to Bb | Bluesy tension |
| Major 7th | 11 | C to B | Strong tension |
| Octave | 12 | C to C | Same note, higher |
Consonant intervals (stable, pleasant): Unison, octave, perfect 5th, major/minor 3rd, major/minor 6th Dissonant intervals (tense, want resolution): 2nds, 7ths, tritone
Chord Construction
A chord is three or more notes played simultaneously. Chords are built by stacking intervals — typically thirds.
Triads (Three-Note Chords)
Major triad: Root + Major 3rd + Perfect 5th - C major: C — E — G (intervals: 4 half steps + 3 half steps)
Minor triad: Root + Minor 3rd + Perfect 5th - A minor: A — C — E (intervals: 3 half steps + 4 half steps)
Diminished triad: Root + Minor 3rd + Diminished 5th - B diminished: B — D — F (3 + 3 half steps) — tense, unstable
Augmented triad: Root + Major 3rd + Augmented 5th - C augmented: C — E — G# (4 + 4 half steps) — dreamy, unresolved
Seventh Chords
Add another third on top of a triad to get a seventh chord:
| Chord | Formula | Example | Sound |
|---|---|---|---|
| Major 7th | Maj triad + Maj 7th | C-E-G-B | Lush, sophisticated |
| Dominant 7th | Maj triad + Min 7th | C-E-G-Bb | Bluesy, wants resolution |
| Minor 7th | Min triad + Min 7th | A-C-E-G | Mellow, common in jazz |
| Half-diminished | Dim triad + Min 7th | B-D-F-A | Jazz, ambiguous |
Chord Inversions
A chord can be played with any note on the bottom (bass): - Root position: C-E-G (C on bottom) - First inversion: E-G-C (E on bottom) - Second inversion: G-C-E (G on bottom)
Inversions create smoother voice leading between chords.
Chord Progressions
Chords in a key are numbered with Roman numerals:
In C major: | Numeral | Chord | Notes | |---------|-------|-------| | I | C major | C-E-G | | ii | D minor | D-F-A | | iii | E minor | E-G-B | | IV | F major | F-A-C | | V | G major | G-B-D | | vi | A minor | A-C-E | | vii° | B diminished | B-D-F |
Uppercase = major; lowercase = minor.
Common Progressions
I-IV-V (the foundation of blues and rock): C — F — G. In any key.
I-V-vi-IV (the "four chord song"): C — G — Am — F. Underlies hundreds of pop songs. Pachelbel's Canon also uses this.
I-vi-IV-V (50s progression): C — Am — F — G. Doo-wop, early rock & roll.
ii-V-I (jazz foundation): Dm7 — G7 — Cmaj7. The cornerstone of jazz harmony.
Time Signatures and Rhythm
Reading Time Signatures
A time signature like 4/4 means: - Top number: 4 beats per measure - Bottom number: the quarter note (4) gets one beat
| Signature | Feel | Example |
|---|---|---|
| 4/4 | Standard, march-like | Most pop/rock |
| 3/4 | Waltz (1-2-3, 1-2-3) | "Happy Birthday" |
| 6/8 | Lilting, compound duple | "House of the Rising Sun" |
| 2/4 | March, fast feel | Polka |
| 5/4 | Asymmetric, complex | "Take Five" |
| 7/8 | Unusual, driving | Progressive rock |
Note Values
| Note | Duration (in 4/4) |
|---|---|
| Whole note | 4 beats |
| Half note | 2 beats |
| Quarter note | 1 beat |
| Eighth note | 1/2 beat |
| Sixteenth note | 1/4 beat |
Syncopation
Emphasis on off-beats or unexpected beats. The backbone of jazz, funk, reggae, and hip-hop. Where the "normal" emphasis is on beats 1 and 3, syncopation accents beats 2 and 4, or the "and" of beats (the off-beats).
Dynamics
Dynamics describe volume and intensity:
| Marking | Italian | Meaning |
|---|---|---|
| ppp | pianississimo | Extremely soft |
| pp | pianissimo | Very soft |
| p | piano | Soft |
| mp | mezzo-piano | Moderately soft |
| mf | mezzo-forte | Moderately loud |
| f | forte | Loud |
| ff | fortissimo | Very loud |
| fff | fortississimo | Extremely loud |
| < | crescendo | Gradually louder |
| > | decrescendo | Gradually softer |
| sfz | sforzando | Sudden strong accent |
Tempo
Tempo is speed, measured in BPM (beats per minute):
| Marking | BPM range | Character |
|---|---|---|
| Larghissimo | <20 | Extremely slow |
| Largo | 40–60 | Very slow, broad |
| Adagio | 66–76 | Slow, stately |
| Andante | 76–108 | Walking pace |
| Moderato | 108–120 | Moderate |
| Allegro | 120–156 | Fast, lively |
| Vivace | 156–176 | Very fast |
| Presto | 168–200 | Very fast |
| Prestissimo | >200 | As fast as possible |
Putting It Together
Music theory is a language, and like language, its grammar only matters insofar as it serves communication. You can know every rule and play music that moves no one. You can know no rules and move everyone.
The value of theory is not to constrain but to explain — to give you vocabulary for what you're hearing and hearing, and to expand your toolkit when you get stuck. When a song you love sounds "right," theory can tell you why. When something you write sounds wrong, theory can point you toward what might fix it.
Start with the major scale in C. Learn the I-IV-V. Learn the minor pentatonic. Then listen actively — when music moves, ask: what's happening? Theory is the discipline of answering that question systematically.
Part of the Observatory Almanac — Section 21: Music & Performance