Music Theory & Composition

# Music Theory & Composition

## Fundamentals

### Pitch & Intervals
Western music divides the oct into 12 equal semitones (equal temperament). An int is the distance between two pitches. Naming: count letter names inclusively from bottom to top. C to E = third (C-D-E, three letters). Quality modifiers: maj, min, perfect, dim, aug.

Perfect int (unison, 4th, 5th, oct): the most consonant, found in virtually all world music traditions. The perfect 5th (7 semitones) is the foundation of harm — it's the first non-oct overtone in the harmonic series and the basis of Pythagorean tuning.

maj int: 2nd (2 semitones), 3rd (4), 6th (9), 7th (11). min int: 2nd (1), 3rd (3), 6th (8), 7th (10). The maj 3rd vs min 3rd distinction is the primary source of the "happy" vs "sad" quality in Western music — though this association is culturally conditioned, not universal.

int inversions: subtract from 9 for number (3rd inverts to 6th), quality flips (maj→min, aug→dim, perfect stays perfect). Knowing inversions halves the int you need to memorize.

### Scales & Keys
A scale is a collection of pitches arranged in ascending order. The maj scale (W-W-H-W-W-W-H, where W=whole step, H=half step) is the reference point for Western music. Every other scale is described relative to it.

Natural min: same pitches as the maj scale starting from the 6th degree (C maj = A min). Relationship: every maj key has a relative min, and vice versa. The min scale's defining feature: flat 3rd (min 3rd above ton).

Harmonic min: raised 7th degree creates a leading tone (half step below ton), enabling a dom function (V chd) in min keys. The augmented 2nd between flat 6th and raised 7th gives harmonic min its distinctive "exotic" sound.

Modes: rotating the starting point of the maj scale creates 7 modes, each with a distinct character. Ionian (maj), Dorian (min with raised 6th — versatile, slightly brighter min), Phrygian (min with flat 2nd — Spanish/flamenco character), Lydian (maj with raised 4th — dreamy, floating quality), Mixolydian (maj with flat 7th — rock, blues, folk), Aeolian (natural min), Locrian (dim — rarely used as a key center, inherently unstable).

Pentatonic scales (5 notes): maj pentatonic removes the 4th and 7th (the two notes that create half steps), producing a scale with no semitone tension — universally consonant across cultures. min pentatonic (1-b3-4-5-b7) is the foundation of blues, rock, and much folk music worldwide.

### Rhythm & Meter
Meter organizes beats into recurring groups. Simple meters: beats divide into two (4/4, 3/4, 2/4). Compound meters: beats divide into three (6/8, 9/8, 12/8). 6/8 vs 3/4: same number of eighth notes but different grouping — 6/8 feels like two groups of three, 3/4 feels like three groups of two.

Syncopation: accenting weak beats or off-beats. The driving force of jazz, funk, Latin, and most popular music. Displacing expected accents creates rhythmic tension and forward momentum. The "and" of beats (upbeats) are the most common syncopation targets.

Polyrhythm: two or more conflicting rhy patterns simultaneously. 3-against-2 (hemiola) is the most basic: one voice plays three equal notes while another plays two. West African drumming traditions develop polyrhythm to extraordinary complexity. In Western classical music, Brahms used hemiola extensively.

## Harmony

### Chord Construction
Triads: three notes stacked in 3rds. Four qualities: maj (maj 3rd + min 3rd = 1-3-5), min (min 3rd + maj 3rd = 1-b3-5), dim (min 3rd + min 3rd = 1-b3-b5), aug (maj 3rd + maj 3rd = 1-3-#5).

Seventh chds add another 3rd: maj7 (maj triad + maj 7th — smooth, jazzy), dom7 (maj triad + min 7th — tense, wants to resolve), min7 (min triad + min 7th — warm, mellow), half-dim7 (dim triad + min 7th — used as ii in min keys), fully-dim7 (dim triad + dim 7th — symmetrical, highly unstable, used for dramatic modulation).

Extended chds continue stacking 3rds: 9ths, 11ths, 13ths. In jazz, a "13th chd" theoretically contains all 7 scale tones. In practice, notes are omitted (usually the 5th, sometimes the root when a bass player covers it). Extensions add color without changing fundamental function.

### Chord Progressions
Roman numeral analysis labels chds by scale degree: in C maj, C=I, Dm=ii, Em=iii, F=IV, G=V, Am=vi, Bdim=vii°. Uppercase = maj, lowercase = min.

Functional harm groups chds into three categories:
- **Tonic** (I, iii, vi): Stability, home, rest
- **Subdominant** (ii, IV): Movement away from home, preparation
- **Dominant** (V, vii°): Maximum tension, strongest pull back to ton

The fundamental prog: ton → sub → dom → ton (I → IV → V → I). Every common prog is a variation of this principle. The V→I resolution (authentic cad) is the strongest harmonic motion in tonal music — the tritone within the dom chd (between the 3rd and 7th of V) resolves by half steps to the root and 3rd of I.

Common progs and their contexts:
- I-V-vi-IV: The "axis of awesome" — hundreds of pop songs ("Let It Be," "No Woman No Cry," "With or Without You")
- ii-V-I: The fundamental jazz prog. The ii provides smooth voice leading into V. Adding 7ths: ii7-V7-Imaj7
- I-vi-IV-V: 1950s doo-wop prog ("Stand By Me," "Every Breath You Take")
- i-bVII-bVI-V: Andalusian cad — flamenco, much rock ("Hit the Road Jack")
- 12-bar blues: I-I-I-I-IV-IV-I-I-V-IV-I-V (with dom7 chds throughout)

### Voice Leading
The art of moving individual voices smoothly between chds. Core principles: (1) Move each voice the shortest possible distance (prefer stepwise motion or common tones over leaps). (2) Resolve tendency tones: the 7th of a dom chd resolves down by step, the leading tone resolves up to ton. (3) Avoid parallel 5ths and oct between voices (they erase voice independence). (4) Contrary motion between outer voices (bass and soprano moving in opposite directions) creates the strongest sense of independence.

Good voice leading makes even simple progs sound professional. Poor voice leading makes complex harm sound amateur. Voice leading is what separates a "chd chart" from actual music.

### Modulation
Changing key within a piece. Methods:
- **Pivot chd**: A chd that functions in both the old and new keys. C maj's vi (Am) is also D min's v — reinterpret it and you've modulated. Smoothest technique.
- **Direct/phrase**: Simply start a new phrase in the new key. Abrupt but effective, especially up a half or whole step for energy (the "truck driver's modulation" in pop ballad final choruses).
- **Chromatic**: Use chromatic voice leading to slide into the new key. Secondary dominants (V/V, V/vi, etc.) are the most common tool — temporarily tonicize a non-ton chd.
- **Enharmonic**: Exploit enharmonic equivalents (dim7 chds are symmetrical — each inv is a root position dim7 of a different key, enabling mod to 4 different keys from one chd).

## Composition & Arrangement

### Form
**Binary (AB)**: Two contrasting sections. The foundation of dance forms (minuet, march). Each section typically repeats: ||:A:||:B:||

**Ternary (ABA)**: Statement, contrast, return. The A section returns after B, providing satisfying closure. Da capo arias, minuet-and-trio, many pop songs follow this.

**Verse-Chorus**: The dominant popular music form. Verse (changing lyrics, same music) and chorus (same lyrics and music each time — the hook). Bridge provides contrast before the final chorus. Pre-chorus builds energy into the chorus.

**Sonata form**: The intellectual architecture of classical music. Exposition (theme 1 in ton key, transition, theme 2 in dom key), Development (themes fragmented, combined, explored through remote keys), Recapitulation (both themes return in ton key — the dramatic resolution). The entire form is a large-scale ton→dom→ton journey.

**Rondo (ABACA...)**: A recurring theme alternates with contrasting episodes. Accessible form — the familiar A section provides an anchor.

### Melodic Construction
Strong mel share common traits: (1) Mostly stepwise motion with occasional leaps for expressiveness (leaps > 4th should be followed by stepwise motion in the opposite direction). (2) Clear contour — a single climactic high point per phrase, typically around 2/3 through. (3) Rhythmic variety — mix of long and short notes. (4) Repetition with variation — repeat a motif but change the ending (antecedent-consequent phrase structure, like a musical question-and-answer).

Motivic development: take a short musical idea (motif) and transform it — trp (shift pitch), inv (flip upside down), retrograde (reverse), augmentation (stretch rhy), diminution (compress rhy), seq (repeat at different pitch levels). Beethoven's 5th Symphony: the entire first movement develops from a 4-note motif (short-short-short-long).

### Orchestration & Arrangement
orch is the art of assigning musical material to specific instruments, exploiting their unique timbres, reg, and capabilities.

Reg considerations: instruments have different characters across their range. Clarinet: chalumeau (low, dark, rich) vs clarion (mid, bright, clear) vs altissimo (high, piercing). Trumpet: low reg (dark, mellow) vs high reg (brilliant, heroic). Writing in the instrument's sweet spot ensures the best tone quality.

dyn layering: not all instruments at all times. Build texture by adding layers — start sparse, add instruments for climactic moments, thin for contrast. The orch's power comes from contrast: a single oboe mel after a full tutti passage is more expressive than the full orch playing the same mel.

Doubling: having multiple instruments play the same line adds volume and timbral richness. Doubling at the oct creates fullness without muddiness. Same-oct doubling blends timbres (flute + violin at unison creates a unique combined timbre). Over-doubling makes everything sound the same — restraint is key.

Balance: Brass naturally overpowers strings and woodwinds. A single trumpet can match 8-10 violins in volume. orch balance requires fewer brass or marked-down dyn, and more strings/winds on mel lines. In arr for smaller ensembles, the piano's sustain pedal and reg span can substitute for many orch functions.