Acoustics & Music Theory
why it sounds like that
Theme

The same shape, moved

A chord, a scale and a rhythm are all patterns that keep their identity when shifted. What survives the shift is what the theory is about.
CC♯DE♭EFF♯GA♭AB♭B2 · 2 · 1 · 2 · 2 · 2 · 1steps, in semitonesthe short chords are the semitones — two of them, unevenly spaced Scales and modes

Seven of the twelve, chosen unevenly

A major scale is a selection of seven positions out of twelve, and the selection is lopsided on purpose. The two semitones sit where they do because an even choice would destroy the thing that makes a scale usable.

 CC♯DE♭EFF♯GA♭AB♭BCLydianIonianMixolydianDorianAeolianPhrygianLocrianbrightest at the top, darkest at the bottomeach row drops exactly one note by a semitone from the row above Scales and modes

The same seven, started later

A mode is not a new scale. It is the same seven notes with a different one treated as home, and the entire change in character comes from reassigning which degree the semitones fall next to.

 CaGeDbAf♯Ec♯Ba♭F♯e♭C♯b♭A♭fE♭cB♭gFdone step= one fifth= one sharpouter ring: major keys · inner ring: their relative minors Scales and modes

Keys are neighbours, and the map is computed

Two keys a fifth apart share six of their seven notes. That single fact generates the circle of fifths, the key signatures, the shape of nearly every modulation, and the sense that some keys are far away.

 C1/1E5/4G3/243major0–4–7C1/1E♭6/5G3/234minor0–3–7C1/1E♭6/5F♯33diminished0–3–6C1/1E5/4A♭8/544augmented0–4–8semitones above the root Harmony and voice leading

Three notes at once, and why these three

A triad is two thirds stacked, and the four ways of stacking them behave completely differently. The difference is entirely in whether the resulting ratios are simple.

 2C majorA minortotal 2 semitones12C majorF majortotal 3 semitones231C majorF♯ majortotal 6 semitonesthe shortest change is the one nobody has to sing far Harmony and voice leading

The shortest move, which is what a chord change is

Between any two chords there is an assignment of voices that moves the least. Compute it and the changes that composers actually use turn out to be the short ones.

 ICiiDiiiEIVFVGviAvii°BI – vi – IV – Vradius = semitones of voice motion from the tonic chord Harmony and voice leading

A progression is a path, and the map can be drawn

Chords in a key are not a list. They sit at measurable distances from home, and a progression is a walk across that space — which explains why some sequences feel like journeys and others like wandering.

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