Acoustics & Music Theory
why it sounds like that
Concept

Modal harmony — where it appears

What chords do when a mode rather than a key is in force, with no leading note on most degrees and closure achieved by other means. Only one of the seven diatonic modes has a leading note and a major triad on its fifth degree.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The seven modes, brightest first. The same seven pitch classes started on each of its degrees in turn, ordered by how many of their notes are raised. Each row differs from the one below it by exactly one note, and that note moves down one semitone each time.

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.

scales · Modes How often the chord changes, and what a room allows. Chord changes a second implied by each style's stated rate and tempo, on a logarithmic axis, with the rate above which a room leaves more than one earlier chord above 20 dB marked for six rooms. The style rates are conventions rather than corpus measurements and the figure says so; the room rates are arithmetic from the reverberation time.

How often the chord changes

Two pieces can use the same chords in the same order and be nothing alike, because a progression says which chords and not how fast. Harmonic rhythm is the second variable, it runs over a factor of thirty between the styles that use it, and both of its limits are set by things that are not harmony — a listener's memory at the slow end and a building at the fast one.

harmony · Progression The triad on every degree of every rotation. The quality of the triad built on each degree of each rotation, computed from the set rather than tabulated. The triad on the fifth degree is major in 3 of the 7: Lydian, Ionian, Locrian. Of those, Locrian has no triad on its own first degree to resolve to, and Lydian has its fifth degree on the note the parent collection is built from, so the cadence would confirm the parent rather than the mode. What is left is Ionian — one rotation of the 7, and the others have to end some other way.

One dominant among seven

The triad on the fifth degree is major in three of the seven rotations. One of those three has no triad on its own first degree, and one has its fifth degree on the note the parent collection is built from — so exactly one rotation of the seven has a dominant, and the other six end by moves that cost twice as much in voice leading.

harmony · Modes The rotations of the diatonic set, brought to one tonic. The same rotations started on the same note rather than on their own, ordered by how many of their degrees are raised. Every step lowers exactly one note by a semitone, and the notes it lowers, in order, are F♯, B, E, A, D, G — which is the chain of fifths read backwards. A rotation is a rotation whatever the scale; the chain is a property of a set generated by a single interval, and it disappears the moment the set is not.

Parallel and relative are two different maps

Bring the seven modes to one tonic and order them by brightness, and each step lowers exactly one note by a semitone — and the notes it lowers, in order, are F♯, B, E, A, D, G, the chain of fifths read backwards. Do the same to harmonic minor's rotations and each step moves two, three or four notes at once. The famous chain belongs to the generator, not to rotation.

scales · Modes

Named alongside it

The objects these essays reach for when they reach for this one.

ModeBrightnessRotationCadenceChain of fifthsDominantHarmonic rhythmIntegration windowLeading noteOstinatoPhraseProgression

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