Symmetric Scales

A scale is symmetric when its interval pattern repeats at regular divisions of the octave.

Transposing it by the length of the repeating cell can reproduce the same pitch classes in a new order.

This differs from a major scale, whose uneven pattern normally identifies one tonic through context and interval placement.

The whole-tone scale uses six consecutive whole steps.

From C:

C-D-E-F sharp-G sharp-A sharp-C

Every step spans two semitones. Transpose the collection up one whole step and the pitch classes stay the same.

There are only two distinct whole-tone pitch collections in twelve-tone equal temperament.

C-E-G sharp forms C augmented. D-F sharp-A sharp forms D augmented.

Dominant structures such as C7 sharp 5 can draw C, E, G sharp and B flat from the collection when B flat is spelled enharmonically instead of A sharp for chord function.

The scale has no perfect fifth above C. Its augmented triads and whole-step motion create its recognizable sonority.

The diminished scale contains eight notes and alternates whole and half steps.

C whole-half diminished is:

C-D-E flat-F-G flat-A flat-A-B-C

C half-whole diminished begins with the opposite step:

C-D flat-E flat-E-G flat-G-A-B flat-C

The two forms are rotations of the same interval pattern and support different chord-centered uses.

Transposing an octatonic collection by a minor third reproduces the same pitch classes.

That leaves three distinct diminished collections in twelve-tone equal temperament.

Within one collection, several roots can sound structurally important. Harmony and bass determine which chord or center the listener follows.

Whole-half diminished contains diminished-seventh structures and is commonly used over a diminished seventh chord.

Half-whole diminished fits dominant chords with combinations of flat 9, sharp 9, sharp 11 and 13.

Over C7, C half-whole diminished contains C, E and B flat plus D flat, E flat, G flat, G and A. Spell notes according to their chord roles.

The augmented scale alternates minor thirds and semitones.

From C, one form is:

C-E flat-E-G-A flat-B-C

It contains two augmented triads, C-E-G sharp and E flat-G-B, with enharmonic spelling adjusted for each structure.

Its repeating four-semitone-plus-one-semitone cell creates a six-note collection and a limited number of distinct transpositions.

The pitch collection alone offers several equivalent starting points. Musical context can still establish a tonic through bass, duration, repetition and resolution.

A C whole-tone line over C7 sharp 5 will be heard relative to C because the chord and bass define it.

Symmetry weakens unique scale-degree hierarchy; it does not prevent composition from creating a center.

The chromatic scale repeats one-semitone steps and contains all twelve pitch classes.

Whole-tone, diminished and augmented scales select smaller repeating cells and omit pitches. Those omissions create specific chord structures.

All are symmetric, but their interval patterns and harmonic applications differ.

Whole-tone collections appear in impressionist, film and game music and over augmented dominants.

Diminished scales appear in jazz improvisation, diminished passing harmony and twentieth-century composition.

Augmented scales appear over augmented-major structures and in music using repeating minor-third and semitone cells.

Play C whole tone and transpose it up a whole step. Confirm that the keys are unchanged.

Play C whole-half diminished, then transpose it up a minor third. Again compare the pitch classes.

Finally, hold C7 and compare C whole tone with C half-whole diminished. Name which altered chord tones each scale supplies.