Limited Transposition

Limited Transposition


Perfectly even chords and scales are limited in their voice leading possibilities partly because they have a limited number of transpositions. The Limited Transposition index lists all possible modes of limited transposition for 12-TET. More 


Examples of perfectly even chords and scales are the diminished seventh, augmented triad, and hexatonic whole-tone scale.

There are three transpositions of the diminished seventh chord, not twelve: C dim 7 = E dim 7 = F# dim 7 = A dim 7 (one), D dim 7 = ... (two), D dim 7 = ... (three).

animation of four clocks with three evenly-spaced dots animating forever clockwise, but only taking four rotations to do so

There are only four different augmented triads: C Aug = E Aug = A Aug (one), D Aug = ... (two), D Aug = ... (three), Eb Aug = ... (four).

See Grouping Clocks for more.