Isomorphic

An isomorphic table of notes is one where every instance of the same offset represents the same interval, every step in the same direction is the same size of interval, and the same chord always has the same shape, even when moved to different notes. When used as a note entry device, it is called an isomorphic keyboard, and the Lumatone is an example. The standard keyboard layout is not isomorphic, because a C major chord and an A minor chord have the same shape, while a C major chord and an A major chord have different shapes. Similarly, the standard guitar fretting is not isomorphic, because one string is offset by a major third, while the rest are offset by perfect fourths.

Examples

Isomorphic tables of notes for several MOSes associated with common ploidacot signatures

- Any just intonation lattice is isomorphic up to octave-reduction.

- The Kite Guitar is isomorphic, as all strings are offset by a major third from one another.

- The harmonic table in 12edo is isomorphic.

- An isomorphic layout can be designed based on any MOS scale, by setting the large step as the vertical axis and the moschroma as the horizontal axis.