Erose–McClain double mode

Erose–McClain double modes, or simply double modes, are a family of heptatonic scales in 31edo.

They are constructed by taking one of the modes of the diatonic scale, but flattening the interval of equivalence by one normal diesis, from 31\31 to 30\31. This creates a scale with pseudo-octaves.

The first double mode to be described was double Lydian, by Zhea Erose. The other six were described by Levi McClain, who was inspired by the work of Erose, and by his own McClain toy piano tuning, which resembles double Phrygian.

Taxonomy

Erose–McClain double modes are warped diatonic scales, containing strings of 6 diatonic steps, but every 7th step is slightly shortened.

Double modes are ternary scales, because they posess exactly 3 step sizes. Double Lydian and double Ionian are 5L 1M 1s, the other five are 4L 1M 2s.

Examples

There are 7 Erose-McClain double modes:

• Double Lydian – 5 5 5 3 5 5 2
• Double Ionian – 5 5 3 5 5 5 2
• Double Mixolydian – 5 5 3 5 5 3 4
• Double Dorian – 5 3 5 5 5 3 4
• Double Aeolian – 5 3 5 5 3 5 5
• Double Phrygian – 3 5 5 5 3 5 4
• Double Locrian – 3 5 5 3 5 5 4

When generating these in Scale Workshop, you need to add a "1" at the end, then delete the last scale degree manually.

For example, to make double Lydian, enter 5 5 5 3 5 5 2 1, and after the scale generates, just manually remove the 31\31.

Generalization

The concept of double modes can be generalized to produce even more scales.

To modmos scales

More double modes could be constructed by using a modmos of the 5L 2s diatonic scale in 31edo.

For example, melodic minor, harmonic minor, harmonic major, or any of their modes (rotations) could be used.

These may not always retain all properties of ordinary double modes. For example, if the modmos itself is ternary, then the double mode may become quaternary.

A sampling of examples (not exhaustive):

• Double-modal harmonic minor – 5 3 5 5 3 7 2
• Double-modal melodic minor – 5 3 5 5 5 5 2
• Double-modal harmonic major – 5 5 3 5 3 5 4

To other edos

Double modes could be generalized to any edo that contains both a diatonic scale and a diesis – that is, an interval in the range between 25 cents and 45 cents.

Double modes in other edos are constructed the same way as in 31edo – start with a diatonic mode (or modmos thereof), then flatten the octave by one diesis.

If the edo has multiple dieses available, then the one closest to 38.7 cents (i.e. the 31edo diesis) should be used.

To other mos scales

Double modes could be generalized to any mode of any mos or modmos scale, especially any with around 5 to 10 tones.

These would still be constructed the same way:

1. Generate the mos or modmos scale inside an edo that has a diesis
2. Choose the desired mode of mos or modmos
3. Flatten the octave of that mode by 1 diesis