User:Zastari

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JI scales on the Harmonic Series

/2^n Scales of Interest

3-Limit

Pyth (2.3)

Lydian-like: 9/8 81/64 729/512 3/2 27/16 243/128 2/1

5-Limit
Zarlino (2.3.5)

Lydian-like: 9/8 5/4 45/32 3/2 27/16 15/8 2/1

Chromatic version: 135/128 9/8 75/64 5/4 675/512 45/32 3/2 25/16 27/16 225/128 15/8 2/1 (aka Duodene in the maximally otonal frame)


7-Limit

Tas Family (2.3.7)

Fundamental pentatonic: 9/8 21/16 3/2 7/4 2/1

Nonatonic: 9/8 81/64 (or 5/4) 21/16 189/128 3/2 27/16 7/4 63/32 2/1

Marveldene Family (2.3.5.7)

Mixolydian-like: 9/8 5/4 21/16 3/2 27/16 7/4 2/1

Lydian-like: see Zarlino

Locrian-like: 135/125 75/64 21/16 45/32 25/16 7/4 2/1

Chromatic version: 135/128 9/8 75/64 5/4 21/16 45/32 3/2 25/16 27/16 7/4 15/8 2/1 (aka a Marveldene detempering)


Zil Family (2.3.5.7)

Unknown hexatonic: 35/32 5/4 175/128 25/16 7/4 2/1

Chromatic Extension (3/2 offset): 525/512 35/32 75/64 5/4 21/16 175/128 3/2 25/16 105/64 7/4 15/8 2/1

  • Offsetting this scale by 9/8 yields zil[24]

Contains tas[14] with 81/64 warped to 5/4 instead.

Diatonic-like Modes:

All Marveldene[12] modes.

Unknown mode (2.3.7.25): 525/512 75/64 21/16 175/128 25/16 7/4 2/1 Unknown mode (2.3.5.7): 35/32 5/4 21/16 3/2 105/64 7/4 2/1