User:Zastari

/2^n JI Scales of Interest

3-Limit

Pyth (2.3)

• [7]: 9/8 81/64 729/512 3/2 27/16 243/128 2/1

5-Limit

Zarlino (2.3.5)

• [7]: 9/8 5/4 45/32 3/2 27/16 15/8 2/1

Duodene

AGS: (8/5, 8/5, 25/24)

• [12]: 135/128 9/8 75/64 5/4 675/512 45/32 3/2 25/16 27/16 225/128 15/8 2/1

7-Limit

Tas Family (2.3.7)

• [5]: 9/8 21/16 3/2 7/4 2/1

• [9]: 9/8 81/64 21/16 189/128 3/2 27/16 7/4 63/32 2/1

Marveldene Family (2.3.5.7)

• [7] (Mixolydian): 9/8 5/4 21/16 3/2 27/16 7/4 2/1

• [7] (Lydian): 9/8 5/4 45/32 3/2 27/16 15/8 2/1 (aka Zarlino[7])

• [7] (Locrian): 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)

Zil is a 4x3x2 rectangle in the (3, 5, 7) space. It can be traversed along the prime axes in any order yielding 6 possible AGS recipes that generate it.

AGS generators (all operations are downwards starting at 1/1):

• Tas frame (7->3->5) : AGS(8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160)
  • [5]: 9/8 21/16 3/2 7/4 2/1
  • [9]: 9/8 5/4 21/16 189/128 3/2 27/16 7/4 63/32 2/1
  • [14]: 35/32 9/8 315/256 5/4 21/16 45/32 189/128 3/2 105/64 27/16 7/4 15/8 63/32 2/1
• Hexatonic septimal-pental frame (7->5->3): AGS(8/7, 7/5, 8/7, 7/5, 8/7, 175/96)
  • [6]: 35/32 5/4 175/128 25/16 7/4 2/1 (same as Hexatonic pental-septimal)
  • [12]: 525/512 35/32 75/64 5/4 21/16 175/128 3/2 25/16 105/64 7/4 15/8 2/1
• Hexatonic pental-septimal frame (5->7->3):
  • [6]: 35/32 5/4 175/128 25/16 7/4 2/1 (same as Hexatonic septimal-pental)
  • [9]: 35/32 75/64 5/4 175/128 3/2 25/16 7/4 15/8 2/1
• Duodene frame (5->3->7): AGS(8/5, 8/5, 25/24, 8/5, 8/5, 25/24, 8/5, 8/5, 25/24, 8/5, 8/5, 675/448)
  • [6]: 75/64 5/4 3/2 25/16 15/8 2/1
  • [9]: 9/8 75/64 5/4 45/32 3/2 25/16 225/128 15/8 2/1

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