JI scales on the Harmonic Series
/2^n Scales of Interest
3-Limit
Pyth (2.3)
- [7] Lydian: 9/8 81/64 729/512 3/2 27/16 243/128 2/1
5-Limit
Zarlino (2.3.5)
- [7] Lydian: 9/8 5/4 45/32 3/2 27/16 15/8 2/1
Duodene (2.3.5)
AGS(8/5, 8/5, 25/24)
- [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
- [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 (2.3.7)
AGS(7/6, 8/7)
- [5]: 9/8 21/16 3/2 7/4 2/1
- [9]: 9/8 81/64 (or 5/4) 21/16 189/128 3/2 27/16 7/4 63/32 2/1
Detempered Marveldene (2.3.5.7)
- [7] Mixolydian: 9/8 5/4 21/16 3/2 27/16 7/4 2/1
- [7] Lydian (aka Zarlino[7]): 9/8 5/4 45/32 3/2 27/16 15/8 2/1
- [7] Locrian: 135/125 75/64 21/16 45/32 25/16 7/4 2/1
- [12]: 135/128 9/8 75/64 5/4 21/16 45/32 3/2 25/16 27/16 7/4 15/8 2/1
Zil (2.3.5.7)
Note: Zil is sometimes defined as a chiral version that contains 405/256 and 2835/2048 in place of 25/16 and 175/128 which yields the AGS (8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 8/7, 189/160, 8/7, 7/6). The version discussed below uses 25/16 and 175/128 yielding the truncated AGS (8/7, 7/6, 8/7, 7/6, 8/7, 7/6, 189/160).
Zil is a 4x3x2 rectangular prism 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.
- 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
- [19]: 135/128 35/32 9/8 75/64 315/256 5/4 21/16 175/128 45/32 189/128 3/2 25/16 105/64 27/16 7/4 945/512 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): AGS(8/5, 8/5, 25/14, 8/5, 8/5, 175/96)
- [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
- [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 (same as Hexatonic septimal-pental)
- [15]: 525/512 35/32 9/8 75/64 5/4 21/16 175/128 45/32 3/2 25/16 105/64 7/4 225/128 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], [9], and [12] are the same as Duodene 2.3.5.
Transitional 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