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Zastari

Joined 10 September 2023
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== JI scales on the Harmonic Series ==
== /2^n JI Scales of Interest ==


=== /2^n Scales of Interest ===
=== 3-Limit ===
 
==== 3-Limit ====


====== Pyth (2.3) ======
====== Pyth (2.3) ======
Lydian-like: 9/8 81/64 729/512 3/2 27/16 243/128 2/1
[7]: 9/8 81/64 729/512 3/2 27/16 243/128 2/1


==== 5-Limit ====
=== 5-Limit ===


====== [[Zarlino|Zarlino (2.3.5)]] ======
====== [[Zarlino|Zarlino (2.3.5)]] ======
Lydian-like: 9/8 5/4 45/32 3/2 27/16 15/8 2/1  
[7]: 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)
'''Duodene'''


==== 7-Limit ====
AGS: (8/5, 8/5, 25/24)


===== Tas Family (2.3.7) =====
* [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
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
==='''7-Limit'''===
'''Tas Family (2.3.7)'''


===== Marveldene Family (2.3.5.7) =====
* [5]: 9/8 21/16 3/2 7/4 2/1
Mixolydian-like: 9/8 5/4 21/16 3/2 27/16 7/4 2/1


Lydian-like: see Zarlino
* [9]: 9/8 81/64 21/16 189/128 3/2 27/16 7/4 63/32 2/1


Locrian-like: 135/125 75/64 21/16 45/32 25/16 7/4 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)
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 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.
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):
AGS generators (all operations are downwards starting at 1/1):
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