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Zastari

Joined 10 September 2023
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====== Pyth (2.3) ======
====== Pyth (2.3) ======
 
Pyth is a line in (3) space. It can be traversed only by stacking 4/3. It forms constant structure at the same sizes that it forms a MOS.
* [7] Lydian: 9/8 81/64 729/512 3/2 27/16 243/128 2/1
* [5]: 9/8 81/64 3/2 27/16 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)]]=====
===== Duodene (2.3.5) =====
Duodene is a 4x3 rectangular prism in the (3, 5) space. It can be traversed along prime axes in any order yielding 2 possible AGS recipes that generate it.


* [7] Lydian: 9/8 5/4 45/32 3/2 27/16 15/8 2/1  
* Augmented frame (5->3): AGS(8/5, 8/5, 25/24):
 
** [6]: 75/64 5/4 3/2 25/16 15/8 2/1
===== Duodene (2.3.5) =====
** [9]: 9/8 75/64 5/4 45/32 3/2 25/16 225/128 15/8 2/1
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
* [6]: 75/64 5/4 3/2 25/16 15/8 2/1
* Zarlino frame (3->5) AGS(4/3, 4/3, 4/3, 40/27):
* [9]: 9/8 75/64 5/4 45/32 3/2 25/16 225/128 15/8 2/1
** [5]: 9/8 5/4 3/2 27/16 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]: 9/8 5/4 45/32 3/2 27/16 15/8 2/1 (aka Zarlino[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 (aka Duodene[12])


==== 7-Limit ====
==== 7-Limit ====
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** [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 (aka Hexatonic septimal-pental[12])
** [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 (aka Hexatonic septimal-pental[12])
** [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
** [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)
* Duodene Augmented 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.
** [6], [9], and [12] are the same as the Duodene Augmented frame in 2.3.5.
* Pyth-Pental frame (3->5->7) AGS(4/3, 4/3, 4/3, 40/27, 4/3, 4/3, 4/3, 40/27, 4/3, 4/3, 4/3, 896/675)
* Duodene Zarlino frame (3->5->7) AGS(4/3, 4/3, 4/3, 40/27, 4/3, 4/3, 4/3, 40/27, 4/3, 4/3, 4/3, 896/675)
** [5]: 9/8 5/4 3/2 27/16 2/1
** [5], [7], and [12] are the same as Duodene Zarlino frame in 2.3.5.
** [7]: 9/8 5/4 45/32 3/2 27/16 15/8 2/1 (aka Zarlino[7])


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