User:Zastari: Difference between revisions

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== JI scales on the Harmonic Series ==

=== SV3 scales ===

* 2.3.5

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

** ???[7]: 10/9 6/5 4/3 3/2 5/3 9/5 2/1

* 2.3.7

** Omnidiatonic[7]: 9/8 7/6 4/3 3/2 14/9 7/4 2/1

** ???[7]: 8/7 7/6 4/3 3/2 12/7 7/4 2/1

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

* 2.3.19

** 9/8 19/16 171/128 3/2 27/16 57/32 2/1

=== /2^n Scales of Interest ===

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===== Duodene (2.3.5) =====

Duodene is a 4x3 ~~rectangular prism~~ in 2.3.5 space. It can be traversed along prime axes in any order yielding 2 possible AGS recipes that generate it.

Duodene is a 4x3 rectangle in 2.3.5 space. It can be traversed along prime axes in any order yielding 2 possible AGS recipes that generate it.

* Augmented frame (5->3): AGS(8/5, 8/5, 25/24):

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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

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

===== Detempered Marveldene (2.3.5.7) =====

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===== 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).

''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, 8/7,189/160).

* zil[24]: 525/512 135/128 35/32 9/8 4725/4096 75/64 315/256 5/4 21/16 675/512 175/128 45/32 189/128 3/2 1575/1024 25/16 105/64 27/16 7/4 225/128 945/512 15/8 63/32 2/1

Zil is a 4x3x2 rectangular prism in 2.3.5.7 space. It can be traversed along the prime axes in any order yielding 6 possible AGS recipes that generate it.

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* 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

===== Unnamed Ambitonal Scale (2.3.5.7) =====

* 36/35 21/20 10/9 8/7 7/6 6/5 80/63 21/16 4/3 48/35 35/24 3/2 32/21 63/40 5/3 12/7 7/4 9/5 40/21 35/18 2/1

=== Chromatic Families ===

* 2.3.5 base: 16/15 10/9 6/5 5/4 27/20 45/32 3/2 8/5 5/3 9/5 15/8 2/1 2.3.5

** L=27/25, m=16/15, s=25/24. msLsLsmmsLsm

* 2.3.5 extension: 81/80 16/15 27/25 10/9 9/8 6/5 243/200 5/4 81/64 27/20 2187/1600 45/32 729/512 3/2 243/160 8/5 81/50 5/3 27/16 9/5 729/400 15/8 243/128 2/1

** L=16/15, m=256/243, s=250/243, c=81/80. cmcscLcscLcscmcmcscLcscm

* 2.3.5.7 extension: 64/63 16/15 1024/945 10/9 640/567 6/5 128/105 5/4 80/63 27/20 48/35 45/32 10/7 3/2 32/21 8/5 512/315 5/3 320/189 9/5 64/35 15/8 40/21 2/1

** L=1701/1600, m=21/20, s=525/512, c=64/63. cmcscLcscLcscmcmcscLcscm

* 2.3.5.11 extension: 33/32 16/15 11/10 10/9 55/48 6/5 99/80 5/4 165/128 27/20 891/640 45/32 1485/1024 3/2 99/64 8/5 33/20 5/3 55/32 9/5 297/160 15/8 495/256 2/1

** L=288/275, m=512/495, s=33/32, c=100/99. Pattern: smscsLscsLscsmsmscsLscsm

* 2.3.5.13 extension: 65/64 16/15 13/12 10/9 325/288 6/5 39/32 5/4 325/256 27/20 351/256 45/32 2925/2048 3/2 195/128 8/5 13/8 5/3 325/192 9/5 117/64 15/8 975/512 2/1

** L=1728/1625 m=1024/975 s=40/39 c=65/64. cmcscLcscLcscmcmcscLcscm

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 == JI scales on the Harmonic Series ==
+=== SV3 scales ===
+* 2.3.5
+** Zarlino[7]: 9/8 5/4 45/32 3/2 27/16 15/8 2/1
+** ???[7]: 10/9 6/5 4/3 3/2 5/3 9/5 2/1
+* 2.3.7
+** Omnidiatonic[7]: 9/8 7/6 4/3 3/2 14/9 7/4 2/1
+** ???[7]: 8/7 7/6 4/3 3/2 12/7 7/4 2/1
+** Diasem[9]: 9/8 81/64 21/16 189/128 3/2 27/16 7/4 63/32 2/1
+* 2.3.19
+** 9/8 19/16 171/128 3/2 27/16 57/32 2/1
 === /2^n Scales of Interest ===
@@ Line 21: / Line 33: @@
 ===== Duodene (2.3.5) =====
-Duodene is a 4x3 rectangular prism in 2.3.5 space. It can be traversed along prime axes in any order yielding 2 possible AGS recipes that generate it.
+Duodene is a 4x3 rectangle in 2.3.5 space. It can be traversed along prime axes in any order yielding 2 possible AGS recipes that generate it.
 * Augmented frame (5->3): AGS(8/5, 8/5, 25/24):
@@ Line 37: / Line 49: @@
 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
+* [9]: 9/8 81/64 21/16 189/128 3/2 27/16 7/4 63/32 2/1
 ===== Detempered Marveldene (2.3.5.7) =====
@@ Line 47: / Line 59: @@
 ===== 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).
+''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, 8/7,189/160).
+* zil[24]: 525/512 135/128 35/32 9/8 4725/4096 75/64 315/256 5/4 21/16 675/512 175/128 45/32 189/128 3/2 1575/1024 25/16 105/64 27/16 7/4 225/128 945/512 15/8 63/32 2/1
 Zil is a 4x3x2 rectangular prism in 2.3.5.7 space. It can be traversed along the prime axes in any order yielding 6 possible AGS recipes that generate it.
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 * 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
+===== Unnamed Ambitonal Scale (2.3.5.7) =====
+* 36/35 21/20 10/9 8/7 7/6 6/5 80/63 21/16 4/3 48/35 35/24 3/2 32/21 63/40 5/3 12/7 7/4 9/5 40/21 35/18 2/1
+=== Chromatic Families ===
+* 2.3.5 base: 16/15 10/9 6/5 5/4 27/20 45/32 3/2 8/5 5/3 9/5 15/8 2/1 2.3.5
+** L=27/25, m=16/15, s=25/24. msLsLsmmsLsm
+* 2.3.5 extension: 81/80 16/15 27/25 10/9 9/8 6/5 243/200 5/4 81/64 27/20 2187/1600 45/32 729/512 3/2 243/160 8/5 81/50 5/3 27/16 9/5 729/400 15/8 243/128 2/1
+** L=16/15, m=256/243, s=250/243, c=81/80. cmcscLcscLcscmcmcscLcscm
+* 2.3.5.7 extension: 64/63 16/15 1024/945 10/9 640/567 6/5 128/105 5/4 80/63 27/20 48/35 45/32 10/7 3/2 32/21 8/5 512/315 5/3 320/189 9/5 64/35 15/8 40/21 2/1
+** L=1701/1600, m=21/20, s=525/512, c=64/63. cmcscLcscLcscmcmcscLcscm
+* 2.3.5.11 extension: 33/32 16/15 11/10 10/9 55/48 6/5 99/80 5/4 165/128 27/20 891/640 45/32 1485/1024 3/2 99/64 8/5 33/20 5/3 55/32 9/5 297/160 15/8 495/256 2/1
+** L=288/275, m=512/495, s=33/32, c=100/99. Pattern: smscsLscsLscsmsmscsLscsm
+* 2.3.5.13 extension: 65/64 16/15 13/12 10/9 325/288 6/5 39/32 5/4 325/256 27/20 351/256 45/32 2925/2048 3/2 195/128 8/5 13/8 5/3 325/192 9/5 117/64 15/8 975/512 2/1
+** L=1728/1625 m=1024/975 s=40/39 c=65/64. cmcscLcscLcscmcmcscLcscm