User:Zastari: Difference between revisions
Created page with "== JI scales on the Harmonic Series == === /2^n Scales of Interest === ==== 3-Limit ==== ====== Pyth ====== Lydian-like: 9/8 81/64 729/512 3/2 27/16 243/128 2/1 ===== 5-Li..." |
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==== 3-Limit ==== | ==== 3-Limit ==== | ||
====== Pyth ====== | ====== Pyth (2.3) ====== | ||
Lydian-like: 9/8 81/64 729/512 3/2 27/16 243/128 2/1 | Lydian-like: 9/8 81/64 729/512 3/2 27/16 243/128 2/1 | ||
===== 5-Limit ===== | ===== 5-Limit ===== | ||
====== [[Zarlino]] ====== | ====== [[Zarlino|Zarlino (2.3.5)]] ====== | ||
Lydian-like: 9/8 5/4 45/32 3/2 27/16 15/8 2/1 | Lydian-like: 9/8 5/4 45/32 3/2 27/16 15/8 2/1 | ||
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'''7-Limit''' | '''7-Limit''' | ||
'''Marveldene Family''' | '''Tas Family (2.3.7)''' | ||
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 | |||
'''Marveldene Family (2.3.5.7)''' | |||
Mixolydian-like: 9/8 5/4 21/16 3/2 27/16 7/4 2/1 | Mixolydian-like: 9/8 5/4 21/16 3/2 27/16 7/4 2/1 | ||
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'''Zil Family''' | '''Zil Family (2.3.5.7)''' | ||
Unknown hexatonic: 35/32 5/4 175/128 25/16 7/4 2/1 | Unknown hexatonic: 35/32 5/4 175/128 25/16 7/4 2/1 | ||
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* Offsetting this scale by 9/8 yields zil[24] | * 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: 35/32 5/4 21/16 3/2 105/64 7/4 2/1 | 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 | |||
Revision as of 00:19, 5 December 2023
JI scales on the Harmonic Series
/2^n Scales of Interest
3-Limit
Pyth (2.3)
Lydian-like: 9/8 81/64 729/512 3/2 27/16 243/128 2/1
5-Limit
Zarlino (2.3.5)
Lydian-like: 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)
7-Limit
Tas Family (2.3.7)
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
Marveldene Family (2.3.5.7)
Mixolydian-like: 9/8 5/4 21/16 3/2 27/16 7/4 2/1
Lydian-like: see Zarlino
Locrian-like: 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)
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