Amity: Difference between revisions
From Xenharmonic Reference
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* 5 gens = '''4/3''' | * 5 gens = '''4/3''' | ||
* 6 gens = '''13/8''' ~ 21/13 (=> S13 is tempered out) | * 6 gens = '''13/8''' ~ 21/13 (=> S13 is tempered out) | ||
* 7 gens = | * 7 gens = 80/81 ~ 63/64 ~ 64/65 | ||
* 8 gens = 6/5 | * 8 gens = 6/5 | ||
* 9 gens = '''16/11''' ~ 22/15 (=> S11 is tempered out) | * 9 gens = '''16/11''' ~ 22/15 (=> S11 is tempered out) | ||
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* 12 gens = 21/16 | * 12 gens = 21/16 | ||
* 13 gens = '''8/5''' | * 13 gens = '''8/5''' | ||
* 14 gens = | * 14 gens = 35/36 ~ 32/33 | ||
* 15 gens = 32/27 ~ 13/11 | * 15 gens = 32/27 ~ 13/11 | ||
* 16 gens = 36/25 ~ 13/9 | * 16 gens = 36/25 ~ 13/9 | ||
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* 19 gens = 13/10 | * 19 gens = 13/10 | ||
* 20 gens = 128/81 | * 20 gens = 128/81 | ||
* 21 gens = | * 21 gens = 20/21 ~ 21/22 ~ 24/25 | ||
* 22 gens = 7/6 | * 22 gens = 7/6 | ||
* 23 gens = 64/45 | * 23 gens = 64/45 | ||
Revision as of 22:52, 24 March 2026
Amity (from "acute minor third"), 46 & 53, is a complex temperament splitting 8/3 into 5 supraminor thirds about 339c-340c in size. While it has a tuning that is very accurate in the 7-limit (namely 99edo), its 11 and 13 mappings tend to be flat due to tempering out S11 and S13.
Amity is a 7-cluster temperament due to its generator being only slightly flatter than 2\7.
Interval chain
(Note: 243/200 is 6/5 sharpened by 81/80)
- 1 gen = 128/105 ~ 243/200 ~ 39/32 ~ 11/9 (=> tempers out 5120/5103 = S8/S9 and 4096/4095 = S64)
- 2 gens = 40/27
- 3 gens = 9/5
- 4 gens = 35/32 ~ 12/11 ~ 11/10
- 5 gens = 4/3
- 6 gens = 13/8 ~ 21/13 (=> S13 is tempered out)
- 7 gens = 80/81 ~ 63/64 ~ 64/65
- 8 gens = 6/5
- 9 gens = 16/11 ~ 22/15 (=> S11 is tempered out)
- 10 gens = 16/9
- 11 gens = 13/12 ~ 14/13
- 12 gens = 21/16
- 13 gens = 8/5
- 14 gens = 35/36 ~ 32/33
- 15 gens = 32/27 ~ 13/11
- 16 gens = 36/25 ~ 13/9
- 17 gens = 7/4
- 18 gens = 16/15
- 19 gens = 13/10
- 20 gens = 128/81
- 21 gens = 20/21 ~ 21/22 ~ 24/25
- 22 gens = 7/6
- 23 gens = 64/45
- 24 gens = 26/15
- 25 gens = 256/243
- 26 gens = 32/25 ~ 14/11
- 27 gens = 14/9
