Amity: Difference between revisions
From Xenharmonic Reference
| Line 5: | Line 5: | ||
Notes: | Notes: | ||
* 243/200 is 6/5 sharpened by 81/80. | * 243/200 is 6/5 sharpened by 81/80. | ||
* The 13 | * The extension to 13 given is called Hitchcock, whose 13 mapping tend to be flat due to tempering out S13. | ||
<br/> | <br/> | ||
* 1 gen = 128/105 ~ 243/200 ~ 39/32 | * 1 gen = 128/105 ~ 243/200 ~ 39/32 (=> tempers out 5120/5103 = S8/S9 and 4096/4095 = S64) | ||
* 2 gens = 40/27 | * 2 gens = 40/27 | ||
* 3 gens = 9/5 | * 3 gens = 9/5 | ||
* 4 gens = 35/32 | * 4 gens = 35/32 | ||
* 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 = 80/81 ~ 63/64 ~ 64/65 | * 7 gens = 80/81 ~ 63/64 ~ 64/65 | ||
* 8 gens = 6/5 | * 8 gens = 6/5 | ||
* 9 gens = | * 9 gens = 48/35 | ||
* 10 gens = '''16/9''' | * 10 gens = '''16/9''' | ||
* 11 gens = 13/12 ~ 14/13 | * 11 gens = 13/12 ~ 14/13 | ||
* 12 gens = 21/16 | * 12 gens = 21/16 | ||
* 13 gens = '''8/5''' | * 13 gens = '''8/5''' | ||
* 14 gens = 35/36 | * 14 gens = 35/36 | ||
* 15 gens = 32/27 | * 15 gens = 32/27 | ||
* 16 gens = 36/25 ~ 13/9 | * 16 gens = 36/25 ~ 13/9 | ||
* 17 gens = '''7/4''' | * 17 gens = '''7/4''' | ||
| Line 27: | Line 27: | ||
* 19 gens = 13/10 | * 19 gens = 13/10 | ||
* 20 gens = 128/81 | * 20 gens = 128/81 | ||
* 21 gens = 20/21 | * 21 gens = 20/21 ~ 24/25 | ||
* 22 gens = 7/6 | * 22 gens = 7/6 | ||
* 23 gens = 64/45 | * 23 gens = 64/45 | ||
* 24 gens = 26/15 | * 24 gens = 26/15 | ||
* 25 gens = 256/243 | * 25 gens = 256/243 | ||
* 26 gens = 32/25 | * 26 gens = 32/25 | ||
* 27 gens = 14/9 | * 27 gens = 14/9 | ||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|temperaments}} | {{Cat|temperaments}} | ||
Revision as of 00:57, 28 March 2026
Amity (from "acute minor third"), 2.3.5.7[46 & 53], is a complex temperament splitting 8/3 into 5 supraminor thirds about 339c-340c in size. It has a tuning that is very accurate in the 7-limit (namely 99edo).
Amity is a 7-cluster temperament due to its generator being only slightly flatter than 2\7.
Interval chain
Notes:
- 243/200 is 6/5 sharpened by 81/80.
- The extension to 13 given is called Hitchcock, whose 13 mapping tend to be flat due to tempering out S13.
- 1 gen = 128/105 ~ 243/200 ~ 39/32 (=> tempers out 5120/5103 = S8/S9 and 4096/4095 = S64)
- 2 gens = 40/27
- 3 gens = 9/5
- 4 gens = 35/32
- 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 = 48/35
- 10 gens = 16/9
- 11 gens = 13/12 ~ 14/13
- 12 gens = 21/16
- 13 gens = 8/5
- 14 gens = 35/36
- 15 gens = 32/27
- 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 ~ 24/25
- 22 gens = 7/6
- 23 gens = 64/45
- 24 gens = 26/15
- 25 gens = 256/243
- 26 gens = 32/25
- 27 gens = 14/9
