Amity: Difference between revisions

From Xenharmonic Reference
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Line 10: Line 10:
* 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 = 2/1 complement of 81/80 ~ 64/63 ~ 65/64
* 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)
Line 17: Line 17:
* 12 gens = 21/16
* 12 gens = 21/16
* 13 gens = '''8/5'''
* 13 gens = '''8/5'''
* 14 gens = 2/1-complement of 36/35 ~ 33/32
* 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
Line 24: Line 24:
* 19 gens = 13/10
* 19 gens = 13/10
* 20 gens = 128/81
* 20 gens = 128/81
* 21 gens = 2/1 complement of 21/20 ~ 22/21 ~ 25/24
* 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