Amity

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 tends 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

List of patent vals

Main article: Amity/Patent vals