Amity

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Amity is a temperament for the 5, 7, 11, and 13 prime limits. EDOs that support amity include 46edo, 53edo, 99edo, 152edo, and 205edo.

See Ragismic microtemperaments for more information.

Interval chain

Generators Cents*
(octave-reduced)
Approximate ratios
Amity
(53&205)
Hitchcock
(46&53)
0 0.000 1/1
1 339.43 11/9
2 678.86 40/27
3 1018.30 9/5
4 157.73 35/32 12/11~35/32~11/10
5 497.16 4/3
6 836.59 21/13~13/8
7 1176.03 65/33, 77/39~160/81 63/32~128/65~65/33,
77/39~160/81
8 315.46 6/5
9 654.89 16/11~22/15
10 994.32 16/9
11 133.75 27/25 14/13~27/25~13/12
12 473.19 21/16
13 812.62 8/5
14 1152.05 35/18 64/33~35/18
15 291.48 13/11~32/27
16 630.92 13/9
17 970.35 7/4
18 109.78 16/15
19 449.21 13/10
20 788.64
21 1128.08 48/25~25/13 21/11~48/25
22 267.51 7/6
23 606.94
24 946.37 26/15
25 85.81 21/20
26 425.24 32/25 14/11~32/25
27 764.67 14/9
28 1104.10
29 243.53 15/13
30 582.97 7/5
31 922.40
32 61.83 28/27~27/26 28/27
33 401.26
34 740.69 20/13
35 1080.13 28/15
36 219.56 25/22
37 558.99 18/13

*in 7-limit POTE tuning

Tuning Spectra

Spectrum of Amity Tunings (53&205)

13-limit commas: 352/351, 540/539, 625/624, 729/728

Eigenmonzo Generator
10/9 339.199
13/11 339.281
8/7 339.343
7/6 339.403
7/5 339.417 (7 limit minimax)
9/7 339.441 (9 limit minimax)
15/14 339.444
6/5 339.455
14/11 339.462 (11 limit minimax)
11/9 339.473
15/11 339.476
12/11 339.485
11/10 339.490
11/8 339.495 (13, 15 limit minimax)
14/13 339.505
5/4 339.514 (5 limit minimax)
16/15 339.541
18/13 339.551
13/12 339.558
16/13 339.563
15/13 339.577
13/10 339.582
4/3 339.609

Spectrum of Hitchcock Tunings (46&53)

13-limit commas: 121/120, 169/168, 176/175, 325/324

Eigenmonzo Generator
12/11 337.659
11/8 338.742
14/13 338.936
14/11 339.135
10/9 339.199
13/11 339.281
8/7 339.343
7/6 339.403
7/5 339.417 (7 limit minimax)
9/7 339.441 (9, 11, 13 limit minimax)
15/14 339.444 (15 limit minimax)
6/5 339.455
5/4 339.514 (5 limit minimax)
16/15 339.541
4/3 339.609
15/13 339.677
13/10 339.695
18/13 339.789
13/12 339.870
16/13 340.088
15/11 340.339
11/10 341.251
11/9 347.408