Amity
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 Amity family or Ragismic microtemperaments #Amity 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 | Comment |
|---|---|---|
| 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 | Comment |
|---|---|---|
| 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 |