Septidiasemi
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Septidiasemi, in this article, is the rank-two regular temperament for the 2.3.5.7.13.17 subgroup defined by tempering out 2401/2400 and 2152828125/2147483648 in the 7-limit; 2205/2197 and 4096/4095 in the 13-limit; 833/832, 1275/1274, and 2025/2023 in the 17-limit.
It can be seen as implying a rank-two tuning which is generated by a large semitone of about 119.3 cents which represents 15/14 (septimal diatonic semitone) and from this it derives its name. Equal temperaments that support septidiasemi include 10EDO (generator 1\10), 151EDO (generator 15\151), 161EDO (generator 16\161), and 171EDO (generator 17\171).
See Breedsmic temperaments #Septidiasemi for more technical data.
Intervals
| Generator steps |
Cents* | Approximate ratios† |
|---|---|---|
| 0 | 0.000 | 1/1 |
| 1 | 119.297 | 15/14 |
| 2 | 238.593 | 39/34 |
| 3 | 357.890 | 16/13 |
| 4 | 477.186 | 112/85, 120/91 |
| 5 | 596.483 | 24/17 |
| 6 | 715.779 | 68/45 |
| 7 | 835.076 | 34/21 |
| 8 | 954.372 | 26/15 |
| 9 | 1073.669 | 13/7 |
| 10 | 1192.965 | 448/225, 255/128, 544/273, 576/289 |
| 11 | 112.262 | 16/15 |
| 12 | 231.559 | 8/7 |
| 13 | 350.855 | 60/49, 49/40 |
| 14 | 470.152 | 21/16 |
| 15 | 589.448 | 45/32 |
| 16 | 708.745 | 128/85 |
| 17 | 828.041 | 21/13 |
| 18 | 947.338 | |
| 19 | 1066.634 | (close to 50/27) |
| 20 | 1185.931 | 119/60, 135/68 |
| 21 | 105.227 | 17/16 |
| 22 | 224.524 | |
| 23 | 343.820 | 39/32 |
| 24 | 463.117 | 17/13 |
| 25 | 582.414 | 7/5 |
| 26 | 701.710 | 3/2 |
| 27 | 821.007 | |
| 28 | 940.303 | |
| 29 | 1059.600 | 24/13 |
| 30 | 1178.896 | (close to 160/81) |
| 31 | 98.193 | 18/17 |
| 32 | 217.489 | 17/15 |
| 33 | 336.786 | 17/14 |
| 34 | 456.082 | 13/10 |
| 35 | 575.379 | |
| 36 | 694.676 | 112/75 |
| 37 | 813.972 | 8/5 |
| 38 | 933.269 | 12/7 |
| 39 | 1052.565 | |
| 40 | 1171.862 | 63/32, 128/65 |
| 41 | 91.158 | |
| 42 | 210.455 | |
| 43 | 329.751 | |
| 44 | 449.048 | |
| 45 | 568.344 | |
| 46 | 687.641 | |
| 47 | 806.937 | |
| 48 | 926.234 | |
| 49 | 1045.531 | 64/35 |
| 50 | 1164.827 | |
| 51 | 84.124 | 21/20 |
| 52 | 203.420 | 9/8 |
| 53 | 322.717 | |
| 54 | 442.013 | |
| 55 | 561.310 | 18/13 |
| 56 | 680.606 | |
| 57 | 799.903 | |
| 58 | 919.199 | 17/10 |
| 59 | 1038.496 | |
| 60 | 1157.793 | 39/20 |
| 61 | 77.089 | |
| 62 | 196.386 | 28/25 |
| 63 | 315.682 | 6/5 |
| 64 | 434.979 | 9/7 |
| 65 | 554.275 | (close to 11/8) |
| 66 | 673.572 | |
| 67 | 792.868 | |
| 68 | 912.165 | |
| 69 | 1031.461 | |
| 70 | 1150.758 | |
| 71 | 70.054 | |
| 72 | 189.351 | |
| 73 | 308.648 | |
| 74 | 427.944 | 32/25 |
| 75 | 547.241 | |
| 76 | 666.537 | |
| 77 | 785.834 | |
| 78 | 905.130 | 27/16 |
| 79 | 1024.427 | |
| 80 | 1143.723 | |
| 81 | 63.020 | (close to 28/27) |
| 82 | 182.316 | (close to 10/9) |
| 83 | 301.613 | |
| 84 | 420.910 | |
| 85 | 540.206 | |
| 86 | 659.503 | |
| 87 | 778.799 | |
| 88 | 898.096 | 42/25 |
| 89 | 1017.392 | 9/5 |
| 90 | 1136.689 | 27/14 |
- * in 2.3.5.7.13.17 POTE tuning
- † 2.3.5.7.13.17 ratio interpretations
See also
- 15/14 - septimal diatonic semitone
- 15/14s equal temperament