User:Moremajorthanmajor/13edIX
This scale occurs in 12edo, where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.
Tuning spectrum
| Period | Octatonic (5L 3s) | Notes | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| L | s | Tetrachord | ||||||||
| 1\1edo | 184.615 | 92.308 | 184.615 | 369.231 | 461.5385 | Phrygian Mode (aka Double) Neapolitan Temperament from here … | ||||
| 15\14 | 197.802 | 98.901 | 197.802 | 395.604 | 494.5055 | |||||
| 14\13 | 198.817 | 99.408 | 198.817 | 397.633 | 497.041 | |||||
| 27\25 | 199.385 | 99.692 | 199.385 | 398.769 | 498.4615 | |||||
| 13\12 | 200 | 100 | 200 | 400 | 500 | |||||
| 38\35 | 200.44 | 100.22 | 200.44 | 400.879 | 501.099 | |||||
| 25\23 | 200.669 | 100.334 | 200.669 | 401.338 | 501.672 | |||||
| 37\34 | 200.905 | 100.4525 | 200.905 | 401.81 | 502.262 | |||||
| 12\11 | 201.399 | 100.699 | 201.399 | 402.797 | 503.4965 | |||||
| 47\43 | 201.789 | 100.8945 | 201.789 | 403.578 | 504.472 | |||||
| 35\32 | 201.923 | 100.9615 | 201.923 | 403.846 | 504.808 | |||||
| 58\53 | 202.032 | 101.016 | 202.032 | 404.064 | 505.08 | |||||
| 23\21 | 202.198 | 101.099 | 202.198 | 404.396 | 505.4945 | |||||
| 57\52 | 202.367 | 101.183 | 202.367 | 404.734 | 505.917 | |||||
| 34\31 | 202.481 | 101.241 | 202.481 | 404.963 | 506.2035 | |||||
| 45\41 | 202.627 | 101.313 | 202.627 | 405.253 | 506.567 | |||||
| 11\10 | 203.077 | 101.5385 | 203.077 | 406.154 | 507.692 | …to here
Phrygian-Aeolian Mode Neapolitan Temperament from here … | ||||
| 54\49 | 203.454 | 101.757 | 203.454 | 406.907 | 508.634 | |||||
| 43\39 | 203.55 | 101.775 | 203.55 | 407.101 | 508.876 | |||||
| 75\68 | 203.62 | 101.81 | 203.62 | 407.24 | 509.05 | |||||
| 32\29 | 203.7135 | 101.857 | 203.7135 | 407.427 | 509.284 | |||||
| 85\77 | 203.796 | 101.898 | 203.796 | 407.592 | 509.4905 | |||||
| 53\48 | 203.846 | 101.923 | 203.846 | 407.692 | 509.615 | |||||
| 74\67 | 203.904 | 101.952 | 203.904 | 407.807 | 509.759 | Square root of 9/8 is near here | ||||
| 21\19 | 204.049 | 102.024 | 204.049 | 408.097 | 510.1215 | |||||
| 73\66 | 204.196 | 102.098 | 204.196 | 408.392 | 510.4895 | |||||
| 52\47 | 204.255 | 102.128 | 204.255 | 408.511 | 510.638 | |||||
| 83\75 | 204.308 | 102.154 | 204.308 | 409.615 | 510.769 | |||||
| 31\28 | 204.396 | 102.198 | 204.396 | 408.792 | 510.989 | |||||
| 72\65 | 204.497 | 102.248 | 204.497 | 408.994 | 511.242 | |||||
| 41\37 | 204.574 | 102.287 | 204.574 | 409.148 | 511.4345 | |||||
| 51\46 | 204.682 | 102.341 | 204.682 | 409.3645 | 511.706 | |||||
| 10\9 | 205.128 | 102.564 | 205.128 | 410.256 | 512.8205 | |||||
| 49\44 | 205.594 | 102.797 | 205.594 | 411.189 | 513.986 | |||||
| 39\35 | 205.714 | 102.857 | 205.714 | 411.429 | 514.286 | |||||
| 68\61 | 205.801 | 102.9 | 205.801 | 411.6015 | 514.502 | |||||
| 29\26 | 205.917 | 102.959 | 205.917 | 411.824 | 514.799 | |||||
| 77\69 | 206.02 | 103.01 | 206.02 | 412.04 | 515.05 | |||||
| 48\43 | 206.082 | 103.041 | 206.082 | 412.165 | 515.205 | |||||
| 67\60 | 206.154 | 103.077 | 206.154 | 412.308 | 515.385 | |||||
| 19\17 | 206.335 | 103.167 | 206.335 | 412.67 | 515.837 | |||||
| 66\59 | 206.519 | 103.2595 | 206.519 | 413.038 | 516.297 | |||||
| 47\42 | 206.593 | 103.297 | 206.593 | 413.187 | 516.4835 | |||||
| 75\67 | 206.659 | 103.3295 | 206.659 | 413.318 | 516.6475 | |||||
| 28\25 | 206.769 | 103.385 | 206.769 | 413.5385 | 516.923 | |||||
| 65\58 | 206.897 | 103.443 | 206.897 | 413.793 | 517.241 | |||||
| 37\33 | 206.993 | 103.4965 | 206.993 | 413.986 | 517.4825 | |||||
| 46\41 | 207.1295 | 103.565 | 207.1295 | 414.259 | 517.824 | |||||
| 9\8 | 207.692 | 103.846 | 207.692 | 415.385 | 519.231 | |||||
| 44\39 | 208.284 | 104.142 | 208.284 | 416.568 | 520.71 | |||||
| 35\31 | 208.437 | 104.218 | 208.437 | 416.873 | 521.092 | |||||
| 61\54 | 208.547 | 104.2735 | 208.547 | 417.094 | 521.3675 | |||||
| 26\23 | 208.696 | 104.348 | 208.696 | 417.391 | 521.739 | |||||
| 69\61 | 208.827 | 104.414 | 208.827 | 417.6545 | 522.068 | |||||
| 43\38 | 208.907 | 104.453 | 208.907 | 417.814 | 522.267 | |||||
| 60\53 | 208.9985 | 104.499 | 208.9985 | 417.997 | 522.496 | |||||
| 17\15 | 209.231 | 104.615 | 209.231 | 418.4615 | 523.077 | |||||
| 59\52 | 209.4675 | 104.734 | 209.4675 | 418.935 | 523.669 | |||||
| 42\37 | 209.563 | 104.782 | 209.563 | 419.127 | 523.9085 | |||||
| 67\59 | 209.648 | 104.824 | 209.648 | 419.296 | 524.12 | |||||
| 25\22 | 209.79 | 104.895 | 209.79 | 419.58 | 524.4755 | |||||
| 58\51 | 209.955 | 104.977 | 209.955 | 419.91 | 524.887 | |||||
| 33\29 | 210.08 | 105.04 | 210.08 | 420.159 | 525.199 | |||||
| 41\36 | 210.256 | 105.128 | 210.256 | 420.513 | 525.641 | |||||
| 8\7 | 210.989 | 105.4945 | 210.989 | 421.978 | 527.4725 | …to here
Aeolian Mode Neapolitan Temperament from here … | ||||
| 39\34 | 211.765 | 105.882 | 211.765 | 423.529 | 529.412 | |||||
| 31\27 | 211.966 | 105.983 | 211.966 | 423.932 | 529.9145 | |||||
| 54\47 | 212.111 | 106.056 | 212.111 | 424.223 | 530.278 | |||||
| 23\20 | 212.308 | 106.154 | 212.308 | 424.615 | 530.769 | |||||
| 61\53 | 212.482 | 106.241 | 212.482 | 424.964 | 531.205 | |||||
| 38\33 | 212.587 | 106.294 | 212.587 | 425.175 | 531.4685 | |||||
| 53\46 | 212.709 | 106.3595 | 212.709 | 425.418 | 531.773 | |||||
| 15\13 | 213.018 | 106.509 | 213.018 | 426.0355 | 532.544 | |||||
| 52\45 | 213.333 | 106.667 | 213.333 | 426.667 | 533.333 | |||||
| 37\32 | 213.4615 | 106.731 | 213.4615 | 426.923 | 533.654 | |||||
| 59\51 | 213.575 | 106.787 | 213.575 | 427.149 | 533.937 | |||||
| 22\19 | 213.765 | 106.883 | 213.765 | 427.52 | 534.413 | |||||
| 51\44 | 213.986 | 106.993 | 213.986 | 427.972 | 534.965 | |||||
| 29\25 | 214.154 | 107.077 | 214.154 | 428.308 | 535.385 | |||||
| 36\31 | 214.392 | 107.196 | 214.392 | 428.784 | 535.98 | |||||
| 7\6 | 215.385 | 107.692 | 215.385 | 430.769 | 538.4615 | |||||
| 34\29 | 216.446 | 108.223 | 216.446 | 432.891 | 541.114 | |||||
| 27\23 | 216.722 | 108.361 | 216.722 | 433.445 | 541.806 | |||||
| 47\40 | 216.923 | 108.4615 | 216.923 | 433.846 | 542.308 | |||||
| 20\17 | 217.195 | 108.597 | 217.195 | 434.389 | 542.986 | |||||
| 53\45 | 217.436 | 108.718 | 217.436 | 434.872 | 543.59 | |||||
| 33\28 | 217.582 | 108.791 | 217.582 | 435.165 | 543.956 | |||||
| 46\39 | 217.7515 | 108.876 | 217.7515 | 435.503 | 544.679 | |||||
| 13\11 | 218.182 | 109.091 | 218.182 | 436.364 | 545.4545 | |||||
| 45\38 | 218.6235 | 109.312 | 218.6235 | 437.247 | 546.5559 | |||||
| 32\27 | 218.803 | 109.402 | 218.803 | 437.606 | 547.0085 | |||||
| 51\43 | 218.962 | 109.461 | 218.962 | 406.6445 | 547.406 | |||||
| 19\16 | 219.231 | 109.615 | 219.231 | 438.4615 | 548.077 | |||||
| 44\37 | 219.543 | 109.771 | 219.543 | 439.085 | 548.8565 | |||||
| 25\21 | 219.78 | 109.89 | 219.78 | 439.56 | 549.4505 | |||||
| 31\26 | 220.118 | 110.059 | 220.118 | 440.237 | 550.296 | |||||
| 6\5 | 221.5385 | 110.769 | 221.5385 | 443.077 | 553.846 | …to here | ||||