User:Moremajorthanmajor/14edIX: Difference between revisions
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This scale occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis MOS with a 2:1 ratio of large against small. | This scale occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis MOS with a 2:1 ratio of large against small. | ||
== | ==Tuning spectrum== | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
Revision as of 19:09, 26 September 2018
This scale occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis MOS with a 2:1 ratio of large against small.
Tuning spectrum
| Period | Octatonic (6L 2s) | Notes | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| L | s | Pentachord | |||||||||
| 1\1edo | 171.429 | 85.714 | 171.429 | 342.857 | 514.286 | 600 | Phrygian Mode (aka Double) Neapolitan Temperament from here … | ||||
| 15\14 | 183.6735 | 91.837 | 183.6735 | 367.347 | 551.02 | 642.857 | |||||
| 14\13 | 184.615 | 92.308 | 184.615 | 369.231 | 553.846 | 646.154 | |||||
| 27\25 | 185.143 | 92.571 | 185.143 | 370.286 | 555.571 | 648 | |||||
| 13\12 | 185.714 | 92.857 | 185.714 | 371.429 | 557.143 | 650 | |||||
| 38\35 | 186.122 | 93.061 | 186.122 | 372.245 | 558.367 | 651.429 | |||||
| 25\23 | 186.335 | 93.168 | 186.335 | 372.671 | 559.006 | 652.174 | |||||
| 37\34 | 186.555 | 93.278 | 186.555 | 373.109 | 559.664 | 652.941 | |||||
| 12\11 | 187.013 | 93.5065 | 187.013 | 374.026 | 561.039 | 654.5455 | |||||
| 46\43 | 187.375 | 93.688 | 187.375 | 374.751 | 562.126 | 655.813 | |||||
| 35\32 | 187.5 | 93.75 | 187.5 | 375 | 562.5 | 656.25 | |||||
| 58\53 | 187.601 | 93.8005 | 187.601 | 375.202 | 562.803 | 656.604 | |||||
| 23\21 | 187.755 | 93.878 | 187.755 | 375.51 | 563.265 | 657.143 | |||||
| 57\52 | 187.912 | 93.956 | 187.912 | 375.824 | 563.736 | 658.242 | |||||
| 34\31 | 188.018 | 94.009 | 188.018 | 376.037 | 564.055 | 658.0645 | |||||
| 45\41 | 188.153 | 94.077 | 188.153 | 376.307 | 564.46 | 658.537 | |||||
| 11\10 | 188.571 | 94.286 | 188.571 | 377.143 | 565.714 | 660 | …to here
Phrygian-Aeolian Mode Neapolitan Temperament from here … | ||||
| 54\49 | 188.921 | 94.461 | 188.921 | 377.842 | 566.764 | 661.2245 | |||||
| 43\39 | 189.011 | 94.5055 | 189.011 | 378.022 | 567.033 | 661.5385 | |||||
| 75\68 | 189.076 | 94.538 | 189.076 | 378.151 | 567.227 | 661.765 | |||||
| 32\29 | 189.163 | 94.581 | 189.163 | 378.325 | 567.488 | 662.069 | |||||
| 85\77 | 189.239 | 94.62 | 189.239 | 378.478 | 567.717 | 662.338 | |||||
| 53\48 | 189.286 | 94.643 | 189.286 | 378.571 | 567.857 | 662.5 | |||||
| 74\67 | 189.339 | 94.6695 | 189.339 | 378.678 | 568.017 | 662.687 | |||||
| 21\19 | 189.474 | 94.736 | 189.474 | 378.947 | 568.421 | 663.158 | |||||
| 73\66 | 189.61 | 94.805 | 189.61 | 379.221 | 568.831 | 663.636 | |||||
| 52\47 | 189.666 | 94.833 | 189.666 | 379.331 | 568.997 | 663.83 | |||||
| 83\75 | 189.714 | 94.857 | 189.714 | 379.429 | 569.143 | 664 | |||||
| 31\28 | 189.796 | 94.898 | 189.796 | 379.591 | 569.388 | 664.286 | |||||
| 72\65 | 189.89 | 94.945 | 189.89 | 379.78 | 569.67 | 664.615 | |||||
| 41\37 | 189.961 | 94.981 | 189.961 | 379.923 | 569.884 | 644.865 | |||||
| 51\46 | 190.062 | 95.031 | 190.062 | 380.124 | 570.186 | 665.217 | |||||
| 10\9 | 190.476 | 95.238 | 190.476 | 380.952 | 571.429 | 666.667 | |||||
| 49\44 | 190.909 | 95.4545 | 190.909 | 381.818 | 572.727 | 668.182 | |||||
| 39\35 | 191.02 | 95.51 | 191.02 | 382.041 | 573.061 | 668.571 | |||||
| 68\61 | 191.101 | 95.55 | 191.101 | 382.201 | 573.302 | 668.8525 | |||||
| 29\26 | 191.209 | 95.604 | 191.209 | 382.418 | 573.626 | 669.231 | |||||
| 77\69 | 191.304 | 95.652 | 191.304 | 382.609 | 573.913 | 669.567 | |||||
| 48\43 | 191.362 | 95.681 | 191.362 | 382.724 | 574.086 | 669.767 | |||||
| 67\60 | 191.429 | 95.714 | 191.429 | 382.857 | 574.286 | 670 | |||||
| 19\17 | 191.597 | 95.798 | 191.597 | 383.193 | 574.79 | 670.588 | |||||
| 66\59 | 191.768 | 95.884 | 191.768 | 383.535 | 575.303 | 671.187 | |||||
| 47\42 | 191.837 | 95.918 | 191.837 | 383.675 | 575.51 | 671.429 | |||||
| 75\67 | 191.898 | 95.949 | 191.898 | 383.795 | 575.693 | 671.642 | |||||
| 28\25 | 192 | 96 | 192 | 384 | 576 | 672 | |||||
| 65\58 | 192.118 | 96.059 | 192.118 | 384.236 | 576.355 | 672.414 | |||||
| 37\33 | 192.208 | 96.104 | 192.208 | 384.416 | 576.623 | 672.727 | |||||
| 46\41 | 192.334 | 96.167 | 192.334 | 384.669 | 577.0035 | 673.171 | |||||
| 9\8 | 192.857 | 96.429 | 192.857 | 385.714 | 578.571 | 675 | |||||
| 44\39 | 193.407 | 96.703 | 193.407 | 386.813 | 580.22 | 676.923 | |||||
| 35\31 | 193.548 | 96.774 | 193.548 | 387.097 | 580.645 | 677.419 | |||||
| 61\54 | 193.651 | 96.825 | 193.651 | 387.302 | 580.952 | 677.778 | |||||
| 26\23 | 193.789 | 96.894 | 193.789 | 387.578 | 581.3665 | 678.261 | |||||
| 69\61 | 193.911 | 96.9555 | 193.911 | 387.822 | 581.733 | 678.6885 | |||||
| 43\38 | 193.985 | 96.9925 | 193.985 | 387.97 | 581.955 | 678.947 | |||||
| 60\53 | 194.07 | 97.035 | 194.07 | 388.14 | 582.21 | 679.245 | |||||
| 17\15 | 194.286 | 97.143 | 194.286 | 388.571 | 582.857 | 680 | |||||
| 59\52 | 194.5055 | 97.253 | 194.5055 | 389.011 | 583.5165 | 680.769 | |||||
| 42\37 | 194.595 | 94.297 | 194.595 | 389.189 | 583.784 | 681.081 | |||||
| 67\59 | 194.673 | 97.337 | 194.673 | 389.346 | 584.019 | 681.356 | |||||
| 25\22 | 194.805 | 97.403 | 194.805 | 389.61 | 584.416 | 681.818 | |||||
| 58\51 | 194.958 | 97.479 | 194.958 | 389.916 | 584.874 | 682.353 | |||||
| 33\29 | 195.074 | 97.537 | 195.074 | 390.148 | 585.222 | 682.759 | |||||
| 41\36 | 195.238 | 97.619 | 195.238 | 390.476 | 585.714 | 683.333 | |||||
| 8\7 | 195.918 | 97.959 | 195.918 | 391.836 | 587.755 | 685.714 | …to here
Aeolian Mode Neapolitan Temperament from here … | ||||
| 39\34 | 196.639 | 98.314 | 196.639 | 393.277 | 589.916 | 688.235 | |||||
| 31\27 | 196.825 | 98.413 | 196.825 | 393.651 | 590.476 | 688.889 | |||||
| 54\47 | 196.9605 | 98.48 | 196.9605 | 393.921 | 590.8815 | 689.362 | |||||
| 23\20 | 197.143 | 98.571 | 197.143 | 394.286 | 591.429 | 690 | |||||
| 61\53 | 197.305 | 98.602 | 197.305 | 394.609 | 591.914 | 690.566 | |||||
| 38\33 | 197.403 | 98.701 | 197.403 | 394.805 | 592.208 | 690.909 | |||||
| 53\46 | 197.5155 | 98.758 | 197.5155 | 395.031 | 592.547 | 691.304 | |||||
| 15\13 | 197.802 | 98.901 | 197.802 | 395.604 | 593.407 | 692.308 | |||||
| 52\45 | 198.095 | 99.048 | 198.095 | 396.1905 | 594.286 | 693.333 | |||||
| 37\32 | 198.214 | 99.107 | 198.214 | 396.429 | 594.643 | 693.75 | |||||
| 59\51 | 198.319 | 99.16 | 198.319 | 396.639 | 594.958 | 694.118 | |||||
| 22\19 | 198.496 | 99.248 | 198.496 | 396.9925 | 595.489 | 694.737 | |||||
| 51\44 | 198.701 | 99.351 | 198.701 | 397.403 | 596.104 | 695.4545 | |||||
| 29\25 | 198.857 | 99.429 | 198.857 | 397.714 | 596.571 | 696 | |||||
| 36\31 | 199.078 | 99.539 | 199.078 | 398.157 | 597.235 | 696.774 | |||||
| 7\6 | 200 | 100 | 200 | 400 | 600 | 700 | |||||
| 34\29 | 200.985 | 100.493 | 200.985 | 400.97 | 602.956 | 703.448 | |||||
| 27\23 | 201.242 | 101.621 | 201.242 | 402.4845 | 603.727 | 704.348 | |||||
| 47\40 | 201.429 | 100.714 | 201.429 | 403.857 | 603.286 | 705 | |||||
| 20\17 | 201.681 | 100.84 | 201.681 | 403.361 | 605.045 | 705.882 | |||||
| 53\45 | 201.905 | 100.952 | 201.905 | 403.8095 | 605.714 | 706.667 | |||||
| 33\28 | 202.041 | 101.02 | 202.041 | 404.082 | 606.122 | 707.143 | |||||
| 46\39 | 202.198 | 101.099 | 202.198 | 404.396 | 606.593 | 707.692 | |||||
| 13\11 | 202.597 | 101.299 | 202.597 | 405.195 | 607.792 | 709.091 | |||||
| 45\38 | 203.0075 | 101.504 | 203.0075 | 406.015 | 609.023 | 710.526 | |||||
| 32\27 | 203.175 | 101.587 | 203.175 | 406.349 | 609.524 | 711.111 | |||||
| 51\43 | 203.322 | 101.661 | 203.322 | 406.6445 | 609.967 | 711.629 | |||||
| 19\16 | 203.571 | 101.786 | 203.571 | 407.143 | 610.714 | 712.5 | |||||
| 44\37 | 203.861 | 101.9305 | 203.861 | 407.722 | 611.583 | 713.5135 | |||||
| 25\21 | 204.082 | 102.041 | 204.082 | 408.163 | 612.245 | 714.286 | |||||
| 31\26 | 204.396 | 102.198 | 204.396 | 408.791 | 613.187 | 715.384 | |||||
| 6\5 | 205.714 | 102.857 | 205.714 | 411.429 | 617.143 | 720 | …to here | ||||