14edf: Difference between revisions
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| Line 11: | Line 11: | ||
!Golden (~ed10\17) | !Golden (~ed10\17) | ||
!ed34\57 (~47ed4!) | !ed34\57 (~47ed4!) | ||
|Approximate Ratios* | |||
|- | |- | ||
|1 | |1 | ||
| Line 18: | Line 19: | ||
|50.41825 | |50.41825 | ||
|51.1278 | |51.1278 | ||
|1/1 | |||
|- | |- | ||
|2 | |2 | ||
| Line 25: | Line 27: | ||
|100.8365 | |100.8365 | ||
|102.2556 | |102.2556 | ||
|33/32, 34/33 | |||
|- | |- | ||
|3 | |3 | ||
| Line 32: | Line 35: | ||
|151.2547 | |151.2547 | ||
|153.3835 | |153.3835 | ||
|17/16, 18/17 | |||
|- | |- | ||
|4 | |4 | ||
| Line 39: | Line 43: | ||
|201.673 | |201.673 | ||
|204.5113 | |204.5113 | ||
|12/11 | |||
|- | |- | ||
|5 | |5 | ||
| Line 46: | Line 51: | ||
|252.0912 | |252.0912 | ||
|255.6391 | |255.6391 | ||
|9/8 | |||
|- | |- | ||
|6 | |6 | ||
| Line 53: | Line 59: | ||
|302.5095 | |302.5095 | ||
|306.7669 | |306.7669 | ||
|22/19 | |||
|- | |- | ||
|7 | |7 | ||
| Line 60: | Line 67: | ||
|352.9277 | |352.9277 | ||
|357.8947 | |357.8947 | ||
|19/16 | |||
|- | |- | ||
|8 | |8 | ||
| Line 67: | Line 75: | ||
|403.346 | |403.346 | ||
|409.0226 | |409.0226 | ||
|11/9 | |||
|- | |- | ||
|9 | |9 | ||
| Line 74: | Line 83: | ||
|453.7642 | |453.7642 | ||
|460.1504 | |460.1504 | ||
|24/19 | |||
|- | |- | ||
|10 | |10 | ||
| Line 81: | Line 91: | ||
|504.1825 | |504.1825 | ||
|511.2781 | |511.2781 | ||
|22/17 | |||
|- | |- | ||
|11 | |11 | ||
| Line 88: | Line 99: | ||
|554.6007 | |554.6007 | ||
|562.406 | |562.406 | ||
|4/3 | |||
|- | |- | ||
|12 | |12 | ||
| Line 95: | Line 107: | ||
|605.019 | |605.019 | ||
|613.5338 | |613.5338 | ||
|11/8 | |||
|- | |- | ||
|13 | |13 | ||
| Line 102: | Line 115: | ||
|655.4372 | |655.4372 | ||
|664.66165 | |664.66165 | ||
|17/12 | |||
|- | |- | ||
|14 | |14 | ||
| Line 109: | Line 123: | ||
|705.85545 | |705.85545 | ||
|715.7895 | |715.7895 | ||
|16/11 | |||
|- | |- | ||
|15 | |15 | ||
| Line 116: | Line 131: | ||
|756.2736 | |756.2736 | ||
|766.9173 | |766.9173 | ||
|3/2 | |||
|- | |- | ||
|16 | |16 | ||
| Line 123: | Line 139: | ||
|806.6919 | |806.6919 | ||
|818.0451 | |818.0451 | ||
|17/11 | |||
|- | |- | ||
|17 | |17 | ||
| Line 130: | Line 147: | ||
|857.1102 | |857.1102 | ||
|869.1729 | |869.1729 | ||
|19/12 | |||
|- | |- | ||
|18 | |18 | ||
| Line 137: | Line 155: | ||
|907.5284 | |907.5284 | ||
|920.30075 | |920.30075 | ||
|18/11 | |||
|- | |- | ||
|19 | |19 | ||
| Line 144: | Line 163: | ||
|957.9467 | |957.9467 | ||
|971.4286 | |971.4286 | ||
|32/19 | |||
|- | |- | ||
|20 | |20 | ||
| Line 151: | Line 171: | ||
|1008.3649 | |1008.3649 | ||
|1022.5564 | |1022.5564 | ||
|19/11 | |||
|- | |- | ||
|21 | |21 | ||
| Line 158: | Line 179: | ||
|1058.7832 | |1058.7832 | ||
|1073.6842 | |1073.6842 | ||
|16/9 | |||
|- | |- | ||
|22 | |22 | ||
| Line 165: | Line 187: | ||
|1109.2014 | |1109.2014 | ||
|1124.812 | |1124.812 | ||
|11/6 | |||
|- | |- | ||
|23 | |23 | ||
| Line 172: | Line 195: | ||
|1159.6297 | |1159.6297 | ||
|1175.93985 | |1175.93985 | ||
|17/9, 32/17 | |||
|- | |- | ||
|24 | |24 | ||
| Line 179: | Line 203: | ||
|1210.0379 | |1210.0379 | ||
|1227.0677 | |1227.0677 | ||
|33/17, 64/33 | |||
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|2/1 | |||
|} | |} | ||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category:todo:improve synopsis]] | [[Category:todo:improve synopsis]] | ||
Revision as of 22:35, 20 February 2019
Division of the just perfect fifth into 14 equal parts (14EDF) is related to 24 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 50.1396 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.
Intervals
| ed31\54 | ed121/81 | ed3/2 | Golden (~ed10\17) | ed34\57 (~47ed4!) | Approximate Ratios* | |
|---|---|---|---|---|---|---|
| 1 | 49.20635 | 49.6297 | 50.1396 | 50.41825 | 51.1278 | 1/1 |
| 2 | 98.4127 | 99.2594 | 100.2793 | 100.8365 | 102.2556 | 33/32, 34/33 |
| 3 | 147.61905 | 148.8891 | 150.4189 | 151.2547 | 153.3835 | 17/16, 18/17 |
| 4 | 196.8254 | 198.5188 | 200.5586 | 201.673 | 204.5113 | 12/11 |
| 5 | 246.03175 | 248.1485 | 250.6982 | 252.0912 | 255.6391 | 9/8 |
| 6 | 295.2381 | 297.782 | 300.8379 | 302.5095 | 306.7669 | 22/19 |
| 7 | 344.4444 | 347.408 | 350.9775 | 352.9277 | 357.8947 | 19/16 |
| 8 | 393.6508 | 397.03765 | 401.1171 | 403.346 | 409.0226 | 11/9 |
| 9 | 442.8571 | 446.66735 | 451.2568 | 453.7642 | 460.1504 | 24/19 |
| 10 | 492.0635 | 496.2971 | 501.3964 | 504.1825 | 511.2781 | 22/17 |
| 11 | 541.2698 | 545.9268 | 551.536 | 554.6007 | 562.406 | 4/3 |
| 12 | 590.4762 | 595.5565 | 601.6757 | 605.019 | 613.5338 | 11/8 |
| 13 | 639.6825 | 645.1862 | 651.8154 | 655.4372 | 664.66165 | 17/12 |
| 14 | 688.8889 | 694.8158 | 701.955 | 705.85545 | 715.7895 | 16/11 |
| 15 | 738.0952 | 744.4456 | 752.0946 | 756.2736 | 766.9173 | 3/2 |
| 16 | 787.3016 | 794.0753 | 802.2343 | 806.6919 | 818.0451 | 17/11 |
| 17 | 836.5079 | 843.705 | 852.3739 | 857.1102 | 869.1729 | 19/12 |
| 18 | 885.7143 | 893.3347 | 902.5136 | 907.5284 | 920.30075 | 18/11 |
| 19 | 934.9206 | 942.9644 | 952.6532 | 957.9467 | 971.4286 | 32/19 |
| 20 | 984.127 | 992.5941 | 1002.7929 | 1008.3649 | 1022.5564 | 19/11 |
| 21 | 1033.333 | 1042.2238 | 1052.9235 | 1058.7832 | 1073.6842 | 16/9 |
| 22 | 1082.5397 | 1091.8535 | 1103.0721 | 1109.2014 | 1124.812 | 11/6 |
| 23 | 1131.7646 | 1141.4832 | 1153.2118 | 1159.6297 | 1175.93985 | 17/9, 32/17 |
| 24 | 1180.9524 | 1191.1129 | 1203.3514 | 1210.0379 | 1227.0677 | 33/17, 64/33 |
| 2/1 |