71edt: Difference between revisions
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'''[[Edt|Division of the third harmonic]] into 71 equal parts''' (71edt) is related to [[45edo|45 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 5.4644 cents stretched and the step size is about 26.7881 cents. | '''[[Edt|Division of the third harmonic]] into 71 equal parts''' (71edt) is related to [[45edo|45 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 5.4644 cents stretched and the step size is about 26.7881 cents. It is related to the 13-limit temperament which tempers out 540/539, 1575/1573, 2200/2197, and 4375/4374, which is supported by [[45edo]] (45ef val), [[179edo]] (179ef val), [[224edo]], [[269edo]] (269ce val), and [[403edo]] (403def val). | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 40: | Line 40: | ||
| | 6 | | | 6 | ||
| | 160.7286 | | | 160.7286 | ||
| | | | | 169/154 | ||
| | | | | | ||
|- | |- | ||
| Line 55: | Line 55: | ||
| | 9 | | | 9 | ||
| | 241.0929 | | | 241.0929 | ||
| | | | | 169/147 | ||
| | | | | | ||
|- | |- | ||
| Line 80: | Line 80: | ||
| | 14 | | | 14 | ||
| | 375.0334 | | | 375.0334 | ||
| | | | | 273/220 | ||
| | | | | | ||
|- | |- | ||
| | 15 | | | 15 | ||
| | 401.8215 | | | 401.8215 | ||
| | | | | 63/50 | ||
| | | | | | ||
|- | |- | ||
| Line 130: | Line 130: | ||
| | 24 | | | 24 | ||
| | 642.9144 | | | 642.9144 | ||
| | | | | 132/91 | ||
| | | | | | ||
|- | |- | ||
| Line 140: | Line 140: | ||
| | 26 | | | 26 | ||
| | 696.4906 | | | 696.4906 | ||
| | | | | 486/325, 220/147 | ||
| | | | | | ||
|- | |- | ||
| Line 150: | Line 150: | ||
| | 28 | | | 28 | ||
| | 750.0668 | | | 750.0668 | ||
| | | | | 54/35 | ||
| | | | | | ||
|- | |- | ||
| Line 225: | Line 225: | ||
| | 43 | | | 43 | ||
| | 1151.8882 | | | 1151.8882 | ||
| | | | | 35/18 | ||
| | | | | | ||
|- | |- | ||
| Line 235: | Line 235: | ||
| | 45 | | | 45 | ||
| | 1205.4644 | | | 1205.4644 | ||
| | | | | 441/220, 325/162 | ||
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|- | |- | ||
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| | 47 | | | 47 | ||
| | 1259.0406 | | | 1259.0406 | ||
| | | | | 91/44 | ||
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|- | |- | ||
| Line 290: | Line 290: | ||
| | 56 | | | 56 | ||
| | 1500.1335 | | | 1500.1335 | ||
| | | | | 50/21 | ||
| | | | | | ||
|- | |- | ||
| | 57 | | | 57 | ||
| | 1526.9216 | | | 1526.9216 | ||
| | | | | 220/91 | ||
| | | | | | ||
|- | |- | ||
| Line 310: | Line 310: | ||
| | 60 | | | 60 | ||
| | 1607.2859 | | | 1607.2859 | ||
| | | | | 195/77 | ||
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|- | |- | ||
| Line 320: | Line 320: | ||
| | 62 | | | 62 | ||
| | 1660.8621 | | | 1660.8621 | ||
| | | | | 441/169 | ||
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|- | |- | ||
| Line 330: | Line 330: | ||
| | 64 | | | 64 | ||
| | 1714.4383 | | | 1714.4383 | ||
| | 35/13 | | | 35/13, 132/49 | ||
| | | | | | ||
|- | |- | ||
| | 65 | | | 65 | ||
| | 1741.2264 | | | 1741.2264 | ||
| | | | | 462/169 | ||
| | | | | | ||
|- | |- | ||
Revision as of 00:36, 29 January 2019
Division of the third harmonic into 71 equal parts (71edt) is related to 45 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 5.4644 cents stretched and the step size is about 26.7881 cents. It is related to the 13-limit temperament which tempers out 540/539, 1575/1573, 2200/2197, and 4375/4374, which is supported by 45edo (45ef val), 179edo (179ef val), 224edo, 269edo (269ce val), and 403edo (403def val).
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 26.7881 | 66/65 | |
| 2 | 53.5762 | 65/63 | |
| 3 | 80.3643 | 22/21 | |
| 4 | 107.1524 | 117/110 | |
| 5 | 133.9405 | 27/25 | |
| 6 | 160.7286 | 169/154 | |
| 7 | 187.5167 | 39/35 | |
| 8 | 214.3048 | 147/130, 198/175 | |
| 9 | 241.0929 | 169/147 | |
| 10 | 267.8810 | 7/6 | |
| 11 | 294.6691 | 77/65 | |
| 12 | 321.4572 | ||
| 13 | 348.2453 | 11/9 | |
| 14 | 375.0334 | 273/220 | |
| 15 | 401.8215 | 63/50 | |
| 16 | 428.6096 | ||
| 17 | 455.3977 | 13/10 | |
| 18 | 482.1858 | 33/25 | |
| 19 | 508.9739 | ||
| 20 | 535.7620 | 15/11 | |
| 21 | 562.5501 | 18/13 | |
| 22 | 589.3382 | ||
| 23 | 616.1263 | 10/7 | |
| 24 | 642.9144 | 132/91 | |
| 25 | 669.7025 | ||
| 26 | 696.4906 | 486/325, 220/147 | |
| 27 | 723.2787 | ||
| 28 | 750.0668 | 54/35 | |
| 29 | 776.8549 | ||
| 30 | 803.6430 | 35/22 | |
| 31 | 830.4311 | 21/13 | |
| 32 | 857.2192 | ||
| 33 | 884.0073 | 5/3 | |
| 34 | 910.7954 | 22/13 | |
| 35 | 937.5835 | 189/110 | |
| 36 | 964.3715 | 110/63 | |
| 37 | 991.1596 | 39/22 | |
| 38 | 1017.9477 | 9/5 | |
| 39 | 1044.7358 | ||
| 40 | 1071.5239 | 13/7 | |
| 41 | 1098.3120 | 66/35 | |
| 42 | 1125.1001 | ||
| 43 | 1151.8882 | 35/18 | |
| 44 | 1178.6763 | ||
| 45 | 1205.4644 | 441/220, 325/162 | |
| 46 | 1232.2525 | ||
| 47 | 1259.0406 | 91/44 | |
| 48 | 1285.8287 | 21/10 | |
| 49 | 1312.6168 | ||
| 50 | 1339.4049 | 13/6 | |
| 51 | 1366.1930 | 11/5 | |
| 52 | 1392.9811 | ||
| 53 | 1419.7692 | 25/11 | |
| 54 | 1446.5573 | 30/13 | |
| 55 | 1473.3454 | ||
| 56 | 1500.1335 | 50/21 | |
| 57 | 1526.9216 | 220/91 | |
| 58 | 1553.7097 | 27/11 | |
| 59 | 1580.4978 | ||
| 60 | 1607.2859 | 195/77 | |
| 61 | 1634.0740 | 18/7 | |
| 62 | 1660.8621 | 441/169 | |
| 63 | 1687.6502 | 175/66, 130/49 | |
| 64 | 1714.4383 | 35/13, 132/49 | |
| 65 | 1741.2264 | 462/169 | |
| 66 | 1768.0145 | 25/9 | |
| 67 | 1794.8026 | 110/39 | |
| 68 | 1821.5907 | 63/22 | |
| 69 | 1848.3788 | 189/65 | |
| 70 | 1875.1669 | 65/22 | |
| 71 | 1901.9550 | exact 3/1 | just perfect fifth plus an octave |