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{{Infobox ET}} | {{Infobox ET}} | ||
31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of [[39edo|39edo]] where each degree gets ~.185 cents flatter than the corresponding degree of 39edo. It [[support]]s the same higher-limit meantone temperament as 12 edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father scales. | 31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of [[39edo|39edo]] where each degree gets ~.185 cents flatter than the corresponding degree of 39edo. It [[support]]s the same higher-limit meantone temperament as 12 edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father scales. | ||
{{Harmonics in equal|31|3|1|intervals=prime|columns=15}} | |||
=<span style="background-color: #ffffff;">Intervals</span>= | =<span style="background-color: #ffffff;">Intervals</span>= | ||
See also: [[Specific intervals in 31edt]] | See also: [[Specific intervals in 31edt]] | ||
{{Interval table}} | {{Interval table}} | ||
Revision as of 00:31, 25 September 2024
| ← 30edt | 31edt | 32edt → |
31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of 39edo where each degree gets ~.185 cents flatter than the corresponding degree of 39edo. It supports the same higher-limit meantone temperament as 12 edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father scales.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +27.1 | +0.0 | -25.4 | +5.6 | +20.7 | -23.1 | +3.3 | -5.2 | -29.2 | -1.0 | +6.2 | +6.7 | +13.0 | -8.1 | +22.0 |
| Relative (%) | +44.1 | +0.0 | -41.4 | +9.1 | +33.8 | -37.6 | +5.4 | -8.4 | -47.6 | -1.6 | +10.2 | +10.9 | +21.3 | -13.1 | +35.9 | |
| Steps (reduced) |
20 (20) |
31 (0) |
45 (14) |
55 (24) |
68 (6) |
72 (10) |
80 (18) |
83 (21) |
88 (26) |
95 (2) |
97 (4) |
102 (9) |
105 (12) |
106 (13) |
109 (16) | |
Intervals
See also: Specific intervals in 31edt
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 61.4 | 41.9 | 27/26 |
| 2 | 122.7 | 83.9 | |
| 3 | 184.1 | 125.8 | 10/9, 19/17 |
| 4 | 245.4 | 167.7 | 15/13 |
| 5 | 306.8 | 209.7 | |
| 6 | 368.1 | 251.6 | 21/17, 26/21 |
| 7 | 429.5 | 293.5 | 9/7 |
| 8 | 490.8 | 335.5 | |
| 9 | 552.2 | 377.4 | 26/19 |
| 10 | 613.5 | 419.4 | 10/7, 27/19 |
| 11 | 674.9 | 461.3 | |
| 12 | 736.2 | 503.2 | 23/15, 26/17 |
| 13 | 797.6 | 545.2 | 27/17 |
| 14 | 858.9 | 587.1 | 18/11 |
| 15 | 920.3 | 629 | 17/10 |
| 16 | 981.7 | 671 | 23/13 |
| 17 | 1043 | 712.9 | 11/6, 20/11 |
| 18 | 1104.4 | 754.8 | 17/9, 19/10 |
| 19 | 1165.7 | 796.8 | |
| 20 | 1227.1 | 838.7 | |
| 21 | 1288.4 | 880.6 | 19/9, 21/10 |
| 22 | 1349.8 | 922.6 | |
| 23 | 1411.1 | 964.5 | |
| 24 | 1472.5 | 1006.5 | 7/3 |
| 25 | 1533.8 | 1048.4 | 17/7 |
| 26 | 1595.2 | 1090.3 | |
| 27 | 1656.5 | 1132.3 | 13/5 |
| 28 | 1717.9 | 1174.2 | 27/10 |
| 29 | 1779.2 | 1216.1 | |
| 30 | 1840.6 | 1258.1 | 26/9 |
| 31 | 1902 | 1300 | 3/1 |