31edt: Difference between revisions
Jump to navigation
Jump to search
CompactStar (talk | contribs) No edit summary |
m Sort key |
||
| (4 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of [[ | '''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 ~0.185 cents flatter than the corresponding degree of 39edo. It [[support]]s the same higher-limit meantone temperament as 12edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father scales. | ||
= | == Intervals == | ||
See also | {{See also|Specific intervals in 31edt}} | ||
{{Interval table}} | {{Interval table}} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 31 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 31 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
{{todo|expand}} | |||
[[Category:31edt| ]] | |||
Latest revision as of 16:01, 31 July 2025
| ← 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 ~0.185 cents flatter than the corresponding degree of 39edo. It supports the same higher-limit meantone temperament as 12edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father scales.
Intervals
| 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 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +27.1 | +0.0 | -7.2 | -25.4 | +27.1 | +5.6 | +19.8 | +0.0 | +1.7 | +20.7 | -7.2 |
| Relative (%) | +44.1 | +0.0 | -11.8 | -41.4 | +44.1 | +9.1 | +32.4 | +0.0 | +2.7 | +33.8 | -11.8 | |
| Steps (reduced) |
20 (20) |
31 (0) |
39 (8) |
45 (14) |
51 (20) |
55 (24) |
59 (28) |
62 (0) |
65 (3) |
68 (6) |
70 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -23.1 | -28.7 | -25.4 | -14.4 | +3.3 | +27.1 | -5.2 | +28.7 | +5.6 | -13.6 | -29.2 |
| Relative (%) | -37.6 | -46.7 | -41.4 | -23.5 | +5.4 | +44.1 | -8.4 | +46.8 | +9.1 | -22.1 | -47.6 | |
| Steps (reduced) |
72 (10) |
74 (12) |
76 (14) |
78 (16) |
80 (18) |
82 (20) |
83 (21) |
85 (23) |
86 (24) |
87 (25) |
88 (26) | |