29ed7: Difference between revisions
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Created page with "'''29ED7''' is the equal division of the 7th harmonic into 29 parts of 116.1664 cents each. It is similar to every third step of 31edo. {| class="wikitab..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
{{ED intro}} It is similar to every third step of [[31edo]]. | |||
{| class="wikitable" | == Intervals == | ||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 29ed7 | |||
|- | |- | ||
! | degree | ! | degree | ||
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|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 29 | |||
| num = 7 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 29 | |||
| num = 7 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
{{stub}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 28ed7 | 29ed7 | 30ed7 → |
29 equal divisions of the 7th harmonic (abbreviated 29ed7) is a nonoctave tuning system that divides the interval of 7/1 into 29 equal parts of about 116 ¢ each. Each step represents a frequency ratio of 71/29, or the 29th root of 7. It is similar to every third step of 31edo.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 116.1664 | 77/72, 15/14 | |
| 2 | 232.3328 | 8/7 | |
| 3 | 348.4992 | 11/9, 49/40 | |
| 4 | 464.6656 | 98/75 | |
| 5 | 580.8321 | 7/5 | |
| 6 | 696.9985 | 112/75, 121/81, 136/91, 187/125 | |
| 7 | 813.1649 | 8/5 | |
| 8 | 929.3313 | 65/38 | |
| 9 | 1045.4977 | 64/35 | |
| 10 | 1161.6641 | 88/45, 96/49, 49/25 | |
| 11 | 1277.8305 | 44/21 | |
| 12 | 1393.9969 | 38/17, 85/38 | |
| 13 | 1510.1633 | ||
| 14 | 1626.3297 | 64/25 | |
| 15 | 1742.4962 | 52/19 | |
| 16 | 1858.6626 | 38/13 | |
| 17 | 1974.8290 | 25/8 | |
| 18 | 2090.9954 | ||
| 19 | 2207.1618 | 68/19 | |
| 20 | 2323.3282 | 65/17 | |
| 21 | 2439.4946 | 45/11 | |
| 22 | 2555.6610 | 35/8 | |
| 23 | 2671.8274 | ||
| 24 | 2787.9939 | 5/1 | |
| 25 | 2904.1603 | 75/14 | |
| 26 | 3020.3267 | 40/7, 63/11 | |
| 27 | 3136.4931 | 49/8 | |
| 28 | 3252.6595 | 98/15, 72/11 | |
| 29 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -38.3 | -43.3 | +39.5 | +1.7 | +34.5 | +0.0 | +1.2 | +29.6 | -36.7 | +30.7 | -3.8 |
| Relative (%) | -33.0 | -37.3 | +34.0 | +1.4 | +29.7 | +0.0 | +1.0 | +25.5 | -31.6 | +26.4 | -3.3 | |
| Steps (reduced) |
10 (10) |
16 (16) |
21 (21) |
24 (24) |
27 (27) |
29 (0) |
31 (2) |
33 (4) |
34 (5) |
36 (7) |
37 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -26.2 | -38.3 | -41.6 | -37.2 | -26.0 | -8.8 | +13.8 | +41.2 | -43.3 | -7.7 | +31.5 |
| Relative (%) | -22.6 | -33.0 | -35.8 | -32.0 | -22.4 | -7.5 | +11.9 | +35.4 | -37.3 | -6.6 | +27.2 | |
| Steps (reduced) |
38 (9) |
39 (10) |
40 (11) |
41 (12) |
42 (13) |
43 (14) |
44 (15) |
45 (16) |
45 (16) |
46 (17) |
47 (18) | |
|
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