36ed7: Difference between revisions
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Created page with "36ED7 is the equal division of the 7th harmonic into 36 parts of 93.57850 cents each (very close to Boethius' semitone, 19/18, 93.6030 cents)." |
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{{Infobox ET}} | |||
{{ED intro}} | |||
One step of 36ed7 is very close to Boethius' semitone, [[19/18]], 93.6030 cents. Making 36ed7 close to the equal multiplication of 19/18 ([[1ed19/18]]). | |||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 36 | |||
| num = 7 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 36 | |||
| num = 7 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
{{stub}} | |||
Latest revision as of 00:25, 23 December 2024
| ← 35ed7 | 36ed7 | 37ed7 → |
36 equal divisions of the 7th harmonic (abbreviated 36ed7) is a nonoctave tuning system that divides the interval of 7/1 into 36 equal parts of about 93.6 ¢ each. Each step represents a frequency ratio of 71/36, or the 36th root of 7.
One step of 36ed7 is very close to Boethius' semitone, 19/18, 93.6030 cents. Making 36ed7 close to the equal multiplication of 19/18 (1ed19/18).
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 93.6 | 18/17, 19/18 |
| 2 | 187.2 | 19/17, 29/26 |
| 3 | 280.7 | |
| 4 | 374.3 | 26/21 |
| 5 | 467.9 | 17/13 |
| 6 | 561.5 | 18/13, 29/21 |
| 7 | 655 | 19/13, 22/15 |
| 8 | 748.6 | 17/11 |
| 9 | 842.2 | |
| 10 | 935.8 | 12/7 |
| 11 | 1029.4 | |
| 12 | 1122.9 | 21/11, 23/12 |
| 13 | 1216.5 | |
| 14 | 1310.1 | |
| 15 | 1403.7 | |
| 16 | 1497.3 | 26/11 |
| 17 | 1590.8 | 5/2 |
| 18 | 1684.4 | 29/11 |
| 19 | 1778 | 14/5 |
| 20 | 1871.6 | |
| 21 | 1965.1 | 25/8 |
| 22 | 2058.7 | 23/7 |
| 23 | 2152.3 | |
| 24 | 2245.9 | 11/3 |
| 25 | 2339.5 | |
| 26 | 2433 | |
| 27 | 2526.6 | |
| 28 | 2620.2 | |
| 29 | 2713.8 | 24/5 |
| 30 | 2807.4 | |
| 31 | 2900.9 | |
| 32 | 2994.5 | |
| 33 | 3088.1 | |
| 34 | 3181.7 | |
| 35 | 3275.2 | |
| 36 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.5 | -30.4 | +33.0 | +21.0 | -13.9 | +0.0 | -44.0 | +32.8 | +37.6 | -33.9 | +2.7 |
| Relative (%) | +17.7 | -32.5 | +35.3 | +22.5 | -14.8 | +0.0 | -47.0 | +35.1 | +40.1 | -36.2 | +2.8 | |
| Steps (reduced) |
13 (13) |
20 (20) |
26 (26) |
30 (30) |
33 (33) |
36 (0) |
38 (2) |
41 (5) |
43 (7) |
44 (8) |
46 (10) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -42.3 | +16.5 | -9.3 | -27.5 | -38.9 | -44.2 | -44.3 | -39.5 | -30.4 | -17.3 | -0.7 |
| Relative (%) | -45.2 | +17.7 | -10.0 | -29.4 | -41.5 | -47.3 | -47.3 | -42.2 | -32.5 | -18.5 | -0.8 | |
| Steps (reduced) |
47 (11) |
49 (13) |
50 (14) |
51 (15) |
52 (16) |
53 (17) |
54 (18) |
55 (19) |
56 (20) |
57 (21) |
58 (22) | |
|
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