User:Agent 19/51ed19
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| ← 50ed19 | 51ed19 | 52ed19 → |
(semiconvergent)
51 equal divisions of the 19th harmonic (abbreviated 51ed19) is a nonoctave tuning system that divides the interval of 19/1 into 51 equal parts of about 100 ¢ each. Each step represents a frequency ratio of 191/51, or the 51st root of 19.
Theory
51ed19 is very closely related to 12edo, but with the 19/1 rather than the 2/1 being just. The enneadectave is too wide to be a useful equivalence, so this is more of a way to sneak in an equal division of it while keeping music made with it familiar.
Prime Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.6 | -2.9 | +12.3 | +29.5 | +46.6 | -42.7 | -7.3 | +0.0 | -30.9 | -32.4 | -47.9 | +45.6 | -32.2 | -14.7 | +31.2 | +23.1 | +37.4 | -20.3 | +17.1 |
| Relative (%) | -0.6 | -2.9 | +12.3 | +29.5 | +46.7 | -42.7 | -7.3 | +0.0 | -30.9 | -32.4 | -47.9 | +45.6 | -32.2 | -14.7 | +31.2 | +23.1 | +37.4 | -20.4 | +17.1 | |
| Steps (reduced) |
12 (12) |
19 (19) |
28 (28) |
34 (34) |
42 (42) |
44 (44) |
49 (49) |
51 (0) |
54 (3) |
58 (7) |
59 (8) |
63 (12) |
64 (13) |
65 (14) |
67 (16) |
69 (18) |
71 (20) |
71 (20) |
73 (22) | |
Subsets and supersets
51ed19 contains 3ed19 and 17ed19 as subsets.