43ed5: Difference between revisions
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== Theory == | == Theory == | ||
43ed5 misses [[2/1]] and cannot be considered equal to [[18edo]] or [[19edo]]. | 43ed5 misses [[2/1]] and cannot be considered equal to [[18edo]] or [[19edo]]. It’s actually similar to [[37ed4]] (18.5edo). | ||
In terms of no-twos no-threes [[subgroup]]s, 43ed5 excels in the 5.7.11 [[subgroup]]. It supports [[Pentadacus]] temperament and is a nearly-optimal tuning of it. Unfortunately, it completely misses the 13th harmonic and has mediocre approximations for the 17th and 19th harmonics. | In terms of no-twos no-threes [[subgroup]]s, 43ed5 excels in the 5.7.11 [[subgroup]]. It supports [[Pentadacus]] temperament and is a nearly-optimal tuning of it. Unfortunately, it completely misses the 13th harmonic and has mediocre approximations for the 17th and 19th harmonics. | ||
===Prime harmonics=== | ===Prime harmonics=== | ||
Revision as of 02:49, 6 August 2026
| ← 42ed5 | 43ed5 | 44ed5 → |
43 equal divisions of the 5th harmonic (abbreviated 43ed5) is a nonoctave tuning system that divides the interval of 5/1 into 43 equal parts of about 64.8 ¢ each. Each step represents a frequency ratio of 51/43, or the 43rd root of 5.
Theory
43ed5 misses 2/1 and cannot be considered equal to 18edo or 19edo. It’s actually similar to 37ed4 (18.5edo).
In terms of no-twos no-threes subgroups, 43ed5 excels in the 5.7.11 subgroup. It supports Pentadacus temperament and is a nearly-optimal tuning of it. Unfortunately, it completely misses the 13th harmonic and has mediocre approximations for the 17th and 19th harmonics.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +31.2 | -22.8 | +0.0 | +0.7 | -4.2 | +30.5 | +19.7 | +21.5 | +14.8 | +2.2 | +16.4 |
| Relative (%) | +48.1 | -35.2 | +0.0 | +1.0 | -6.6 | +47.1 | +30.4 | +33.2 | +22.8 | +3.5 | +25.3 | |
| Steps (reduced) |
19 (19) |
29 (29) |
43 (0) |
52 (9) |
64 (21) |
69 (26) |
76 (33) |
79 (36) |
84 (41) |
90 (4) |
92 (6) | |
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