User:Eliora/80edn: Difference between revisions
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Prime factorization
24 × 5
Step size
21.6404 ¢
Octave
55\80edn (1190.22 ¢) (→ 11\16edn)
Twelfth
88\80edn (1904.36 ¢) (→ 11\10edn)
Consistency limit
2
Distinct consistency limit
2
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'''80 equal divisions of the natave''' '''(80edn, 80ede)''' is a tuning that divides the [[natave]], e/1 into steps of 21.640 [[cents]] each, a size close to [[81/80]], the syntonic comma. The step size arises from the limit definition of the number e. | '''80 equal divisions of the natave''' '''(80edn, 80ede)''' is a tuning that divides the [[natave]], e/1 into steps of 21.640 [[cents]] each, a size close to [[81/80]], the syntonic comma. The step size arises from the limit definition of the number e. | ||
== Theory == | == Theory == | ||
{{Harmonics in equal|80|2.718281828459|1|intervals=prime|columns=10}} | {{Harmonics in equal|80|2.718281828459|1|intervals=prime|columns=10}} | ||
80edn is | 80edn is approximates the 3.5.11.13.23 [[subgroup]] well. It can also be used as a [[dual-n|dual-2]] tuning for the full [[17-limit]]. | ||
In the 2.3.5.11.13 subgroup on the minor octave it shares the [[mapping]] with the 55bcceeeff [[val]] in [[55edo]], and tempers out 100/99, 256/243, 624/605, 704/675. | In the 2.3.5.11.13 subgroup on the minor octave it shares the [[mapping]] with the 55bcceeeff [[val]] in [[55edo]], and tempers out 100/99, 256/243, 624/605, 704/675. | ||
Latest revision as of 14:43, 1 August 2025
| ← 79edn | 80edn | 81edn → |
80 equal divisions of the natave (80edn, 80ede) is a tuning that divides the natave, e/1 into steps of 21.640 cents each, a size close to 81/80, the syntonic comma. The step size arises from the limit definition of the number e.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.78 | +2.40 | +5.30 | +7.08 | +3.64 | -4.24 | +7.42 | +9.63 | +3.47 | -8.30 |
| Relative (%) | -45.2 | +11.1 | +24.5 | +32.7 | +16.8 | -19.6 | +34.3 | +44.5 | +16.0 | -38.4 | |
| Steps (reduced) |
55 (55) |
88 (8) |
129 (49) |
156 (76) |
192 (32) |
205 (45) |
227 (67) |
236 (76) |
251 (11) |
269 (29) | |
80edn is approximates the 3.5.11.13.23 subgroup well. It can also be used as a dual-2 tuning for the full 17-limit.
In the 2.3.5.11.13 subgroup on the minor octave it shares the mapping with the 55bcceeeff val in 55edo, and tempers out 100/99, 256/243, 624/605, 704/675.