1178edo: Difference between revisions
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The '''1178 equal tuning''' divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It is also distinctly [[consistent]] through to the 21-odd-limit, and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984. It supports and provides a great tuning for [[semihemienneadecal]]. | The '''1178 equal tuning''' divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It is also distinctly [[consistent]] through to the 21-odd-limit, and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984. It supports and provides a great tuning for [[semihemienneadecal]]. | ||
Revision as of 22:08, 4 October 2022
| ← 1177edo | 1178edo | 1179edo → |
The 1178 equal tuning divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a zeta peak, integral and gap edo. It is also distinctly consistent through to the 21-odd-limit, and is the first edo past 742 with a lower 19-limit relative error. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984. It supports and provides a great tuning for semihemienneadecal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.087 | -0.236 | -0.065 | -0.214 | -0.120 | -0.032 | -0.060 | +0.249 | +0.304 | -0.044 |
| Relative (%) | +0.0 | -8.6 | -23.1 | -6.4 | -21.0 | -11.8 | -3.1 | -5.9 | +24.4 | +29.8 | -4.3 | |
| Steps (reduced) |
1178 (0) |
1867 (689) |
2735 (379) |
3307 (951) |
4075 (541) |
4359 (825) |
4815 (103) |
5004 (292) |
5329 (617) |
5723 (1011) |
5836 (1124) | |
Miscellaneous properties
Since 1178 = 2 × 19 × 31, 1178edo is notable for containing both 19 and 31. Its subset edos are 2, 19, 31, 38, 62, and 589.