1178edo: Difference between revisions
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{{EDO intro|1178}} | {{EDO intro|1178}} | ||
1178edo is a very strong 19-limit system, and is a [[ | 1178edo is a very strong 19-limit system, and is a [[zeta edo|zeta peak, integral and gap edo]]. It is also [[consistency|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 [[comma]]s is [[2500/2499]], [[3025/3024]], 3250/3249, 4200/4199, [[4375/4374]], [[4914/4913]] and 5985/5984. It [[support]]s and provides a great tuning for [[semihemienneadecal]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1178 = | Since 1178 = {{factorization|1178}}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}. | ||
[[Category:Enneadecal]] | [[Category:Enneadecal]] | ||
[[Category:Hemienneadecal]] | [[Category:Hemienneadecal]] | ||
[[Category:Semihemienneadecal]] | [[Category:Semihemienneadecal]] | ||
Revision as of 10:13, 31 October 2023
| ← 1177edo | 1178edo | 1179edo → |
1178edo 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) | |
Subsets and supersets
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.