1178edo: Difference between revisions
→Music: added music |
→Theory: +regular temperament properties |
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=== Subsets and supersets === | === Subsets and supersets === | ||
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 }}. | 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 }}. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo|-1867 1178}} | |||
|{{val|1178 1867}} | |||
| 0.0276 | |||
| 0.0276 | |||
| 2.71 | |||
|- | |||
|2.3.5 | |||
|{{monzo|-14 -19-19}}, {{monzo|-99 61 1}} | |||
|{{val|1178 1867 2735}} | |||
| 0.0522 | |||
| 0.0415 | |||
| 4.07 | |||
|- | |||
|2.3.5.7 | |||
|4375/4374, 703125/702464, 2460375/2458624 | |||
|{{val|1178 1867 2735 3307}} | |||
| 0.0450 | |||
| 0.0380 | |||
| 3.73 | |||
|- | |||
|2.3.5.7.11 | |||
|3025/3024, 4375/4374, 9801/9800, 43923/43904 | |||
|{{val|1178 1867 2735 3307 4075}} | |||
| 0.0484 | |||
| 0.0347 | |||
| 3.41 | |||
|- | |||
|2.3.5.7.11.13 | |||
|3025/3024, 4225/4224, 9801/9800, 91125/91091, 1664000/1663893 | |||
|{{val|1178 1867 2735 3307 4075 4359}} | |||
| 0.0457 | |||
| 0.0322 | |||
| 3.16 | |||
|- | |||
|2.3.5.7.11.13.17 | |||
|3025/3024, 4225/4224, 5832/5831, 9801/9800, 14875/14872, 31213/31212 | |||
|{{val|1178 1867 2735 3307 4075 4359 4815}} | |||
| 0.0403 | |||
| 0.0327 | |||
| 3.21 | |||
|- | |||
|2.3.5.7.11.13.17.19 | |||
|4200/4199, 5985/5984, 9801/9800, 10830/10829, 12636/12635, 14365/14364, 23409/23408 | |||
|{{val|1178 1867 2735 3307 4075 4359 4815 5004}} | |||
| 0.0370 | |||
| 0.0318 | |||
| 3.12 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
|1 | |||
|337\1178 | |||
|343.29 | |||
|8000/6561 | |||
|[[Raider]] | |||
|- | |||
|19 | |||
|489\1178<br>(7\1178) | |||
|498.13<br>(7.13) | |||
|4/3<br>(225/224) | |||
|[[Enneadecal]] | |||
|- | |||
|38 | |||
|489\1178<br>(7\1178) | |||
|498.13<br>(7.13) | |||
|4/3<br>(225/224) | |||
|[[Hemienneadecal]] | |||
|} | |||
== Music == | == Music == | ||