1178edo: Difference between revisions
→Regular temperament properties: +semihemienneadecal |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1178 | Since 1178 factors into {{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 == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
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| 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872 | | 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872 | ||
| {{mapping| 1178 1867 2735 3307 4075 4359 4815 }} | | {{mapping| 1178 1867 2735 3307 4075 4359 4815 }} | ||
| 0.0403 | | +0.0403 | ||
| 0.0327 | | 0.0327 | ||
| 3.21 | | 3.21 | ||
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| 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913 | | 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913 | ||
| {{mapping| 1178 1867 2735 3307 4075 4359 4815 5004 }} | | {{mapping| 1178 1867 2735 3307 4075 4359 4815 5004 }} | ||
| 0.0370 | | +0.0370 | ||
| 0.0318 | | 0.0318 | ||
| 3.12 | | 3.12 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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|- | |- | ||
| 19 | | 19 | ||
| 489\1178<br>(7\1178) | | 489\1178<br />(7\1178) | ||
| 498.13<br>(7.13) | | 498.13<br />(7.13) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Enneadecal]] | | [[Enneadecal]] | ||
|- | |||
| 31 | |||
| 581\1178<br />(11\1178) | |||
| 591.851<br />(11.205) | |||
| 936/665<br />(?) | |||
| [[31st-octave temperaments#217 & 1178|217 & 1178]] | |||
|- | |- | ||
| 38 | | 38 | ||
| 260\1178<br>(12\1178) | | 260\1178<br />(12\1178) | ||
| 264.86<br>(12.22) | | 264.86<br />(12.22) | ||
| 500/429<br>(144/143) | | 500/429<br />(144/143) | ||
| [[Semihemienneadecal]] | | [[Semihemienneadecal]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 489\1178<br>(7\1178) | | 489\1178<br />(7\1178) | ||
| 498.13<br>(7.13) | | 498.13<br />(7.13) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Eliora]] | ; [[Eliora]] | ||
* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) – 217 & 1178 and enneadecal in 1178edo tuning | * [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) – {{nowrap|217 & 1178}} and enneadecal in 1178edo tuning | ||
[[Category:Enneadecal]] | [[Category:Enneadecal]] | ||
[[Category:Hemienneadecal]] | [[Category:Hemienneadecal]] | ||
[[Category:Listen]] | |||
[[Category:Semihemienneadecal]] | [[Category:Semihemienneadecal]] | ||