User:Francium/1031edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} == Theory == 1031edo is consistent to the 9-odd-limit. It is strong in the 2.3.5.13.17 subgroup. === Prime harmonics === {{Harmonics in equal|1031}} === Subsets and supersets === 1031edo is the 273rd prime edo." |
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== Theory == | == Theory == | ||
1031edo is [[consistent]] to the [[9-odd-limit]]. It is strong in the 2.3.5.13.17 [[subgroup]]. | 1031edo is [[consistent]] to the [[9-odd-limit]], [[tempering out]] [[420175/419904]], 5250987/5242880 and 152946081792/152587890625 in the [[7-limit]]. It is strong in the 2.3.5.13.17 [[subgroup]], tempering out [[2601/2600]], 1601613/1600000, 33564375/33554432 and 4782969/4780672. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
1031edo is the 273rd [[prime edo]]. | 1031edo is the 273rd [[prime edo]]. [[3093edo]], which triples it, gives a good correction to its [[harmonic]] [[11/1|11]]. | ||
== 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|-1634 1031}} | |||
| {{mapping|1031 1634}} | |||
| 0.0354 | |||
| 0.0354 | |||
| 3.04 | |||
|- | |||
| 2.3.5 | |||
| {{monzo|38 -2 -15}}, {{monzo|-38 65 -28}} | |||
| {{mapping|1031 1634 2394}} | |||
| 0.0082 | |||
| 0.0481 | |||
| 4.13 | |||
|- | |||
| 2.3.5.7 | |||
| 420175/419904, 5250987/5242880, 152946081792/152587890625 | |||
| {{mapping|1031 1634 2394 2894}} | |||
| 0.0458 | |||
| 0.0774 | |||
| 6.65 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>Ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 166\1031 | |||
| 193.210 | |||
| 262144/234375 | |||
| [[Luna]] | |||
|} | |||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | |||
; [[Francium]] | |||
* "sweet gravy" from ''have nice day'' (2025) – [https://open.spotify.com/track/6F1HyBmCUC6t7FUaGswzK1 Spotify] | [https://francium223.bandcamp.com/track/sweet-gravy Bandcamp] | [https://www.youtube.com/watch?v=5YC--2hRyms YouTube] – in Sycamore, 1031edo tuning | |||