751edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|751}} == Theory == 751edo is only consistent to the 3-odd-limit, with rather large errors in the harmonics 3, 7 and 1..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
751edo is | 751edo is in[[consistent]] in the [[5-odd-limit]], with rather large errors in the [[harmonic]]s [[3/1|3]], [[7/1|7]] and [[17/1|17]]. It has two mappings possible for the 7-limit: | ||
* {{val|751 1190 1744 2108}} ([[patent val]]) | * {{val| 751 1190 1744 2108 }} ([[patent val]]) | ||
* {{val|751 1190 '''1743''' 2108}} (751c val) | * {{val| 751 1190 '''1743''' 2108 }} (751c val) | ||
Using the patent val, it [[tempers out]] [[2460375/2458624]] (breeze comma), 26873856/26796875 and {{monzo|-14 7 -6 6}} in the 7-limit. | Using the patent val, it [[tempering out|tempers out]] [[2460375/2458624]] (breeze comma), 26873856/26796875 and {{monzo|-14 7 -6 6}} in the 7-limit. | ||
Using the 751c val, it tempers out [[420175/419904]], [[2109375/2097152]] and [[1640558367/1638400000]] in the 7-limit, [[support]]ing [[quinwell]]. | Using the 751c val, it tempers out [[420175/419904]], [[2109375/2097152]] and [[1640558367/1638400000]] in the 7-limit, [[support]]ing [[quinwell]]. | ||
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== 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" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-1190 751}} | | {{monzo|-1190 751}} | ||
| {{mapping|751 1190}} | | {{mapping|751 1190}} | ||
| 0.1547 | | +0.1547 | ||
| 0.1547 | | 0.1547 | ||
| 9.68 | | 9.68 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "jelly birds" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1RUQJkLybUfnDfL0WTOjWi Spotify] | [https://francium223.bandcamp.com/track/jelly-birds Bandcamp] | [https://www.youtube.com/watch?v=cuL1FRF24Ho YouTube] – in Bluebirds, 751edo tuning | |||
{{todo|inline=1|explain its xenharmonic value}} | |||