3079edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
3079edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[43046721/43025920]], 1220703125/1219784832 and {{monzo| 51 -13 -1 -10 }} in the 7-limit, [[support]]ing [[acrosextilifourths]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
3079edo is the 440th [[prime | 3079edo is the 440th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.3 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|-4880 3079}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|3079 4880}} | ! rowspan="2" | [[Mapping]] | ||
| 0.0122 | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo|-4880 3079}} | |||
| {{mapping|3079 4880}} | |||
| +0.0122 | |||
| 0.0122 | | 0.0122 | ||
| 3.13 | | 3.13 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-69 45 -1}}, {{monzo|-50 -71 70}} | | {{monzo| -69 45 -1 }}, {{monzo| -50 -71 70 }} | ||
|{{mapping|3079 4880 7149}} | | {{mapping| 3079 4880 7149 }} | ||
| 0.0203 | | +0.0203 | ||
| 0.0151 | | 0.0151 | ||
| 3.87 | | 3.87 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|43046721/43025920, 1220703125/1219784832, {{monzo|51 -13 -1 -10}} | | 43046721/43025920, 1220703125/1219784832, {{monzo| 51 -13 -1 -10 }} | ||
|{{mapping|3079 4880 7149 8644}} | | {{mapping| 3079 4880 7149 8644 }} | ||
| 0.0099 | | +0.0099 | ||
| 0.0223 | | 0.0223 | ||
| 5.72 | | 5.72 | ||
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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 | ||
|- | |- | ||
|1 | | 1 | ||
|1278\3079 | | 1278\3079 | ||
|498.084 | | 498.084 | ||
|4/3 | | 4/3 | ||
|[[Counterschismic]] | | [[Counterschismic]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | |||
; [[Francium]] | |||
* "mfdreamshoppedfashionforyou" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6paD6q5WZKPjgVW32P81sh Spotify] | [https://francium223.bandcamp.com/track/mfdreamshoppedfashionforyou Bandcamp] | [https://www.youtube.com/watch?v=xPxStKUUpFU YouTube] – acrosextilifourths[13] in 3079edo tuning | |||