337edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
337edo is [[consistent]] to the [[9-odd-limit]], but the error of [[harmonic]] [[5/1|5]] is quite large. If the harmonic is used at all, it tends very flat. The equal temperament [[tempering out|tempers out]] [[16875/16807]], 420175/419904, and 5250987/5242880 in the 7-limit. It [[support]]s | 337edo is [[consistent]] to the [[9-odd-limit]], but the error of [[harmonic]] [[5/1|5]] is quite large. If the harmonic is used at all, it tends very flat. The equal temperament [[tempering out|tempers out]] [[16875/16807]], [[420175/419904]], and 5250987/5242880 in the 7-limit. It [[support]]s [[tokko]] and [[sqrtphi]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 13: | Line 13: | ||
== 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]] (%) | ||
| Line 25: | Line 26: | ||
| {{monzo| -534 337 }} | | {{monzo| -534 337 }} | ||
| {{mapping| 337 534 }} | | {{mapping| 337 534 }} | ||
| 0.1487 | | +0.1487 | ||
| 0.1487 | | 0.1487 | ||
| 4.18 | | 4.18 | ||
| Line 32: | Line 33: | ||
| 15625/15552, {{monzo| -88 57 -1 }} | | 15625/15552, {{monzo| -88 57 -1 }} | ||
| {{mapping| 337 534 782 }} | | {{mapping| 337 534 782 }} | ||
| 0.3495 | | +0.3495 | ||
| 0.3089 | | 0.3089 | ||
| 8.67 | | 8.67 | ||
| Line 39: | Line 40: | ||
| 15625/15552, 16875/16807, 7381125/7340032 | | 15625/15552, 16875/16807, 7381125/7340032 | ||
| {{mapping| 337 534 782 946 }} | | {{mapping| 337 534 782 946 }} | ||
| 0.2870 | | +0.2870 | ||
| 0.2886 | | 0.2886 | ||
| 8.10 | | 8.10 | ||
|} | |} | ||
=== 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 | ||
|- | |- | ||
| Line 63: | Line 66: | ||
| 6/5 | | 6/5 | ||
| [[Hanson]] | | [[Hanson]] | ||
|- | |||
| 1 | |||
| 117\337 | |||
| 416.62 | |||
| 14/11 | |||
| [[Sqrtphi]] (337, 11-limit) | |||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | |||
; [[Francium]] | |||
* "The End Of A Good Day" from ''Mysteries'' (2023) – [https://open.spotify.com/track/1yaSXn4u2TVWClwXBtMVs4 Spotify] | [https://francium223.bandcamp.com/track/the-end-of-a-good-day Bandcamp] | [https://www.youtube.com/watch?v=2ixL8YQmJig YouTube] | |||
[[Category:Listen]] | |||