349edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
349edo is only [[consistent]] to the [[5-odd-limit]]. Omitting the [[harmonic]] [[7/1|7]], it is consistent to the [[13-odd-limit]] with a flat tendency. In the 2.3.5.11.13 [[subgroup]], the equal temperament [[tempering out|tempers out]] [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072 and 166375/165888. | 349edo is only [[consistent]] to the [[5-odd-limit]]. Omitting the [[harmonic]] [[7/1|7]], it is consistent to the [[13-odd-limit]] with a flat tendency. In the 2.3.5.11.13 [[subgroup]], the equal temperament [[tempering out|tempers out]] [[625/624]], 17303/17280, 28561/28512, 41067/40960, 43940/43923, 85293/85184, 131625/131072, and 166375/165888. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| -553 349 }} | | {{monzo| -553 349 }} | ||
| {{mapping| 349 553 }} | | {{mapping| 349 553 }} | ||
| 0.1648 | | +0.1648 | ||
| 0.1648 | | 0.1648 | ||
| 4.79 | | 4.79 | ||
| Line 24: | Line 33: | ||
| 2109375/2097152, {{monzo| -31 43 -16 }} | | 2109375/2097152, {{monzo| -31 43 -16 }} | ||
| {{mapping| 349 553 810 }} | | {{mapping| 349 553 810 }} | ||
| 0.2841 | | +0.2841 | ||
| 0.2158 | | 0.2158 | ||
| 6.28 | | 6.28 | ||
| Line 31: | Line 40: | ||
| 166375/165888, 1366875/1362944, 1953125/1948617 | | 166375/165888, 1366875/1362944, 1953125/1948617 | ||
| {{mapping| 349 553 810 1207 }} | | {{mapping| 349 553 810 1207 }} | ||
| 0.2980 | | +0.2980 | ||
| 0.1884 | | 0.1884 | ||
| 5.48 | | 5.48 | ||
| Line 38: | Line 47: | ||
| 625/624, 17303/17280, 41067/40960, 216513/216320 | | 625/624, 17303/17280, 41067/40960, 216513/216320 | ||
| {{mapping| 349 553 810 1207 1291 }} | | {{mapping| 349 553 810 1207 1291 }} | ||
| 0.3227 | | +0.3227 | ||
| 0.1756 | | 0.1756 | ||
| 5.11 | | 5.11 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 51: | Line 67: | ||
| 75/64 | | 75/64 | ||
| [[Orson]] | | [[Orson]] | ||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) | * "chill futuristic lounge" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/3p2RNlmQieZA2fh3ZwQzVw Spotify] | [https://francium223.bandcamp.com/track/chill-futuristic-lounge Bandcamp] | [https://www.youtube.com/watch?v=B_P7zp5Zmio YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||