2129edo: Difference between revisions
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m Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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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]] (%) | |||
|- | |- | ||
| 2.9 | | 2.9 | ||
| {{monzo| -6749 2129 }} | | {{monzo| -6749 2129 }} | ||
| {{mapping| 2129 6749 }} | | {{mapping| 2129 6749 }} | ||
| | | −0.0204 | ||
| 0.0204 | | 0.0204 | ||
| 3.62 | | 3.62 | ||
Line 24: | Line 33: | ||
| {{monzo| 37 29 -33 }}, {{monzo| 209 -61 -4 }} | | {{monzo| 37 29 -33 }}, {{monzo| 209 -61 -4 }} | ||
| {{mapping| 2129 6749 8318 }} | | {{mapping| 2129 6749 8318 }} | ||
| | | −0.0247 | ||
| 0.0177 | | 0.0177 | ||
| 3.14 | | 3.14 | ||
Line 31: | Line 40: | ||
| 24414062500/24407490807, 13841287201/13839609375, 2199023255552/2197176384375 | | 24414062500/24407490807, 13841287201/13839609375, 2199023255552/2197176384375 | ||
| {{mapping| 2129 6749 8318 5977 }} | | {{mapping| 2129 6749 8318 5977 }} | ||
| | | −0.0256 | ||
| 0.0154 | | 0.0154 | ||
| 2.73 | | 2.73 | ||
Line 38: | Line 47: | ||
| 9800/9801, 5767168/5764801, 104857600/104825259, 13841287201/13839609375 | | 9800/9801, 5767168/5764801, 104857600/104825259, 13841287201/13839609375 | ||
| {{mapping| 2129 6749 8318 5977 7365 }} | | {{mapping| 2129 6749 8318 5977 7365 }} | ||
| | | −0.0162 | ||
| 0.0232 | | 0.0232 | ||
| 4.12 | | 4.12 | ||
Line 45: | Line 54: | ||
| 10648/10647, 9801/9800, 196625/196608, 36924979/36905625, 304117528/303807105 | | 10648/10647, 9801/9800, 196625/196608, 36924979/36905625, 304117528/303807105 | ||
| {{mapping| 2129 6749 8318 5977 7365 7878 }} | | {{mapping| 2129 6749 8318 5977 7365 7878 }} | ||
| | | −0.0075 | ||
| 0.0288 | | 0.0288 | ||
| 5.11 | | 5.11 | ||
Line 52: | Line 61: | ||
| 2431/2430, 10648/10647, 9801/9800, 845325/845152, 297440/297381, 11275335/11275264, 15980544/15978655 | | 2431/2430, 10648/10647, 9801/9800, 845325/845152, 297440/297381, 11275335/11275264, 15980544/15978655 | ||
| {{mapping| 2129 6749 8318 5977 7365 7878 8702 }} | | {{mapping| 2129 6749 8318 5977 7365 7878 8702 }} | ||
| | | −0.0024 | ||
| 0.0295 | | 0.0295 | ||
| 5.2 | | 5.2 | ||
|} | |||
=== 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 | ||
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| 498.262 | | 498.262 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Scales == | == Scales == | ||
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== Music == | == Music == | ||
; [[User:Francium|Francium]] | ; [[User:Francium|Francium]] | ||
* "Brid Dance" from ''HemischisMatic EP'' (2023) | * "Brid Dance" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/6yXO4yHFM0EWk3pCjop8Dp Spotify] | [https://francium223.bandcamp.com/track/brid-dance Bandcamp] | [https://youtu.be/xF_1MKMlsjY?si=8Db0YVe6GQ9ZgPET YouTube] – [[hemischis]] in 2129edo tuning | ||
[[Category:Listen]] | [[Category:Listen]] |