619edo: 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 == | ||
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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 | ||
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| {{mapping|619 981}} | | {{mapping|619 981}} | ||
| 0.0561 | | 0.0561 | ||
| 0.0561 | | +0.0561 | ||
| 2.89 | | 2.89 | ||
|- | |- | ||
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| {{mapping|619 981 1437}} | | {{mapping|619 981 1437}} | ||
| 0.1135 | | 0.1135 | ||
| 0.0932 | | +0.0932 | ||
| 4.81 | | 4.81 | ||
|- | |- | ||
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| {{mapping|619 981 1437 2141}} | | {{mapping|619 981 1437 2141}} | ||
| 0.1395 | | 0.1395 | ||
| 0.0925 | | +0.0925 | ||
| 4.77 | | 4.77 | ||
|} | |} | ||
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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 | ||
|- | |- | ||
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| 498.223 | | 498.223 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |} | ||
<nowiki>* | <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]] | ||
* "Would You Like An Egg?" from ''Questions'' (2024) | * "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] | [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] | [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning | ||