593edo: Difference between revisions
→Regular temperament properties: since it tempers out the garischisma, it obviously supports the 2.3.7 gary temp |
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" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
593edo is [[consistent]] to the [[9-odd-limit]]. | 593edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]], [[33554432/33480783]], 52734375/52706752, and 67108864/66976875 in the 7-limit. It [[support]]s [[vulture]] and [[squarschmidt]]. It is also notable in the 2.3.5.7.17 [[subgroup]], tempering out [[2500/2499]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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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" | [[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]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 940 -593 }} | ||
| {{ | | {{Mapping| 593 940 }} | ||
| | | −0.0748 | ||
| 0.0748 | | 0.0748 | ||
| 3.70 | | 3.70 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 24 -21 4 }}, {{monzo| 37 25 -33 }} | ||
| {{ | | {{Mapping| 593 940 1377 }} | ||
| | | −0.0780 | ||
| 0.0613 | | 0.0613 | ||
| 3.03 | | 3.03 | ||
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| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 33554432/33480783, 52734375/52706752 | | 4375/4374, 33554432/33480783, 52734375/52706752 | ||
| {{ | | {{Mapping| 593 940 1377 1665 }} | ||
| | | −0.1015 | ||
| 0.0669 | | 0.0669 | ||
| 3.31 | | 3.31 | ||
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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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| 435.08 | | 435.08 | ||
| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor (temperament)|Supermajor]] | ||
|- | |- | ||
| 1 | | 1 | ||
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| [[Whoosh]] | | [[Whoosh]] | ||
|} | |} | ||
<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 == | |||
; [[Francium]] | |||
* "theshocks" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/3EmJ9swIvLJ8NPLvT7qnV4 Spotify] | [https://francium223.bandcamp.com/track/theshocks Bandcamp] | [https://www.youtube.com/watch?v=fwgy5bpHh5U YouTube] – in Vulture[13], 593edo tuning | |||
[[Category:Listen]] | |||