593edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
593edo is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[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 === | ||
| 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" | ||
|- | |- | ||
|2.3 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|940 -593}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|593 940}} | ! rowspan="2" | [[Mapping]] | ||
| | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 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}} | | {{monzo| 24 -21 4 }}, {{monzo| 37 25 -33 }} | ||
|{{mapping|593 940 1377}} | | {{mapping| 593 940 1377 }} | ||
| | | −0.0780 | ||
| 0.0613 | | 0.0613 | ||
| 3.03 | | 3.03 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 52734375/52706752 | | 4375/4374, 33554432/33480783, 52734375/52706752 | ||
|{{mapping|593 940 1377 1665}} | | {{mapping| 593 940 1377 1665 }} | ||
| | | −0.1015 | ||
| 0.0669 | | 0.0669 | ||
| 3.31 | | 3.31 | ||
| Line 46: | Line 47: | ||
=== 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 | ||
|- | |- | ||
|1 | | 1 | ||
|196\593 | | 196\593 | ||
|396.63 | | 396.63 | ||
|98304/78125 | | 98304/78125 | ||
|[[Squarschmidt]] | | [[Squarschmidt]] | ||
|- | |- | ||
|1 | | 1 | ||
|215\593 | | 215\593 | ||
|435.08 | | 435.08 | ||
|9/7 | | 9/7 | ||
|[[Supermajor]] | | [[Supermajor]] | ||
|- | |- | ||
|1 | | 1 | ||
|235\593 | | 235\593 | ||
|475.55 | | 475.55 | ||
|320/243 | | 320/243 | ||
|[[Vulture]] | | [[Vulture]] | ||
|- | |- | ||
|1 | | 1 | ||
|277\593 | | 246\593 | ||
|560.54 | | 497.81 | ||
|864/625 | | 4/3 | ||
|[[Whoosh]] | | [[Gary]] | ||
|- | |||
| 1 | |||
| 277\593 | |||
| 560.54 | |||
| 864/625 | |||
| [[Whoosh]] | |||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|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] – vulture[13] in 593edo tuning | |||
[[Category:Listen]] | |||