593edo: Difference between revisions
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Preserve the distinction between ET and edo. "Supporting speric" can be better worded as tempering out 2500/2499 in the 2.3.5.7.17 subgroup, same for garischismic and decovulture |
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 === | ||
| 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" | ||
|- | |||
! 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 | ||
| Line 38: | Line 39: | ||
| 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 | ||
| 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 | ||
|- | |- | ||
| Line 63: | Line 65: | ||
| 435.08 | | 435.08 | ||
| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor (temperament)|Supermajor]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 70: | Line 72: | ||
| 320/243 | | 320/243 | ||
| [[Vulture]] | | [[Vulture]] | ||
|- | |||
| 1 | |||
| 246\593 | |||
| 497.81 | |||
| 4/3 | |||
| [[Gary]] | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 77: | Line 85: | ||
| [[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]] | |||
Latest revision as of 13:30, 13 March 2026
| ← 592edo | 593edo | 594edo → |
593 equal divisions of the octave (abbreviated 593edo or 593ed2), also called 593-tone equal temperament (593tet) or 593 equal temperament (593et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 593 equal parts of about 2.02 ¢ each. Each step represents a frequency ratio of 21/593, or the 593rd root of 2.
Theory
593edo is consistent to the 9-odd-limit. As an equal temperament, it tempers out 4375/4374, 33554432/33480783, 52734375/52706752, and 67108864/66976875 in the 7-limit. It supports vulture and squarschmidt. It is also notable in the 2.3.5.7.17 subgroup, tempering out 2500/2499.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.237 | +0.196 | +0.483 | -0.896 | -0.730 | +0.272 | -0.043 | -0.956 | +0.440 | +0.327 |
| Relative (%) | +0.0 | +11.7 | +9.7 | +23.9 | -44.3 | -36.1 | +13.5 | -2.1 | -47.2 | +21.7 | +16.2 | |
| Steps (reduced) |
593 (0) |
940 (347) |
1377 (191) |
1665 (479) |
2051 (272) |
2194 (415) |
2424 (52) |
2519 (147) |
2682 (310) |
2881 (509) |
2938 (566) | |
Subsets and supersets
593edo is the 108th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [940 -593⟩ | [⟨593 940]] | −0.0748 | 0.0748 | 3.70 |
| 2.3.5 | [24 -21 4⟩, [37 25 -33⟩ | [⟨593 940 1377]] | −0.0780 | 0.0613 | 3.03 |
| 2.3.5.7 | 4375/4374, 33554432/33480783, 52734375/52706752 | [⟨593 940 1377 1665]] | −0.1015 | 0.0669 | 3.31 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 196\593 | 396.63 | 98304/78125 | Squarschmidt |
| 1 | 215\593 | 435.08 | 9/7 | Supermajor |
| 1 | 235\593 | 475.55 | 320/243 | Vulture |
| 1 | 246\593 | 497.81 | 4/3 | Gary |
| 1 | 277\593 | 560.54 | 864/625 | Whoosh |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct