593edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|593}} == Theory == 593et is consistent to the 9-odd-limit. It tempers out 4375/4374, 52734375/52706752 and 3276800000/3268642167 in the..."
 
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}}
{{EDO intro|593}}
{{ED intro}}


== Theory ==
== Theory ==
593et is [[consistent]] to the [[9-odd-limit]]. It tempers out [[4375/4374]], 52734375/52706752 and 3276800000/3268642167 in the 7-limit, [[support]]ing [[speric]], [[garischismic]], [[decovulture]], [[septimal vulture]] and [[squarschmidt]].  
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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|940 -593}}
! rowspan="2" | [[Comma list]]
|{{mapping|593 940}}
! rowspan="2" | [[Mapping]]
| -0.0748
! 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
| −0.0780
| 0.0613
| 0.0613
| 3.03
| 3.03
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 52734375/52706752, 3276800000/3268642167
| 4375/4374, 33554432/33480783, 52734375/52706752
|{{mapping|593 940 1377 1665}}
| {{Mapping| 593 940 1377 1665 }}
| -0.1015
| −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>Ratio*
! 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 (temperament)|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 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


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Listen]]

Latest revision as of 13:30, 13 March 2026

← 592edo 593edo 594edo →
Prime factorization 593 (prime)
Step size 2.02361 ¢ 
Fifth 347\593 (702.192 ¢)
Semitones (A1:m2) 57:44 (115.3 ¢ : 89.04 ¢)
Consistency limit 9
Distinct consistency limit 9

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

Approximation of prime harmonics in 593edo
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

Table of rank-2 temperaments by generator
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

Music

Francium
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