653edo: Difference between revisions

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== Theory ==

653edo is [[distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo| 39 -29 3 }} ([[~~tricot~~ comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.

653edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], and the [[23-odd-limit]] if not for the [[23/13]] and its [[octave complement]] barely missing the mark. Although the [[25/1|25]] is flat enough to create more inconsistencies, the [[29/1|29]] and [[31/1|31]] blend well with the lower primes, together making it a fairly strong [[31-limit]] system.

As an equal temperament, it [[tempering out|tempers out]] {{monzo| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]]; [[875/874]], [[1105/1104]] among others in the [[23-limit]].

=== Prime harmonics ===

{{Harmonics in equal|653|columns=10|start=12|collapsed=true|title=Approximation of prime harmonics in 653edo (continued)}}

{{Harmonics in equal|653|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 653edo (continued)}}

=== Subsets and supersets ===

653edo is the 119th [[prime edo]].

653edo is the 119th [[prime edo]]. As such, it does not contain any nontrivial subset edo.

== Regular temperament properties ==

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! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve stretch (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning error

|-

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|-

| 2.3

| {{~~monzo~~| 1035 -653 }}

| {{Monzo| 1035 -653 }}

| {{~~mapping~~| 653 1035 }}

| {{Mapping| 653 1035 }}

| −0.0113

| 0.0113

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|-

| 2.3.5

| {{~~monzo~~| 39 -29 3 }}, {{monzo| -20 -24 25 }}

| {{Monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }}

| {{~~mapping~~| 653 1035 1516 }}

| {{Mapping| 653 1035 1516 }}

| +0.0503

| 0.0875

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| 2.3.5.7

| 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }}

| {{~~mapping~~| 653 1035 1516 1833 }}

| {{Mapping| 653 1035 1516 1833 }}

| +0.0709

| 0.0838

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| 2.3.5.7.11

| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617

| {{~~mapping~~| 653 1035 1516 1833 2259 }}

| {{Mapping| 653 1035 1516 1833 2259 }}

| +0.0576

| 0.0795

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| 2.3.5.7.11.13

| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536

| {{~~mapping~~| 653 1035 1516 1833 2259 2416 }}

| {{Mapping| 653 1035 1516 1833 2259 2416 }}

| +0.0801

| 0.0882

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| 2.3.5.7.11.13.17

| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976

| {{~~mapping~~| 653 1035 1516 1833 2259 2416 2669 }}

| {{Mapping| 653 1035 1516 1833 2259 2416 2669 }}

| +0.0759

| 0.0823

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| 2.3.5.7.11.13.17.19

| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400

| {{~~mapping~~| 653 1035 1516 1833 2259 2416 2669 2774 }}

| {{Mapping| 653 1035 1516 1833 2259 2416 2669 2774 }}

| +0.0608

| 0.0867

| 4.72

|-

| 2.3.5.7.11.13.17.19.23

| 875/874, 1105/1104, 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079

| {{Mapping| 653 1035 1516 1833 2259 2416 2669 2774 2954 }}

| +0.0489

| 0.0884

| 4.81

|}

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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Associated ratio*

! Temperaments

|-

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| 566.00

| 81920/59049

| [[~~Tricot~~]]

| [[Alphatricot]]

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<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]]

* "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] | [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] | [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|653}}
+{{ED intro}}
 == Theory ==
-edo is [[distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo| 39 -29 3 }} ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.
+edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], and the [[23-odd-limit]] if not for the [[23/13]] and its [[octave complement]] barely missing the mark. Although the [[25/1|25]] is flat enough to create more inconsistencies, the [[29/1|29]] and [[31/1|31]] blend well with the lower primes, together making it a fairly strong [[31-limit]] system.
+As an equal temperament, it [[tempering out|tempers out]] {{monzo| 39 -29 3 }} ([[alphatricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the [[5-limit]]; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} in the [[7-limit]]; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the [[11-limit]]; [[2080/2079]], [[4459/4455]], [[6656/6655]], [[10985/10976]], and 170625/170368 in the [[13-limit]]; [[1225/1224]], [[2058/2057]], [[2431/2430]], [[2500/2499]], [[4914/4913]], and 11271/11264 in the [[17-limit]]; [[1445/1444]], [[1521/1520]], [[1540/1539]], [[1729/1728]], [[3136/3135]], [[4200/4199]], and 4394/4389 in the [[19-limit]]; [[875/874]], [[1105/1104]] among others in the [[23-limit]].
 === Prime harmonics ===
 {{Harmonics in equal|653|columns=11}}
-{{Harmonics in equal|653|columns=10|start=12|collapsed=true|title=Approximation of prime harmonics in 653edo (continued)}}
+{{Harmonics in equal|653|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 653edo (continued)}}
 === Subsets and supersets ===
-edo is the 119th [[prime edo]].
+edo is the 119th [[prime edo]]. As such, it does not contain any nontrivial subset edo.
 == Regular temperament properties ==
@@ Line 18: / Line 20: @@
 ! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br />8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve stretch (¢)
 ! colspan="2" | Tuning error
 |-
@@ Line 25: / Line 27: @@
 |-
 | 2.3
-| {{monzo| 1035 -653 }}
+| {{Monzo| 1035 -653 }}
-| {{mapping| 653 1035 }}
+| {{Mapping| 653 1035 }}
 | −0.0113
 | 0.0113
@@ Line 32: / Line 34: @@
 |-
 | 2.3.5
-| {{monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }}
+| {{Monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }}
-| {{mapping| 653 1035 1516 }}
+| {{Mapping| 653 1035 1516 }}
 | +0.0503
 | 0.0875
@@ Line 40: / Line 42: @@
 | 2.3.5.7
 | 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }}
-| {{mapping| 653 1035 1516 1833 }}
+| {{Mapping| 653 1035 1516 1833 }}
 | +0.0709
 | 0.0838
@@ Line 47: / Line 49: @@
 | 2.3.5.7.11
 | 2401/2400, 3025/3024, 65625/65536, 1953125/1948617
-| {{mapping| 653 1035 1516 1833 2259 }}
+| {{Mapping| 653 1035 1516 1833 2259 }}
 | +0.0576
 | 0.0795
@@ Line 54: / Line 56: @@
 | 2.3.5.7.11.13
 | 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536
-| {{mapping| 653 1035 1516 1833 2259 2416 }}
+| {{Mapping| 653 1035 1516 1833 2259 2416 }}
 | +0.0801
 | 0.0882
@@ Line 61: / Line 63: @@
 | 2.3.5.7.11.13.17
 | 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976
-| {{mapping| 653 1035 1516 1833 2259 2416 2669 }}
+| {{Mapping| 653 1035 1516 1833 2259 2416 2669 }}
 | +0.0759
 | 0.0823
@@ Line 68: / Line 70: @@
 | 2.3.5.7.11.13.17.19
 | 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400
-| {{mapping| 653 1035 1516 1833 2259 2416 2669 2774 }}
+| {{Mapping| 653 1035 1516 1833 2259 2416 2669 2774 }}
 | +0.0608
 | 0.0867
 | 4.72
+|-
+| 2.3.5.7.11.13.17.19.23
+| 875/874, 1105/1104, 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079
+| {{Mapping| 653 1035 1516 1833 2259 2416 2669 2774 2954 }}
+| +0.0489
+| 0.0884
+| 4.81
 |}
@@ Line 78: / Line 87: @@
 |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
 |-
-! Periods<br />per 8ve
+! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br />ratio*
+! Associated<br>ratio*
 ! Temperaments
 |-
@@ Line 106: / Line 115: @@
 | 566.00
 | 81920/59049
-| [[Tricot]]
+| [[Alphatricot]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<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]]
 * "Seamless Toggle-Style" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/6nGhaXwzE85erYFtxGB9Dt Spotify] | [https://francium223.bandcamp.com/track/seamless-toggle-style Bandcamp] | [https://www.youtube.com/watch?v=TQP9W0vIvqw YouTube]