653edo: Difference between revisions

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{{Infobox ET
| Prime factorization = 653 (prime)
| Step size = 1.83767¢
| Fifth = 382\653 (701.99¢)
| Semitones = 62:49 (113.94¢ : 90.05¢)
| Consistency = 21
}}
{{EDO intro|653}}
{{EDO intro|653}}


== Theory ==
653edo is consistent to the [[21-odd-limit]], tempering out 68719476736000/68630377364883 ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], 65625/65536, and 7656250000000/7625597484987 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 consistent to the [[21-odd-limit]], tempering out 68719476736000/68630377364883 ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], 65625/65536, and 7656250000000/7625597484987 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.


=== Prime harmonics ===
{{Harmonics in equal|653|columns=11}}
=== Miscellaneous properties ===
653edo is the 119th [[prime EDO]].
653edo is the 119th [[prime EDO]].


{{Harmonics in equal|653|columns=11}}
== Regular temperament properties ==
{| 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
| {{monzo| 1035 -653 }}
| [{{val| 653 1035 }}]
| -0.0113
| 0.0113
| 0.61
|-
| 2.3.5
| {{monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }}
| [{{val| 653 1035 1516 }}]
| +0.0503
| 0.0875
| 4.76
|-
| 2.3.5.7
| 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }}
| [{{val| 653 1035 1516 1833 }}]
| +0.0709
| 0.0838
| 4.56
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617
| [{{val| 653 1035 1516 1833 2259 }}]
| +0.0576
| 0.0795
| 4.33
|-
| 2.3.5.7.11.13
| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536
| [{{val| 653 1035 1516 1833 2259 2416 }}]
| +0.0801
| 0.0882
| 4.80
|-
| 2.3.5.7.11.13.17
| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 10985/10976, 11271/11264
| [{{val| 653 1035 1516 1833 2259 2416 2669 }}]
| +0.0759
| 0.0823
| 4.48
|-
| 2.3.5.7.11.13.17.19
| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400
| [{{val| 653 1035 1516 1833 2259 2416 2669 2774 }}]
| +0.0608
| 0.0867
| 4.72
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per Octave
! Generator<br>(Reduced)
! Cents<br>(Reduced)
! Associated<br>Ratio
! Temperaments
|-
| 1
| 21\653
| 38.59
| 45/44
| [[Hemitert]]
|-
| 1
| 42\653
| 77.18
| 256/245
| [[Tertiaseptal]]
|-
| 1
| 172/653
| 316.08
| 6/5
| [[Counterhanson]]
|-
| 1
| 308/653
| 566.00
| 81920/59049
| [[Tricot]]
|}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 01:49, 30 September 2022

← 652edo 653edo 654edo →
Prime factorization 653 (prime)
Step size 1.83767 ¢ 
Fifth 382\653 (701.991 ¢)
Semitones (A1:m2) 62:49 (113.9 ¢ : 90.05 ¢)
Consistency limit 21
Distinct consistency limit 21

Template:EDO intro

Theory

653edo is consistent to the 21-odd-limit, tempering out 68719476736000/68630377364883 (tricot comma) and [-20 -24 25⟩ (counterhanson comma) in the 5-limit; 2401/2400, 65625/65536, and 7656250000000/7625597484987 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.

Prime harmonics

Approximation of prime harmonics in 653edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.036 -0.403 -0.373 -0.016 -0.711 -0.208 +0.190 +0.210 -0.481 -0.166
Relative (%) +0.0 +1.9 -21.9 -20.3 -0.9 -38.7 -11.3 +10.3 +11.4 -26.2 -9.0
Steps
(reduced) 		653
(0) 		1035
(382) 		1516
(210) 		1833
(527) 		2259
(300) 		2416
(457) 		2669
(57) 		2774
(162) 		2954
(342) 		3172
(560) 		3235
(623)

Miscellaneous properties

653edo is the 119th prime EDO.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [1035 -653⟩ [⟨653 1035]] -0.0113 0.0113 0.61
2.3.5 [39 -29 3⟩, [-20 -24 25⟩ [⟨653 1035 1516]] +0.0503 0.0875 4.76
2.3.5.7 2401/2400, 65625/65536, [7 -27 13 2⟩ [⟨653 1035 1516 1833]] +0.0709 0.0838 4.56
2.3.5.7.11 2401/2400, 3025/3024, 65625/65536, 1953125/1948617 [⟨653 1035 1516 1833 2259]] +0.0576 0.0795 4.33
2.3.5.7.11.13 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536 [⟨653 1035 1516 1833 2259 2416]] +0.0801 0.0882 4.80
2.3.5.7.11.13.17 1225/1224, 2058/2057, 2080/2079, 2401/2400, 10985/10976, 11271/11264 [⟨653 1035 1516 1833 2259 2416 2669]] +0.0759 0.0823 4.48
2.3.5.7.11.13.17.19 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400 [⟨653 1035 1516 1833 2259 2416 2669 2774]] +0.0608 0.0867 4.72

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per Octave 		Generator
(Reduced) 		Cents
(Reduced) 		Associated
Ratio 		Temperaments
1 21\653 38.59 45/44 Hemitert
1 42\653 77.18 256/245 Tertiaseptal
1 172/653 316.08 6/5 Counterhanson
1 308/653 566.00 81920/59049 Tricot
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