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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]]
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