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{{Infobox ET
| Prime factorization = 643 (prime)
| Step size = 1.86625¢
| Fifth = 376\643 (701.71¢)
| Semitones = 60:49 (111.98¢ : 91.45¢)
| Consistency = 21
}}
{{EDO intro|643}}
{{EDO intro|643}}


== Theory ==
643edo is uniquely [[consistent]] to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], 2431/2430 and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.
643edo is uniquely [[consistent]] to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], 2431/2430 and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.


=== Prime harmonics ===
{{Harmonics in equal|643|columns=11}}
=== Miscellaneous properties ===
643edo is the 117th [[prime edo]].
643edo is the 117th [[prime edo]].


{{Harmonics in equal|643|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| -1019 643 }}
| [{{val| 643 1019 }}]
| +0.0771
| 0.0771
| 4.13
|-
| 2.3.5
| 32805/32768, {{monzo| 1 99 -68 }}
| [{{val| 643 1019 1493 }}]
| +0.0513
| 0.7270
| 3.90
|-
| 2.3.5.7
| 2401/2400, 32805/32768, {{monzo| 9 21 -17 -1 }}
| [{{val| 643 1019 1493 1805 }}]
| +0.0600
| 0.0647
| 3.47
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 32805/32768, 391314/390625
| [{{val| 643 1019 1493 1805 2224 }}]
| +0.0927
| 0.0874
| 4.68
|-
| 2.3.5.7.11.13
| 1001/1000, 1716/1715, 3025/3024, 4225/4224, 32805/32768
| [{{val| 643 1019 1493 1805 2224 2379 }}]
| +0.1094
| 0.0881
| 4.72
|-
| 2.3.5.7.11.13.17
| 1001/1000, 1089/1088, 1701/1700, 1716/1715, 2601/2600, 4225/4224
| [{{val| 643 1019 1493 1805 2224 2379 2628 }}]
| +0.1094
| 0.0816
| 4.37
|-
| 2.3.5.7.11.13.17.19
| 1001/1000, 1089/1088, 1521/1520, 1701/1700, 1716/1715, 1729/1728, 2601/2600
| [{{val| 643 1019 1493 1805 2224 2379 2628 2731 }}]
| +0.1186
| 0.0801
| 4.29
|}
 
=== 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
| 94\643
| 175.43
| 448/405
| [[Sesquiquartififths]]
|-
| 1
| 267\643
| 498.29
| 4/3
| [[Helmholtz]]
|}


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