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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|433}}
{{ED intro}}
 
== Theory ==
== Theory ==
433et tempers out 4096000/4084101, 95703125/95551488 and [[1640558367/1638400000]] in the 7-limit; 161280/161051, 25165824/25109315, 1019215872/1019046875, [[4000/3993]], 2359296/2358125, [[6250/6237]], 180224/180075, 17537553/17500000, [[3025/3024]] and 1362944/1361367 in the 11-limit.
443edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. To start with, the [[patent val]] {{val| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val| 433 686 1005 '''1215''' }} are worth considering.
===Subsets and supersets===
 
433edo is the 84th [[prime edo]].
Using the patent val, it [[tempering out|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.
===Odd harmonics===
 
=== Odd harmonics ===
{{Harmonics in equal|433}}
{{Harmonics in equal|433}}
==Regular temperament properties==
 
=== Subsets and supersets ===
433edo is the 84th [[prime edo]]. It might be interesting due to being the smallest subset edo of the nanotemperament [[2901533edo]], an extremely high-precision/complexity [[microtemperament]].
 
== 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]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
|2.3
! [[TE error|Absolute]] (¢)
|{{monzo|-686 433}}
! [[TE simple badness|Relative]] (%)
|{{val|433 686}}
|-
| 0.2525
| 2.3
| {{monzo| -686 433 }}
| {{mapping| 433 686 }}
| +0.2525
| 0.2525
| 0.2525
| 9.11
| 9.11
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-21 3 7}}, {{monzo|-29 52 -23}}
| 2109375/2097152, {{monzo| -29 52 -23 }}
|{{val|433 686 1005}}
| {{mapping| 433 686 1005 }}
| 0.3254
| +0.3254
| 0.2306
| 0.2306
| 8.32
| 8.32
|-
|-
|2.3.5.7
| 2.3.5.7
|19683/19600, 4096000/4084101, 2109375/2097152
| 19683/19600, 4096000/4084101, 2109375/2097152
|{{val|433 686 1005 1216}}
| {{mapping| 433 686 1005 1216 }}
| 0.1414
| +0.1414
| 0.3759
| 0.3759
| 13.56
| 13.56
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|3025/3024, 6250/6237, 30375/30184, 180224/180075
| 3025/3024, 6250/6237, 30375/30184, 180224/180075
|{{val|433 686 1005 1216 1498}}
| {{mapping| 433 686 1005 1216 1498 }}
| 0.1026
| +0.1026
| 0.3451
| 0.3451
| 12.45
| 12.45
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|2080/2079, 625/624, 3025/3024, 18954/18865, 41472/41405
| 2080/2079, 625/624, 3025/3024, 18954/18865, 41472/41405
|{{val|433 686 1005 1216 1498 1602}}
| {{mapping| 433 686 1005 1216 1498 1602 }}
| 0.1217
| +0.1217
| 0.3179
| 0.3179
| 11.47
| 11.47
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|2080/2079, 375/374, 715/714, 936/935, 1377/1372, 76032/75803
| 2080/2079, 375/374, 715/714, 936/935, 1377/1372, 76032/75803
|{{val|433 686 1005 1216 1498 1602 1770}}
| {{mapping| 433 686 1005 1216 1498 1602 1770 }}
| 0.0919
| +0.0919
| 0.3033
| 0.3033
| 10.94
| 10.94
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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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|98\433
| 98\433
|271.594
| 271.594
|75/64
| 75/64
|[[Orson]]
| [[Orson]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* [https://www.youtube.com/watch?v=M4CFR4yYF_U ''sleeping as we don't know''] (2023)


==Music==
[[Category:Listen]]
* [https://www.youtube.com/watch?v=M4CFR4yYF_U sleeping as we don't know] by Francium
Retrieved from "https://en.xen.wiki/w/433edo"