432edo: Difference between revisions

ArrowHead294 (talk | contribs)
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Francium (talk | contribs)
m changed EDO intro to ED intro
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|432}}
{{ED intro}}


== Theory ==
== Theory ==
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== Regular temperament properties ==
== Regular temperament properties ==
{{comma basis begin}}
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 685 -432 }}
| {{monzo| 685 -432 }}
| {{mapping| 432 685 }}
| {{mapping| 432 685 }}
| &minus;0.2596
| −0.2596
| 0.2595
| 0.2595
| 9.34
| 9.34
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| {{monzo| 41 -20 -4 }}, {{monzo| -3 -23 17 }}
| {{monzo| 41 -20 -4 }}, {{monzo| -3 -23 17 }}
| {{mapping| 432 685 1003 }}
| {{mapping| 432 685 1003 }}
| &minus;0.1440
| −0.1440
| 0.2676
| 0.2676
| 9.63
| 9.63
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| 5120/5103, 703125/702464, 6565234375/6530347008
| 5120/5103, 703125/702464, 6565234375/6530347008
| {{mapping| 432 685 1003 1213 }}
| {{mapping| 432 685 1003 1213 }}
| &minus;0.1631
| −0.1631
| 0.2341
| 0.2341
| 8.43
| 8.43
{{comma basis end}}
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{{rank-2 begin}}
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
|-
| 1
| 1
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| 4/3
| 4/3
| [[Undim]]
| [[Undim]]
{{rank-2 end}}
|}
{{orf}}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct