315edo: Difference between revisions

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Francium (talk | contribs)
m changed EDO intro to ED intro
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|315}}
{{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|-499 315}}
| {{monzo|-499 315}}
| {{mapping|315 499}}
| {{mapping|315 499}}
| 0.3163
| +0.3163
| 0.3164
| 0.3164
| 8.31
| 8.31
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| {{monzo| -27 -2 13 }}, {{monzo| -28 25 -5 }}
| {{monzo| -27 -2 13 }}, {{monzo| -28 25 -5 }}
| {{mapping| 315 499 731 }}
| {{mapping| 315 499 731 }}
| 0.4337
| +0.4337
| 0.3071
| 0.3071
| 8.06
| 8.06
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| 2401/2400, 4375/4374, {{monzo| -21 6 11 -5 }}
| 2401/2400, 4375/4374, {{monzo| -21 6 11 -5 }}
| {{mapping| 315 499 731 884 }}
| {{mapping| 315 499 731 884 }}
| 0.4328
| +0.4328
| 0.2659
| 0.2659
| 6.98
| 6.98
{{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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| 6/5<br />(36/35)
| 6/5<br />(36/35)
| [[Ennealimmal]]
| [[Ennealimmal]]
{{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