397edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|397}}
{{ED intro}}


== Theory ==
== Theory ==
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
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| {{monzo| -629 397 }}
| {{monzo| -629 397 }}
| {{mapping| 397 629 }}
| {{mapping| 397 629 }}
| 0.2194
| +0.2194
| 0.2195
| 0.2195
| 7.26
| 7.26
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| 129140163/128000000, {{monzo| 55 -1 -23 }}
| 129140163/128000000, {{monzo| 55 -1 -23 }}
| {{mapping| 397 629 922 }}
| {{mapping| 397 629 922 }}
| 0.0618
| +0.0618
| 0.2859
| 0.2859
| 9.46
| 9.46
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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
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Cotritone]] (397cd)
| [[Cotritone]] (397cd)
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Music ==
== Music ==