337edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|337}}
{{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| -534 337 }}
| {{monzo| -534 337 }}
| {{mapping| 337 534 }}
| {{mapping| 337 534 }}
| 0.1487
| +0.1487
| 0.1487
| 0.1487
| 4.18
| 4.18
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| 15625/15552, {{monzo| -88 57 -1 }}
| 15625/15552, {{monzo| -88 57 -1 }}
| {{mapping| 337 534 782 }}
| {{mapping| 337 534 782 }}
| 0.3495
| +0.3495
| 0.3089
| 0.3089
| 8.67
| 8.67
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| 15625/15552, 16875/16807, 7381125/7340032
| 15625/15552, 16875/16807, 7381125/7340032
| {{mapping| 337 534 782 946 }}
| {{mapping| 337 534 782 946 }}
| 0.2870
| +0.2870
| 0.2886
| 0.2886
| 8.10
| 8.10
{{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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| 14/11
| 14/11
| [[Sqrtphi]] (337, 11-limit)
| [[Sqrtphi]] (337, 11-limit)
{{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


== Music ==
== Music ==