164edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! 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]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3.5
| 2.3.5
| 393216/390625, {{monzo| 24 -21 4 }}
| 393216/390625, {{monzo| 24 -21 4 }}
| {{mapping| 164 260 381 }}
| {{mapping| 164 260 381 }}
| -0.316
| &minus;0.316
| 0.262
| 0.262
| 3.58
| 3.58
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| 676/675, 256000/255879, 393216/390625
| 676/675, 256000/255879, 393216/390625
| {{mapping| 164 260 381 607 }}
| {{mapping| 164 260 381 607 }}
| -0.300
| &minus;0.300
| 0.229
| 0.229
| 3.13
| 3.13
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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|-
|-
| 4
| 4
| 68\164<br>(14\164)
| 68\164<br />(14\164)
| 497.56<br>(102.44)
| 497.56<br />(102.44)
| 4/3<br>(35/33)
| 4/3<br />(35/33)
| [[Undim]] (164deff) / [[unlit]] (164f)
| [[Undim]] (164deff) / [[unlit]] (164f)
|-
|-
| 41
| 41
| 53\164<br>(1\164)
| 53\164<br />(1\164)
| 387.80<br>(7.32)
| 387.80<br />(7.32)
| 5/4<br>(32805/32768)
| 5/4<br />(32805/32768)
| [[Countercomp]]
| [[Countercomp]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


[[Category:Würschmidt]]
[[Category:Würschmidt]]