357edo: 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
| 2.3
| {{monzo| 566 -357 }}
| {{monzo| 566 -357 }}
| {{mapping| 357 566 }}
| {{mapping| 357 566 }}
| -0.1786
| &minus;0.1786
| 0.1785
| 0.1785
| 5.31
| 5.31
Line 34: Line 26:
| 1600000/1594323, {{monzo| 61 4 -29 }}
| 1600000/1594323, {{monzo| 61 4 -29 }}
| {{mapping| 357 566 829 }}
| {{mapping| 357 566 829 }}
| -0.1536
| &minus;0.1536
| 0.1500
| 0.1500
| 4.46
| 4.46
Line 41: Line 33:
| 10976/10935, 235298/234375, 2100875/2097152
| 10976/10935, 235298/234375, 2100875/2097152
| {{mapping| 357 566 829 1002 }}
| {{mapping| 357 566 829 1002 }}
| -0.0477
| &minus;0.0477
| 0.2248
| 0.2248
| 6.69
| 6.69
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| 3025/3024, 5632/5625, 10976/10935, 102487/102400
| 3025/3024, 5632/5625, 10976/10935, 102487/102400
| {{mapping| 357 566 829 1002 1235 }}
| {{mapping| 357 566 829 1002 1235 }}
| -0.0348
| &minus;0.0348
| 0.2027
| 0.2027
| 6.03
| 6.03
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| 676/675, 1001/1000, 3025/3024, 4096/4095, 10976/10935
| 676/675, 1001/1000, 3025/3024, 4096/4095, 10976/10935
| {{mapping| 357 566 829 1002 1235 1321 }}
| {{mapping| 357 566 829 1002 1235 1321 }}
| -0.0204
| &minus;0.0204
| 0.1879
| 0.1879
| 5.59
| 5.59
|}
{{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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| 192/175
| 192/175
| [[Pnict]]
| [[Pnict]]
|}
{{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}}