624edo: Difference between revisions

m Music: -redundant bold; +year
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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
Line 34: Line 26:
| {{monzo| 23 6 -14 }}, {{monzo| -69 45 -1 }}
| {{monzo| 23 6 -14 }}, {{monzo| -69 45 -1 }}
| {{mapping| 624 989 1449 }}
| {{mapping| 624 989 1449 }}
| -0.0256
| &minus;0.0256
| 0.0510
| 0.0510
| 2.65
| 2.65
Line 41: Line 33:
| 250047/250000, 2460375/2458624, {{monzo| 27 0 -8 -3 }}
| 250047/250000, 2460375/2458624, {{monzo| 27 0 -8 -3 }}
| {{mapping| 624 989 1449 1752 }}
| {{mapping| 624 989 1449 1752 }}
| -0.0552
| &minus;0.0552
| 0.0678
| 0.0678
| 3.52
| 3.52
Line 48: Line 40:
| 9801/9800, 46656/46585, 131072/130977, 151263/151250
| 9801/9800, 46656/46585, 131072/130977, 151263/151250
| {{mapping| 624 989 1449 1752 2159 }}
| {{mapping| 624 989 1449 1752 2159 }}
| -0.0792
| &minus;0.0792
| 0.0772
| 0.0772
| 4.02
| 4.02
Line 55: Line 47:
| 1716/1715, 2080/2079, 4096/4095, 34398/34375, 39366/39325
| 1716/1715, 2080/2079, 4096/4095, 34398/34375, 39366/39325
| {{mapping| 624 989 1449 1752 2159 2309 }}
| {{mapping| 624 989 1449 1752 2159 2309 }}
| -0.0595
| &minus;0.0595
| 0.0831
| 0.0831
| 4.32
| 4.32
Line 62: Line 54:
| 936/935, 1701/1700, 1716/1715, 2025/2023, 4096/4095, 11016/11011
| 936/935, 1701/1700, 1716/1715, 2025/2023, 4096/4095, 11016/11011
| {{mapping| 624 989 1449 1752 2159 2309 2551 }}
| {{mapping| 624 989 1449 1752 2159 2309 2551 }}
| -0.0795
| &minus;0.0795
| 0.0911
| 0.0911
| 4.74
| 4.74
Line 69: Line 61:
| 936/935, 1521/1520, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 11016/11011
| 936/935, 1521/1520, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 11016/11011
| {{mapping| 624 989 1449 1752 2159 2309 2551 2651 }}
| {{mapping| 624 989 1449 1752 2159 2309 2551 2651 }}
| -0.0861
| &minus;0.0861
| 0.0870
| 0.0870
| 4.53
| 4.53
|}
{{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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|-
|-
| 6
| 6
| 177\624<br>(31\624)
| 177\624<br />(31\624)
| 340.38<br>(59.62)
| 340.38<br />(59.62)
| 162/133<br>(88/85)
| 162/133<br />(88/85)
| [[Semiseptichrome]]
| [[Semiseptichrome]]
|-
|-
| 12
| 12
| 259\624<br>(1\624)
| 259\624<br />(1\624)
| 498.08<br>(1.92)
| 498.08<br />(1.92)
| 4/3<br>(32805/32768)
| 4/3<br />(32805/32768)
| [[Atomic]]
| [[Atomic]]
|-
|-
| 13
| 13
| 259\624<br>(19\624)
| 259\624<br />(19\624)
| 498.08<br>(36.54)
| 498.08<br />(36.54)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Aluminium]]
| [[Aluminium]]
|-
|-
| 16
| 16
| 259\624<br>(14\624)
| 259\624<br />(14\624)
| 498.08<br>(48.077)
| 498.08<br />(48.077)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Sulfur]]
| [[Sulfur]]
|-
|-
| 24
| 24
| 303\624<br>(17\624)
| 303\624<br />(17\624)
| 582.692<br>(32.692)
| 582.692<br />(32.692)
| 7/5<br>(?)
| 7/5<br />(?)
| [[Chromium]]
| [[Chromium]]
|-
|-
| 26
| 26
| 259\624<br>(19\624)
| 259\624<br />(19\624)
| 498.08<br>(36.54)
| 498.08<br />(36.54)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Iron]]
| [[Iron]]
|}
{{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}}


== Music ==
== Music ==