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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 8ve<br>Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 2452 -1547 }}
| {{monzo| 2452 -1547 }}
| {{mapping| 1547 2542 }}
| {{mapping| 1547 2542 }}
| -0.015
| &minus;0.015
| 0.015
| 0.015
| 1.99
| 1.99
Line 38: Line 30:
| {{monzo| -52 -17 34 }}, {{monzo| 40 -56 21 }}
| {{monzo| -52 -17 34 }}, {{monzo| 40 -56 21 }}
| {{mapping| 1547 2542 3592 }}
| {{mapping| 1547 2542 3592 }}
| -0.008
| &minus;0.008
| 0.017
| 0.017
| 2.14
| 2.14
Line 45: Line 37:
| 4375/4374, {{monzo| -1 4 11 -11 }}, {{monzo| 46 -14 -3  -6 }}
| 4375/4374, {{monzo| -1 4 11 -11 }}, {{monzo| 46 -14 -3  -6 }}
| {{mapping| 1547 2542 3592 4343 }}
| {{mapping| 1547 2542 3592 4343 }}
| -0.007
| &minus;0.007
| 0.014
| 0.014
| 1.86
| 1.86
Line 52: Line 44:
| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325
| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325
| {{mapping| 1547 2542 3592 4343 5352 }}
| {{mapping| 1547 2542 3592 4343 5352 }}
| -0.017
| &minus;0.017
| 0.024
| 0.024
| 3.10
| 3.10
Line 59: Line 51:
| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683
| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683
| {{mapping| 1547 2542 3592 4343 5352 5725 }}
| {{mapping| 1547 2542 3592 4343 5352 5725 }}
| -0.029
| &minus;0.029
| 0.034
| 0.034
| 4.42
| 4.42
|}
{{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
Line 87: Line 72:
|-
|-
| 7
| 7
| 670\1547<br>(7\1547)
| 670\1547<br />(7\1547)
| 519.715<br>(5.429)
| 519.715<br />(5.429)
| 27/20<br>(325/324)
| 27/20<br />(325/324)
| [[Brahmagupta]] (7-limit)
| [[Brahmagupta]] (7-limit)
|-
|-
Line 99: Line 84:
|-
|-
| 13
| 13
| 642\1547<br>(47\1547)
| 642\1547<br />(47\1547)
| 497.996<br>(36.458)
| 497.996<br />(36.458)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Aluminium]]
| [[Aluminium]]
|-
|-
| 17
| 17
| 321\1547<br>(48\1547)
| 321\1547<br />(48\1547)
| 248.998<br>(37.233)
| 248.998<br />(37.233)
| {{monzo| -23 5 9 -2 }}<br>(100352/98415)
| {{monzo| -23 5 9 -2 }}<br />(100352/98415)
| [[Chlorine]]
| [[Chlorine]]
|-
|-
| 91
| 91
| 642\1547<br>(13\1547)
| 642\1547<br />(13\1547)
| 497.996<br>(10.084)
| 497.996<br />(10.084)
| 4/3<br>(176/175)
| 4/3<br />(176/175)
| [[Protactinium]]
| [[Protactinium]]
|}
{{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 ==
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