509edo: 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| 807 -509 }}
| {{monzo| 807 -509 }}
| {{mapping| 509 807 }}
| {{mapping| 509 807 }}
| -0.1890
| &minus;0.1890
| 0.1889
| 0.1889
| 8.01
| 8.01
Line 34: Line 26:
| {{monzo| 9 -13 5 }}, {{monzo| 93 -3 -38 }}
| {{monzo| 9 -13 5 }}, {{monzo| 93 -3 -38 }}
| {{mapping| 509 807 1182 }}
| {{mapping| 509 807 1182 }}
| -0.1729
| &minus;0.1729
| 0.1559
| 0.1559
| 6.61
| 6.61
Line 41: Line 33:
| 2401/2400, 1600000/1594323, 29360128/29296875
| 2401/2400, 1600000/1594323, 29360128/29296875
| {{mapping| 509 807 1182 1429 }}
| {{mapping| 509 807 1182 1429 }}
| -0.1415
| &minus;0.1415
| 0.1456
| 0.1456
| 6.18
| 6.18
Line 48: Line 40:
| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323
| 2401/2400, 3025/3024, 5632/5625, 1600000/1594323
| {{mapping| 509 807 1182 1429 1761 }}
| {{mapping| 509 807 1182 1429 1761 }}
| -0.1335
| &minus;0.1335
| 0.1312
| 0.1312
| 5.57
| 5.57
Line 55: Line 47:
| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625
| 2080/2079, 2200/2197, 2401/2400, 3025/3024, 5632/5625
| {{mapping| 509 807 1182 1429 1761 1884 }}
| {{mapping| 509 807 1182 1429 1761 1884 }}
| -0.1618
| &minus;0.1618
| 0.1354
| 0.1354
| 5.74
| 5.74
Line 62: Line 54:
| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913
| 1225/1224, 2080/2079, 2200/2197, 2401/2400, 2431/2430, 4914/4913
| {{mapping| 509 807 1182 1429 1761 1884 2081 }}
| {{mapping| 509 807 1182 1429 1761 1884 2081 }}
| -0.1784
| &minus;0.1784
| 0.1318
| 0.1318
| 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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| 243/200
| 243/200
| [[Amity]]
| [[Amity]]
|}
{{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 ==