369edo: Difference between revisions

Cleanup; clarify the title row of the rank-2 temp table; -redundant categories
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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
| {{monzo| 32 -7 -9 }}, {{monzo| 1 -27 18 }}
| {{monzo| 32 -7 -9 }}, {{monzo| 1 -27 18 }}
| {{mapping| 369 585 857 }}
| {{mapping| 369 585 857 }}
| -0.1991
| &minus;0.1991
| 0.1409
| 0.1409
| 4.33
| 4.33
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| 2401/2400, 4375/4374, {{monzo| 32 -7 -9 }}
| 2401/2400, 4375/4374, {{monzo| 32 -7 -9 }}
| {{mapping| 369 585 857 1036 }}
| {{mapping| 369 585 857 1036 }}
| -0.1743
| &minus;0.1743
| 0.1294
| 0.1294
| 3.98
| 3.98
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| 2401/2400, 4000/3993, 4375/4374, 5632/5625
| 2401/2400, 4000/3993, 4375/4374, 5632/5625
| {{mapping| 369 585 857 1036 1277 }}
| {{mapping| 369 585 857 1036 1277 }}
| -0.2277
| &minus;0.2277
| 0.1576
| 0.1576
| 4.85
| 4.85
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| 1575/1573, 2080/2079, 2200/2197, 2401/2400, 3584/3575
| 1575/1573, 2080/2079, 2200/2197, 2401/2400, 3584/3575
| {{mapping| 369 585 857 1036 1277 1366 }} (369f)
| {{mapping| 369 585 857 1036 1277 1366 }} (369f)
| -0.2685
| &minus;0.2685
| 0.1703
| 0.1703
| 5.24
| 5.24
|}
{{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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|-
|-
| 9
| 9
| 77\369<br>(5\369)
| 77\369<br />(5\369)
| 250.41<br>(16.26)
| 250.41<br />(16.26)
| 140/121<br>(100/99)
| 140/121<br />(100/99)
| [[Semiennealimmal]]
| [[Semiennealimmal]]
|-
|-
| 9
| 9
| 97\369<br>(15\369)
| 97\369<br />(15\369)
| 315.45<br>(48.78)
| 315.45<br />(48.78)
| 6/5<br>(36/35)
| 6/5<br />(36/35)
| [[Ennealimmal]]
| [[Ennealimmal]]
|-
|-
| 9
| 9
| 68\369<br>(14\369)
| 68\369<br />(14\369)
| 221.14<br>(45.53)
| 221.14<br />(45.53)
| 25/22<br>(77/75)
| 25/22<br />(77/75)
| [[Quadraennealimmal]]
| [[Quadraennealimmal]]
|-
|-
| 41
| 41
| 55\369<br>(1\369)
| 55\369<br />(1\369)
| 178.86<br>(3.25)
| 178.86<br />(3.25)
| 567/512<br>(352/351)
| 567/512<br />(352/351)
| [[Hemicountercomp]]
| [[Hemicountercomp]]
|}
{{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:Semiporwellismic]]
[[Category:Semiporwellismic]]