84edo: Difference between revisions

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! #
! #
! Cents
! Cents
! Approximate Ratios*
! Approximate ratios*
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
| 0
| 0
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| D
| D
|}
|}
<nowiki>*</nowiki> as a 2.3.5.7.13.19.23-subgroup temperament
<nowiki />* {{sg|2.3.5.7.13.19.23 subgroup}}


== Notation ==
== Notation ==
=== 4L 5s (gramitonic) notation ===
=== 4L 5s (gramitonic) notation ===
The notation of Orwell[9]. Notes are denoted as LsLsLsLss = JKLMNOPQRJ, and raising and lowering by a chroma (L s), 3 steps in this instance, is denoted by & "amp" and @ "at".  
The notation of Orwell[9]. Notes are denoted as {{nowrap|LsLsLsLss {{=}} JKLMNOPQRJ}}, and raising and lowering by a chroma {{nowrap|(L &minus; s)}}, 3 steps in this instance, is denoted by & "amp" and @ "at".  


{| class="wikitable center-1 right-2 center-3"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! #
! &#35;
! Cents
! Cents
! Note
! Note
! Name
! Name
! Associated Ratio
! Associated ratio
|-
|-
| 0
| 0
Line 742: Line 742:


== 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
Line 769: Line 761:
| 225/224, 351/350, 640/637, 1701/1690
| 225/224, 351/350, 640/637, 1701/1690
| {{mapping| 84 133 195 236 311 }}
| {{mapping| 84 133 195 236 311 }}
| -0.013
| &minus;0.013
| 0.754
| 0.754
| 5.28
| 5.28
|-style="border-top: double;"
|- style="border-top: double;"
| 2.3.5.7.11
| 2.3.5.7.11
| 225/224, 441/440, 1344/1331, 1728/1715
| 225/224, 441/440, 1344/1331, 1728/1715
| {{mapping| 84 133 195 236 291 }} (84)
| {{mapping| 84 133 195 236 291 }} (84)
| -0.225
| &minus;0.225
| 1.003
| 1.003
| 7.02
| 7.02
Line 783: Line 775:
| 144/143, 225/224, 351/350, 441/440, 975/968
| 144/143, 225/224, 351/350, 441/440, 975/968
| {{mapping| 84 133 195 236 291 311 }} (84)
| {{mapping| 84 133 195 236 291 311 }} (84)
| -0.292
| &minus;0.292
| 0.928
| 0.928
| 6.50
| 6.50
|-style="border-top: double;"
|- style="border-top: double;"
| 2.3.5.7.11
| 2.3.5.7.11
| 99/98, 121/120, 176/175, 78732/78125
| 99/98, 121/120, 176/175, 78732/78125
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| 1.146
| 1.146
| 8.02
| 8.02
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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| 4/3<br>(105/104)
| 4/3<br>(105/104)
| [[Oquatonic]]
| [[Oquatonic]]
|}
{{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}}


== Scales ==
== Scales ==
=== MOS ===
=== MOS ===
Brightest mode is listed.
Brightest mode is listed.


* [[Orwell]]
* [[Orwell]]
** Orwell[9], [[4L 5s]] - 11 8 11 8 11 8 11 8 8  
** Orwell[9], [[4L 5s]] &ndash; 11 8 11 8 11 8 11 8 8  
** Orwell[13] - [[9L 4s]] - 8 8 8 3 8 8 3 8 8 3 8 8 3
** Orwell[13] &ndash; [[9L 4s]] &ndash; 8 8 8 3 8 8 3 8 8 3 8 8 3
** Orwell[22] - [[13L 9s]]
** Orwell[22] &ndash; [[13L 9s]]
** Orwell[31] - [[22L 9s]]
** Orwell[31] &ndash; [[22L 9s]]


=== Other ===
=== Other ===