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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| 165 -104 }}
| {{monzo| 165 -104 }}
| {{mapping| 104 165 }}
| {{mapping| 104 165 }}
| -0.597
| &minus;0.597
| 0.596
| 0.596
| 5.17
| 5.17
Line 38: Line 30:
| 2048/2025, {{monzo| 0 22 -15 }}
| 2048/2025, {{monzo| 0 22 -15 }}
| {{mapping| 104 165 242 }} (104c)
| {{mapping| 104 165 242 }} (104c)
| -1.258
| &minus;1.258
| 1.054
| 1.054
| 9.14
| 9.14
Line 45: Line 37:
| 126/125, 2048/2025, 117649/116640
| 126/125, 2048/2025, 117649/116640
| {{mapping| 104 165 242 292 }} (104c)
| {{mapping| 104 165 242 292 }} (104c)
| -0.980
| &minus;0.980
| 1.032
| 1.032
| 8.95
| 8.95
Line 52: Line 44:
| 126/125, 176/175, 896/891, 14641/14580
| 126/125, 176/175, 896/891, 14641/14580
| {{mapping| 104 165 242 292 360 }} (104c)
| {{mapping| 104 165 242 292 360 }} (104c)
| -0.930
| &minus;0.930
| 0.929
| 0.929
| 8.05
| 8.05
Line 59: Line 51:
| 126/125, 176/175, 196/195, 364/363, 2197/2187
| 126/125, 176/175, 196/195, 364/363, 2197/2187
| {{mapping| 104 165 242 292 360 385 }} (104c)
| {{mapping| 104 165 242 292 360 385 }} (104c)
| -0.855
| &minus;0.855
| 0.864
| 0.864
| 7.49
| 7.49
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
==== In patent val ====
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
! Periods<br>per 8ve
|+ style="font-size: 105%;" | Patent val
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperament
! Temperament
|-
|-
Line 92: Line 85:
|}
|}


==== In 104c val ====
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
! Periods<br>per 8ve
|+ style="font-size: 105%;" | 104c val
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperament
! Temperament
|-
|-
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|-
|-
| 2
| 2
| 43\104<br>(9\104)
| 43\104<br />(9\104)
| 496.15<br>(103.85)
| 496.15<br />(103.85)
| 4/3<br>(17/16)
| 4/3<br />(17/16)
| [[Diaschismic]]
| [[Diaschismic]]
|-
|-
| 8
| 8
| 49\104<br>(2\104)
| 49\104<br />(2\104)
| 565.38<br>(34.62)
| 565.38<br />(34.62)
| 168/121<br>(55/54)
| 168/121<br />(55/54)
| [[Octowerck]] / octowerckis
| [[Octowerck]] / octowerckis
|-
|-
| 26
| 26
| 43\104<br>(1\104)
| 43\104<br />(1\104)
| 496.15<br>(11.54)
| 496.15<br />(11.54)
| 4/3<br>(225/224)
| 4/3<br />(225/224)
| [[Bosonic]]
| [[Bosonic]]
|}
|}
<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}}


== Intervals ==
== Intervals ==
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{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2" | #
! rowspan="2" | &#35;
! rowspan="2" | Cents
! rowspan="2" | Cents
! colspan="3" | Approximate Ratios
! colspan="3" | Approximate Ratios
|-
|-
! of 2.3.7.11.13.17.19.25 <br> Subgroup
! of 2.3.7.11.13.17.19.25<br />subgroup
! Additional Ratios of 5 <br> Tending Sharp (104c Val)
! Additional ratios of 5<br />tending sharp (104c val)
! Additional Ratios of 5 <br> Tending Flat (Patent Val)
! Additional ratios of 5<br />tending flat (patent val)
|-
|-
| 0
| 0
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|}
|}


[[Category:Apollo]]
[[Category:Diaschismic]]
[[Category:Diaschismic]]
[[Category:Apollo]]
[[Category:Magic]]
[[Category:Magic]]
[[Category:Necromancy]]
[[Category:Necromancy]]
Retrieved from "https://en.xen.wiki/w/104edo"