99edo: Difference between revisions

Theory: +subsets and supersets
ArrowHead294 (talk | contribs)
mNo edit summary
Line 21: Line 21:


== 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| 157 -99 }}
| {{monzo| 157 -99 }}
| {{mapping| 99 157 }}
| {{mapping| 99 157 }}
| -0.339
| &minus;0.339
| 0.339
| 0.339
| 2.80
| 2.80
Line 41: Line 33:
| 393216/390625, 1600000/1594323
| 393216/390625, 1600000/1594323
| {{mapping| 99 157 230 }}
| {{mapping| 99 157 230 }}
| -0.451
| &minus;0.451
| 0.319
| 0.319
| 2.63
| 2.63
Line 48: Line 40:
| 2401/2400, 3136/3125, 4375/4374
| 2401/2400, 3136/3125, 4375/4374
| {{mapping| 99 157 230 278 }}
| {{mapping| 99 157 230 278 }}
| -0.416
| &minus;0.416
| 0.283
| 0.283
| 2.33
| 2.33
|-style="border-top: double;"
|- style="border-top: double;"
| 2.3.5.7.11
| 2.3.5.7.11
| 243/242, 441/440, 896/891, 3136/3125
| 243/242, 441/440, 896/891, 3136/3125
| {{mapping| 99 157 230 278 343 }} (99e)
| {{mapping| 99 157 230 278 343 }} (99e)
| -0.694
| &minus;0.694
| 0.612
| 0.612
| 5.05
| 5.05
|-style="border-top: double;"
|- style="border-top: double;"
| 2.3.5.7.11
| 2.3.5.7.11
| 121/120, 176/175, 1375/1372, 2200/2187
| 121/120, 176/175, 1375/1372, 2200/2187
Line 65: Line 57:
| 0.881
| 0.881
| 7.27
| 7.27
|}
{{comma basis end}}
* 99et is lower in relative error than any previous equal temperaments in the 7-limit. Not until 171 do we find a better equal temperament in terms of either absolute error or relative error.  
* 99et is lower in relative error than any previous equal temperaments in the 7-limit. Not until 171 do we find a better equal temperament in terms of either absolute error or relative error.  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all right-3 left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperament
|-
|-
| 1
| 1
Line 162: Line 148:
|-
|-
| 3
| 3
| 41\99<br>(8\99)
| 41\99<br />(8\99)
| 496.970<br>(96.970)
| 496.970<br />(96.970)
| 4/3<br>(18/17~19/18)
| 4/3<br />(18/17~19/18)
| [[Misty]]
| [[Misty]]
|-
|-
Line 171: Line 157:
| 48.485
| 48.485
| 36/35
| 36/35
| [[Ennealimmal]] (99e) / ennealimmia (99) / <br>ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)
| [[Ennealimmal]] (99e) / ennealimmia (99) / <br />ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)
|-
|-
| 11
| 11
| 41\99<br>(4\99)
| 41\99<br />(4\99)
| 496.970<br>(48.485)
| 496.970<br />(48.485)
| 4/3<br>(36/35)
| 4/3<br />(36/35)
| [[Hendecatonic]]
| [[Hendecatonic]]
|}
{{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 ==
Line 193: Line 179:


; [[Mundoworld]]
; [[Mundoworld]]
* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) zeus[7] in 99edo tuning
* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) &ndash; zeus[7] in 99edo tuning


; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
Line 200: Line 186:


== See also ==
== See also ==
* [[157edt]] relative [[edt]]
* [[157edt]] &ndash; relative [[edt]]
* [[58edf]] relative [[edf]]
* [[58edf]] &ndash; relative [[edf]]
* [[87edo]], [[94edo]], [[111edo]] similarly sized edos all with consistency in higher harmonics.
* [[87edo]], [[94edo]], [[111edo]] &ndash; similarly sized edos all with consistency in higher harmonics.
* [[198edo]], the half-sized edo to reconcile the mappings of 11 and 13.
* [[198edo]], the half-sized edo to reconcile the mappings of 11 and 13.
* [[105edo]], a similarly sized edo that supports meantone, septimal meantone, undecimal meantone and grosstone
* [[105edo]], a similarly sized edo that supports meantone, septimal meantone, undecimal meantone, and grosstone


[[Category:Hemifamity]]
[[Category:Hemifamity]]
Line 210: Line 196:
[[Category:Hendecatonic]]
[[Category:Hendecatonic]]
[[Category:Hitchcock]]
[[Category:Hitchcock]]
[[Category:Listen]]
[[Category:Zeus]]
[[Category:Zeus]]
[[Category:Listen]]