99edo: Difference between revisions
→Theory: +subsets and supersets |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 157 -99 }} | | {{monzo| 157 -99 }} | ||
| {{mapping| 99 157 }} | | {{mapping| 99 157 }} | ||
| | | −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 | ||
| 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 | ||
| 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 | ||
| 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 === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 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}} | |||
{{orf}} | |||
== Scales == | == Scales == | ||
| Line 193: | Line 179: | ||
; [[Mundoworld]] | ; [[Mundoworld]] | ||
* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) | * [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – zeus[7] in 99edo tuning | ||
; [[Gene Ward Smith]] | ; [[Gene Ward Smith]] | ||
| Line 200: | Line 186: | ||
== See also == | == See also == | ||
* [[157edt]] | * [[157edt]] – relative [[edt]] | ||
* [[58edf]] | * [[58edf]] – relative [[edf]] | ||
* [[87edo]], [[94edo]], [[111edo]] | * [[87edo]], [[94edo]], [[111edo]] – 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]] | ||