99edo: Difference between revisions
→Music: linking |
Cleanup |
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| Line 30: | Line 30: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 157 -99 }} | | {{monzo| 157 -99 }} | ||
| | | {{mapping| 99 157 }} | ||
| -0.339 | | -0.339 | ||
| 0.339 | | 0.339 | ||
| Line 37: | Line 37: | ||
| 2.3.5 | | 2.3.5 | ||
| 393216/390625, 1600000/1594323 | | 393216/390625, 1600000/1594323 | ||
| | | {{mapping| 99 157 230 }} | ||
| -0.451 | | -0.451 | ||
| 0.319 | | 0.319 | ||
| Line 44: | Line 44: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 3136/3125, 4375/4374 | | 2401/2400, 3136/3125, 4375/4374 | ||
| | | {{mapping| 99 157 230 278 }} | ||
| -0.416 | | -0.416 | ||
| 0.283 | | 0.283 | ||
| 2.33 | | 2.33 | ||
|- | |-style="border-top: double;" | ||
| 2.3.5.7.11 | |||
| 243/242, 441/440, 896/891, 3136/3125 | |||
| | | {{mapping| 99 157 230 278 343 }} (99e) | ||
| -0.694 | |||
| 0.612 | |||
| 5.05 | |||
|- | |-style="border-top: double;" | ||
| 2.3.5.7.11 | |||
| 121/120, 176/175, 1375/1372, 2200/2187 | |||
| | | {{mapping| 99 157 230 278 342 }} (99) | ||
| +0.006 | |||
| 0.881 | |||
| 7.27 | |||
|} | |} | ||
* 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. | ||
| Line 69: | Line 69: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| Line 176: | Line 176: | ||
| [[Hendecatonic]] | | [[Hendecatonic]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Scales == | == Scales == | ||
| Line 196: | Line 197: | ||
== See also == | == See also == | ||
* [[157edt]] – relative | * [[157edt]] – relative [[edt]] | ||
* [[58edf]] – relative | * [[58edf]] – relative [[edf]] | ||
* [[87edo]], [[94edo]], [[111edo]] – similarly sized edos all with consistency in higher harmonics. | * [[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. | ||