198edo: Difference between revisions
→Theory: discuss the extensions beyond the 13-limit |
→Regular temperament properties: +no-17 19-limit and no-17 23-limit |
||
| Line 32: | Line 32: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 40: | Line 40: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 3136/3125, 4375/4374 | | 2401/2400, 3025/3024, 3136/3125, 4375/4374 | ||
| {{ | | {{Mapping| 198 314 460 556 685 }} | ||
| −0.344 | | −0.344 | ||
| 0.291 | | 0.291 | ||
| Line 47: | Line 47: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 352/351, 676/675, 847/845, 1716/1715, 3025/3024 | | 352/351, 676/675, 847/845, 1716/1715, 3025/3024 | ||
| {{ | | {{Mapping| 198 314 460 556 685 733 }} | ||
| −0.372 | | −0.372 | ||
| 0.273 | | 0.273 | ||
| 4.50 | | 4.50 | ||
|- | |||
| 2.3.5.7.11.13.19 | |||
| 352/351, 361/360, 456/455, 676/675, 847/845, 1331/1330 | |||
| {{Mapping| 198 314 460 556 685 733 841 }} | |||
| −0.301 | |||
| 0.307 | |||
| 5.07 | |||
|- | |||
| 2.3.5.7.11.13.19.23 | |||
| 352/351, 361/360, 456/455, 484/483, 576/575, 676/675, 847/845 | |||
| {{Mapping| 198 314 460 556 685 733 841 896 }} | |||
| −0.319 | |||
| 0.291 | |||
| 4.81 | |||
|} | |} | ||
* 198et has a lower absolute error in the 13-limit than any previous equal temperaments, past [[190edo|190]] and followed by [[224edo|224]]. | * 198et has a lower absolute error in the 13-limit than any previous equal temperaments, past [[190edo|190]] and followed by [[224edo|224]]. | ||
| Line 60: | Line 74: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 127: | Line 141: | ||
|- | |- | ||
| 2 | | 2 | ||
| 52\198<br | | 52\198<br>(47\198) | ||
| 315.15<br | | 315.15<br>(284.85) | ||
| 6/5<br | | 6/5<br>(33/28) | ||
| [[Semiparakleismic]] | | [[Semiparakleismic]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 58\198<br | | 58\198<br>(41\198) | ||
| 351.52<br | | 351.52<br>(248.48) | ||
| 49/40<br | | 49/40<br>(15/13) | ||
| [[Semihemi]] | | [[Semihemi]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 67\198<br | | 67\198<br>(32\198) | ||
| 406.06<br | | 406.06<br>(193.94) | ||
| 495/392<br | | 495/392<br>(28/25) | ||
| [[Semihemiwürschmidt]] | | [[Semihemiwürschmidt]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 74\198<br | | 74\198<br>(25\198) | ||
| 448.48<br | | 448.48<br>(151.51) | ||
| 35/27<br | | 35/27<br>(12/11) | ||
| [[Neusec]] | | [[Neusec]] | ||
|- | |- | ||
| Line 157: | Line 171: | ||
|- | |- | ||
| 3 | | 3 | ||
| 41\198<br | | 41\198<br>(25\198) | ||
| 248.48<br | | 248.48<br>(151.51) | ||
| 15/13<br | | 15/13<br>(12/11) | ||
| [[Hemimist]] | | [[Hemimist]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 82\198<br | | 82\198<br>(16\198) | ||
| 496.97<br | | 496.97<br>(96.97) | ||
| 4/3<br | | 4/3<br>(200/189) | ||
| [[Semimist]] | | [[Semimist]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 52\198<br | | 52\198<br>(3\198) | ||
| 315.15<br | | 315.15<br>(18.18) | ||
| 6/5<br | | 6/5<br>(99/98) | ||
| [[Hemiennealimmal]] | | [[Hemiennealimmal]] | ||
|- | |- | ||
| 22 | | 22 | ||
| 82\198<br | | 82\198<br>(1\198) | ||
| 496.97<br | | 496.97<br>(6.06) | ||
| 4/3<br | | 4/3<br>(385/384) | ||
| [[Icosidillic]] | | [[Icosidillic]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
[[Category:99edo]] | [[Category:99edo]] | ||
[[Category:Major minthmic]] | [[Category:Major minthmic]] | ||
[[Category:Namaka]] | [[Category:Namaka]] | ||