285edo: Difference between revisions
Expansion |
Cleanup |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
285edo has a sharp tendency. | 285edo has a sharp tendency. The equal temperament [[tempering out|tempers out]] the [[misty comma]] and the [[enneadeca]] in the 5-limit; [[3136/3125]] and [[5120/5103]] in the 7-limit; [[3025/3024]] and [[3388/3375]] in the 11-limit; [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], and [[2080/2079]] in the 13-limit. It supports the 13-limit [[hemimist]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|285}} | {{Harmonics in equal|285|intervals=prime}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
| Line 24: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 452 -285 }} | | {{monzo| 452 -285 }} | ||
| | | {{mapping| 285 452 }} | ||
| -0.3795 | | -0.3795 | ||
| 0.3794 | | 0.3794 | ||
| Line 31: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| 67108864/66430125, {{monzo| -14 -19 19 }} | | 67108864/66430125, {{monzo| -14 -19 19 }} | ||
| | | {{mapping| 285 452 662 }} | ||
| -0.4043 | | -0.4043 | ||
| 0.3117 | | 0.3117 | ||
| Line 38: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 3136/3125, 5120/5103, 40353607/39858075 | | 3136/3125, 5120/5103, 40353607/39858075 | ||
| | | {{mapping| 285 452 662 800 }} | ||
| -0.2673 | | -0.2673 | ||
| 0.3596 | | 0.3596 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 3136/3125, 5120/5103, 12005/11979 | | 3025/3024, 3136/3125, 5120/5103, 12005/11979 | ||
| | | {{mapping| 285 452 662 800 986 }} | ||
| -0.2289 | | -0.2289 | ||
| 0.3307 | | 0.3307 | ||
| Line 52: | Line 52: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 352/351, 676/675, 847/845, 3025/3024, 12005/11979 | | 352/351, 676/675, 847/845, 3025/3024, 12005/11979 | ||
| | | {{mapping| 285 452 662 800 986 1055 }} | ||
| -0.2618 | | -0.2618 | ||
| 0.3107 | | 0.3107 | ||
| Line 62: | Line 62: | ||
|+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* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 91: | Line 91: | ||
| [[Enneadecal]] (5-limit) | | [[Enneadecal]] (5-limit) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||