359edo: Difference between revisions
Cleanup; +commas; +subset and supersets |
Cleanup; clarify the title row of the rank-2 temp table; request a citation |
||
| Line 5: | Line 5: | ||
359edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. In the 5-limit it tempers out the [[würschmidt comma]] and the [[counterschisma]]; in the 7-limit [[2401/2400]] and [[3136/3125]], supporting [[hemiwürschmidt]]; in the 11-limit, [[8019/8000]], providing the [[optimal patent val]] for 11-limit [[hera]]. | 359edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. In the 5-limit it tempers out the [[würschmidt comma]] and the [[counterschisma]]; in the 7-limit [[2401/2400]] and [[3136/3125]], supporting [[hemiwürschmidt]]; in the 11-limit, [[8019/8000]], providing the [[optimal patent val]] for 11-limit [[hera]]. | ||
359edo [[support]]s a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359edo this is the step 203\359 of 678.55153¢. | 359edo [[support]]s a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America{{citation needed}}; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359edo this is the step 203\359 of 678.55153¢. | ||
Pythagorean diatonic scale: 61 61 27 61 61 61 27 | Pythagorean diatonic scale: 61 61 27 61 61 61 27 | ||
| Line 30: | Line 30: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -569 359 }} | | {{monzo| -569 359 }} | ||
| | | {{mapping| 359 569 }} | ||
| +0.0016 | | +0.0016 | ||
| 0.0016 | | 0.0016 | ||
| Line 37: | Line 37: | ||
| 2.3.5 | | 2.3.5 | ||
| 393216/390625, {{monzo| -69 45 -1 }} | | 393216/390625, {{monzo| -69 45 -1 }} | ||
| | | {{mapping| 359 569 834 }} | ||
| -0.2042 | | -0.2042 | ||
| 0.2910 | | 0.2910 | ||
| Line 44: | Line 44: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 3136/3125, {{monzo| -18 24 -5 -3 }} | | 2401/2400, 3136/3125, {{monzo| -18 24 -5 -3 }} | ||
| | | {{mapping| 359 569 834 1008 }} | ||
| -0.2007 | | -0.2007 | ||
| 0.2521 | | 0.2521 | ||
| Line 51: | Line 51: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3136/3125, 8019/8000, 42592/42525 | | 2401/2400, 3136/3125, 8019/8000, 42592/42525 | ||
| | | {{mapping| 359 569 834 1008 1242 }} | ||
| -0.1729 | | -0.1729 | ||
| 0.2322 | | 0.2322 | ||
| Line 58: | Line 58: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 729/728, 847/845, 1001/1000, 1716/1715, 3136/3125 | | 729/728, 847/845, 1001/1000, 1716/1715, 3136/3125 | ||
| | | {{mapping| 359 569 834 1008 1242 1328 }} (359f) | ||
| -0.2257 | | -0.2257 | ||
| 0.2426 | | 0.2426 | ||
| Line 67: | Line 67: | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 91: | Line 91: | ||
| [[Counterschismic]] | | [[Counterschismic]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[Category:Hera]] | [[Category:Hera]] | ||