359edo: Difference between revisions
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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{{citation needed}}; the | 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 678.495{{c}} [[262144/177147|Pythagorean diminished sixth]]; in 359edo this is reached using 203 steps, or 678.55153{{c}}. | ||
Pythagorean diatonic scale: 61 61 27 61 61 61 27 | Pythagorean diatonic scale: 61 61 27 61 61 61 27 | ||
| Line 39: | Line 39: | ||
| 393216/390625, {{monzo| -69 45 -1 }} | | 393216/390625, {{monzo| -69 45 -1 }} | ||
| {{mapping| 359 569 834 }} | | {{mapping| 359 569 834 }} | ||
| | | −0.2042 | ||
| 0.2910 | | 0.2910 | ||
| 8.71 | | 8.71 | ||
| Line 46: | Line 46: | ||
| 2401/2400, 3136/3125, {{monzo| -18 24 -5 -3 }} | | 2401/2400, 3136/3125, {{monzo| -18 24 -5 -3 }} | ||
| {{mapping| 359 569 834 1008 }} | | {{mapping| 359 569 834 1008 }} | ||
| | | −0.2007 | ||
| 0.2521 | | 0.2521 | ||
| 7.54 | | 7.54 | ||
| Line 53: | Line 53: | ||
| 2401/2400, 3136/3125, 8019/8000, 42592/42525 | | 2401/2400, 3136/3125, 8019/8000, 42592/42525 | ||
| {{mapping| 359 569 834 1008 1242 }} | | {{mapping| 359 569 834 1008 1242 }} | ||
| | | −0.1729 | ||
| 0.2322 | | 0.2322 | ||
| 6.95 | | 6.95 | ||
| Line 60: | Line 60: | ||
| 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) | | {{mapping| 359 569 834 1008 1242 1328 }} (359f) | ||
| | | −0.2257 | ||
| 0.2426 | | 0.2426 | ||
| 7.26 | | 7.26 | ||
| Line 93: | Line 93: | ||
| [[Counterschismic]] | | [[Counterschismic]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "This Madness Won't Stop!" from ''End Of Sartorius Membranes'' (2024) | * "This Madness Won't Stop!" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/50O9nTxeMafR8AyBtsPSKa Spotify] | [https://francium223.bandcamp.com/track/this-madness-wont-stop Bandcamp] | [https://www.youtube.com/watch?v=UJyIKzgLVQU YouTube] | ||
[[Category:Hera]] | [[Category:Hera]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||