35edo: Difference between revisions
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== Theory == | == Theory == | ||
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71{{c}} and 5edo's wide fifth of 720{{c}}. Because it includes 7edo, 35edo tunes the 29th harmonic with only 1{{c}} of error. | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71{{c}} and 5edo's wide fifth of 720{{c}}. Because it includes 7edo, 35edo tunes the 29th harmonic with only 1{{c}} of error. | ||
35edo can also represent the 2.3.5.7.11.17 [[subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among [[whitewood]] tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. | 35edo can also represent the 2.3.5.7.11.17 [[subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among [[whitewood]] tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. | ||
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0-9-20-29 = C vE G vB = Cv7 = C down seven | 0-9-20-29 = C vE G vB = Cv7 = C down seven | ||
For a more complete list, see [[Ups and | For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]]. | ||
== JI Intervals == | == JI Intervals == | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable" | {| class="wikitable" | ||
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== Instruments == | == Instruments == | ||
=== Lumatone === | |||
35edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 35edo]] | 35edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 35edo]] | ||
=== Skip fretting === | |||
'''Skip fretting system 35 3 8''' is a [[skip fretting]] system for [[35edo]]. All examples on this page are for 7-string [[guitar]]. | |||
; Prime harmonics | |||
1/1: string 2 open | |||
2/1: string 3 fret 9 and string 6 fret 1 | |||
3/2: string 3 fret 4 and string 4 fret 13 | |||
5/4: string 3 fret 1, string 4 fret 10, and string 7 fret 2 | |||
7/4: string 4 fret 4 | |||
11/8: string 1 fret 8, string 4 open, and string 5 fret 9 | |||
13/8: string 1 fret 11, string 4 fret 3, and string 5 fret 12 | |||
17/16: string 2 fret 1 and string 3 fret 10 | |||
== Music == | == Music == | ||
; [[dotuXil]] | ; [[dotuXil]] | ||
* [https:// | * [https://www.youtube.com/watch?v=61ssLv9H6rk "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024) | ||
; [[E8 Heterotic]] | ; [[E8 Heterotic]] | ||