35edo: Difference between revisions

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== 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¢~~ and 5edo's wide fifth of ~~720¢~~. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 ~~cent~~ 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.

35edo has the optimal [[patent val]] for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a [[diatonic scale]] (unless 7edo is considered a diatonic scale).

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0-9-20-29 = C vE G vB = Cv7 = C down seven

For a more complete list, see [[Ups and ~~Downs Notation~~#Chords and Chord Progressions|Ups and ~~Downs Notation~~ - Chords and Chord Progressions]].

For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]].

== JI Intervals ==

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* A good place to start using 35-EDO is with the sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.

* Also available is the amulet scale{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3

* Approximations of [[gamelan]] scales:

** 5-tone pelog: 3 5 12 3 12

** 7-tone pelog: 3 5 7 5 3 8 4

** 5-tone slendro: 7 7 7 7 7

== Instruments ==

=== Lumatone ===

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 ==

; [[dotuXil]]

* [https://~~dotuxil~~.~~bandcamp~~.com/~~track/icebound-gallery-of-refractions-2~~ "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)

* [https://www.youtube.com/watch?v=61ssLv9H6rk "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)

; [[E8 Heterotic]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|35}}
+{{ED intro}}
 == 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¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent 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.
-edo 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.
+edo 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.
 edo has the optimal [[patent val]] for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a [[diatonic scale]] (unless 7edo is considered a diatonic scale).
@@ Line 321: / Line 321: @@
 -9-20-29 = C vE G vB = Cv7 = C down seven
-For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
+For a more complete list, see [[Ups and downs notation#Chords and Chord Progressions|Ups and downs notation - Chords and Chord Progressions]].
 == JI Intervals ==
@@ Line 788: / Line 788: @@
 * A good place to start using 35-EDO is with the sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.
 * Also available is the amulet scale{{idiosyncratic}}, approximated from [[magic]] in [[25edo]]: 3 1 3 3 1 3 4 3 3 1 3 4 3
+* Approximations of [[gamelan]] scales:
+** 5-tone pelog: 3 5 12 3 12
+** 7-tone pelog: 3 5 7 5 3 8 4
+** 5-tone slendro: 7 7 7 7 7
 == Instruments ==
+=== Lumatone ===
 edo 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: string 2 open
+/1: string 3 fret 9 and string 6 fret 1
+/2: string 3 fret 4 and string 4 fret 13
+/4: string 3 fret 1, string 4 fret 10, and string 7 fret 2
+/4: string 4 fret 4
+/8: string 1 fret 8, string 4 open, and string 5 fret 9
+/8: string 1 fret 11, string 4 fret 3, and string 5 fret 12
+/16: string 2 fret 1 and string 3 fret 10
 == Music ==
 ; [[dotuXil]]
-* [https://dotuxil.bandcamp.com/track/icebound-gallery-of-refractions-2 "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)
+* [https://www.youtube.com/watch?v=61ssLv9H6rk "Icebound Gallery of Refractions"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)
 ; [[E8 Heterotic]]