35edo: Difference between revisions

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35-tET or 35-[[EDO|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each.

As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal_edos|macrotonal edos]]: [[5edo|5edo]] and [[7edo|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. 35edo can also represent the 2.3.5.7.11.17 [[Just_intonation_subgroups|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|22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[~~Greenwoodmic_temperaments|~~greenwood]] and [[~~Greenwoodmic_temperaments#Secund|~~secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles.

As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal_edos|macrotonal edos]]: [[5edo|5edo]] and [[7edo|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. 35edo can also represent the 2.3.5.7.11.17 [[Just_intonation_subgroups|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|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.

A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[MOS|MOS]] of 3L2s: 9 4 9 9 4.

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 -tET or 35-[[EDO|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[cent|34.29¢]] each.
-As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal_edos|macrotonal edos]]: [[5edo|5edo]] and [[7edo|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. 35edo can also represent the 2.3.5.7.11.17 [[Just_intonation_subgroups|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|22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[Greenwoodmic_temperaments|greenwood]] and [[Greenwoodmic_temperaments#Secund|secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles.
+As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal_edos|macrotonal edos]]: [[5edo|5edo]] and [[7edo|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. 35edo can also represent the 2.3.5.7.11.17 [[Just_intonation_subgroups|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|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.
 A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[MOS|MOS]] of 3L2s: 9 4 9 9 4.