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. | 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 [[ | 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. | ||
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. | 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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| | 8\35 | | | 8\35 | ||
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| | Messed-up [[ | | | Messed-up [[Orwell]] | ||
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| | 1 | | | 1 | ||
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| | 1 | | | 1 | ||
| | 11\35 | | | 11\35 | ||
| | [[ | | | [[Muggles]] | ||
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| | 1 | | | 1 | ||
| | 13\35 | | | 13\35 | ||
| colspan="2" | Inconsistent 2.9'/7.5/3 [[ | | colspan="2" | Inconsistent 2.9'/7.5/3 [[Sensi]] | ||
|- | |- | ||
| | 1 | | | 1 | ||
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| | 1\35 | | | 1\35 | ||
| | | | | | ||
| | [[ | | | [[Blackwood]] (favoring 7/6) | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 2\35 | | | 2\35 | ||
| | | | | | ||
| | [[ | | | [[Blackwood]] (favoring 6/5 and 20/17) | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 3\35 | | | 3\35 | ||
| | | | | | ||
| | [[ | | | [[Blackwood]] (favoring 5/4 and 17/14) | ||
|- | |- | ||
| | 7 | | | 7 | ||