1-3-7-9 by 11/8 bihexany: Difference between revisions

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[[File:1_3_7_9_by_11-8_Bihexany.png|thumb|Circle diagram.]] The simplest no-5's [[Hexany]], offset by 11/8 to create a bihexany. This creates a scale of 1 33/32 9/8 7/6 77/64 21/16 11/8 3/2 99/64 77/48 7/4 231/128 2/1, with steps of 33/32 12/11 28/27 33/32 12/11 22/21 12/11 33/32 28/27 12/11 33/32 256/231. This is particularly interesting, because it naturally extends the detempered [[archy]] scale of the [[1-3-7-9_hexany|base hexany]] into a detempered version of the the 12 note 2.3.7.11 subgroup [[Archytas_clan#Supra|supra]] scale. It has 8 perfect 5ths, 2 which are sharp by [[64/63]], which means they don't pass as perfect 5ths, but can still be consonant in the right voicings, particularly when used as a harmonic fourth of 21/16, 1 which is sharp by [[896/891]] and is still entirely usable as a regular 5th, and one ultraflat wolf fifth of 77/54 which is better interpreted as a tritone.

While it has no true 5-limit intervals, it does have two [[Keenanismic_chords|keenanismic]] major & minor chords of 154:192:231 and 64:77:96 which can pass as 5-limit to most ears, as they're far closer to just than 12edo majors & minors, which reflects how superpyth naturally reaches 5-limit intervals after 9 generators by tempering that comma out. Since no note deviates from 12edo by more than 100 cents, it can be mapped to a standard keyboard, but the ~~keenanistic~~ chords use the opposite fingerings to usual. (majors have minor fingerings and vice versa)

While it has no true 5-limit intervals, it does have two [[Keenanismic_chords|keenanismic]] major & minor chords of 154:192:231 and 64:77:96 which can pass as 5-limit to most ears, as they're far closer to just than 12edo majors & minors, which reflects how superpyth naturally reaches 5-limit intervals after 9 generators by tempering that comma out. Since no note deviates from 12edo by more than 100 cents, it can be mapped to a standard keyboard, but the keenanismic chords use the opposite fingerings to usual. (majors have minor fingerings and vice versa)

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! 1-3-7-9_by_11/8_Bihexany.scl

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 [[File:1_3_7_9_by_11-8_Bihexany.png|thumb|Circle diagram.]]  The simplest no-5's [[Hexany]], offset by 11/8 to create a bihexany. This creates a scale of 1 33/32 9/8 7/6 77/64 21/16 11/8 3/2 99/64 77/48 7/4 231/128 2/1, with steps of 33/32 12/11 28/27 33/32 12/11 22/21 12/11 33/32 28/27 12/11 33/32 256/231. This is particularly interesting, because it naturally extends the detempered [[archy]] scale of the [[1-3-7-9_hexany|base hexany]] into a detempered version of the the 12 note 2.3.7.11 subgroup [[Archytas_clan#Supra|supra]] scale. It has 8 perfect 5ths, 2 which are sharp by [[64/63]], which means they don't pass as perfect 5ths, but can still be consonant in the right voicings, particularly when used as a harmonic fourth of 21/16, 1 which is sharp by [[896/891]] and is still entirely usable as a regular 5th, and one ultraflat wolf fifth of 77/54 which is better interpreted as a tritone.
-While it has no true 5-limit intervals, it does have two [[Keenanismic_chords|keenanismic]] major & minor chords of 154:192:231 and 64:77:96 which can pass as 5-limit to most ears, as they're far closer to just than 12edo majors & minors, which reflects how superpyth naturally reaches 5-limit intervals after 9 generators by tempering that comma out. Since no note deviates from 12edo by more than 100 cents, it can be mapped to a standard keyboard, but the keenanistic chords use the opposite fingerings to usual. (majors have minor fingerings and vice versa)
+While it has no true 5-limit intervals, it does have two [[Keenanismic_chords|keenanismic]] major & minor chords of 154:192:231 and 64:77:96 which can pass as 5-limit to most ears, as they're far closer to just than 12edo majors & minors, which reflects how superpyth naturally reaches 5-limit intervals after 9 generators by tempering that comma out. Since no note deviates from 12edo by more than 100 cents, it can be mapped to a standard keyboard, but the keenanismic chords use the opposite fingerings to usual. (majors have minor fingerings and vice versa)
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 ! 1-3-7-9_by_11/8_Bihexany.scl