3-7-13-15 by 4/3 bihexany: Difference between revisions

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[[File:3-7-13-15_by_4-3_Hexany.png|thumb|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png|thumb|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany|base hexany]] out to a detemper of the [[Modes_of_Negri-9|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.

[[File:3-7-13-15_by_4-3_Hexany.png|thumb|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png|thumb|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany|base hexany]] out to a detemper of the [[Modes_of_Negri-9|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes, 6 perfect fifths and 1 17 cent flat one which is usable if you can tolerate 7edo fifths. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.

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636.617

756.060

884.358

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-[[File:3-7-13-15_by_4-3_Hexany.png|thumb|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png|thumb|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany|base hexany]] out to a detemper of the [[Modes_of_Negri-9|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.
+[[File:3-7-13-15_by_4-3_Hexany.png|thumb|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png|thumb|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany|base hexany]] out to a detemper of the [[Modes_of_Negri-9|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes, 6 perfect fifths and 1 17 cent flat one which is usable if you can tolerate 7edo fifths. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.
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 .044
 .487
+.617
 .060
 .358