1-5-9-15 by 17/12 bihexany: Difference between revisions

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[[File:1-5-9-15_by_17-12_Bihexany.png|thumb|Circle diagram.]] A [[17-limit]] [[bihexany]]. This creates a scale of 1 17/16 9/8 153/128 51/40 85/64 17/12 3/2 51/32 27/16 9/5 15/8 2/1, with steps of 17/16 18/17 17/16 16/15 25/24 16/15 18/17 17/16 18/17 16/15 25/24 16/15. As all the notes apart from the root in the [[1-5-9-15_hexany|~~1-5-9-15_hexany~~]]~~base hexany~~ have at least one power of three in the top, this is a good way to cancel some of them while also keeping intervals evenly spaced, resulting in a scale entirely composed of superparticular intervals with only 4 different step sizes that maps unambiguously to a 12edo keyboard. 6 of the notes have perfect fifths above them, 2 are sharp by 136/135, 2 are sharp by 256/255, 1 is flat by 51/50 and 1 is flat by 432/425. As it is comprised of chains of 5 semitone steps that average slightly larger than 12edo semitones, then a third tone, this is an unambiguous detemper of the 12 note mos scale of the 2.3.5.17 subgroup [[srutal_archagall]] temperament and music composed in that temperament can be converted to this scale and remain recognisable.

[[File:1-5-9-15_by_17-12_Bihexany.png|thumb|Circle diagram.]] [[File:1-5-9-15_by_17-12_Bihexany_(rotated).png|thumb|Circle diagram. (rotated)]] A [[17-limit]] [[bihexany]]. This creates a scale of 1 17/16 9/8 153/128 51/40 85/64 17/12 3/2 51/32 27/16 9/5 15/8 2/1, with steps of 17/16 18/17 17/16 16/15 25/24 16/15 18/17 17/16 18/17 16/15 25/24 16/15. As all the notes apart from the root in the [[1-5-9-15_hexany|base hexany]] have at least one power of three in the top, this is a good way to cancel some of them while also keeping intervals evenly spaced, resulting in a scale entirely composed of superparticular intervals with only 4 different step sizes that maps unambiguously to a 12edo keyboard. 6 of the notes have perfect fifths above them, 2 are sharp by [[136/135]], 2 are sharp by [[256/255]], 1 is flat by [[51/50]] and 1 is flat by 432/425. As it is comprised of chains of 5 semitone steps that average slightly larger than 12edo semitones, then a third tone, this is an unambiguous detemper of the 12 note mos scale of the 2.3.5.17 subgroup [[srutal_archagall]] temperament and music composed in that temperament can be converted to this scale and remain recognisable.

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Revision as of 22:12, 25 November 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,870 edits Create Page.		Latest revision as of 19:34, 26 November 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,870 edits m add rotated diagram.
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	[[File:1-5-9-15_by_17-12_Bihexany.png\|thumb\|Circle diagram.]] A [[17-limit]] [[bihexany]]. This creates a scale of 1 17/16 9/8 153/128 51/40 85/64 17/12 3/2 51/32 27/16 9/5 15/8 2/1, with steps of 17/16 18/17 17/16 16/15 25/24 16/15 18/17 17/16 18/17 16/15 25/24 16/15. As all the notes apart from the root in the [[1-5-9-15_hexany\|~~1-5-9-15_hexany~~]]~~base hexany~~ have at least one power of three in the top, this is a good way to cancel some of them while also keeping intervals evenly spaced, resulting in a scale entirely composed of superparticular intervals with only 4 different step sizes that maps unambiguously to a 12edo keyboard. 6 of the notes have perfect fifths above them, 2 are sharp by 136/135, 2 are sharp by 256/255, 1 is flat by 51/50 and 1 is flat by 432/425. As it is comprised of chains of 5 semitone steps that average slightly larger than 12edo semitones, then a third tone, this is an unambiguous detemper of the 12 note mos scale of the 2.3.5.17 subgroup [[srutal_archagall]] temperament and music composed in that temperament can be converted to this scale and remain recognisable.		[[File:1-5-9-15_by_17-12_Bihexany.png\|thumb\|Circle diagram.]] [[File:1-5-9-15_by_17-12_Bihexany_(rotated).png\|thumb\|Circle diagram. (rotated)]] A [[17-limit]] [[bihexany]]. This creates a scale of 1 17/16 9/8 153/128 51/40 85/64 17/12 3/2 51/32 27/16 9/5 15/8 2/1, with steps of 17/16 18/17 17/16 16/15 25/24 16/15 18/17 17/16 18/17 16/15 25/24 16/15. As all the notes apart from the root in the [[1-5-9-15_hexany\|base hexany]] have at least one power of three in the top, this is a good way to cancel some of them while also keeping intervals evenly spaced, resulting in a scale entirely composed of superparticular intervals with only 4 different step sizes that maps unambiguously to a 12edo keyboard. 6 of the notes have perfect fifths above them, 2 are sharp by [[136/135]], 2 are sharp by [[256/255]], 1 is flat by [[51/50]] and 1 is flat by 432/425. As it is comprised of chains of 5 semitone steps that average slightly larger than 12edo semitones, then a third tone, this is an unambiguous detemper of the 12 note mos scale of the 2.3.5.17 subgroup [[srutal_archagall]] temperament and music composed in that temperament can be converted to this scale and remain recognisable.

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