5-7-9-15 by 29/18 bihexany: Difference between revisions

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[[File:5-7-9-15_by_29-18_Hexany.png|thumb|Circle diagram.]] A [[29-limit]] [[Bihexany]]. This creates a scale of 1 29/28 15/14 29/24 9/7 29/20 3/2 87/56 29/18 9/5 27/14 2/1, with steps of 29/28 30/29 203/180 218/203 203/180 30/29 29/28 28/27 15/14 756/725 15/14 28/27. This expands the [[5-7-9-15_hexany|base hexany]] out in a way that minimises the size of the smallest step and cancels out many of the factors, turning the steps around the root into a neat 27:28:29:30, a fragment of the harmonic sequence. It does not have any true 5-limit major ~~or minor~~ thirds, but as 29/24 and 36/29 are only [[145/144]] cents out from just, they can still pass as ordinary minors and majors to most ears in the same way that 22edo and 48edo thirds do.

[[File:5-7-9-15_by_29-18_Hexany.png|thumb|Circle diagram.]] A [[29-limit]] [[Bihexany]]. This creates a scale of 1 29/28 15/14 29/24 9/7 29/20 3/2 87/56 29/18 9/5 27/14 2/1, with steps of 29/28 30/29 203/180 218/203 203/180 30/29 29/28 28/27 15/14 756/725 15/14 28/27. This expands the [[5-7-9-15_hexany|base hexany]] out in a way that minimises the size of the smallest step and cancels out many of the factors, turning the steps around the root into a neat 27:28:29:30, a fragment of the harmonic sequence. It has 4 perfect fifths, 2 that are sharp by 406/405 and 2 that are flat by 145/144, which are all still within the diatonic tuning range. by It does not have any true 5-limit major thirds, but as 29/24 and 36/29 are only [[145/144]] cents out from just, they can still pass as ordinary minors and majors to most ears in the same way that 22edo and 48edo thirds do.

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Revision as of 10:01, 18 November 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,974 edits Create Page.		Revision as of 20:55, 18 November 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,974 edits m Fix math error. Newer edit →
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	[[File:5-7-9-15_by_29-18_Hexany.png\|thumb\|Circle diagram.]] A [[29-limit]] [[Bihexany]]. This creates a scale of 1 29/28 15/14 29/24 9/7 29/20 3/2 87/56 29/18 9/5 27/14 2/1, with steps of 29/28 30/29 203/180 218/203 203/180 30/29 29/28 28/27 15/14 756/725 15/14 28/27. This expands the [[5-7-9-15_hexany\|base hexany]] out in a way that minimises the size of the smallest step and cancels out many of the factors, turning the steps around the root into a neat 27:28:29:30, a fragment of the harmonic sequence. It does not have any true 5-limit major ~~or minor~~ thirds, but as 29/24 and 36/29 are only [[145/144]] cents out from just, they can still pass as ordinary minors and majors to most ears in the same way that 22edo and 48edo thirds do.		[[File:5-7-9-15_by_29-18_Hexany.png\|thumb\|Circle diagram.]] A [[29-limit]] [[Bihexany]]. This creates a scale of 1 29/28 15/14 29/24 9/7 29/20 3/2 87/56 29/18 9/5 27/14 2/1, with steps of 29/28 30/29 203/180 218/203 203/180 30/29 29/28 28/27 15/14 756/725 15/14 28/27. This expands the [[5-7-9-15_hexany\|base hexany]] out in a way that minimises the size of the smallest step and cancels out many of the factors, turning the steps around the root into a neat 27:28:29:30, a fragment of the harmonic sequence. It has 4 perfect fifths, 2 that are sharp by 406/405 and 2 that are flat by 145/144, which are all still within the diatonic tuning range. by It does not have any true 5-limit major thirds, but as 29/24 and 36/29 are only [[145/144]] cents out from just, they can still pass as ordinary minors and majors to most ears in the same way that 22edo and 48edo thirds do.

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