1-3-5-7-15 dekany: Difference between revisions

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[[File:1-3-5-7-15_Dekany.png|thumb|Circle diagram.]] [[File:1-3-5-7-15_Dekany_(rotated).png|thumb|Circle diagram (rotated).]] The simplest [[15-odd-limit]] [[dekany]]. This creates a scale of 1 35/32 7/6 5/4 35/24 25/16 5/3 7/4 15/8, with steps of 35/32 16/15 15/14 7/6 15/14 16/15 21/20 15/14 16/15. This is notable because it is the simplest dekany that winds up with fewer than 10 notes, with 5/4 appearing twice as the reduced product of 1x15 and 3x5. This does not have a perfect fifth above the root, but does have four other ones, plus an additional ~~fifth~~ that is flat by a [[marvel comma]] and still entirely usable as a regular fifth. Although it does not contain a diatonic scale, it still has many other simple consonances, making it a highly accessible introduction to xenharmony that contains several notes almost exactly 50 cents out from 12edo, but does not provide so many options as to be overwhelming.

[[File:1-3-5-7-15_Dekany.png|thumb|Circle diagram.]] [[File:1-3-5-7-15_Dekany_(rotated).png|thumb|Circle diagram (rotated).]] The simplest [[15-odd-limit]] [[dekany]]. This creates a scale of 1 35/32 7/6 5/4 35/24 25/16 5/3 7/4 15/8, with steps of 35/32 16/15 15/14 7/6 15/14 16/15 21/20 15/14 16/15. This is notable because it is the simplest dekany that winds up with fewer than 10 notes, with 5/4 appearing twice as the reduced product of 1x15 and 3x5. This does not have a perfect fifth above the root, but does have four other ones, plus two additional fifths that are flat by a [[marvel comma]] and still entirely usable as a regular fifth. Although it does not contain a diatonic scale, it still has many other simple consonances, making it a highly accessible introduction to xenharmony that contains several notes almost exactly 50 cents out from 12edo, but does not provide so many options as to be overwhelming.

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Revision as of 21:19, 18 December 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,859 edits Create Page.		Latest revision as of 23:08, 18 December 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,859 edits m There's actually two marvelous fifths, making this one even better than I thought at first.
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	[[File:1-3-5-7-15_Dekany.png\|thumb\|Circle diagram.]] [[File:1-3-5-7-15_Dekany_(rotated).png\|thumb\|Circle diagram (rotated).]] The simplest [[15-odd-limit]] [[dekany]]. This creates a scale of 1 35/32 7/6 5/4 35/24 25/16 5/3 7/4 15/8, with steps of 35/32 16/15 15/14 7/6 15/14 16/15 21/20 15/14 16/15. This is notable because it is the simplest dekany that winds up with fewer than 10 notes, with 5/4 appearing twice as the reduced product of 1x15 and 3x5. This does not have a perfect fifth above the root, but does have four other ones, plus an additional ~~fifth~~ that is flat by a [[marvel comma]] and still entirely usable as a regular fifth. Although it does not contain a diatonic scale, it still has many other simple consonances, making it a highly accessible introduction to xenharmony that contains several notes almost exactly 50 cents out from 12edo, but does not provide so many options as to be overwhelming.		[[File:1-3-5-7-15_Dekany.png\|thumb\|Circle diagram.]] [[File:1-3-5-7-15_Dekany_(rotated).png\|thumb\|Circle diagram (rotated).]] The simplest [[15-odd-limit]] [[dekany]]. This creates a scale of 1 35/32 7/6 5/4 35/24 25/16 5/3 7/4 15/8, with steps of 35/32 16/15 15/14 7/6 15/14 16/15 21/20 15/14 16/15. This is notable because it is the simplest dekany that winds up with fewer than 10 notes, with 5/4 appearing twice as the reduced product of 1x15 and 3x5. This does not have a perfect fifth above the root, but does have four other ones, plus two additional fifths that are flat by a [[marvel comma]] and still entirely usable as a regular fifth. Although it does not contain a diatonic scale, it still has many other simple consonances, making it a highly accessible introduction to xenharmony that contains several notes almost exactly 50 cents out from 12edo, but does not provide so many options as to be overwhelming.

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