3-5-7-9-11-13 eikosany: Difference between revisions

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[[File:3-5-7-9-11-13_Eikosany.png|thumb|Circle diagram.]] The most complex [[13-odd-limit]] [[eikosany]]. This creates a scale of 1 143/140 13/12 11/10 33/28 143/120 9/7 13/10 39/28 99/70 3/2 429/280 11/7 33/20 117/70 143/84 9/5 11/6 13/7 39/20 2/1, with steps of 143/140 35/33 66/65 15/14 91/90 1080/1001 91/90 15/14 66/65 35/33 143/140 40/39 21/20 78/77 55/54 756/715 55/54 78/77 21/20 40/39. Like its [[3-5-7-9-11-13 pentadekany|corresponding pentadekany]], this is essentially an octotonic scale with many close comma steps concentrated around the cardinal points of the scale. This means it has a pretty even mix of familiar and xenharmonic intervals, including 6 perfect fifths, but no chains of multiple fifths in a row, making it quite usable, but only if you work within its framework rather than trying to ~~fore~~ it into a diatonic one.

[[File:3-5-7-9-11-13_Eikosany.png|thumb|Circle diagram.]] The most complex [[13-odd-limit]] [[eikosany]]. This creates a scale of 1 143/140 13/12 11/10 33/28 143/120 9/7 13/10 39/28 99/70 3/2 429/280 11/7 33/20 117/70 143/84 9/5 11/6 13/7 39/20 2/1, with steps of 143/140 35/33 66/65 15/14 91/90 1080/1001 91/90 15/14 66/65 35/33 143/140 40/39 21/20 78/77 55/54 756/715 55/54 78/77 21/20 40/39. Like its [[3-5-7-9-11-13 pentadekany|corresponding pentadekany]], this is essentially an octotonic scale with many close comma steps concentrated around the cardinal points of the scale. This means it has a pretty even mix of familiar and xenharmonic intervals, including 6 perfect fifths, but no chains of multiple fifths in a row, making it quite usable, but only if you work within its framework rather than trying to force it into a diatonic one.

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	[[File:3-5-7-9-11-13_Eikosany.png\|thumb\|Circle diagram.]] The most complex [[13-odd-limit]] [[eikosany]]. This creates a scale of 1 143/140 13/12 11/10 33/28 143/120 9/7 13/10 39/28 99/70 3/2 429/280 11/7 33/20 117/70 143/84 9/5 11/6 13/7 39/20 2/1, with steps of 143/140 35/33 66/65 15/14 91/90 1080/1001 91/90 15/14 66/65 35/33 143/140 40/39 21/20 78/77 55/54 756/715 55/54 78/77 21/20 40/39. Like its [[3-5-7-9-11-13 pentadekany\|corresponding pentadekany]], this is essentially an octotonic scale with many close comma steps concentrated around the cardinal points of the scale. This means it has a pretty even mix of familiar and xenharmonic intervals, including 6 perfect fifths, but no chains of multiple fifths in a row, making it quite usable, but only if you work within its framework rather than trying to ~~fore~~ it into a diatonic one.		[[File:3-5-7-9-11-13_Eikosany.png\|thumb\|Circle diagram.]] The most complex [[13-odd-limit]] [[eikosany]]. This creates a scale of 1 143/140 13/12 11/10 33/28 143/120 9/7 13/10 39/28 99/70 3/2 429/280 11/7 33/20 117/70 143/84 9/5 11/6 13/7 39/20 2/1, with steps of 143/140 35/33 66/65 15/14 91/90 1080/1001 91/90 15/14 66/65 35/33 143/140 40/39 21/20 78/77 55/54 756/715 55/54 78/77 21/20 40/39. Like its [[3-5-7-9-11-13 pentadekany\|corresponding pentadekany]], this is essentially an octotonic scale with many close comma steps concentrated around the cardinal points of the scale. This means it has a pretty even mix of familiar and xenharmonic intervals, including 6 perfect fifths, but no chains of multiple fifths in a row, making it quite usable, but only if you work within its framework rather than trying to force it into a diatonic one.

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