1-3-7-21 hexany: Difference between revisions

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A [[7-limit]] [[Hexany]]. This creates a scale of 1 7/6 21/16 49/32 7/4 2/1, with steps of 7/6 9/8 7/6 8/7 8/7. This is particularly notable because it is the second simplest hexany that results in a pentatonic scale, with 7/4 appearing twice as the reduced product of 1x21 and 3x7. This means any [[dekany|dekanies]] built using it will also wind up with 9 or fewer notes. Unlike the smallest pentatonic ~~dekany~~, the notes are quite evenly spaced, with a ratio of less than 4:3 between the largest and smallest steps. The most consonant mode is the symmetrical one, which makes the steps 1/1 8/7 4/3 3/2 7/4 2/1, revealing this to be a detemper of [[semaphore]] temperament. As such, songs composed in that temperament can also be played using this scale while remaining recognisable.

A [[7-limit]] [[Hexany]]. This creates a scale of 1 7/6 21/16 49/32 7/4 2/1, with steps of 7/6 9/8 7/6 8/7 8/7. This is particularly notable because it is the second simplest hexany that results in a pentatonic scale, with 7/4 appearing twice as the reduced product of 1x21 and 3x7. This means any [[dekany|dekanies]] built using it will also wind up with 9 or fewer notes. Unlike the smallest pentatonic hexany, the notes are quite evenly spaced, with a ratio of less than 4:3 between the largest and smallest steps. The most consonant mode is the symmetrical one, which makes the steps 1/1 8/7 4/3 3/2 7/4 2/1, revealing this to be a detemper of [[semaphore]] temperament. As such, songs composed in that temperament can also be played using this scale while remaining recognisable.

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	A [[7-limit]] [[Hexany]]. This creates a scale of 1 7/6 21/16 49/32 7/4 2/1, with steps of 7/6 9/8 7/6 8/7 8/7. This is particularly notable because it is the second simplest hexany that results in a pentatonic scale, with 7/4 appearing twice as the reduced product of 1x21 and 3x7. This means any [[dekany\|dekanies]] built using it will also wind up with 9 or fewer notes. Unlike the smallest pentatonic ~~dekany~~, the notes are quite evenly spaced, with a ratio of less than 4:3 between the largest and smallest steps. The most consonant mode is the symmetrical one, which makes the steps 1/1 8/7 4/3 3/2 7/4 2/1, revealing this to be a detemper of [[semaphore]] temperament. As such, songs composed in that temperament can also be played using this scale while remaining recognisable.		A [[7-limit]] [[Hexany]]. This creates a scale of 1 7/6 21/16 49/32 7/4 2/1, with steps of 7/6 9/8 7/6 8/7 8/7. This is particularly notable because it is the second simplest hexany that results in a pentatonic scale, with 7/4 appearing twice as the reduced product of 1x21 and 3x7. This means any [[dekany\|dekanies]] built using it will also wind up with 9 or fewer notes. Unlike the smallest pentatonic hexany, the notes are quite evenly spaced, with a ratio of less than 4:3 between the largest and smallest steps. The most consonant mode is the symmetrical one, which makes the steps 1/1 8/7 4/3 3/2 7/4 2/1, revealing this to be a detemper of [[semaphore]] temperament. As such, songs composed in that temperament can also be played using this scale while remaining recognisable.

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