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 | [[File:Hexany 1 3 7 21.png|thumb|Circle diagram (rotated).]] 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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Latest revision as of 04:39, 5 October 2025
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 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.
! 1-3-7-21_Hexany.scl ! 1 3 5 15 2-combination Hexany 5 ! 7/6 21/16 49/32 7/4 2/1
Suggested keyboard mapping: E G A C D E