1-3-7-9 hexany: Difference between revisions

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[[File:1-3-7-9_Hexany.png|thumb|Circle diagram ~~(rotated)~~.]] The simplest no-5's [[Hexany]]. This creates a scale of 1 9/8 7/6 21/16 3/2 7/4 2/1, with steps of 9/8 28/27 9/8 8/7 7/6 8/7. This is particularly interesting, because it can be viewed as a detemper of the basic [[archy]] diatonic scale in the same way that the [[1-3-5-9 hexany]] detempers [[meantone]]. Like those, the septimal pentatonic scale is more even, but has a smaller diatonic semitone once extended to a hexatonic scale. Similarly, major chords are simpler in the 5-limit, while minor ones are simpler in the 7-limit, making the notes with minor chords above them the more obvious roots. Since the notes are fairly evenly spaced and none are more than 33 cents away from 12edo, it maps unambiguously to a standard keyboard layout.

[[File:1-3-7-9_Hexany.png|thumb|Circle diagram.]] The simplest no-5's [[Hexany]]. This creates a scale of 1 9/8 7/6 21/16 3/2 7/4 2/1, with steps of 9/8 28/27 9/8 8/7 7/6 8/7. This is particularly interesting, because it can be viewed as a detemper of the basic [[archy]] diatonic scale in the same way that the [[1-3-5-9 hexany]] detempers [[meantone]]. Like those, the septimal pentatonic scale is more even, but has a smaller diatonic semitone once extended to a hexatonic scale. Similarly, major chords are simpler in the 5-limit, while minor ones are simpler in the 7-limit, making the notes with minor chords above them the more obvious roots. Since the notes are fairly evenly spaced and none are more than 33 cents away from 12edo, it maps unambiguously to a standard keyboard layout.

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Revision as of 21:03, 10 October 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,869 edits m Replace incorrect circle diagram. ← Older edit		Latest revision as of 21:03, 10 October 2025 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 1,869 edits m Not rotated.
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	[[File:1-3-7-9_Hexany.png\|thumb\|Circle diagram ~~(rotated)~~.]] The simplest no-5's [[Hexany]]. This creates a scale of 1 9/8 7/6 21/16 3/2 7/4 2/1, with steps of 9/8 28/27 9/8 8/7 7/6 8/7. This is particularly interesting, because it can be viewed as a detemper of the basic [[archy]] diatonic scale in the same way that the [[1-3-5-9 hexany]] detempers [[meantone]]. Like those, the septimal pentatonic scale is more even, but has a smaller diatonic semitone once extended to a hexatonic scale. Similarly, major chords are simpler in the 5-limit, while minor ones are simpler in the 7-limit, making the notes with minor chords above them the more obvious roots. Since the notes are fairly evenly spaced and none are more than 33 cents away from 12edo, it maps unambiguously to a standard keyboard layout.		[[File:1-3-7-9_Hexany.png\|thumb\|Circle diagram.]] The simplest no-5's [[Hexany]]. This creates a scale of 1 9/8 7/6 21/16 3/2 7/4 2/1, with steps of 9/8 28/27 9/8 8/7 7/6 8/7. This is particularly interesting, because it can be viewed as a detemper of the basic [[archy]] diatonic scale in the same way that the [[1-3-5-9 hexany]] detempers [[meantone]]. Like those, the septimal pentatonic scale is more even, but has a smaller diatonic semitone once extended to a hexatonic scale. Similarly, major chords are simpler in the 5-limit, while minor ones are simpler in the 7-limit, making the notes with minor chords above them the more obvious roots. Since the notes are fairly evenly spaced and none are more than 33 cents away from 12edo, it maps unambiguously to a standard keyboard layout.

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