1-3-5-7 hexany - Revision history

Yourmusic Productions: /* Expansions */ Still more notable ones to come.

2026-01-17T10:57:17Z

Expansions: Still more notable ones to come.

← Older revision		Revision as of 10:57, 17 January 2026
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	* [[1-3-5-7 by 40/21 bihexany]]		* [[1-3-5-7 by 40/21 bihexany]]
	* [[1-3-5-7 by 48/35 bihexany]]		* [[1-3-5-7 by 48/35 bihexany]]

			All other offset intervals will produce a 12 note scale with at least 4 perfect fifths, although they may not be positioned in a way that provides familiar chord sequences. Ones that have five or more perfect fifths include:

			* [[1-3-5-7 by 9/8 bihexany]]
			* [[1-3-5-7 by 21/16 bihexany]]
			* [[1-3-5-7 by 16/15 bihexany]]
			* [[1-3-5-7 by 56/45 bihexany]]
			* [[1-3-5-7 by 64/35 bihexany]]
			* [[1-3-5-7 by 80/63 bihexany]]

	== Music ==		== Music ==

Yourmusic Productions: /* Expansions */ Complete list of bihexanies with overlapping notes, will fill in links later.

2026-01-10T09:59:13Z

Expansions: Complete list of bihexanies with overlapping notes, will fill in links later.

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 * [[1-3-5-7 by 6/5 bihexany]]
 * [[1-3-5-7 by 12/7 bihexany]]
 == Music ==

Yourmusic Productions: expand expansions

2026-01-09T05:20:25Z

expand expansions

← Older revision		Revision as of 05:20, 9 January 2026
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	== Expansions ==		== Expansions ==

			As it has 1 as a factor, turning this from a standard hexany into a stellated hexany only adds two notes to your options rather than a full 14 due to the large number of repeated notes, which still leaves plenty of gaps on a standard keyboard.
			* [[1-3-5-7 stellated hexany]]

	There are 6 ways of expanding this out to a bihexany that will put a 3/2 above the root, expanding your options in a way that gives you a stable 5-limit chord to centre your scale upon and plenty of other consonant chords. 3 of them produce a full 12 note scale.		There are 6 ways of expanding this out to a bihexany that will put a 3/2 above the root, expanding your options in a way that gives you a stable 5-limit chord to centre your scale upon and plenty of other consonant chords. 3 of them produce a full 12 note scale.

Yourmusic Productions: Various derived bihexanies

2025-11-15T12:46:02Z

Various derived bihexanies

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 [[File:1-3-5-7_hexany.png|thumb|Circle diagram.]]
-[[File:1-3-5-7_hexany_rotated.png|thumb|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9, the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.
+[[File:1-3-5-7_hexany_rotated.png|thumb|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour [[1-3-5-9_hexany|1-3-5-9]], the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.
 <pre>
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 Suggested keyboard mapping: C D# E G A Bb C
 == Music ==
 ; [[Daniel Corral]]

Yourmusic Productions: Give this one extra attention as it's the starting point for hexanies.

2025-10-12T01:55:41Z

Give this one extra attention as it's the starting point for hexanies.

← Older revision		Revision as of 01:55, 12 October 2025
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	[[File:~~Hexany~~ 1 3 5 7.png\|thumb\|Circle diagram (rotated).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9 and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.		[[File:1-3-5-7_hexany.png\|thumb\|Circle diagram.]]
			[[File:1-3-5-7_hexany_rotated.png\|thumb\|Circle diagram (rotated to most consonant mode).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9, the smallest step is also smaller and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.

	<pre>		<pre>

BudjarnLambeth at 03:10, 5 October 2025

2025-10-05T03:10:09Z

← Older revision		Revision as of 03:10, 5 October 2025
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	The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9 and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.		[[File:Hexany 1 3 5 7.png\|thumb\|Circle diagram (rotated).]] The simplest possible [[Hexany]], comprised of two-combination sum products of the first four odd numbers. This creates a scale of 1 7/6 5/4 35/24 5/3 7/4 2/1, with steps of 7/6 15/14 7/6 8/7 21/20 8/7. Despite having simpler factors, it's most complex number (the 35/24) is more complex than that of its immediate neighbour 1-3-5-9 and the overall sound is more xenharmonic as it involves 7-limit intervals. It has two 5-limit chords that can be used to provide stable roots, a major one rooted on the 7/6 and a minor one rooted on the 5/3.

	<pre>		<pre>

Yourmusic Productions: Add music.

2025-08-20T17:52:46Z

Add music.

← Older revision		Revision as of 17:52, 20 August 2025
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	; [[Inhibitd]]		; [[Inhibitd]]
	* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''		* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''

			; [[Kalleaho]]
			* ''[https://soundcloud.com/kalleaho/nocturne Nocturne]''

	; [[Paul Maaswinkel]]		; [[Paul Maaswinkel]]

Yourmusic Productions: Add music.

2025-08-20T17:46:07Z

Add music.

← Older revision		Revision as of 17:46, 20 August 2025
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	; [[Inhibitd]]		; [[Inhibitd]]
	* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''		* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''

			; [[Paul Maaswinkel]]
			* ''[https://soundcloud.com/paulmaaswinkel/dungeon-brunch Dungeon Brunch]''

	; [[Node Audio]]		; [[Node Audio]]

Yourmusic Productions: Add music.

2025-08-20T16:02:41Z

Add music.

← Older revision		Revision as of 16:02, 20 August 2025
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	; [[Elkay & Cee]]		; [[Elkay & Cee]]
	* ''[https://soundcloud.com/elkayandcee/hexany-1357 Hexany1357]''		* ''[https://soundcloud.com/elkayandcee/hexany-1357 Hexany1357]''

			; [[Inhibitd]]
			* ''[https://soundcloud.com/inhibitd/the-sphere-7-limit-hexany The Sphere]''

	; [[Node Audio]]		; [[Node Audio]]

Yourmusic Productions: Add music.

2025-08-20T10:20:02Z

Add music.

← Older revision		Revision as of 10:20, 20 August 2025
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	; [[Daniel Corral]]		; [[Daniel Corral]]
	* ''[https://www.youtube.com/watch?v=tGDaXGdPG5o Stellate Hexany Study #1: Triads]''		* ''[https://www.youtube.com/watch?v=tGDaXGdPG5o Stellate Hexany Study #1: Triads]''

			; [[Dominique Cyprès]]
			* ''[https://soundcloud.com/lunasspecto/canal-street-antique-mall Canal Street Antique Mall]''

	; [[Elkay & Cee]]		; [[Elkay & Cee]]
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	; [[Phexioenesystems]]		; [[Phexioenesystems]]
	* ''[https://phexioenesystems.bandcamp.com/track/shining-sea-hexany-1-3-5-7 Shining Sea]''		* ''[https://phexioenesystems.bandcamp.com/track/shining-sea-hexany-1-3-5-7 Shining Sea]''

			; [[Dave Seidel]]
			* ''[https://soundcloud.com/mysterybear/hexany-dyads Hexany Dyads]''
			* ''[https://soundcloud.com/mysterybear/the-1-3-5-7-hexany-chord-catalog-the-35-three-note-chords-possible-in-one-octave-disquiet0226 The 1-3-5-7 Hexany Chord Catalogue (The 35 three-note chords possible in one octave]''

	; [[Sevish]]		; [[Sevish]]