Gann 8x8 - Revision history

Wilh3lm: /* Properties of the scale */ Correcting properties of the neutral thirds

2026-05-01T13:25:36Z

Properties of the scale: Correcting properties of the neutral thirds

← Older revision		Revision as of 13:25, 1 May 2026
Line 255:		Line 255:
	The most versatile pitches are 15/8 and 45/32 (D and A+ in ''Hyperchromatica''), each appearing in four different harmonic series, which is the reason ''Andromeda Memories'', the first movement of ''Hyperchromatica'', builds its jazz harmonies on D.<ref>https://kylegann.com/HyperchromaticaTech.html</ref>		The most versatile pitches are 15/8 and 45/32 (D and A+ in ''Hyperchromatica''), each appearing in four different harmonic series, which is the reason ''Andromeda Memories'', the first movement of ''Hyperchromatica'', builds its jazz harmonies on D.<ref>https://kylegann.com/HyperchromaticaTech.html</ref>

	On top of 5/4 (G in ''Hyperchromatica'')~~, and nowhere else~~, it is possible to build minor (6/5), major (5/4), and neutral thirds, using [[49/40]] for the neutral third (49/32 relative to 1/1) instead. This minor-neutral-major third sequence, as ~~Bb-Bb^-B~~, is the basis for the movement ''Busted Grooves'', and appears as an ostinato throughout. However, 9/8 (F+) comes close, with relative 11/9 (absolute 11/8, Ab^) for the neutral third, but [[7/6]] (absolute 21/16, Ab7+) for the minor third.		On top of 5/4 (G in ''Hyperchromatica''), it is possible to build minor (6/5), major (5/4), and neutral thirds, using [[49/40]] for the neutral third (49/32 relative to 1/1) instead of the more common 11/9. This minor-neutral-major third sequence, as Bb—Cb77+—B, is the basis for the movement ''Busted Grooves'', and appears as an ostinato throughout. However, 9/8 (F+) comes close, with relative 11/9 (absolute 11/8, Ab^) for the neutral third, but [[7/6]] (absolute 21/16, Ab7+) for the minor third.

	== Works using this scale ==		== Works using this scale ==

Wilh3lm: /* Properties of the scale */ Corrected a missing comma on 121/64

2026-05-01T13:24:21Z

Properties of the scale: Corrected a missing comma on 121/64

← Older revision		Revision as of 13:24, 1 May 2026
Line 245:		Line 245:
	\|121/64		\|121/64
	\|1102.6		\|1102.6
	\|Db^^		\|Db^^-
	\|Bb^^-		\|Bb^^-
	\|-		\|-

Wilh3lm: References header

2026-03-15T21:40:11Z

References header

← Older revision		Revision as of 21:40, 15 March 2026
Line 306:		Line 306:
	</syntaxhighlight>		</syntaxhighlight>

			== References ==
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]

Wilh3lm: Added more information on certain aspects of the scale as used in Hyperchromatica

2026-03-15T21:39:55Z

Added more information on certain aspects of the scale as used in Hyperchromatica

← Older revision		Revision as of 21:39, 15 March 2026
Line 253:		Line 253:
	\|C7+		\|C7+
	\|}		\|}
			The most versatile pitches are 15/8 and 45/32 (D and A+ in ''Hyperchromatica''), each appearing in four different harmonic series, which is the reason ''Andromeda Memories'', the first movement of ''Hyperchromatica'', builds its jazz harmonies on D.<ref>https://kylegann.com/HyperchromaticaTech.html</ref>

			On top of 5/4 (G in ''Hyperchromatica''), and nowhere else, it is possible to build minor (6/5), major (5/4), and neutral thirds, using [[49/40]] for the neutral third (49/32 relative to 1/1) instead. This minor-neutral-major third sequence, as Bb-Bb^-B, is the basis for the movement ''Busted Grooves'', and appears as an ostinato throughout. However, 9/8 (F+) comes close, with relative 11/9 (absolute 11/8, Ab^) for the neutral third, but [[7/6]] (absolute 21/16, Ab7+) for the minor third.

	== Works using this scale ==		== Works using this scale ==

Wilh3lm: Added more info including how it's made and the resulting pitches on Eb and C

2026-03-15T21:21:51Z

Added more info including how it's made and the resulting pitches on Eb and C

Show changes

Wilh3lm: Added more info about scale

2026-03-15T14:45:45Z

Added more info about scale

← Older revision		Revision as of 14:45, 15 March 2026
Line 1:		Line 1:
	<syntaxhighlight lang="text">		The '''8x8 scale''', or '''Gann 8x8''', is a [[13-limit]] [[just intonation]] scale with 33 pitches per octave, developed by [[Kyle Gann]] and used in his cycle ''Hyperchromatica'' for three player pianos.

			The scale is formed by taking the first eight odd harmonics (1, 3, 5, 7, 9, 11, 13, and 15), and then taking the first eight odd harmonics of each of those pitches.<syntaxhighlight lang="text">
	! Gann_8x8.scl		! Gann_8x8.scl
	!		!

Lériendil: Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

2025-06-24T00:40:20Z

Text replacement - "Category:Just intonation scales" to "Category:Just intonation scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:40, 24 June 2025
Line 44:		Line 44:
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
			[[Category:Pages with mostly numerical content]]

Xenwolf: fix syntax error (the lang attribute is required), add categories

2022-03-18T08:26:39Z

fix syntax error (the lang attribute is required), add categories

← Older revision		Revision as of 08:26, 18 March 2022
Line 1:		Line 1:
	<syntaxhighlight>		<syntaxhighlight lang="text">
	! Gann_8x8.scl		! Gann_8x8.scl
	!		!
Line 41:		Line 41:
	2/1		2/1
	</syntaxhighlight>		</syntaxhighlight>

			[[Category:Pages with Scala files]]
			[[Category:Just intonation scales]]

Kaiveran: Created page with " ! Gann_8x8.scl ! ! Harmonics 8-16, reproduced on harmonics 8-16 (or 15-odd-limit order-2 otonal heterodyne) ! Kyle Gann, 8x8 Scale ("Nursery Tunes for Dement..."

2022-03-18T08:21:44Z

Created page with "<syntaxhighlight> ! Gann_8x8.scl ! ! Harmonics 8-16, reproduced on harmonics 8-16 (or 15-odd-limit order-2 otonal heterodyne) ! Kyle Gann, 8x8 Scale ("Nursery Tunes for Dement..."

New page

<syntaxhighlight>
! Gann_8x8.scl
!
! Harmonics 8-16, reproduced on harmonics 8-16 (or 15-odd-limit order-2 otonal heterodyne)
!
Kyle Gann, 8x8 Scale ("Nursery Tunes for Demented Children", "Hyperchromatica")
33
!
65/64
33/32
135/128
35/32
143/128
9/8
75/64
77/64
39/32
5/4
81/64
165/128
21/16
169/128
11/8
45/32
91/64
3/2
195/128
49/32
99/64
25/16
13/8
105/64
27/16
55/32
7/4
225/128
117/64
15/8
121/64
63/32
2/1
</syntaxhighlight>