The 16 most stable triads of 22edo - Revision history

Fredg999: Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

2025-08-20T01:07:18Z

Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

← Older revision		Revision as of 01:07, 20 August 2025
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	[[File:16 most stable triads.png\|thumb\|611x611px\|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and ~~Downs Notation~~\|Ups and Downs]]. Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triples describe the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest. Triads are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample		[[File:16 most stable triads.png\|thumb\|611x611px\|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and downs notation\|Ups and Downs]]. Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triples describe the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest. Triads are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+

YoVariable: Fixed cent errors, most importantly, 1082c to 1091c

2024-02-13T08:44:36Z

Fixed cent errors, most importantly, 1082c to 1091c

← Older revision		Revision as of 08:44, 13 February 2024
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	\|Classic major seventh (no fifth)		\|Classic major seventh (no fifth)
	\|382		\|382
	~~1082~~		1091
	\|5/4, 3/2, 15/14, 8:10:15		\|5/4, 3/2, 15/14, 8:10:15
	\|0.78		\|0.78
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	\|Classic augmented triad		\|Classic augmented triad
	\|382		\|382
	~~765~~		764
	\|5/4, 5/4, 9/7, 16:20:25		\|5/4, 5/4, 9/7, 16:20:25
	\|1.08		\|1.08
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	\|Classic major seventh (no third)		\|Classic major seventh (no third)
	\|709		\|709
	~~1082~~		1091
	\|3/2, 5/4, 15/14, 8:12:15		\|3/2, 5/4, 15/14, 8:12:15
	\|1.10		\|1.10

Lhearne: corrected links

2021-07-13T03:07:32Z

corrected links

← Older revision		Revision as of 03:07, 13 July 2021
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	\|-		\|-
	\|2		\|2
	\|[https://www.dropbox.com/s/gw3zd7teif6klo6/3.aif?dl=0 <nowiki>[0,4,13]</nowiki>]		\|[https://www.dropbox.com/s/gw3zd7teif6klo6/2.aif?dl=0 <nowiki>[0,4,13]</nowiki>]
	\|Suspended triad		\|Suspended triad
	\|491		\|491
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	\|-		\|-
	\|3		\|3
	\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 <nowiki>[0,8,13]</nowiki>]		\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/3.aif?dl=0 <nowiki>[0,8,13]</nowiki>]
	\|Supermajor triad		\|Supermajor triad
	\|436		\|436
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	\|-		\|-
	\|11		\|11
	\|[https://www.dropbox.com/sh/~~5fg5v76hsvhmbr3~~/~~AAB4Ww-MlDTw__FcmE5_9XXEa~~?dl=0 <nowiki>[0,4,7]</nowiki>]		\|[https://www.dropbox.com/s/0tk5wn3ac4gjv7f/11.aif?dl=0 <nowiki>[0,4,7]</nowiki>]
	\|Classic major add 9 (no fifth)		\|Classic major add 9 (no fifth)
	\|218		\|218
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	\|-		\|-
	\|12		\|12
	\|[https://www.dropbox.com/s/z6ck2n622w0s0mt/11.aif?dl=0 <nowiki>[0,5,13]</nowiki>]		\|[https://www.dropbox.com/s/z6ck2n622w0s0mt/12.aif?dl=0 <nowiki>[0,5,13]</nowiki>]
	\|Subminor triad		\|Subminor triad
	\|273		\|273
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	\|-		\|-
	\|14		\|14
	\|[https://www.dropbox.com/s/48w3q0poo3v2ylo/13.aif?dl=0 <nowiki>[0,7,14]</nowiki>]		\|[https://www.dropbox.com/s/48w3q0poo3v2ylo/14.aif?dl=0 <nowiki>[0,7,14]</nowiki>]
	\|Classic augmented triad		\|Classic augmented triad
	\|382		\|382

Lhearne at 02:49, 13 July 2021

2021-07-13T02:49:43Z

← Older revision		Revision as of 02:49, 13 July 2021
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	[[File:16 most stable triads.png\|thumb\|611x611px\|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and Downs Notation\|Ups and Downs]]. Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triples describe the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest. Triads are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample ~~(tbc)~~		[[File:16 most stable triads.png\|thumb\|611x611px\|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and Downs Notation\|Ups and Downs]]. Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triples describe the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest. Triads are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+

Lhearne: added triads 13 and 16

2021-07-13T02:48:30Z

added triads 13 and 16

← Older revision		Revision as of 02:48, 13 July 2021
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	\|-		\|-
	\|13		\|13
	\|[0,7,11]		\|[https://www.dropbox.com/s/e0skc9cg2ilmk7h/triad13.aif?dl=0 <nowiki>[0,7,11]</nowiki>]
	\|Classic major flat 5		\|Classic major flat 5
	\|382		\|382
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	\|-		\|-
	\|16		\|16
	\|[0,7,9]		\|[https://www.dropbox.com/s/f31k6asri0qqec1/triad16.aif?dl=0 <nowiki>[0,7,9]</nowiki>]
	\|Classic major seventh (no third)		\|Classic major seventh (no third)
	\|709		\|709

Lhearne: Added links to audio of most triads

2021-05-09T09:36:21Z

Added links to audio of most triads

← Older revision		Revision as of 09:36, 9 May 2021
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	[[File:16 most stable triads.png\|thumb\|611x611px\|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and Downs Notation\|Ups and Downs]]. Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triples describe the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest. Triads are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample (~~coming soon~~)		[[File:16 most stable triads.png\|thumb\|611x611px\|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and Downs Notation\|Ups and Downs]]. Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triples describe the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest. Triads are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample (tbc)
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
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	\|-		\|-
	\|7		\|7
	\|[0,2,9]		\|[https://www.dropbox.com/s/o47pctm9f36ezo5/7.aif?dl=0 <nowiki>[0,2,9]</nowiki>]
	\|Classic major seventh (no fifth)		\|Classic major seventh (no fifth)
	\|382		\|382
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	\|-		\|-
	\|8		\|8
	\|[0,7,12]		\|[https://www.dropbox.com/s/bprlfpy2f5pdepf/8.aif?dl=0 <nowiki>[0,7,12]</nowiki>]
	\|"Squished" major triad		\|"Squished" major triad
	\|382		\|382
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	\|-		\|-
	\|9		\|9
	\|[0,6,11]		\|[https://www.dropbox.com/s/g9jt3n34vhbpxzb/9.aif?dl=0 <nowiki>[0,6,11]</nowiki>]
	\|Harmonic diminished triad		\|Harmonic diminished triad
	\|327		\|327
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	\|-		\|-
	\|10		\|10
	\|[0,4,11]		\|[https://www.dropbox.com/s/smlmcqgm8tw83qn/10.aif?dl=0 <nowiki>[0,4,11]</nowiki>]
	\|Harmonic dominant seventh (no fifth)		\|Harmonic dominant seventh (no fifth)
	\|382		\|382
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	\|-		\|-
	\|11		\|11
	\|[0,4,7]		\|[https://www.dropbox.com/sh/5fg5v76hsvhmbr3/AAB4Ww-MlDTw__FcmE5_9XXEa?dl=0 <nowiki>[0,4,7]</nowiki>]
	\|Classic major add 9 (no fifth)		\|Classic major add 9 (no fifth)
	\|218		\|218
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	\|-		\|-
	\|12		\|12
	\|[0,5,13]		\|[https://www.dropbox.com/s/z6ck2n622w0s0mt/11.aif?dl=0 <nowiki>[0,5,13]</nowiki>]
	\|Subminor triad		\|Subminor triad
	\|273		\|273
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	\|-		\|-
	\|14		\|14
	\|[0,7,14]		\|[https://www.dropbox.com/s/48w3q0poo3v2ylo/13.aif?dl=0 <nowiki>[0,7,14]</nowiki>]
	\|Classic augmented triad		\|Classic augmented triad
	\|382		\|382
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	\|-		\|-
	\|15		\|15
	\|[0,3,9]		\|[https://www.dropbox.com/s/m6m6a1qmsj22g6z/15.aif?dl=0 <nowiki>[0,3,9]</nowiki>]
	\|Classic minor seventh (no fifth)		\|Classic minor seventh (no fifth)
	\|327		\|327

Lhearne at 09:28, 9 May 2021

2021-05-09T09:28:57Z

← Older revision		Revision as of 09:28, 9 May 2021
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	\|-		\|-
	\|1		\|1
	\|[https://www.dropbox.com/s/ke3deqbdntbn2dg/1.aif?dl=0 </nowiki>[0,7,13]</nowiki>]		\|[https://www.dropbox.com/s/ke3deqbdntbn2dg/1.aif?dl=0 <nowiki>[0,7,13]</nowiki>]
	\|Classic major triad		\|Classic major triad
	\|382		\|382
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	\|-		\|-
	\|2		\|2
	\|[https://www.dropbox.com/s/gw3zd7teif6klo6/3.aif?dl=0 </nowiki>[0,4,13]</nowiki>]		\|[https://www.dropbox.com/s/gw3zd7teif6klo6/3.aif?dl=0 <nowiki>[0,4,13]</nowiki>]
	\|Suspended triad		\|Suspended triad
	\|491		\|491
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	\|-		\|-
	\|3		\|3
	\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 </nowiki>[0,8,13]</nowiki>]		\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 <nowiki>[0,8,13]</nowiki>]
	\|Supermajor triad		\|Supermajor triad
	\|436		\|436
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	\|-		\|-
	\|4		\|4
	\|[https://www.dropbox.com/s/wjoo4lediuyaix6/4.aif?dl=0 </nowiki>[0,6,13]</nowiki>]		\|[https://www.dropbox.com/s/wjoo4lediuyaix6/4.aif?dl=0 <nowiki>[0,6,13]</nowiki>]
	\|Classic minor triad		\|Classic minor triad
	\|327		\|327

Lhearne at 09:28, 9 May 2021

2021-05-09T09:28:15Z

← Older revision		Revision as of 09:28, 9 May 2021
Line 10:		Line 10:
	\|-		\|-
	\|1		\|1
	\|[https://www.dropbox.com/s/ke3deqbdntbn2dg/1.aif?dl=0 [0,7,13]]		\|[https://www.dropbox.com/s/ke3deqbdntbn2dg/1.aif?dl=0 </nowiki>[0,7,13]</nowiki>]
	\|Classic major triad		\|Classic major triad
	\|382		\|382
Line 18:		Line 18:
	\|-		\|-
	\|2		\|2
	\|[[https://www.dropbox.com/s/gw3zd7teif6klo6/3.aif?dl=0 0,4,13]]		\|[https://www.dropbox.com/s/gw3zd7teif6klo6/3.aif?dl=0 </nowiki>[0,4,13]</nowiki>]
	\|Suspended triad		\|Suspended triad
	\|491		\|491
Line 26:		Line 26:
	\|-		\|-
	\|3		\|3
	\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 [0,8,13]]		\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 </nowiki>[0,8,13]</nowiki>]
	\|Supermajor triad		\|Supermajor triad
	\|436		\|436
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	\|-		\|-
	\|4		\|4
	\|[https://www.dropbox.com/s/wjoo4lediuyaix6/4.aif?dl=0 [0,6,13]]		\|[https://www.dropbox.com/s/wjoo4lediuyaix6/4.aif?dl=0 </nowiki>[0,6,13]</nowiki>]
	\|Classic minor triad		\|Classic minor triad
	\|327		\|327
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	\|-		\|-
	\|5		\|5
	\|[https://www.dropbox.com/s/1957ess34prkpmm/5.aif?dl=0 [0,5,9]]		\|[https://www.dropbox.com/s/1957ess34prkpmm/5.aif?dl=0 <nowiki>[0,5,9]</nowiki>]
	\|Subminor seventh (no third)		\|Subminor seventh (no third)
	\|709		\|709

Lhearne at 09:27, 9 May 2021

2021-05-09T09:27:08Z

← Older revision		Revision as of 09:27, 9 May 2021
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	\|-		\|-
	\|6		\|6
	\|[0,4,9]		\|[https://www.dropbox.com/s/u77dk0xz25e9fmc/6.aif?dl=0 <nowiki>[0,4,9]</nowiki>]
	\|Subminor seventh (no fifth)		\|Subminor seventh (no fifth)
	\|273		\|273

Lhearne at 09:25, 9 May 2021

2021-05-09T09:25:28Z

← Older revision		Revision as of 09:25, 9 May 2021
Line 26:		Line 26:
	\|-		\|-
	\|3		\|3
	\|[0,8,13]		\|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 [0,8,13]]
	\|Supermajor triad		\|Supermajor triad
	\|436		\|436
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	\|-		\|-
	\|4		\|4
	\|[0,6,13]		\|[https://www.dropbox.com/s/wjoo4lediuyaix6/4.aif?dl=0 [0,6,13]]
	\|Classic minor triad		\|Classic minor triad
	\|327		\|327
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	\|-		\|-
	\|5		\|5
	\|[0,5,9]		\|[https://www.dropbox.com/s/1957ess34prkpmm/5.aif?dl=0 [0,5,9]]
	\|Subminor seventh (no third)		\|Subminor seventh (no third)
	\|709		\|709