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The 16 most stable triads of 22edo: Difference between revisions

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[[File:16 most stable triads.png|thumb|611x611px|The 16 most stable triads of 22-TET, from an empirical experiment, notated in [[Ups and Downs Notation|Ups and Downs]]]]
[[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
 
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. Triads are written in 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.
 
Click the triad for an audio sample
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 11: Line 7:
!Size in cents
!Size in cents
!Ratios approximated
!Ratios approximated
!Stability
!Relative Instability
|-
|-
|1
|1
|[0,7,13]
|[https://www.dropbox.com/s/ke3deqbdntbn2dg/1.aif?dl=0 <nowiki>[0,7,13]</nowiki>]
|Classic major triad  
|Classic major triad  
|382-709
|382
709
|5/4, 6/5, 4/3, 4:5:6
|5/4, 6/5, 4/3, 4:5:6
|0
|0
|-
|-
|2
|2
|[0,4,13]
|[https://www.dropbox.com/s/gw3zd7teif6klo6/2.aif?dl=0 <nowiki>[0,4,13]</nowiki>]
|Suspended triad
|Suspended triad
|491-709
|491
709
|4/3, 8/7, 4/3, 6:8:9
|4/3, 8/7, 4/3, 6:8:9
|-0.34
|0.34
|-
|-
|3
|3
|[0,8,13]
|[https://www.dropbox.com/s/rw9vbpsbrcveak0/3.aif?dl=0 <nowiki>[0,8,13]</nowiki>]
|Supermajor triad
|Supermajor triad
|436-709
|436
709
|9/7, 7/6, 4/3, 14:18:21
|9/7, 7/6, 4/3, 14:18:21
|-0.40
|0.40
|-
|-
|4
|4
|[0,6,13]
|[https://www.dropbox.com/s/wjoo4lediuyaix6/4.aif?dl=0 <nowiki>[0,6,13]</nowiki>]
|Classic minor triad
|Classic minor triad
|327-709
|327
709
|6/5, 5/4, 4/3, 10:12:15
|6/5, 5/4, 4/3, 10:12:15
|-0.53
|0.53
|-
|-
|5
|5
|[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)
|709-982
|709
982
|3/2, 7/6, 8/7, 4:6:7
|3/2, 7/6, 8/7, 4:6:7
|-0.53
|0.53
|-
|-
|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)
|273-982
|273
982
|7/6, 3/2, 8/7, 12:14:21
|7/6, 3/2, 8/7, 12:14:21
|-0.71
|0.71
|-
|-
|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)
|382-1082
|382
1091
|5/4, 3/2, 15/14, 8:10:15
|5/4, 3/2, 15/14, 8:10:15
|-0.78
|0.78
|-
|-
|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
|382-655
|382
655
|5/4, 7/6, 11/8, 24:30:35
|5/4, 7/6, 11/8, 24:30:35
|-0.84
|0.84
|-
|-
|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
|327-600
|327
600
|6/5, 7/6, 7/5, 5:6:7
|6/5, 7/6, 7/5, 5:6:7
|-0.86
|0.86
|-
|-
|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)
|382-982
|382
982
|5/4, 7/5, 8/7, 4:5:7
|5/4, 7/5, 8/7, 4:5:7
|-0.96
|0.96
|-
|-
|11
|11
|[0,4,7]
|[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)
|218-382 &8/7, 10/9, 8/5,  8:9:10
|218
|-0.99
382
|8/7, 10/9, 8/5,  8:9:10
|0.99
|-
|-
|12
|12
|[0,5,13]
|[https://www.dropbox.com/s/z6ck2n622w0s0mt/12.aif?dl=0 <nowiki>[0,5,13]</nowiki>]
|Subminor triad
|Subminor triad
|273-709
|273
709
|7/6, 9/7, 4/3, 6:7:9
|7/6, 9/7, 4/3, 6:7:9
|-1.03
|1.03
|-
|-
|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
|382-600
|382
600
|5/4, 8/7, 7/5, 12:15:17
|5/4, 8/7, 7/5, 12:15:17
|-1.06
|1.06
|-
|-
|14
|14
|[0,7,14]
|[https://www.dropbox.com/s/48w3q0poo3v2ylo/14.aif?dl=0 <nowiki>[0,7,14]</nowiki>]
|Classic augmented triad
|Classic augmented triad
|382-765
|382
764
|5/4, 5/4, 9/7, 16:20:25
|5/4, 5/4, 9/7, 16:20:25
|-1.08
|1.08
|-
|-
|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)
|327-1036
|327
1036
|6/5, 3/2, 10/9, 5:6:9
|6/5, 3/2, 10/9, 5:6:9
|-1.09
|1.09
|-
|-
|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)
|709-1082
|709
1091
|3/2, 5/4, 15/14, 8:12:15
|3/2, 5/4, 15/14, 8:12:15
|-1.10}
|1.10
|}
 
[[Category: 22edo]]
[[Category: Triad]]
Retrieved from "https://en.xen.wiki/w/The_16_most_stable_triads_of_22edo"