User:DesertFreeze/List of otonal chords: Difference between revisions

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{{Stub}}
Below is a series of justly-intonated chords represented otonally.


Below lies a list of chords that lie in the overtone series.
"With 3/2" denotes that the triads contain a [[3/2|3/2 perfect fifth]] of ~702 ¢. In these tables, the fifth will not be explicitly listed, due to the redundancy of listing "3/2" over and over. "Tertian-based" means that the second note generally counts as a third ([[Interval region|see Margo Schulter's interval regions]]). while "sus-based" denotes that the second note counts as a second or fourth, as in western [[wikipedia:Suspended_chord|sus triads]].
 
Of course, the boundaries between second, third, and fourth are "fuzzy" as described by [[Margo Schulter]], so subjectivity concerning interseptimal intervals such as [[13/10]] may arise. Editors are encouraged to add in their own viewpoints on this topic.{{Stub}}


== Triads ==
== Triads ==
{| class="wikitable"
{| class="wikitable"
|+Third-based (tertian) triads consisting of a [[3/2|3/2 perfect fifth]], going up to the [[33-odd-limit]].
|+Tertian-based triads with a [[3/2]], going up to the [[33-odd-limit]].
!Otonal
! rowspan="2" |Otonal
representation
representation
!Third
! colspan="3" |JI ratios
(ratio)
!
!Third
!
(¢)
!
!
|-
!
!
!
!Third (¢)
!English triad name
!English triad name
![[Limit|Prime]]  
![[Limit|Prime Limit]]  
[[Limit]]
!Steps
|-
|-
|[[4:5:6]]
|[[4:5:6]]
|
|[[5/4]]
|[[5/4]]
|3/2
|386.3
|386.3
|Classic major
|Classic major
|5-limit
|5-limit
|[[5/4]], [[6/5]], 4/3
|-
|-
|[[6:7:9]]
|[[6:7:9]]
|
|[[7/6]]
|[[7/6]]
|3/2
|266.9
|266.9
|Septimal subminor
|Septimal subminor
|7-limit
|7-limit
|[[7/6]], [[9/7]], 4/3
|-
|-
|[[10:12:15]]
|[[10:12:15]]
|
|[[6/5]]
|[[6/5]]
|3/2
|315.6
|315.6
|Classic minor
|Classic minor
|5-limit
|5-limit
|[[6/5]], [[5/4]], 4/3
|-
|-
|[[10:13:15]]
|[[10:13:15]]
|
|[[13/10]]
|[[13/10]]
|3/2
|454.2
|454.2
|Barbados / tridecimal ultramajor
|Barbados / tridecimal ultramajor
|13-limit
|13-limit
|[[13/10]], [[15/13]], 4/3
|-
|-
|[[14:17:21]]
|[[14:17:21]]
|
|[[17/14]]
|[[17/14]]
|3/2
|336.1
|336.1
|Septendecimal minor
|Septendecimal minor
|17-limit
|17-limit
|[[21/17]], [[17/14]], 4/3
|-
|-
|[[14:18:21]]
|[[14:18:21]]
|[[9/7]]
|
|[[9/7]],
|3/2
|435.1
|435.1
|Septimal supermajor
|Septimal supermajor
|7-limit
|7-limit
|[[9/7]], [[7/6]], 4/3
|-
|-
|[[16:19:24]]
|[[16:19:24]]
|
|[[19/16]]
|[[19/16]]
|3/2
|297.5
|297.5
|Undevicesimal minor/otonal minor
|Undevicesimal minor/otonal minor
|19-limit
|19-limit
|[[19/16]], [[24/19]], 4/3
|-
|-
|[[18:22:27]]
|[[18:22:27]]
|
|[[11/9]]
|[[11/9]]
|3/2
|347.4
|347.4
|Undecimal neutral/rastmic
|Undecimal neutral/rastmic
|11-limit
|11-limit
|[[11/9]], [[27/22]], 4/3
|-
|-
|[[18:23:27]]
|[[18:23:27]]
|
|[[23/18]]
|[[23/18]]
|3/2
|424.4
|424.4
|Vicesimotertial supermajor
|Vicesimotertial supermajor
|23-limit
|23-limit
|[[23/18]], [[27/23]], 4/3
|-
|-
|[[20:23:30]]
|[[20:23:30]]
|
|[[23/20]]
|[[23/20]]
|242
|3/2
|242.0
|Vicesimotertial ultraminor
|Vicesimotertial ultraminor
|23-limit
|23-limit
|[[23/20]], [[30/23]], 4/3
|-
|-
|[[22:26:33]]
|[[22:26:33]]
|
|[[13/11]]
|[[13/11]]
|3/2
|289.2
|289.2
|
|
|13-limit
|13-limit
|[[13/11]], [[33/26]], 4/3
|-
|-
|[[22:27:33]]
|[[22:27:33]]
|
|[[27/22]]
|[[27/22]]
|3/2
|354.6
|354.6
|Neutral / Rastmic
|Neutral / Rastmic
|11-limit
|11-limit
|[[27/22]], [[11/9]], 4/3
|-
|-
|[[22:28:33]]
|[[22:28:33]]
|
|[[14/11]]
|[[14/11]]
|3/2
|417.5
|417.5
|
|
|11-limit
|11-limit
|[[14/11]], [[33/28]], 4/3
|-
|-
|[[24:29:36]]
|[[24:29:36]]
|
|[[29/24]]
|[[29/24]]
|3/2
|327.6
|327.6
|
|
|29-limit
|29-limit
|[[29/24]], [[36/29]], 4/3
|-
|-
|[[24:31:36]]
|[[24:31:36]]
|
|[[31/24]]
|[[31/24]]
|3/2
|443.1
|443.1
|
|
|31-limit
|31-limit
|
|}
{| class="wikitable"
|+Sus-based triads with a 3/2, going up to the [[33-odd-limit]].
!Otonal reps.
!2nd/4th (JI)
!(¢)
!English triad name
![[Limit|Prime Limit]]
!Steps
|-
|6:8:9
|4/3, 3/2
|498.0
|Pythagorean sus4
|3-limit
|[[4/3]], [[9/8]]
|-
|8:9:12
|9/8, 3/2
|203.9
|Pythagorean sus2
|3-limit
|[[9/8]], [[4/3]]
|-
|8:11:12
|11/8, 3/2
|551.3
|Undecimal sus4
|11-limit
|[[11/8]], [[12/11]]
|-
|10:11:15
|11/10, 3/2
|165.0
|Undecimal sus2
|11-limit
|[[11/10]], [[15/11]]
|-
|12:13:18
|13/12, 3/2
|138.6
|Tridecimal sus2
|13-limit
|[[13/12]], [[18/13]]
|-
|14:16:21
|8/7, 3/2
|231.2
|Septimal sus2
|7-limit
|
|-
|14:19:21
|19/14, 3/2
|528.9
|Device sus4
|19-limit
|
|}
|}
{{Todo|expand|inline=1}}
{{Todo|expand|inline=2|add audios}}

Revision as of 18:25, 24 July 2026

Below is a series of justly-intonated chords represented otonally.

"With 3/2" denotes that the triads contain a 3/2 perfect fifth of ~702 ¢. In these tables, the fifth will not be explicitly listed, due to the redundancy of listing "3/2" over and over. "Tertian-based" means that the second note generally counts as a third (see Margo Schulter's interval regions). while "sus-based" denotes that the second note counts as a second or fourth, as in western sus triads.

Of course, the boundaries between second, third, and fourth are "fuzzy" as described by Margo Schulter, so subjectivity concerning interseptimal intervals such as 13/10 may arise. Editors are encouraged to add in their own viewpoints on this topic.

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

Triads

Tertian-based triads with a 3/2, going up to the 33-odd-limit.
Otonal

representation

JI ratios
Third (¢) English triad name Prime Limit Steps
4:5:6 5/4 3/2 386.3 Classic major 5-limit 5/4, 6/5, 4/3
6:7:9 7/6 3/2 266.9 Septimal subminor 7-limit 7/6, 9/7, 4/3
10:12:15 6/5 3/2 315.6 Classic minor 5-limit 6/5, 5/4, 4/3
10:13:15 13/10 3/2 454.2 Barbados / tridecimal ultramajor 13-limit 13/10, 15/13, 4/3
14:17:21 17/14 3/2 336.1 Septendecimal minor 17-limit 21/17, 17/14, 4/3
14:18:21 9/7, 3/2 435.1 Septimal supermajor 7-limit 9/7, 7/6, 4/3
16:19:24 19/16 3/2 297.5 Undevicesimal minor/otonal minor 19-limit 19/16, 24/19, 4/3
18:22:27 11/9 3/2 347.4 Undecimal neutral/rastmic 11-limit 11/9, 27/22, 4/3
18:23:27 23/18 3/2 424.4 Vicesimotertial supermajor 23-limit 23/18, 27/23, 4/3
20:23:30 23/20 3/2 242.0 Vicesimotertial ultraminor 23-limit 23/20, 30/23, 4/3
22:26:33 13/11 3/2 289.2 13-limit 13/11, 33/26, 4/3
22:27:33 27/22 3/2 354.6 Neutral / Rastmic 11-limit 27/22, 11/9, 4/3
22:28:33 14/11 3/2 417.5 11-limit 14/11, 33/28, 4/3
24:29:36 29/24 3/2 327.6 29-limit 29/24, 36/29, 4/3
24:31:36 31/24 3/2 443.1 31-limit
Sus-based triads with a 3/2, going up to the 33-odd-limit.
Otonal reps. 2nd/4th (JI) (¢) English triad name Prime Limit Steps
6:8:9 4/3, 3/2 498.0 Pythagorean sus4 3-limit 4/3, 9/8
8:9:12 9/8, 3/2 203.9 Pythagorean sus2 3-limit 9/8, 4/3
8:11:12 11/8, 3/2 551.3 Undecimal sus4 11-limit 11/8, 12/11
10:11:15 11/10, 3/2 165.0 Undecimal sus2 11-limit 11/10, 15/11
12:13:18 13/12, 3/2 138.6 Tridecimal sus2 13-limit 13/12, 18/13
14:16:21 8/7, 3/2 231.2 Septimal sus2 7-limit
14:19:21 19/14, 3/2 528.9 Device sus4 19-limit
Todo: expand, add audios
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