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

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Below is a series of justly-intonated chords represented otonally.
Below is a series of justly-intonated chords represented otonally.{{Stub}}
 
"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"
|+Tertian-based triads with a [[3/2]], going up to the [[33-odd-limit]].
|+[[wikipedia:Tertian|Tertian]], 5th = [[3/2]], [[27-odd-limit|27-oli]]
! rowspan="2" |Otonal
!Harmonics
representation
!Ints. f. root
! colspan="3" |JI ratios
!Cts. f. root
!
!Step ints.
!
!Step cts.
!
![[Prime limit|P-li]], [[Odd-limit|O-li]]
!
!Possible English name(s)
|-
!
!
!
!Third (¢)
!English triad name
![[Limit|Prime Limit]]  
!Steps
|-
|-
|[[4:5:6]]
|[[4:5:6]]
|
|1 - [[5/4]] - 3/2
|[[5/4]]
|3/2
|386.3
|386.3
|[[5/4]], [[6/5]]
|386¢, 316¢
|[[5-limit|5]], 5
|Classic major
|Classic major
|5-limit
|[[5/4]], [[6/5]], 4/3
|-
|-
|[[6:7:9]]
|[[6:7:9]]
|
|1 - [[7/6]] - 3/2
|[[7/6]]
|3/2
|266.9
|266.9
|[[7/6]], [[9/7]]
|267¢, 435¢
|7, 9
|Septimal subminor
|Septimal subminor
|7-limit
|[[7/6]], [[9/7]], 4/3
|-
|-
|[[10:12:15]]
|[[10:12:15]]
|
|1 - [[6/5]] - 3/2
|[[6/5]]
|3/2
|315.6
|315.6
|[[6/5]], [[5/4]]
|316¢, 386¢
|5, 15
|Classic minor
|Classic minor
|5-limit
|[[6/5]], [[5/4]], 4/3
|-
|-
|[[10:13:15]]
|[[10:13:15]]
|
|1 - [[13/10]] - 3/2
|[[13/10]]
|3/2
|454.2
|454.2
|Barbados / tridecimal ultramajor
|[[13/10]], [[15/13]]
|13-limit
|454¢, 248¢
|[[13/10]], [[15/13]], 4/3
|13, 15
|Tridecimal ultramajor, barbados
|-
|-
|[[14:17:21]]
|[[14:17:21]]
|1 - [[17/14]] - 3/2
|336.1
|[[21/17]], [[17/14]]
|
|
|[[17/14]]
|17, 21
|3/2
|Septendecimal (supra)minor
|336.1
|Septendecimal minor
|17-limit
|[[21/17]], [[17/14]], 4/3
|-
|-
|[[14:18:21]]
|[[14:18:21]]
|1- [[9/7]] - 3/2
|435.1
|[[9/7]], [[7/6]]
|
|
|[[9/7]],
|7, 21
|3/2
|435.1
|Septimal supermajor
|Septimal supermajor
|7-limit
|[[9/7]], [[7/6]], 4/3
|-
|-
|[[16:19:24]]
|[[16:19:24]]
|1- [[19/16]] - 3/2
|297.5
|[[19/16]], [[24/19]]
|
|
|[[19/16]]
|19, 19
|3/2
|Otonal minor, novemdecimal minor
|297.5
|Undevicesimal minor/otonal minor
|19-limit
|[[19/16]], [[24/19]], 4/3
|-
|-
|[[18:22:27]]
|[[18:22:27]]
|1 - [[11/9]] - 3/2
|347.4
|[[11/9]], [[27/22]]
|
|
|[[11/9]]
|11, 27
|3/2
|Undecimal/rastmic neutral
|347.4
|Undecimal neutral/rastmic
|11-limit
|[[11/9]], [[27/22]], 4/3
|-
|-
|[[18:23:27]]
|[[18:23:27]]
|1 - [[23/18]] - 3/2
|424.4
|[[23/18]], [[27/23]]
|
|
|[[23/18]]
|23, 27
|3/2
|424.4
|Vicesimotertial supermajor
|Vicesimotertial supermajor
|23-limit
|[[23/18]], [[27/23]], 4/3
|-
|-
|[[20:23:30]]
|[[20:23:30]]
|1 - [[23/20]] - 3/2
|242.0
|[[23/20]], [[30/23]]
|
|23, 23
|Vicesimotertial inframinor
|}
{| class="wikitable"
|+Tertian, 5th ≠ 3/2, 27-oli
!Harmonics
!Intvs. from root
!Step intvs.
!Cts. from root
!Step cts.
!P-li, O-li
!Possible English name(s)
|-
|[[5:6:7]]
|1 - 6/5 - 7/5
|6/5, 7/6
|0¢ - 316¢ - 583¢
|316¢, 267¢
|
|Septimal/harmonic diminished
|-
|[[7:9:11]]
|1 - 9/7 - 11/7
|9/7, 11/9
|0¢ - 435¢ - 782¢
|435¢, 347¢
|
|
|[[23/20]]
|Greeley major, undecimal augmented
|3/2
|242.0
|Vicesimotertial ultraminor
|23-limit
|[[23/20]], [[30/23]], 4/3
|-
|-
|[[22:26:33]]
|[[9:11:13]]
|1 - 11/9, 13/9
|11/9, 13/11
|0¢ - 347¢ - 637¢
|347¢,
|
|
|[[13/11]]
|3/2
|289.2
|
|
|13-limit
|[[13/11]], [[33/26]], 4/3
|-
|-
|[[22:27:33]]
|[[9:11:14]]
|1 - 11/9- 14/9
|11/9 14/11
|0¢ - 347¢ - 765¢
|
|
|
|
|[[27/22]]
|3/2
|354.6
|Neutral / Rastmic
|11-limit
|[[27/22]], [[11/9]], 4/3
|-
|-
|[[22:28:33]]
|[[10:13:16]]
|1 - 13/10 - 8/5
|13/10, 16/13
|0¢ - 454¢ - 814¢
|
|
|
|[[14/11]]
|3/2
|417.5
|
|
|11-limit
|[[14/11]], [[33/28]], 4/3
|-
|-
|[[24:29:36]]
|[[11:13:15]]
|1 - 13/11 - 15/11
|13/11, 15/13
|0¢ - 289¢ - 537¢
|
|
|
|[[29/24]]
|3/2
|327.6
|
|
|29-limit
|[[29/24]], [[36/29]], 4/3
|-
|-
|[[24:31:36]]
|[[11:13:16]]
|1 - 13/11 - 16/11
|13/11, 16/13
|0¢ - 289¢ - 649¢
|
|
|
|-
|[[11:14:17]]
|1 - 14/11 - 17/11
|14/11, 17/14
|0¢ - 418¢ - 754¢
|
|
|[[31/24]]
|3/2
|443.1
|
|
|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
|[[11:14:18]]
|4/3, 3/2
|1 - 14/11 - 18/11
|498.0
|14/11, 9/7
|Pythagorean sus4
|0¢ - 418¢ - 853¢
|3-limit
|
|[[4/3]], [[9/8]]
|
|
|-
|-
|8:9:12
|[[12:15:19]]
|9/8, 3/2
|1 - 5/4 - 19/12
|203.9
|5/4, 19/15
|Pythagorean sus2
|0¢ - 386¢ - 796¢
|3-limit
|
|[[9/8]], [[4/3]]
|
|Novemdecimal augmented
|-
|-
|8:11:12
|[[13:15:18]]
|11/8, 3/2
|1 - 15/13 - 18/13
|551.3
|15/13, 6/5
|Undecimal sus4
|
|11-limit
|
|[[11/8]], [[12/11]]
|
|
|-
|-
|10:11:15
|13:16:19
|11/10, 3/2
|1 - 16/13, 19/13
|165.0
|16/13, 19/16
|Undecimal sus2
|
|11-limit
|
|[[11/10]], [[15/11]]
|
|
|-
|-
|12:13:18
|14:17:20
|13/12, 3/2
|1 - 17/14 - 10/7
|138.6
|
|Tridecimal sus2
|
|13-limit
|
|[[13/12]], [[18/13]]
|
|
|-
|-
|14:16:21
|14:17:22
|8/7, 3/2
|1 - 17/14 - 11/7
|231.2
|
|Septimal sus2
|
|7-limit
|
|
|
|
|-
|-
|14:19:21
|14:18:23
|19/14, 3/2
|1 - 9/7 - 23/14
|528.9
|
|Device sus4
|
|19-limit
|
|
|
|
|}
|}
{{Todo|expand|inline=2|add audios}}
{{Todo|expand|inline=2|add audios}}

Latest revision as of 00:29, 28 July 2026

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

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

Triads

Tertian, 5th = 3/2, 27-oli
Harmonics Ints. f. root Cts. f. root Step ints. Step cts. P-li, O-li Possible English name(s)
4:5:6 1 - 5/4 - 3/2 386.3 5/4, 6/5 386¢, 316¢ 5, 5 Classic major
6:7:9 1 - 7/6 - 3/2 266.9 7/6, 9/7 267¢, 435¢ 7, 9 Septimal subminor
10:12:15 1 - 6/5 - 3/2 315.6 6/5, 5/4 316¢, 386¢ 5, 15 Classic minor
10:13:15 1 - 13/10 - 3/2 454.2 13/10, 15/13 454¢, 248¢ 13, 15 Tridecimal ultramajor, barbados
14:17:21 1 - 17/14 - 3/2 336.1 21/17, 17/14 17, 21 Septendecimal (supra)minor
14:18:21 1- 9/7 - 3/2 435.1 9/7, 7/6 7, 21 Septimal supermajor
16:19:24 1- 19/16 - 3/2 297.5 19/16, 24/19 19, 19 Otonal minor, novemdecimal minor
18:22:27 1 - 11/9 - 3/2 347.4 11/9, 27/22 11, 27 Undecimal/rastmic neutral
18:23:27 1 - 23/18 - 3/2 424.4 23/18, 27/23 23, 27 Vicesimotertial supermajor
20:23:30 1 - 23/20 - 3/2 242.0 23/20, 30/23 23, 23 Vicesimotertial inframinor
Tertian, 5th ≠ 3/2, 27-oli
Harmonics Intvs. from root Step intvs. Cts. from root Step cts. P-li, O-li Possible English name(s)
5:6:7 1 - 6/5 - 7/5 6/5, 7/6 0¢ - 316¢ - 583¢ 316¢, 267¢ Septimal/harmonic diminished
7:9:11 1 - 9/7 - 11/7 9/7, 11/9 0¢ - 435¢ - 782¢ 435¢, 347¢ Greeley major, undecimal augmented
9:11:13 1 - 11/9, 13/9 11/9, 13/11 0¢ - 347¢ - 637¢ 347¢,
9:11:14 1 - 11/9- 14/9 11/9 14/11 0¢ - 347¢ - 765¢
10:13:16 1 - 13/10 - 8/5 13/10, 16/13 0¢ - 454¢ - 814¢
11:13:15 1 - 13/11 - 15/11 13/11, 15/13 0¢ - 289¢ - 537¢
11:13:16 1 - 13/11 - 16/11 13/11, 16/13 0¢ - 289¢ - 649¢
11:14:17 1 - 14/11 - 17/11 14/11, 17/14 0¢ - 418¢ - 754¢
11:14:18 1 - 14/11 - 18/11 14/11, 9/7 0¢ - 418¢ - 853¢
12:15:19 1 - 5/4 - 19/12 5/4, 19/15 0¢ - 386¢ - 796¢ Novemdecimal augmented
13:15:18 1 - 15/13 - 18/13 15/13, 6/5
13:16:19 1 - 16/13, 19/13 16/13, 19/16
14:17:20 1 - 17/14 - 10/7
14:17:22 1 - 17/14 - 11/7
14:18:23 1 - 9/7 - 23/14
Todo: expand, add audios
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