Xenharmonic Wiki

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

VisualWikitext
My goal is to create a list of otonal chords. Needs significant work.
 
 
(3 intermediate revisions by the same user not shown)
Line 1: Line 1:
{{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|Finish tables, expand further. Create tables for sus chords and beyond, finish summary|inline=1}}
{{Todo|expand|inline=2|add audios}}
Retrieved from "https://en.xen.wiki/w/User:DesertFreeze/List_of_otonal_chords"