Hendrix chord

The hendrix chord, a 7#9no5 chord originating from 12edo, has several possible interpretations.

English Wikipedia has an article on:

Dominant seventh sharp ninth chord#Hendrix chord

JI interpretations

Interpretations as a just intonation chord:

5-limit

Chord information

Harmonics	10:20:25:36:40:48
Intervals from root	1/2 – 1/1 – 5/4 – 9/5 – 2/1 – 12/5
Cents from root	-1200¢ 0¢ 386¢ 1018¢ 1200¢ 1516¢
Step intervals	2/1, 5/4, 36/25, 10/9, 6/5
Step cents	1200¢, 386¢, 631¢, 182¢, 316¢
Color name	yo gu-7 guqu-9 no-5 or y,g7gq9no5
Prime limit	5
Genus	32 ⋅ 52 (225)
Intervallic odd limit	25
Otonal odd limit	25
Utonal odd limit	75
Consistent edos (d ≥ 1.5)	12edo, 15edo, 19edo**, 31edo, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

In the 5-limit it may be tuned as 10:20:25:36:40:48, an extended major-minor seventh chord.

7-limit

Chord information

Harmonics	6:12:15:21:24:28
Intervals from root	1/2 – 1/1 – 5/4 – 7/4 – 2/1 – 7/3
Cents from root	-1200¢ 0¢ 386¢ 969¢ 1200¢ 1467¢
Step intervals	2/1, 5/4, 7/5, 8/7, 7/6
Step cents	1200¢, 386¢, 583¢, 231¢, 267¢
Color name	har-7 zoqu-9 no-5 or h7zq9no5
Prime limit	7
Genus	3 ⋅ 5 ⋅ 7 (105)
Intervallic odd limit	15
Otonal odd limit	21
Utonal odd limit	35
Consistent edos (d ≥ 1.5)	10edo*, 12edo, 21edo, 22edo, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

In the 7-limit it may be tuned as 6:12:15:21:24:28, also an extended harmonic seventh chord.

19-limit

Chord information

Harmonics	4:8:10:14:16:19
Intervals from root	1/2 – 1/1 – 5/4 – 7/4 – 2/1 – 19/8
Cents from root	-1200¢ 0¢ 386¢ 969¢ 1200¢ 1498¢
Step intervals	2/1, 5/4, 7/5, 8/7, 19/16
Step cents	1200¢, 386¢, 583¢, 231¢, 298¢
Color name	har-7 noqu-9 no-5 or h7,19oq9no5
Prime limit	19
Genus	5 ⋅ 7 ⋅ 19 (665)
Intervallic odd limit	19
Otonal odd limit	19
Utonal odd limit	665
Consistent edos (d ≥ 1.5)	4edo, 12edo, 16edo*, 25edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

In the 19-limit it may be tuned as 4:8:10:14:16:19, an extended harmonic seventh chord.

Tempered interpretations

Interpretations as a tempered chord.

Essentially tempered

It can also be tuned as an essentially tempered chord that splits the difference between the 19/8 10th and the 7/3 10th. This chord tempers out the hendrix comma of 57/56.

Todo: review The paragraph about tempering 57/56 needs more explanation, and may be incorrect.

In EDOs

EDOs with hendrix chords include the 9, 10, 14, 16, 17, 21, 22, 26, and 31.

Todo: complete section Explain the reasoning for exactly when an EDO is considered to "have" a Hendrix chord and when not.