Hendrix chord

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Dominant seventh sharp ninth chord#Hendrix chord

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

JI interpretations

Interpretations as a just intonation chord.

The only interpretations allowed in this section are ones where all 'intervals from root' have a denominator of 8 or less (to prevent the section becoming too long.

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.

According to this interpretation, the 12edo hendrix chord has 30.2 cents of total error and no more than 17.6 cents error on any single interval.

EDOs with less than 20 cents error on any one interval include: 12, 15, 18, 19, 22, 24, 26, 27, 28... and everything bigger than 28.

EDOs up to 100 with successively lower error include: 4, 5, 6, 7, 12, 19, 34, 46, 53.

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, an extended harmonic seventh chord.

According to this interpretation, the 12edo hendrix chord has 78.0 cents of total error and no more than 33.1 cents error on any single interval.

EDOs with less than 35 cents error on any one interval include: 10, 12, 15, 16, 17... and everything bigger than 17.

EDOs up to 100 with successively lower error include: 4, 6, 9, 10, 19, 21, 22, 31, 68, 99.

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.

According to this interpretation, the 12edo hendrix chord has 47.4 cents of total error and no more than 33.1 cents error on any single interval.

EDOs with less than 35 cents error on any one interval include: 12, 15, 16, 17... and everything bigger than 17.

EDOs up to 100 with successively lower error include: 4, 7, 9, 12, 15, 16, 25, 37, 53, 56, 68, 93.

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.