Hendrix chord: Difference between revisions

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The '''hendrix chord''', a 7#9no5 [[chord]], has several possible [[JI]] interpretations.
The '''hendrix chord''', a 7#9no5 [[chord]], has several possible [[JI]] interpretations.


{{Infobox Chord|4:8:10:14:16:19|Name=19-limit Hendrix}}
{{Infobox Chord|4:8:10:14:16:19|Root=8|Name=19-limit Hendrix}}
In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, or 1/2 - 1/1 - [[5/4]] - [[7/4]] - [[2/1]] - [[19/16|19/8]], an extended [[harmonic seventh chord]].
In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, or 1/2 - 1/1 - [[5/4]] - [[7/4]] - [[2/1]] - [[19/16|19/8]], an extended [[harmonic seventh chord]].


{{Infobox Chord|6:12:15:21:24:28|Name=7-limit Hendrix}}
{{Infobox Chord|6:12:15:21:24:28|Root=12|Name=7-limit Hendrix}}
In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, or 1/2 - 1/1 - 5/4 - 7/4 - 2/1 - [[7/3]], also an extended harmonic seventh chord.
In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, or 1/2 - 1/1 - 5/4 - 7/4 - 2/1 - [[7/3]], also an extended harmonic seventh chord.
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{{Infobox Chord|10:20:25:36:40:48|Name=5-limit Hendrix}}
{{Infobox Chord|10:20:25:36:40:48|Root=20|Name=5-limit Hendrix}}
In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, or 1/2 - 1/1 - 5/4 - [[9/5]] - 2/1 - [[12/5]], an extended [[major-minor seventh chord]].
In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, or 1/2 - 1/1 - 5/4 - [[9/5]] - 2/1 - [[12/5]], an extended [[major-minor seventh chord]].



Revision as of 05:18, 12 August 2024

The hendrix chord, a 7#9no5 chord, has several possible JI interpretations.

Chord information
Harmonics 4:8:10:14:16:19
Intervals from root 1/21/15/47/42/119/8
Cents from root -1200¢386¢969¢1200¢1498¢
Step intervals 2/1, 5/4, 7/5, 8/7, 19/16
Step cents 1200¢, 386¢, 583¢, 231¢, 298¢
Prime limit 19
Genus 5719 (665)
Intervallic odd limit 19
Otonal odd limit 19
Utonal odd limit 665
Consistent edos (d ≥ 1.5) 4edo, 12edo, 16edo*, 25edo*, …

In the 19-limit it may be tuned as 4:8:10:14:16:19, or 1/2 - 1/1 - 5/4 - 7/4 - 2/1 - 19/8, an extended harmonic seventh chord.

Chord information
Harmonics 6:12:15:21:24:28
Intervals from root 1/21/15/47/42/17/3
Cents from root -1200¢386¢969¢1200¢1467¢
Step intervals 2/1, 5/4, 7/5, 8/7, 7/6
Step cents 1200¢, 386¢, 583¢, 231¢, 267¢
Prime limit 7
Genus 357 (105)
Intervallic odd limit 15
Otonal odd limit 21
Utonal odd limit 35
Consistent edos (d ≥ 1.5) 10edo*, 12edo, 21edo, 22edo, …

In the 7-limit it may be tuned as 6:12:15:21:24:28, or 1/2 - 1/1 - 5/4 - 7/4 - 2/1 - 7/3, also an extended harmonic seventh chord.

Chord information
Harmonics 10:20:25:36:40:48
Intervals from root 1/21/15/49/52/112/5
Cents from root -1200¢386¢1018¢1200¢1516¢
Step intervals 2/1, 5/4, 36/25, 10/9, 6/5
Step cents 1200¢, 386¢, 631¢, 182¢, 316¢
Prime limit 5
Genus 3252 (225)
Intervallic odd limit 25
Otonal odd limit 25
Utonal odd limit 75
Consistent edos (d ≥ 1.5) 12edo, 15edo, 19edo**, 31edo, …

In the 5-limit it may be tuned as 10:20:25:36:40:48, or 1/2 - 1/1 - 5/4 - 9/5 - 2/1 - 12/5, an extended major-minor seventh chord.

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. It is notable for existing in 12-EDO; other equal divisions with hendrix chords include the 9, 10, 14, 16, 17, 21, 22, 26, and 31 equal divisions.

Todo: review

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