Hendrix chord: Difference between revisions

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{{Wikipedia|Dominant seventh sharp ninth chord#Hendrix chord}}
{{Wikipedia|Dominant seventh sharp ninth chord#Hendrix chord}}
The '''hendrix chord''', a 7#9no5 [[chord]], has several possible [[JI]] interpretations:
* in the [[19-limit]] 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 [[7-limit]] 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;
* or in the [[5-limit]] 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]].


The '''hendrix chord''', a 7#9no5 [[chord]], has several possible [[JI]] interpretations.
{{Infobox Chord|4:8:10:14:16:19|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]].
{{Infobox Chord|6:12:15:21:24:28|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.
</div>
{{Infobox Chord|10:20:25:36:40:48|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]].
{{Clear}}
It can also be tuned as an [[essentially tempered chord]] that splits the difference between the [[19/16|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 {{EDOs| 9, 10, 14, 16, 17, 21, 22, 26, and 31}} equal divisions.
It can also be tuned as an [[essentially tempered chord]] that splits the difference between the [[19/16|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 {{EDOs| 9, 10, 14, 16, 17, 21, 22, 26, and 31}} equal divisions.
== See also ==
* [[Tetrad]]


[[Category:Hendrix| ]] <!-- main article -->
[[Category:Hendrix| ]] <!-- main article -->
[[Category:19-limit chords]]
[[Category:19-odd-limit chords]]
[[Category:7-limit chords]]
[[Category:15-odd-limit chords]]
[[Category:5-limit chords]]
[[Category:25-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Tetrads]]


{{Todo|review|inline=1|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}
{{Todo|review|inline=1|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}

Revision as of 05:06, 12 August 2024

English Wikipedia has an article on:

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

Chord information
Harmonics 4:8:10:14:16:19
Subharmonics 1/(2660:1330:1064:760:665:560)
Intervals from root 1/1–2/1–5/2–7/2–4/1–19/4
Cents from root 0¢–1200¢–1586¢–2169¢–2400¢–2698¢
Step intervals 2/1, 5/4, 7/5, 8/7, 19/16
Step cents 1200¢, 386¢, 583¢, 231¢, 298¢
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*, …

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
Subharmonics 1/(140:70:56:40:35:30)
Intervals from root 1/1–2/1–5/2–7/2–4/1–14/3
Cents from root 0¢–1200¢–1586¢–2169¢–2400¢–2667¢
Step intervals 2/1, 5/4, 7/5, 8/7, 7/6
Step cents 1200¢, 386¢, 583¢, 231¢, 267¢
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, …

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
Subharmonics 1/(360:180:144:100:90:75)
Intervals from root 1/1–2/1–5/2–18/5–4/1–24/5
Cents from root 0¢–1200¢–1586¢–2218¢–2400¢–2716¢
Step intervals 2/1, 5/4, 36/25, 10/9, 6/5
Step cents 1200¢, 386¢, 631¢, 182¢, 316¢
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, …

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.

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