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]] originating from [[12edo]], has several possible interpretations.
{{clear}}


The '''hendrix chord''', a 7#9no5 [[chord]], has several possible [[JI]] interpretations.
== JI interpretations ==
Interpretations as a [[just intonation]] chord:


=== 5-limit ===
{{Infobox Chord|10:20:25:36:40:48|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5|Root=20}}
In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36|major-minor seventh chord]].
{{clear}}
=== 7-limit ===
{{Infobox Chord|6:12:15:21:24:28|ColorName=har-7 zoqu-9 no-5 or h7zq9no5|Root=12}}
In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, also an extended harmonic seventh chord.
{{clear}}
=== 19-limit ===
{{Infobox Chord|4:8:10:14:16:19|ColorName=har-7 noqu-9 no-5 or h7,19oq9no5|Root=8}}
{{Infobox Chord|4:8:10:14:16:19|ColorName=har-7 noqu-9 no-5 or h7,19oq9no5|Root=8}}
In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7|harmonic seventh chord]].
In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7|harmonic seventh chord]].
{{clear}}


{{Infobox Chord|6:12:15:21:24:28|ColorName=har-7 zoqu-9 no-5 or h7zq9no5|Root=12}}
== Tempered interpretations ==
In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, also an extended harmonic seventh chord.
Interpretations as a [[temperament|tempered]] chord.
</div>


{{Infobox Chord|10:20:25:36:40:48|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5|Root=20}}
=== Essentially tempered ===
In the [[5-limit]] it may be tuned as 10:20:25:36:40:48, an extended [[20:25:30:36|major-minor seventh chord]].
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]].  
{{Todo|review|inline=1|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}


{{Clear}}
=== In EDOs ===
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.
[[EDO]]s with hendrix chords include the {{EDOs|9, 10, 14, 16, 17, 21, 22, 26, and 31}}.
{{Todo|complete section|inline=1|text=Explain the reasoning for exactly when an EDO is considered to "have" a Hendrix chord and when not.}}


[[Category:Hendrix| ]] <!-- main article -->
[[Category:Hendrix| ]] <!-- main article -->
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Just intonation chords]]
[[Category:Just intonation chords]]
{{Todo|review|inline=1|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}

Revision as of 01:55, 27 April 2025

English Wikipedia has an article on:

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

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, …

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, …

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*, …

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.

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