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Hendrix chord: Difference between revisions

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remove redundant names: the prime limit is already listed separately in each infobox, and all of these chords are Hendrix chords (it's in the page name)
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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.


{{Infobox Chord|4:8:10:14:16:19|Root=8}}
<!-- ''The only interpretations allowed in this section are ones where all 'intervals from root'
In the [[19-limit]] it may be tuned as 4:8:10:14:16:19, an extended [[4:5:6:7|harmonic seventh chord]].
''have a denominator of 8 or less (to prevent the section becoming too long).'' -->


{{Infobox Chord|6:12:15:21:24:28|Root=12}}
=== 5-limit ===
In the [[7-limit]] it may be tuned as 6:12:15:21:24:28, also an extended harmonic seventh chord.
{{Infobox Chord|10:20:25:36:40:48|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5|Root=20}}
</div>
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]].


{{Infobox Chord|10:20:25:36:40:48|Root=20}}
This chord appears in [[20afdo]] and all higher [[AFDO]]s.
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}}
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.
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 less than 20 cents error on any one interval include: {{EDOs|12, 15, 18, 19, 22, 24, 26, 27, 28...}} and everything bigger than 28.
 
[[EDO]]s up to 100 with successively lower error include: {{EDOs|4, 5, 6, 7, 12, 19, 34, 46, 53}}.
{{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''', an extended [[4:5:6:7|harmonic seventh chord]].
 
This chord appears in [[12afdo]] and all higher [[AFDO]]s.
 
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.
 
[[EDO]]s with less than 35 cents error on any one interval include: {{EDOs|10, 12, 15, 16, 17...}} and everything bigger than 17.
 
[[EDO]]s up to 100 with successively lower error include: {{EDOs|4, 6, 9, 10, 19, 21, 22, 31, 68, 99}}.
{{clear}}
 
=== 19-limit ===
{{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]].
 
This chord appears in [[8afdo]] and all higher [[AFDO]]s.
 
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.
 
[[EDO]]s with less than 35 cents error on any one interval include: {{EDOs|12, 15, 16, 17...}} and everything bigger than 17.
 
[[EDO]]s up to 100 with successively lower error include: {{EDOs|4, 7, 9, 12, 15, 16, 25, 37, 53, 56, 68, 93}}.
{{clear}}
 
== Tempered interpretations ==
Interpretations as a [[temperament|tempered]] chord.
 
=== Essentially tempered ===
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]].  
 
[[EDO]]s including this chord are {{EDOs|9, 10, 12, 14, 16, 17, 21, 22, 26, and 31}}.
 
{{Todo|review|inline=1|text=The section about tempering 57/56 needs more explanation, and may be incorrect.}}


[[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.}}
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