Hendrix chord: Difference between revisions

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The ''hendrix chord'', a ~~dom7~~#9no5 ~~chord, can be tuned as an 8:10:14:19 chord =~~ [[~~Kite's color notation|h7,19o10no5~~]]~~. An alternate tuning is 12:15:21:28, or 1/1 - 5/4 - 7/4 - 7/3 =~~ [[~~Kite's color notation|h7z10no5~~]].

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

~~It can also be tuned~~ as an [[~~Dyadic_chord|essentially tempered~~]] chord that splits the difference between the [[19/16|19/8]] ino 10th and the [[7/3]] zo 10th. This chord tempers out the ''hendrix comma'' of [[57/56|57/56]]. It is notable for existing in 12-equal, but equal divisions with hendrix chords include, aside from 12, the 9, 10, 14, 16, 17, 21, 22 and 26 equal divisions.

== JI interpretations ==

Interpretations as a [[just intonation]] chord.

[[~~Category~~:19-limit]]

<!-- ''The only interpretations allowed in this section are ones where all 'intervals from root'

[[~~Category~~:7-limit]]

''have a denominator of 8 or less (to prevent the section becoming too long).'' -->

[[~~Category~~:chord]]

[[Category:~~hendrix~~]]

=== 5-limit ===

[[Category:~~tetrad~~]]

{{Infobox Chord|10:20:25:36:40:48|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5|Root=20}}

[[Category:~~todo:add_links~~]]

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]].

This chord appears in [[20afdo]] and all higher [[AFDO]]s.

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.

[[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}}.

=== 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}}.

=== 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}}.

== 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| ]]

[[Category:Essentially tempered chords]]

[[Category:Just intonation chords]]

@@ Line 1: / Line 1: @@
-The ''hendrix chord'', a dom7#9no5 chord, can be tuned as an 8:10:14:19 chord = [[Kite's color notation|h7,19o10no5]]. An alternate tuning is 12:15:21:28, or 1/1 - 5/4 - 7/4 - 7/3 = [[Kite's color notation|h7z10no5]].
+{{Wikipedia|Dominant seventh sharp ninth chord#Hendrix chord}}
+The '''hendrix chord''', a 7#9no5 [[chord]] originating from [[12edo]], has several possible interpretations.
+{{clear}}
-It can also be tuned as an [[Dyadic_chord|essentially tempered]] chord that splits the difference between the [[19/16|19/8]] ino 10th and the [[7/3]] zo 10th. This chord tempers out the ''hendrix comma'' of [[57/56|57/56]]. It is notable for existing in 12-equal, but equal divisions with hendrix chords include, aside from 12, the 9, 10, 14, 16, 17, 21, 22 and 26 equal divisions.
+== JI interpretations ==
+Interpretations as a [[just intonation]] chord.
-[[Category:19-limit]]
+<!-- ''The only interpretations allowed in this section are ones where all 'intervals from root'
-[[Category:7-limit]]
+''have a denominator of 8 or less (to prevent the section becoming too long).'' -->
-[[Category:chord]]
-[[Category:hendrix]]
+=== 5-limit ===
-[[Category:tetrad]]
+{{Infobox Chord|10:20:25:36:40:48|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5|Root=20}}
-[[Category:todo:add_links]]
+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]].
+This chord appears in [[20afdo]] and all higher [[AFDO]]s.
+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.
+[[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:Essentially tempered chords]]
+[[Category:Just intonation chords]]