Hendrix chord: Difference between revisions

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Interpretations as a [[just intonation]] chord.

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

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

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

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

=== 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]].

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.

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=== 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]].

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.

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=== 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]].

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.

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=== 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]].

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.

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

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 6: / Line 6: @@
 Interpretations as a [[just intonation]] chord.
-''The only interpretations allowed in this section are ones where all 'intervals from root'
+<!-- ''The only interpretations allowed in this section are ones where all 'intervals from root'
-have a denominator of 8 or less (to prevent the section becoming too long.''
+''have a denominator of 8 or less (to prevent the section becoming too long).'' -->
 === 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]].
+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.
@@ Line 22: / Line 24: @@
 === 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]].
+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.
@@ Line 33: / Line 37: @@
 === 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]].
+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.
@@ Line 46: / Line 52: @@
 === 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]].
+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.
-{{Todo|review|inline=1|text=The paragraph about tempering 57/56 needs more explanation, and may be incorrect.}}
+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]]