Hendrix chord: Difference between revisions
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== JI interpretations == | == JI interpretations == | ||
Interpretations as a [[just intonation]] chord | Interpretations as a [[just intonation]] chord. | ||
''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.'' | |||
=== 5-limit === | === 5-limit === | ||
{{Infobox Chord|10:20:25:36:40:48|ColorName=yo gu-7 guqu-9 no-5 or y,g7gq9no5|Root=20}} | {{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]]. | ||
According to this interpretation, the 12edo hendrix chord has 30.2 [[cents]] of error relative to JI. | |||
{{clear}} | {{clear}} | ||
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{{Infobox Chord|6:12:15:21:24:28|ColorName=har-7 zoqu-9 no-5 or h7zq9no5|Root=12}} | {{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]]. | ||
According to this interpretation, the 12edo hendrix chord has 78.0 [[cents]] of error relative to JI. | |||
{{clear}} | {{clear}} | ||
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{{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]]. | ||
According to this interpretation, the 12edo hendrix chord has 47.4 [[cents]] of error relative to JI. | |||
{{clear}} | {{clear}} | ||
Revision as of 02:18, 27 April 2025
The hendrix chord, a 7#9no5 chord originating from 12edo, has several possible interpretations.
JI interpretations
Interpretations as a just intonation chord.
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.
5-limit
| Chord information |
In the 5-limit it may be tuned as 10:20:25:36:40:48, an extended major-minor seventh chord.
According to this interpretation, the 12edo hendrix chord has 30.2 cents of error relative to JI.
7-limit
| Chord information |
In the 7-limit it may be tuned as 6:12:15:21:24:28, an extended harmonic seventh chord.
According to this interpretation, the 12edo hendrix chord has 78.0 cents of error relative to JI.
19-limit
| Chord information |
In the 19-limit it may be tuned as 4:8:10:14:16:19, an extended harmonic seventh chord.
According to this interpretation, the 12edo hendrix chord has 47.4 cents of error relative to JI.
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.
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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.
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Todo: complete section Explain the reasoning for exactly when an EDO is considered to "have" a Hendrix chord and when not. |