Augmented chords in just intonation, some: Difference between revisions

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 == harmonic augmented 7th chords based on 8:10:13 ==
-The central triad in all three chords is 8:10:13,
+The central [[triad]] in all three [[chord]]s is 8:10:13, but each uses a different 7th degree, to come as close as possible to the familiar aug7 (without straying into [[17-limit|high harmonics]]).
-but each uses a different 7th degree,
-to come as close as possible to the familiar aug7
-(without straying into high harmonics).
-Some of the intervals are listed below in terms of cents.
+Some of the [[interval]]s are listed below in terms of [[cents]].
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 : 13 : 16 : 18 | aug 7
-: 16 : 20 : 24 | aug neutral 7
+: 16 : 20 : 24 | aug [[neutral]] 7
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 == augmented 7th chords based on 9:11:13 ==
-Interestingly, none of these chords has a 5:4.
+Interestingly, none of these chords has a [[5/4|5:4]]. Someone might argue that a chord with a [[neutral third scale|neutral third]] is not properly augmented, but they certainly sound closer to augmented than they do to anything else in Western music.
-Someone might argue that a chord with a neutral third is not properly augmented,
-but they certainly sound closer to augmented than anything else in Western music.
 Some of the intervals are listed below in terms of cents.
-The central triad in all three chords is 7:9:11,
+The central triad in all three chords is 7:9:11, but each uses a different 7th degree, to come as close as possible to aug7 (without straying into high harmonics).
-but each uses a different 7th degree,
-to come as close as possible to aug7 (without straying into high harmonics).
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 [[Category:Chords]]
 [[Category:Just intonation]]
+[[Category:13-limit chords]]