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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 [[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]]).


== harmonic augmneted 7th chords based on 8:10:13 ==
Some of the [[interval]]s are listed below in terms of [[cents]].


The central triad in all three chords is 8:10:13,
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.
The chords:


8  : 10 : 13 : 14 | aug 7
8  : 10 : 13 : 14 | aug 7
Line 14: Line 12:
10 : 13 : 16 : 18 | aug 7
10 : 13 : 16 : 18 | aug 7


13 : 16 : 20 : 24 | aug neutral 7
13 : 16 : 20 : 24 | aug [[neutral]] 7
 




Line 25: Line 22:


16 : 13 ~ 359 cents
16 : 13 ~ 359 cents


The sevenths (as reduced fractions):
The sevenths (as reduced fractions):
Line 34: Line 32:
24 : 13 ~ 1061 cents
24 : 13 ~ 1061 cents


== agumented 7th chords based on 9:11:13 ==
== Augmented 7th chords based on 9:11:13 ==
 
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.


Interestingly, none of these chords has a 5:4.
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.
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).


The inversions:
The inversions:
Line 70: Line 66:


20 : 11 ~ 1035 cents
20 : 11 ~ 1035 cents
{{todo | intro | discuss title | review | inline=1}}
[[Category:Just intonation chords]]
[[Category:13-limit chords]]
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