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]]). | |||
Some of the [[interval]]s are listed below in terms of [[cents]]. | |||
Some of the | |||
| Line 17: | 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 38: | Line 32: | ||
24 : 13 ~ 1061 cents | 24 : 13 ~ 1061 cents | ||
== | == 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. | |||
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 74: | 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]] | |||
Latest revision as of 22:13, 22 December 2024
Harmonic augmented 7th chords based on 8:10:13
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
10 : 13 : 16 : 18 | aug 7
13 : 16 : 20 : 24 | aug neutral 7
The thirds:
10 : 8 ~ 386 cents
13 : 10 ~ 454 cents
16 : 13 ~ 359 cents
The sevenths (as reduced fractions):
7 : 4 ~ 969 cents
9 : 5 ~ 1018 cents
24 : 13 ~ 1061 cents
Augmented 7th chords based on 9:11:13
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 they do to 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, but each uses a different 7th degree, to come as close as possible to aug7 (without straying into high harmonics).
The inversions:
7 : 9 : 11 : 13 ~ aug #7
9 : 11 : 14 : 16 ~ aug 7
11 : 14 : 18 : 20 ~ aug (neutral?) 7
The thirds:
9 : 7 ~ 435 cents
11 : 9 ~ 347 cents
14 : 11 ~ 418 cents
The sevenths:
13 : 7 ~ 1072 cents
16 : 9 ~ 996 cents
20 : 11 ~ 1035 cents
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Todo: intro , discuss title , review |