Augmented chords in just intonation, some: Difference between revisions
m Capitalisation |
mNo edit summary |
||
| Line 1: | Line 1: | ||
== Harmonic augmented 7th chords based on 8:10:13 == | == Harmonic augmented 7th chords based on 8:10:13 == | ||
| Line 68: | Line 66: | ||
20 : 11 ~ 1035 cents | 20 : 11 ~ 1035 cents | ||
{{todo | intro | discuss title | review | inline=1}} | |||
[[Category:Chords]] | [[Category:Chords]] | ||
[[Category:Just intonation]] | [[Category:Just intonation]] | ||
[[Category:13-limit chords]] | [[Category:13-limit chords]] | ||
Revision as of 06:51, 4 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
|
Todo: intro , discuss title , review |