Augmented chords in just intonation, some

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