Augmented chords in just intonation, some

harmonic augmneted 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.

{| class="wikitable"

! formula ! name

|- 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

agumented 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 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