the augmented 5th

[cadenz]

Hello. I am curious about the history of the interval of an augmented fifth and the augmented triad (ie three major third intervals)..
As I understand it, most classical and romantic harmonies can be traced back to counterpoint, which can provide reasoning for their harmonic 'purpose'.
When were the first instances of augmented triads properly used? and how did they tend to be resolved?
I imagine that it may have something to do with the harmonic minor scale, going from the minor third up to the leading note would create such an interval.
so i'm basically just interested to know if anybody has any ideas or knows any theory and history behind this interval and the chord. i am also especially interested if anyone is familiar with any baroque pieces for instance, which blatantly use such a chord.

[mike_lang]

Generally can go to a IV64 (or any IV, for that matter).  The augmented fifth (of the triad) resolves upward.

Best,
ML

[pianistimo]

i don't know why i'm thinking bach's italian concerto - but let me go check.  i'd say that the wavering back and forth from major to minor is bach's favorite little thing.  he does this in the first prelude.  but, in terms of adding it to counterpoint - i'm not sure.  i was thinking it would probably (and this is speculation) be a sort of link to go wherever u wanted.  mozart did this too - but within the diatonic key that he was in.  it always led back home.

they probably use the aug 5th on ornaments more than the main notes.  the goldberg variations probably gives u some ideas about the wild ornamentation that bach gets into (adding more and more of 'auxillary' notes).

[pianistimo]

here's a site about intervals with examples:
www.smirnov.fsworld.co.uk/Intervals.html

they suggested listening to bach's st. matthew passion, schubert octet in F, and wagner's siegfried act III (o heil der mutter).  also, instead of calling it an augmented 5th - the term minor sixth is used.  interesting what it 'represents' in composer's minds.