Augmented triads. Augmented triads could be found in minor on III (C, E, G# in A minor harmonic/melodic ascending) and in major on the lowered VI (A flat, C, E in C major). As chromatically altered chords, they result from the "raising" of the fith in the 3 major triads available in any major key (I, V, and IV). For the way they resolve, see Piston.
Since augmented triads are built only of major thirds, (e.g. C-E, E-G#, and G#-C = diminished 4th which has a size of 4 semitones, the same size as a major third) they invite the same kind of ambiguity as the "fully diminished" seventh chords.
Consequently, any augmented triad could function in nine different keys. The C, E, G# triad could be:
Inversion: root first second C-E-G# C-E-A flat B#-E-G# (B#-E-G#) (C-F flat-A flat) _____________________________________________________________________ Function: VI E C A flat diatonic III a f d flat(c#) -------------------------------------------------- I C A flat(G#) E chromatic V F D flat(C#) A IV G E flat B (C flat)
Since these chords are built around the major third interval, one can transpose them one semitone at a time, in the same direction, only 3 times. Which means that there are all together four different augmented trids possible in the tonal system (see J.C.'s comment in the Welcome 104 conference in answer to Janossy James question about the Lecture 9-8).
Secondary functions on multile layers. We started the discussion on this day and continued on 9/10 - see September 10
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