extended triad types ii

In this post we're going to examine the whole-half diminished scale. It is, like the whole tone scale, a symmetric arrangement of tones, and its name is the formula of the arrangement (i.e. a whole tone followed by a half tone followed by a whole tone...). This scale is different from many, many others in that it has more than 7 tones, in fact it is octatonic (8 toned). Here it is along with its triads:



Since it's composed of more than 7 tones some problems of nomenclature occur. For instance, at some point a scale tone (degree) has to be duplicated. Above we've made it F and F#, though it could've been D and D# (which would've produced an E#, then F#), etc. A massive ramification of this is that there is not a unique, one-to-one correspondence between scale degrees and triads -- some triads will manifest in 2 different forms. Above it is II, IV and VII (because they each contain F, which scale degree also exists as F#).

In this scale there are two triads which are "extended": the I and III. But these extended triads are a bit different from the ones which occurred in the previous post, and that's because they are enharmonically equivalent to basic triads. Put another way, the first two extended triads we encountered have no sonic equivalents, whereas these two that hail from the whole-half diminished scale do. Here they are:



The I chord sounds like a 1st inversion Ab major triad; the III chord sounds like a 2nd inversion G# minor one. But even though this is the case it's still important to be able to analyze these triads as extended types, if only for consistency's sake (most likely from a performer's point of view). But there is precedent for this sort of thing. Consider the Fr+6 chord: it is enharmonically equivalent to a dominant 7th chord, but its function is quite different in common practice harmony (that is its resolution is different from that of a dominant 7th chord).

So, back to the chords at hand: the I chord can be called a minor augmented (min Aug) and the III chord a diminished 3rd augmented (°3 Aug).