A couple of years ago I decided to formalize my harmony studies (I'm a mathematician) by reading Schoenberg's book Theory of Harmony, however I left it since it felt a little too difficult for my current knowledge. Since then, I've been teaching myself harmony from different books and a couple of weeks ago decided to give a second try to this book, and even though I can follow the ideas in a fairly fast way now I seem to be loosing something because I still can't understand the last sentence of the next paragraph (I also added the examples quoted in the paragraph just to give it more context):
So far, Schoenberg has stated several (mostly temporary) rules in order to introduce a scheme which allows to link chords in a way that respects the nature of the harmonic series, however in this paragraph he states that in the minor mode one can not resolve (using his temporary rules) I7 to any triad which contain a raised interval (that is IV# and V#) because "g cannot go to f#". This claim seems a little odd to me since the rules that I can recall and that are related to this are the following:
- The seventh degree must go down a step, and
- The tonic must go up a fourth.
In this scenario the reasonable resolution should be I7 - IV, where IV should be major (and thus moving g, the seventh of a, to f#, the major third of d). With that said my question would be: What is the "rule" that does not allows us to use this cadence to resolve I7?
- So far, resolutions have taken place by means of diatonic triads in the corresponding mode, so if that where a rule I'd understand that resolutions in general wouldn't be possible by means of any triad with a raised interval (since they do not belong to the diatonic triads of the minor mode), however in the same paragraph they state the resolution II7 - V, where V is major, which contradicts the latter reasoning (unless V being major where some sort of exception to the rule, which would actually make a lot of sense, since, well, it is the dominant chord of the minor mode).
- For the people that reads this question but have not read the book and does not understand the notation, it's because I'm using the notation of the book, which is pretty different from the one in most jazz harmony books I've seen so far.