Here's today's AAC sound file:
Invention in A Minor v4.5
The exposition hasn't changed any, but beginning in measure seven there is an episode that modulates to the subdominant minor region. This is actually a harmonized version of the subject, which you can see if you look at the first dotted-eighth note of every group: It's the note at the corresponding location in the subject until I prepare to modulate at the end. Since the tonic A minor is the dominant degree of the upcoming D minor region, this was easy to accomplish by using the written-out trill on the proper level and introducing the C-sharp leading tone at the end.
An interesting aspect of working in two voices is that you can't easily just work your rhythmic velocity up to a constant eighth note motoric motion - or alternating dotted-eighths and sixteenths, as the case would be here - so that makes one think about how to make the combined rhythm breathe smoothly. This actually requires a bit of thought. Fortunately, the subject has six different rhythmic values in it and the trill tends to scrub out any buildup and so allows for a new beginning, so to speak. That's why I put the trill figure at the end of the episode: Going back into a constant quarter cumulative rhythm sounds excellent with that trill as a re-transition.
Since I've now established that there will be no perpetual motion cumulative rhythm, the stretti beginning in eleven breathe quite naturally from a rhythmic standpoint.
This culminates in a virtual stop in the rhythm at fifteen, which sounds quite dramatically cool at the new pitch climax of B-flat.
There is another episode based on the harmonized subject beginning at eighteen, but I've modified the counterpoint to facilitate a modulation from the subdominant minor region to the relative major. This took a little more head scratching and chin rubbing than the more obvious and easy previous episode, but the result is more interesting, which is what you want in succeeding versions of a musical idea.
The relative major statement is the last confirmed bit of the piece from the beginning - I'm sure the first 23 measures won't change any - but I had to resort to a lineal link to get to the final episode based on the harmonized subject, which is back in the tonic minor. I'm just not sure what will replace measure 24 at this point, but I'm thinking of statements of some kind on the dominant minor level, which would provide an overall pitch climax on C above the previous high of B-flat. I must admit to being stuck here, but that's usually a good sign, as what comes after much consideration is always - in my experience, at least - the final element that makes the piece perfect (Or pluperfect, if I'm particularly inspired).
For the final version of the harmonized subject episode, I discovered that two consecutive statements of that harmony, with slight variation, would work with a descending chromatic tetrachord as the counterpoint. this is goosebump-inducing cool if the listener is astute enough to follow what's going on, and it's one of those musical effects that can only be perceived with a bit of retrospection. So, 25-27 have the first statement over do, ti, and te...
... while the second statement is over la, le, and sol. It isn't really possible to perceive the new beginning of the subject until half-way through 28, so the effect is quite surprising. Tres cool, non?
There is no change to the closest stretto that begins at 31 - which functions as a recapitulation here - but the hyper-stretto coda that starts at 35 has been improved with some very nifty chromatic, rhythmic, and contrapuntal action.
The last quarter of 38 now has an augmented sixth on it - the only one of those in the piece at this point - and then there is an ascending chromatic tetrachord in 39. Then, the descending quarter triplet that starts in 40 has some cool contrapuntal relationships over the rhythmically augmented trill: m7-M6, m6-P5, and d5-m6 into the m6-m7 and d5 last two-beat triplet. It sounds a bit awkward in the m4a version because MIDI assumes every note is attacked, but when played the trill will be executed with hammer-ons and pull-offs, so it should be very smooth and cool. It's a nice closing contrapuntal device.
Almost more interesting to me though is the cumulative rhythm produced. If you consider a half note as the basic rhythmic unit, starting in 39 the cumulative attacks are 2, 4, 6, 3, 1, which is a very nice accelerating and decelerating rhythmic ratio.
I'm learning some cool things about the musico-psychological effects of rhythm with this piece.
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