This is the first of two examples.
The contention of this pitch Quixote is that symmetrical structures extend themselves in our brains without being presented in actuality. In this example, the contention is that the whole tone scale completes itself in our brain. We hear the G# that completes the whole tone scale. And then the low G natural in the guitar displaces a note that we hear only in our heads.
What to make of this? Whatever you like. My take--this is a last frontier. I'm bored with only hearing things that are THERE. I'm happy in this realm where we're counting angels on the head of a pin.And it makes for interesting tunes, regardless of who wins the argument.
Another example in the same piece: look for measure 6. The contention here is that our ears are soooo diatonic that major thirds always imply the intervening note, symmetrically in between. So here, between the F# and the Bb our brain supplies the G#.
In both examples it is G# that's not there. In fact, there are no G#s in this piece.
There's more to the last example. The complement to the prevailing D, E, F#, G, A, B is heard in measure 6, although it's mixed up with D's and other suspensions from the other hexachord.. The complement is Ab, Bb, C, Db, Eb, F (the tritone transposition of the D diatonic hexachord).
So in measure 6 we have all but the Ab, which, according to this contention about major thirds, we supply without it actually being there. Fact is, I felt this measure first as the complement. After playing the piece dozens of times the sense that I was hearing the complement became very clear.
Then I looked at the score and realized that complements don't have to be complete. Is it not the case that augmented 6 chords imply the rest of the complement? In Beethoven this seems clear enough. Even in Fernando Sor. Who needs all the rest of the tritone-transposition???
Oren & I record Genius Loci on July 18! It's an innocent little doodle, with these devilish deals going on under the table.Another example---->
In this example there's an 8-note scale, with only 7 of the 8 notes. The line stops abruptly before the 8th note, which should be B natural. Instead, we get a Bb, displacing downwards the note that we imagine we heard, but didn't.
The passage has 0235s continually displacing implied 0245s. Before the first notes of the melody in the example below, a full Bb scale is instated, with the leading tone, A natural. The G is displaced down to Gb and the A down to Ab. Through these precedents the downward tendancy comes to be expected. This habitual downward semitone displacement helps to reinforce the sense that Bb displaces the unheard B natural. The fact that this passage comes preceded by a full Bb scale in the instruments makes this harder to argue. It (the passage) argues that a symmetry (the octotonic scale) can have more strength than an instated diatonic region. The passage also argues that the voice part had no Bbs and that each party in the conversation tallies independently. That's quite a contention, and yet there is much to it. I don't dismiss it. I'm on the fence. Nevertheless, I admire this chutzpah, and that's what it is because in this "aggregate", there is no B natural. In fact the actual appearance of that note is delayed for a long, long time. Notice also that the last downward displacement is the completion (Fb), assuming that we really did imagine the B natural. Completions are not heard in a vacuum. They are heard in the context of moves. Here he teaches us to hear 0245 being displaced by 1235s, repeatedly. The last time, the 4 is F and the 3 is Fb. We learn moves that fill holes. Hole filling for the sake of hole filling is not really the point.
Here's the whole passage--->
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