Polytonality?

One goal I set for myself for my new motets was to develop some form of approach to pitch material.

In Si el clima, I generally focussed on controlling the long-range trajectory of lines, but did not have any structural approach to the specific pitch or intervallic content. What I did on that front was largely intuitive (with the exception of the chordal passage and a handful of passages in the middle section where I had a kind of extended-‘modal’ approach). In general I enjoy the aural results that came from this intuitive approach, but I decided I wanted to develop some kind of systematic way of dealing with harmony, in order to be able to use it for articulating formal development, contrast etc. The somewhat academic question was also in my mind: ‘what form of harmonic structure would suit a modern counterpoint?’

Now, the historical perspective implied by the term counterpoint is a potential trap, and it’s true that a part of my initial thoughts with regard to developing a harmonic approach was to find a way of re-founding the contradiction between harmony and line (the vertical and the horizontal) that in different ways was at the heart of counterpoint in earlier eras.

I am now quite happy to say that this is no longer the aim. I’m not interested in developing a new system of ‘dissonance treatment’ that would regulate the relations between lines (and against which they could push). This is an old logic of counterpoint, belonging to an age that can’t come back. Basically this means forsaking any pretence to a 1-to-1 relationship between composer and audience (or score and audience, or performers and audience). But this is both a good and unavoidable thing in any case: new music is an alienated medium, its alienation still carries great potential, but you have to face up to it first.

What I do want to do is develop an approach to pitch material that heightens my ability to control relations between lines. That is to say, it is part of an overall concept of ‘imitation’ that is increasingly at the basis of my approach to counterpoint.

So, what I decided to do in motets 1 and 3 of this set (motet 2 is a little different, though related), is to set up not one harmonic framework, nor just define certain interval or pitch structures for each line, but instead to lay out three different simultaneous harmonic fields running through the one piece.

This is not dissimilar to the old idea of polytonality or polymodality that people like Ives and Bartok developed over 100 years ago (which reminds me, I should go back and check them out a bit for the ol’ PhD). The differences being: 1) the harmonies are considerably more varied (coming from a variety of different approaches) and extended (including up to 8th-tone distinctions); 2) the control over these harmonies and their development is significantly rationalised (the computer helps here); 3) the harmonies are not generally associated to a rhythmic layer (even if they each have their own structure of harmonic rhythm); 4) their degree of differentiation is itself subject to control, since individual lines can partake of two or more harmonic layers at once. Those differences aside, I am definitely trying to draw in some of that striking cognitive dissonance between two identifiable harmonic layers that you can find in some of Ives’s work.

To be more concrete, in my first motet ‘Sappho/Matilde/Flora’ the three harmonies are laid out thus: 1) An abstract, atonal harmonic field across the entire possible range of the instruments, constructed by an intervallic sequence repeating every 10 semitones, and subject to transformations and transpositions; 2) A folkish layer in D-minor derived from a Spanish funeral march sung during the Civil War, this is microtonally distorted in a fairly random manner, as though the guitar that was playing these chords was going in and out of tune; 3)  A ‘spectral’ band taking every third partial between the 15th and 30th of Db3 (I put spectral in ‘scare-quotes’ because while I start with this spectral chord, I immediately treat the pitches in a more abstract manner, modulating the chord in different ways).

While the first layer covers the entire range of the instruments, the second and third are kept within their respective band-widths: the spectral layer goes from the middle to just above the treble staff, and the folkish layer goes from a low G below the staff to a D in on the second line from the top.

I worked out their various processes of modulation and change of harmonic rhythm in OpenMusic and then exported them into Finale to make a harmonic ‘plot’ of the piece. Here’s what it looks like:

Motet_1 plot

Ugly huh? The export to Finale never really comes off so well…

In general each layer was associated with an instrumental line (themselves representing a different text in the ‘triple motet’), at least initially: the clarinet, crossing a largish register, was the first, abstract field; the flute, weaving around the top of the staff, was the bottom, spectral harmony; and the violin alternated between the abstract layer and the middle, folkish layer.

Across the work, the lines make some forays into each others’ harmonic terrains, thus bringing them closer together in terms of their identity relation, but mostly stick to their own original field.

What this all means is that the resulting harmony is a kind of ‘meta-harmony’ whose verticality is not envisaged as a unified chord, but nor is it completely stratified, or at least not always – plenty of times there will be weird admixtures of the various harmonic layers fusing into something perceptually different.

One thing that these pieces will test is the discernibility of these layers. I’ve tried to make it so that the D-minor quality of the violin line stands out strongly at some points; and the contrast between the 12-tone clarinet and the very microtonal flute (often criss-crossing each other in register), should also be noticeable. But the overall effect of stratification? That remains to be seen. I’m also unsure how much I want it to be discernible. In any case, that’s the experiment at this point.

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