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piano+guitar 1

Piano and Guitar duet v.1

Because this is based on Linda Catlin Smith's gtr/pno piece Drifter, I know the general 'feel' of it but not the details. I know there'll be lots of moving between unisons and broken unisons, but what's the basic material, and how do I vary it. Unlike Smith I'll also be using a lot of different piano/guitar timbres; guitar harmonics, prepared guitar, and prepared piano, etc.

It took me a while to settle on a pitch strategy. Initially I wanted to use a random number system to generate the pitches for a motif/harmony that I could re-order and sequence. And I'd use a system of weighting to make sure that some pitches are more prevalent than others, to give it a more coherent harmonic identity. At this time I also decided to avoid traditional metric notation and instead use stemless notation, with points of togetherness (connecting lines): this means I can have a notation that implies togetherness but allows the parts to drift (both players see both parts so they can follow each other), and I can use connecting lines to specify places where they must be together.

I generated random numbers from 0–15 (e.g. 10, 13, 10, 11, 7, 3, 7, 5, 1, 13, 11, 4, 15, 11, 10, 11, 2, 7, 13, 10): these map to pitches as follows 0=C, 1=C#, 2=D etc, with the numbers from 12–15 as doubles of other pitches so that they come up more often and stand out more in the harmony. I chose 15 so that it would be a long line that I could break up and re-order/vary, maybe also use for a magic square.

However, this didn't work because there’s so many possible numbers that when you randomise you get too much bias (see above example), not enough even distribution. It would have worked better maybe if I generated a continuous line of 200 pitches, then the doubled pitches would stand out better. The new plan is to use a repeating ‘head’ motif of specific preferred pitches and use the randomisation as a way to vary that by inserting passing notes, grace notes, harmonies etc.

To come up with head motif… Should it be a quotation? maybe use the Berio ‘O King’ pitches (2nd movement of his Sinfonia where the same 7-note line is slowly permuted/overlapped and accented differently by the ensemble), then vary that quotation with random pitches or something...? Or it might be interesting to use the head motif in a heterophonic way, an extreme heterophony where the head is spaced out across a section multiple times overlapping, perhaps in a canon, perhaps also transposed etc. And then the random notes fill in gaps. This idea comes from Martin Iddon’s music but also from this quote in a student's thesis discussing models in folk musics (where everyone plays their own variation of a the model tune).
According to [Bruno] Nettl, the 'model' must be articulated at certain 'points of reference': 'obligatory musical events which must be observed [...] in order that the model remain intact.' 'Points of reference' or 'signposts', as Nettl sometimes calls this phenomenon, can be 'certain central tones, opening and closing motifs, melodic indications signalling the coming of closing sections, etc.' In heterophony, the 'points of reference' are the tones of the skeletal melody or the melodic pattern, respectively; additionally, culture-specific conventions underlying the 'actualisation' of the 'model' can also be regulated by a system of 'signposts.' For example, in the traditional music of Myanmar, one layer of the texture is based on the skeletal melody; another layer is made up of the 'segments' that are used to 'actualise' this 'model' and that are themselves organised according to certain conventions: they are classified as 'opening' and 'closing' segments, 'static' segments, segments 'approaching a cadence', etc.
I decided not to follow the heterophony idea settled on a short head motif (E, G#, D, F#, A#) which will be permuted using a markov chain that adds random extra pitches; see below. This head motif a clear tonal centre on E, but also ambiguous because of the dominant 7th D and the lydian 4th A#. Having this tonal centre gives me a 'ground' from which to make more-or-less radical harmonic variations using random numbers.

The markov chain is a simple way to vary something using probabilities. Here's a great explanation with examples. I use it to generate a stream of pitches based on my motif. In mine, each of the five notes has a 90% probability of simply moving to the next note in the motif (repeating in a loop), but the 10% probability of escaping this loop into a new loop that generates random pitches instead ("N" in ex.2 below): the random loop then also has a 10% probability of escaping back into the main five pitches. I change these probabilities to get different versions of the pitch-stream that move between extremely repetitive to extremely varied. Here's three graphs of test pitch streams. You can see the repeating ascending lines of the motif, especially in the bottom graph which has a high probability of repetition: To make the graph look sensible here, the random pitches are only in the upper octave; because the motif spans an octave and a half, and I didn't want to make the decision about which octave the pitches should be in.

ex.1: graphs of markov-chain varied repeats.
My markov-chain sketch is below, see ex.2. Initially my markov harmony failed, but this later turned out to be because I hadn’t yet got a clear idea of how the harmony for the piece should be done. I needed to work through it by trying it several different times and playing through those (rather slowly, on a piano) to hear the shape of the harmony over time. If you're interested in the MAX patch I used to generate the markov-chain harmony, it's here, email me if it's not clear.

ex.2a: markov chain
ex.2b: markov chain original sketch
In the meantime I also tried to use the magic squares to make this pitch-stream, but this didn’t work. I was taking the head motif (E, G#, D, F#, A#) and transposing successive versions (as Maxwell Davies does), but they were all rubbish. Because my motif was whole-tone (not deliberate, just worked out that way), I had to use non-whole-tone transpositions to ensure I was generating all 12-tones; which was what I wanted to get the widest range of variation, but as insertions within a more familiar set of pitches (from the head motif).

ex.3: failed magic squares using head-motif

After the failed magic squares I went back to the markov-chain and fine-tuned it. Ex.4 shows a notated version of this.

ex.4: notated version of markov-chain harmony
The notation here is intended to be loose, at a slow tempo, with points of synchronisation shown by lines between the parts. Where the two lines have the same amount of notes they'll probably be together, though they can drift, but where one part has more notes than the other then they certainly will go out of time momentarily: later in the process I'll be adding another layer of grace notes to destabilise it more, see below. The section was written by taking the pitch-stream generated by the markov process and mostly having both instruments play all the notes, but intuitively giving one part more notes than the other at times. Often this was influenced by instrumental questions such as when harmonics were available, or not, on the guitar part. The guitar here uses a scordatura tuning (probably retuned before performance but maybe during, we'll see) which is just detuning strings 2, 3, and 5 by a semitone to A#, F#, and G# respectively, which allows my head motif to be played entirely on natural harmonics: this also means that for balance I may have to put the piano part up an octave later, we'll see... But by using harmonics exclusively then I get to keep the standard guitar tone in reserve for later. eventually the section will use a mosaic of different timbres. The guitar string 1 (e-string) is prepared using blue-tack which gives it a sound like metal percussion, while the piano will eventually have metal/rubber preparations; as used in John Cage's Sonatas and Interludes for Prepared Piano.

Key Commentary points

  • it's taken several attempts at randomising and markov chains to find something that works for what I want. In the commentary I'd use an appendix to explain the final technique that I use, and in the commentary just briefly explain what wasn't working in the earlier versions. Not much to say now because I think this will change again later.


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