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Showing posts with the label magic square

Opening Section + Magic Squares

This section has no solos, it's a simple contrast of two strata: (1) descending rapid scales, and (2) sustained chords swelling and receding. Listen to the opening page (score below) here: If you cannot see the audio controls, your browser does not support the audio element Ex.1: score p.1 The pitches for both are derived from the magic square. The chords are most straightforward, they simply read the horizontals of the square as 6-note chords. The piece starts with the uppermost vertical (the main material + high G), and works its way down. E G# D F# A# G B F A C# A# D G# C E C# F B D# G F A D# G B G# C F# A# D B D# A C# F A# Ex.2: magic square, showing different transposed 5-note sequences (alternating red and blue) Here are the voicings; which I just worked on the piano intuitively by starting with the horizontal as written, then moving notes around to form triads where possible. Note also that I opted for a smoother orchestration across the t...

Magic Squares

--> I took my original 5-note sequence (E, G#, D, F#, A#) and extended it into a 6x6 magic square following Maxwell Davies' approach of (a) ensuring the sequence goes out of phase from line to line (because sequence of 5 pitches along lines 6 units long), and (b) transposing each subsequent sequence. The transpositions aren't always the same, because I was getting repetitions; because going up in minor-3rds ends up in the same place after four cycles (12 chromatics divided by 3 semitones = 4), so after the 4th cycle (when it should return to E) I transposed up a further semitone to push the whole cycle of four sequences a semitone higher than the first four. The square is (mostly) transposed by minor 3rds because the original 5-note sequence is whole-tone (the two possible whole-tone sets are six notes each), so minor 3rds give pitches not in the original whole-tone set. [commentary point] This solves the whole-tone problem of only having six notes to work with (...

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 (bo...