This is a long-term study plan to help in looking out for scores.

I have, or have on order, study or full scores for works highlighted in yellow..

Classical study matrix covering genres and periods

This is a long-term study plan to help in looking out for scores.

I have, or have on order, study or full scores for works highlighted in yellow..

Classical study matrix covering genres and periods

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Listened to Steve Reich’s Music for Pieces of wood (which requires tuned claves). His style is to set up a rhythmic pattern and then subtly undermine it with a cross-rhythm. If the asynchronised rhythms start to converge again this is like ‘entrainment’ in classical mechanics theory of oscillators – why two mechanical clocks on the same wall with the same pendulum length will converge to beat in time:

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0007057

This inspired me to think about planning a percussion piece with the bar (for notational simplicity, a pair of bars) representing the average interval between high tides; the time of high and the low tide represented by wood blocks at two distinct pitches (temple blocks?) diverging outside and inside the bar. Depending on temp this needs to be rounded to the nearest demi- or semiquaver. The tidal range varies with the lunar cycle and this can set dynamics in the obvious way. The highest and lowest tides (spring tides) have the largest intervals about them. Assuming also a side drum (or pair of side drums handing over between each other, for practicality), playing at 12 quavers in half a day, and also that the average time between tides is 12.5 hours, then the basic bar pattern is 12/8 alternating with 13/8, and a Reich-like progressive syncopation is set up as a day ‘beat’ say on triangle every 24 quavers, returning to synchrony after (2 x (12+13) = 50 bars

Added interest can be from bass drum for waves overspilling the promenade (randomly chosen around ‘spring high tides) and by contrast a suspended cymbal roll around neap tides – e.g. sand blowing in the wind. A speaker could say the tide height in metres at spring high and low tides – the whole piece ending after some multiple of the lunar month 28 days to say ‘come in number 56’ or 84 – to fit allowed length. 84 lunar days (around three months) would last 168 bars at dotted crotchet = 100 is nearly 7 minutes; a reasonable performance length for the audience to get the hang of the shifting rhythms and not get bored. For comparison, Steve Reich’s piece is 9 minutes on youtube.

A tide table for three months at Aberystwyth is:

The source for this was entitled ‘Discover Ceredigion’ which could be the working title of the piece:

http://www.discoverceredigion.co.uk/English/where/coast/TideTables/Pages/TideTables.aspx

Slightly sideways idea for a composition for ‘untuned percussion’ that would break all records for the metronome mark, number of instruments and length. Conceptual composition really. May be possible to implement this as custom software…

Instrument 1 enters with a pulse defining interval 1 (essentially a click track) at a fast but discernible beat e.g. MM=240.

Instrument 2 at interval 2, 3 at interval 3, 4 at interval 5, 5 at interval 7

Instrument m at the interval of n the m’th prime number

Subtlety: the novelty would get spaced wider and wider in time, so the tempo needs to be progressively increased in a log ratio, i.e. constant multiplicative rate. This will lead to pulses eventually being interpreted as a pitch e.g. a click track at MM=6000 is a tone of 100 Hz.

To the extent that prime numbers become less frequent with size then the increase in tempo should balance the scarcity of prime numbers. I think that this will lead to a pseudo random sequence of chords – the Wiki link at foot of this post is interesting as a source.

Clearly the progression is infinite. With a continuously rising pitch, the original click track and then, soon after, multiples of this would become inaudible above around 15kHz so the calculation can be truncated, but the speed of processing to test primality and need for special large number formats will lead to slower processing so the implementation of this in practice needs a cached list of prime numbers. A further challenge is that with the exponential increase in tempo the number of numbers to be tested increases exponentially also. So the piece needs to be ‘precalculated’ up to some duration, or parts of the piece between set starting and ending ‘beats’ could be calculated on demand.

A further refinement likely to be more tolerable to hear for a sustained period would be to disguise the pitch change (falling as primes become less frequent) by doubling at multiple octaves and as the frequency of finding primes falls, transfer amplitudes upwards through the octaves and so use Shepard’s illusion – ‘the auditory equivalent of Escher’s continuous descending staircase’:

Andrew