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2007: Approximating Pi
Point of departure: the converging series π = 4 – 4/3 + 4/5 – 4/7 + 4/9 ···
Each convergence gets a time window of 5040 samples, in which ten square waves at frequency multiples of 83⁄4n Hz and at amplitudes 2dn are set up, ’83⁄4′ deriving from the 5040 samples, ‘n’ being the partial number and ‘dn’ the nth digit in the convergence’s decimal representation; e.g. for ’3.141592654′, the ten partials’ amplitudes are 23, 21, 24, 21 ,25, 29 etc., thereafter rescaled by the arbitrary sawtooth spectral factor 2π/n, where ‘n’ is still the partial number. The convergences make the digits stabilize from left to right to a value approaching π , the resultant timbre moving from turbulence to constancy over 4 x109 x 5040 = 20.16 x 1012 samples or ~141⁄2 years. The installation can be pitch- transposed (by sample dropping) and/or time-truncated. Here 16 sound channels are transposed from 83⁄4 Hz to frequencies 9 to 402 times higher according to the formula 9π(1 + 1/2 + 1/3 + ·· + 1/X), where X is the channel number plus one); the duration is truncated to a millionth of the total, i.e. 7′ 37″, the highest transposition thereby reaching the 700,000th approximation of π, where the first six digits are already stable.

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