131
Varieties of Particle Synthesis
synthesis technique is to ®lter the impulses with a bandpass characteristic to carve out a speci®c peak in the spectrum. When the ®lter is very narrow, a single impulse causes the ®lter to resonate at a speci®c frequency, yielding the sensation of pitch. Another processing trick is to pass the impulse train through a variable delay and feedback loop, so that the density of impulses accumulates under the control of the composer. Karlheinz Stockhausen and Gottfried Michael Koenig used these kinds of techniques in the synthesis of Kontakte in 1960. (See also Kaegi 1967.) Ultimately, all electronic signals, whether analog or digital, are bandlimited. An analog IG has an obvious advantage over a digital IG, which is strictly bandlimited by the Nyquist theorem. As is clear from the speci®cations in table 4.1, the bandwidth of analog IGs is much broader. Theory and Practice of Trainlets A trainlet cloud contains one or more trainlets. The main variables in the synthesis of a trainlet cloud are: 1 Density per second of trainlets 1 Trainlet pulse period 1 Trainlet harmonic structure 1 Trainlet spectral energy pro®le An amplitude envelope shapes each trainlet, and the generator projects each trainlet to a speci®c location in space. The parameters vary for each trainlet, so each trainlet may be unique. Since trainlet synthesis operates in the digital domain, it is important that the impulses be bandlimited to avoid aliasing. A standard bandlimited impulse generator for modern synthesis languages is Godfrey Winham's buzz unit generator and its variant, gbuzz (Winham 1966; Winham and Steiglitz 1970; Howe 1975; Steiglitz 1996). Buzz emits a set of N harmonic partials of equal amplitude. As the number of harmonics N increases, the pulse width becomes narrower (®gure 4.6). Gbuzz emits a set of N harmonic partials with more ¯exible control of the spectrum. In the 1998 prototype implementation of trainlet synthesis, I wrote the synthesis engine in the Csound language (Boulanger 2000). Csound's gbuzz unit generator emits harmonic cosines aligned to a fundamental frequency. It scales the amplitudes of the cosines so their sum equals a stipulated peak value. One