In his research and book on ‘Sinusoidal Run Rhythm’, Steffen Krebber describes a way of generating non-discrete rhythmical patterns by adding up in-phase cosine functions in integer ratios.
‘Sinusoidal Run Rhythm’ comes with shifts in timing relative to discrete rhythmic or polyrhythmic patterns and also adds volume weighting.
This temporal shifting is significant because it illustrates how rhythms generated from wave interference behave differently from manually constructed or performed rhythms. These shifts and volume variations introduce a nuanced, fluid quality to the rhythm that is not easily replicable through traditional musical notation or performance. Therefore, Krebber considers ‘Sinusoidal Run Rhythm’ to allow a ‘subobjective’ perspective on rhythmic patterns.
“‘sinusoidal run rhythm’ proposes a definition of rhythm as a wave. It does not conceive of time as discrete subdivisions, but makes it continuously quantifiable. Concurrently, through the aesthetics of wave additions, it does not present physicality as a merely subjective concept and thus liberates it from mystification.”
Steffen Krebber (2024)
In electronic music, similar kinds of rhythmic patterns often appear in low frequency oscillator based modulations e.g. in sound synthesis or filtering.
Pure Data implementation
PD-SRR is an implementation of Krebber’s concept of ‘Sinusoidal Run Rhythm’ in Pure Data. It comes as both a standalone (pd-srr.pd) and modular (srrmod.pd) version, the latter for use in compositions. You can find it on GitHub.
The standalone implementation works with ‘Sinusoidal Run Rhythm’ applied to the amplitude modulation of a white noise generator similar to the web based application Steffen Krebber presents on his website.
As suggested by Krebber, the implementation works with combinations of 2 partials (derived from the Farey sequence of order 8) and 3 partials (coprime triples up to 16) through dedicated selectors. For further experimentation, up to 4 partials can be set by using the manual selection option.
The modular version of the implementation allows setting the partial combination from the calling patch and outputs the result through its outlet for use in signal modulation.
In the following video, I’m showing three scenarios where srrmod.pd is used to modulate both sound synthesis parameters as well as a filter in a compact setup.
It should be interesting to expand the concept of ‘Sinusoidal Run Rhythm’ to larger compositions both incorporating it as rhythmical baseline for sound generators and modulators alike but also experiment with an application on a compositional level.
Thanks to Steffen, whom I had the pleasure to meet and talk to at the ArtSearch 2024 symposium at ligeti zentrum in Hamburg recently. His presentation on ‘Sinusoidal Run Rhythm’ sparked quite a few new ideas on my end.
