In search for perfectly imperfect interpolation (by Reiko Yamada)
The development of Western tuning systems offers an interesting example of interpolation evolving in relation to the development of musical instruments and ensemble performance practices. Rather than trying to tackle the topic of interpolation in the tuning system itself, I explored two tuning systems (Just Intonation Pythagorean and Meantone 1/4 Syntonic Comma) as a tool to experiment with interpolation in a voice leading practice. Concretely, by using the digital organ at Zentrum für Orgelforschung (directed by Prof. Gunther Rost) with DynTune (system developed by Jan Ročnik, that allows to move between two tuning systems using a pedal), I tried to create an environment where perfection and imperfection coexist in interpolation.
Below is an excerpt from the experiment, in which four-voice chorale-like texture demonstrates how otherwise simple piecewise constant interpolation (sustained pitches) turns into a complex interpolating phenomenon caused by a linear interpolation, itself created by the tuning pedal.
While the interpolating relationship between voices are vertically consistent in every performance, a performer provides inconsistent horizontal measurement by a subtle change of tempo and an imprecise human operation of the pedal. The result is a mixture of preprogrammed, multi part interpolations constantly changing their relationship to each other, with a performer’s musical judgement intervening the calculation in real time. Photo: Approximate visual representation of the discussion