Output details

fur Johannes Kepler

Concert work for voice, viola and sine-tone keyboard

The principal innovative research content in this work lies in its unique tuning system, based on a set of interlocking frequency ratios. These ratios are derived from the inter-planetary ‘harmonies’ described by Johannes Kepler in his astronomical treatise, ‘Harmonices Mundi’ (1619), and are heard as sine-tones in the keyboard part of the work.

By measuring the widest and narrowest orbital ellipses of the planets then visible in the solar system, Kepler was able to calculate the difference between these paths and propose a harmonic ratio for each planet (for example, Saturn is a major third, Mars a perfect fifth). On closer examination, however, it is evident that Kepler simplified the results of his observations in order to produce simple, Pythagorean ratios; in the present work the tuning ratios return to that original data to produce much more complex harmonies. Each section of ‘für Johannes Kepler’ focuses on a different ratio.

The use of interlocking ratios first occurred in Fox’s ‘BLANK’ (2002) which in turn acknowledged the influence of that work’s dedicatee, James Tenney. In the present work, however, ratio-based tunings are combined with sixth-tune tuning in the voice and viola parts to create a hybrid tuning system which juxtaposes the celestial domain of the keyboard part with the human domain of the voice and viola.

The Latin text of ‘für Johannes Kepler’ is taken from the end of the fifth volume of ‘Harmonices Mundi’. In keeping with the era in which the texts were written and with their subject matter, the work’s formal structure is based on the 17th century ‘cantata da chiesa’. ‘für Johannes Kepler’ was commissioned by Trio Scordatura who premiered it at the 2008 Transit Festival in Leuven (Belgium). They subsequently recorded it for the CD ‘Natural Science’, released on Metier in 2011.