Bach in just intonation by Erik Zuurbier

Articles

Erik Zuurbier Bach in just intonation
Het ORGEL 112 (2016), nr. 6, 22-27 [summary]

Many temperaments are available for organs. This article treats just intonation, but with many more than the customary 12 pitches per octave. For this, a different division of the keyboard is required. Existing designs, e.g. that in On the Sensations of Tone by Hermann Helmholtz / Alexander Ellis, are complicated. The article describes an alternative that adapts the idea used in the double-pedal harp: with but 7 strings per octave it is possible to play all the tones. On the new keyboard you have for each key the choice of 3 or more tones, at intervals of a syntonic comma. So if Bach writes an E, you have to decide which E to play. The article describes a computer program that does this. The result can be heard on 4 sound files:

Triosonate, BWV 525 – Adagio
Nun komm, der Heiden Heiland, BWV 659
Fuga in g, BWV 578
Fantasia in c, BWV 562 a
Fantasia in c, BWV 562 b

This last work is very dissonant. It makes use of 38 different pitches per octave. For comparison, a sound file of the Fantasia in c is provided in 12-tone equal temperament.