Farey systems of musical intonation
Rudolf A. Rasch · Contemporary Music Review · 1988
The distinction between consonant and dissonant intervals, represented in their just forms by frequency ratios expressible in low and high integer numbers respectively, is of prime importance in Western music. It is easy to tell just consonances from tempered ones on the basis of beat perception. Research by Vos & van Vianen (1985) with low‐number frequency‐ratio intervals has shown that beat detection can be predicted by the sum of the ratio numbers in the perfect (just) interval. We investigated the discrimination of perfect and imperfect (tempered) intervals with ratio numbers up to and including 16, thus mainly so‐called dissonances. Beat detection and discrimination are still possible, but are probably determined by other factors that simply the ratio‐numbers magnitude, such as the pattern of interferences in the sound stimulus. We investigated the practical possibilities of the high‐number ratio intervals by describing them as part of a Farey series of musical intervals. These investigations show that low‐number ratio intervals (roughly the classical consonances) have much “space” around them. High‐number ratio intervals have little space around them; they should be tuned very accurately in order not to be confused with neighbouring ratios. These spaces around intervals should be taken into account when applying the high‐number ratio intervals in music compositions.