«Suspended in Ratios» is an electroacoustic drone composition that explores the relationships between intonation, microtonality and harmony within the framework of the 7-Limit Just Intonation System.
The main inspiration and starting point for this work was the tuning system of the American minimalist La Monte Young, presented in *The Well-Tuned Piano*. This system, also known as "natural," is based on a type of xenharmonic scale used in 7-Limit-Just intonation, where musical intervals are based on ratios between whole numbers (hence the ratios in the title). Unlike equal temperament, the intervals between successive scale degrees are not equal. Young's system is based on the ratios between the prime numbers 2, 3, and 7 and their multiples. The constant fundamental frequency, which forms the basis for other ratios, is that of E-flat.
I am developing Young's concept of microtonality further by applying this difficult-to-execute tuning in an even more challenging context—that of an orchestra, rather than a piano. Pure intonation systems are those in which the frequency ratios of all intervals are rational numbers. However, these ratios are not fixed and can change depending on the harmony and context in which a particular interval occurs. The "7-Limit" ratios are created using only the prime numbers 2, 3, 5, 7, and their multiples. The proportions are calculated from a single fundamental frequency, usually referred to as 1:1 or 1/1. The tuning process becomes more fluid and less precise, which enhances the possibilities for working with tone types and timbres.
Due to the highly precise results of these calculations, implementing this system with pure intervals (often adapted to the equal temperament of Western music) can pose a significant challenge for both the composer and the performers. Extraordinary precision and full commitment are required from all orchestra members as they actively listen to one another to ensure all harmonies are correctly tuned.
“Suspended in Ratios” demonstrates the potential advantages of understanding sound as an acoustic phenomenon and employing a tuning method that deviates from the equal-tempered system common in Western classical music. By incorporating such an approach, one can potentially gain a deeper understanding of the complexities of musical performance. Despite the difficulties outlined above, I find ample justification for using pure intonation. Most importantly, the tuning system physically corresponds to the harmonic series. This can be illustrated by plucking a string, which always produces the lowest partial (in this case, the constant fundamental frequency) and a series of overtones corresponding to those produced by dividing the string in the ratios 2:3, 3:4, and so on. In brass instruments, the overtone series corresponds to that used in most natural tuning systems. To achieve precise intonation within the Young system, I have the wind instruments retune, apply scordatura to the strings, and use preparation on the percussion. A large part of the string sound is based on natural overtones, which are much closer to pure intonation than to equal temperament. The constant electronics support the Basel Sinfonietta ensemble by enriching and unifying the acoustic sound of all instruments, reinforcing each individual chord, and significantly simplifying the process of tuning and interpreting the harmony for the performers.
Aleksandra Słyż
