Printed set (Score & Parts)
As represented in the ratio test equation, it may seem counterintuitive that a series, in which the limit of its terms approaches 0 yet it diverges, accurately expresses the concept of overtones in music.
In other words, the overtone wavelengths are 1/2, 1/3, 1/4, and so on, in relation to the fundamental tone. To put it simply, this is equivalent to the sequences of notes produced by the same fingering on brass instruments, for example.
Furthermore, this concept led to the development of alternating harmonic series (Leibniz's formula), general harmonic series, Kempner series (a kind of depleted harmonic series), and more.
This piece comprises the following elements: harmonic series-based overtone sequences, a Brazilian scene influenced by a rhythm approach, Modes of Limited Transposition (MLT) Mode No. 3, and an improvised sequence using all of them.
However, even without such complex explanations, performers can create their own interpretations from the notes. When they come together across the eight parts, it gives birth to music.
(Masamicz Amano)
