Keyboards for pure music
Jan Mycielski · The Journal of the Acoustical Society of America · 1978
Let S45 be the set all rational numbers of the form m/n, where m and n are positive integers with mn?45. We define an instrument M with three keyboards I, II, and III. Keyboards I and II permit one to play all consonant chords for which there exists a value φ such that the ratio of φ to the frequency of each simple tone of the chord belongs to S45. Keyboard II is organized so that pressing the keys on some straight lines yields the consonant chords. Keyboard III controls the quality of tones. The purpose of M is not to perform the music of today, but, hopefully, to inspire a new kind of music.