All of these three microtonal double-stop intonation studies are based on a flexible non-tempered sixth-tone scale. The sixth-tones, which were already promoted by Ferruccio Busoni more than 100 years ago, seem to be the smallest intervals that can easily be perceived as melodic steps, whereas yet smaller intervals tend to create the impression of an enharmonic retuning of the previous pitch.

I have employed various micro-chromatic scales during the past fifteen years in order to establish interesting and comprehensible microtonal harmonic modulations; but in this composition I have limited the number of scale degrees to 31 per octave to keep the steps between them melodic. Unlike in the tone system of 31-tone Equal Temperament, however, any scale degree may be represented by one of several different, yet similar pitches, each of which has a particular harmonic function within the musical context. – This flexible sixth-tone scale (from D-4 to D-5), which serves as a “cantus firmus” or theme for all three of the etudes, is a conceptual variation of James Tenney’s magnificent Koan for string quartet; and I also regard it as an homage to Marc Sabat’s ground-breaking List of Intervals Tunable by Ear.

Etude 2 also features the small chromatic semitone (with a frequency ratio of 25 : 24, i.e. circa 71 cents), which comes about in harmonic common-tone modulations into one of the upper or lower mediants, as already explored in the music of Nicola Vicentino and Don Carlo Gesualdo di Venosa. The 3rd etude emphasizes the familiar diatonic steps in order to preserve the old distinction between diatonic and chromatic melodic elements and redefine it within the new microtonal context. How to establish an elegant symbiosis between them, this is an issue György Ligeti was very concerned with; and that is why I dedicated this piece to my former teacher. But as my music also includes the melodic ¾-tone steps known from Persian music, it is paying tribute to Gérard Grisey as well, who embraced this powerful interval so unforgettably in his Quatre Chants pour franchir leseuil.

Wolfgang von Schweinitz