Henry Cowell’s (1897-1965) New Musical Resources (Cowell 1996), first published in 1930, proposes an analogy between rhythmic patterns and just intonation ratios. Since each harmonic in the overtone series is an integer multiple of a given fundamental (i.e., f, 2f, 3f, 4f, 5f, ...), Cowell imports this spectral information to rhythmically articulate harmony, thus redefining pitch and rhythm as different time scales of the same phenomenon (Roads 2002). A major triad in close position, would be rhythmically notated, so that the number of articulations and respective duration are in correspondence to the harmonics 2f, 3f, and 5f. In this case, the root of the triad (second harmonic) would be rhythmically articulated as two eighth-notes, the fifth of the triad (third harmonic) as an eighth-note triplet and the third of the triad (fifth harmonic) as a sixteenth-note quintuplet, respectively 2f, 3f, and 5f where f =quarter-note. Joseph Schillinger (1895-1943) idealized one of his composing machines, Rhythmicon (built by Leon Theremin), to compose and perform patterns according to Cowell’s principle of spectral rhythm (Schillinger 1948).
In “.... How time passes....” (Stockhausen 1961), Stockhausen describes the creation of a tempered chromatic scale of duration paralleling the equal-tempered pitch scale. Since, traditional note values cannot properly represent the values resulting from the division of the octave ratio in twelve equal parts, Stockhausen opted for a common note value set to a tempered chromatic scale of metronome settings. Such scale, within the octave of whole-note (w) = 60 to whole-note = 120, is represented as w= 60, w= 63.6, w= 67.4, w= 71.4, w= 75.6, w=80.1, w= 84.9, w = 89.9, w = 95.2, w= 100.9, w= 106.9, w= 113.3, w= 120.
See also Periodically Aperiodical - Aperiodically Periodical .
In “.... How time passes....” (Stockhausen 1961), Stockhausen describes the creation of a tempered chromatic scale of duration paralleling the equal-tempered pitch scale. Since, traditional note values cannot properly represent the values resulting from the division of the octave ratio in twelve equal parts, Stockhausen opted for a common note value set to a tempered chromatic scale of metronome settings. Such scale, within the octave of whole-note (w) = 60 to whole-note = 120, is represented as w= 60, w= 63.6, w= 67.4, w= 71.4, w= 75.6, w=80.1, w= 84.9, w = 89.9, w = 95.2, w= 100.9, w= 106.9, w= 113.3, w= 120.
See also Periodically Aperiodical - Aperiodically Periodical .
