By Susan Francis
On the finish of the varsity time period Kai's summer season used to be all deliberate out: get together, date the most well liked lady round, play soccer, play basketball and pursue his pastime, capturing along with his digicam. He lands a task operating for a qualified photographer, and will get to spend the final weekend of summer season on the analyzing track pageant. existence is sweet for Kai. that's, till a brand new arrival to Aintree strikes into the home throughout from his.... Tasha's summer season was once all deliberate out too: settle in her new domestic and maintain a low profile. She will get sucked into becoming a member of the clique of kids within the quarter yet she quickly discovers that no longer every body in Aintree is overjoyed to have her round. Homesick and not able to slot in, existence isn't really precisely nice for Tasha. that's, till she gets an unforeseen, real provide of friendship… or is it?
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Extra resources for Butterfly Porcupine
Young professes a dislike for the intervals based on the integer five (Gann 135); in his tuning lattice for The Well-Tuned Piano, he replaces the 5/4 major third with the 7/4 septimal minor seventh. Just as the just diatonic and chromatic scales can be understood as regions within an infinite harmonic fabric, Young's twelve-note scale is a subset of the harmonic space defined by 7 and 3. ) mingle with the clearly ringing perfect fifths—which are subtly different from the slightly smaller (by two cents) fifths of standard twelve-tone equal temperament.
An effect of rootedness is that we group pitches together which can fit into the same overtone series: this suggests a mechanism of "harmonic templates" supported by the research of Albert Bregman and Ernst Terhardt. Pitches fitting into the same harmonic template will be grouped together in our aural perceptions. In our discussion ofKoan, we saw how the overtone series of a single complex sound had deep implications for the consonance or dissonance of pairs of complex sounds. In the following examples—Lucier's Music on a Long Thin Wire and Tenney's string quartet version oiKoan—we will see some ways that composers have exploited the as Klangspaltung or tone-splitting: see Haas, "Mikrotonalitaten," in Musik der anderen Tradition: Mikrotonale Tonwelten (Munich: Musik-Konzepte, Edition Text+Kritik, 2003), 59-65.
The next overtone, at 165 Hz, is an octave and a fifth above (3/1), followed by a double octave (4/1) at 220 Hz. The next overtone after this is in a 5/1 ratio with the fundamental, sounding two octaves and a just major third above: 275 Hz. Despite Mersenne's doubts, a vibrating string can simultaneously vibrate in multiple modes, each corresponding to some division of the string into equal parts. 1 draw here on Christensen's research on the history of overtones and vibrational theory, particularly on the discussion in pages 133-168.