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Todd Harrop

In 2012 we collaborated on a solo work for Bohlen–Pierce (BP) clarinet in both the BP scale and Carlos alpha scale. Neither has a 1200 cent octave, however they share an interval of 1170 cents which we attempted to use as a substitute for... more
In 2012 we collaborated on a solo work for Bohlen–Pierce (BP) clarinet in both the BP scale and Carlos alpha scale. Neither has a 1200 cent octave, however they share an interval of 1170 cents which we attempted to use as a substitute for motivic transposition. Some computer code assisted us during the creation period in managing up to five staves for one line of music: sounding pitch, MIDI keyboard notation for the composer in both BP and alpha, and a clarinet fingering notation for the performer in both BP and alpha. Although there are programs today that can interactively handle microtonal notation, e.g., MaxScore and the Bach library for Max/MSP, we show how a computer can assist composers in navigating poly-microtonal scales or, for advanced composer-theorists, to interpret equal-tempered scales as just intonation frequency ratios situated in a harmonic lattice. This project was unorthodox for the following reasons: playing two microtonal scales on one clarinet, appropriating a quasi-octave as interval of equivalency, and composing with non-octave scales.
This paper discusses non–octave-based microtonal scales which can express a septimal minor triad formed by the 6th, 7th and 9th partials of the harmonic series. Three methods are proposed for modulating or transferring between each scale:... more
This paper discusses non–octave-based microtonal scales which can express a septimal minor triad formed by the 6th, 7th and 9th partials of the harmonic series. Three methods are proposed for modulating or transferring between each scale: by pivoting on common tones, building joint chords with pitches unique to each scale, or dynamically changing the sizes of generator and period to transform one scale into another. Motivation for this project was to shed light on two relatively unexplored possibilities in microtonality: scales without octaves, and multiple scales within a single piece of music. With today's computers and synthesizers these areas can be explored more easily. The author borrows a goodness-of-fit strategy for a 6:7:9 chord and chooses three scales that divide the perfect fifth into 8, 13 and 18 equal steps. In addition to septimal triads other common tones are identified, e.g. a major seventh 1/6th-tone sharp, and the paper touches on less obvious manners of modulation. This project may be of interest to composers wishing to explore new facets of microtonality in their work.
The author uses just intonation to introduce the Bohlen–Pierce non-octave scale by way of lattices, unison vectors and periodicity blocks. Although these techniques are already documented in BP literature the examples presented may be of... more
The author uses just intonation to introduce the Bohlen–Pierce non-octave scale by way of lattices, unison vectors and periodicity blocks. Although these techniques are already documented in BP literature the examples presented may be of interest to intermediate composers/theorists who wish to strengthen their understanding of just music systems.
The author examines excerpts from three unusual clarinet duets by Fredrik Schwenk, Sascha Lino Lemke and Roger Feria. These quasi-poly-microtonal works explore different approaches to combining the conventional chromatic scale with the... more
The author examines excerpts from three unusual clarinet duets by Fredrik Schwenk, Sascha Lino Lemke and Roger Feria. These quasi-poly-microtonal works explore different approaches to combining the conventional chromatic scale with the Bohlen-Pierce scale of 13 steps per perfect twelfth.