A microtonal wind controller building on Yamaha’s technology to facilitate the performance of music based on the “19-EDO” scale

We describe a project in which several collaborators adapted an existing instrument to make it capable of playing expressively in music based on the microtonal scale characterised by equal divsion of the octave into 19 tones (“19-EDO”). Our objective was not just to build this instrument, however, but also to produce a well-formed piece of music which would exploit it idiomatically, in a performance which would provide listeners with a pleasurable and satisfying musical experience. Hence, consideration of the extent and limits of the playing-techniques of the resulting instrument (a “Wind-Controller”) and of appropriate approaches to the composition of music for it were an integral part of the project from the start. Moreover, the intention was also that the piece, though grounded in the musical characteristics of the 19-EDO scale, would nevertheless have a recognisable relationship with what Dimitri Tymoczko (2010) has called the “Extended Common Practice” of the last millennium. So the article goes on to consider these matters, and to present a score of the resulting new piece, annotated with comments documenting some of the performance issues which it raises. Thus, bringing the project to fruition involved elements of composition, performance, engineering and computing, and the article describes how such an inter-disciplinary, multi-disciplinary and cross-disciplinary collaboration was co-ordinated in a unified manner to achieve the envisaged outcome. Finally, we consider why the building of microtonal instruments is such a problematic issue in a contemporary (“high-tech”) society like ours

Generalized Tonnetze and Zeitnetze, and the topology of music concepts

The music-theoretic idea of a Tonnetz can be generalized at different levels: as a network of chords relating by maximal intersection, a simplicial complex in which vertices represent notes and simplices represent chords, and as a triangulation of a manifold or other geometrical space. The geometrical construct is of particular interest, in that allows us to represent inherently topological aspects to important musical concepts. Two kinds of music-theoretical geometry have been proposed that can house Tonnetze: geometrical duals of voice-leading spaces and Fourier phase spaces. Fourier phase spaces are particularly appropriate for Tonnetze in that their objects are pitch-class distributions (real-valued weightings of the 12 pitch classes) and proximity in these space relates to shared pitch-class content. They admit of a particularly general method of constructing a geometrical Tonnetz that allows for interval and chord duplications in a toroidal geometry. This article examines how these duplications can relate to important musical concepts such as key or pitch height, and details a method of removing such redundancies and the resulting changes to the homology of the space. The method also transfers to the rhythmic domain, defining Zeitnetze for cyclic rhythms. A number of possible Tonnetze are illustrated: on triads, seventh chords, ninth chords, scalar tetrachords, scales, etc., as well as Zeitnetze on common cyclic rhythms or timelines. Their different topologies – whether orientable, bounded, manifold, etc. – reveal some of the topological character of musical concepts.Accepted manuscrip

Converting images to music using their colour properties

Presented at the 12th International Conference on Auditory Display (ICAD), London, UK, June 20-23, 2006.Music is associated to colors since ancient years. Different mappings between attributes of sound and images allow the efficient conversion between the two types of media. The proposed method for converting images to music using the concept of chromaticism provides the area of computer music with a parameterized environment for audio-visual presentations. The auditory display of colour images may bring the different ways that a listener perceives a musical piece (because of colour transitions) to light. A design template for chromatic synthesis is described. A short example, based on a graphical digital icon, demonstrates the preliminary results

Sonority and Linear Structure in Three Early Works of Olivier Messiaen

In this study I examine three early works of Olivier Messiaen: the motet O sacrum convivium (1937), La colombe from the eight piano preludes (1928-9), and the closing passage of La fiancée perdue from the song cycle Trois méodies (1930). All three works exhibit varying degrees of tonal behavior in combination with a foreground focus on harmonic sonority. As such, I approach each of them with two contrasting analytic methods: modified Schenkerian linear-reductive analysis, informed by the interaction of diatonic and octatonic collections, and set-class analysis. The latter approach incorporates the harmonic complexity index (HCI) as an innovative harmonic measure calculated from the interval-class vector of each set-class. Informed by established and recent scholarly work, the introduction to the thesis provides a background for the application of these analytic techniques to this repertoire, while the thesis itself demonstrates that form is revealed powerfully through the combination of these two separate perspectives

An alternative approach to generalized Pythagorean scales: generation and properties derived in the frequency domain

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of mathematics and music on march 2020, available online at: http://www.tandfonline.com/10.1080/17459737.2020.1726690.Abstract scales are formalized as a cyclic group of classes of projection functions related to iterations of the scale generator. Their representatives in the frequency domain are used to built cyclic sequences of tone iterates satisfying the closure condition. The refinement of cyclic sequences with regard to the best closure provides a constructive algorithm that allows to determine cyclic scales avoiding continued fractions. New proofs of the main properties are obtained as a consequence of the generating procedure. When the scale tones are generated from the two elementary factors associated with the generic widths of the step intervals we get the partition of the octave leading to the fundamental Bézout’s identity relating several characteristic scale indices. This relationship is generalized to prove a new relationship expressing the partition that the frequency ratios associated with the two sizes composing the different step-intervals induce to a specific set of octaves.Peer ReviewedPostprint (author's final draft