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An Application of Calculated Consonance in Computer-Assisted Microtonal Music

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University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2013-12-23 An Application of Calculated Consonance in Computer-Assisted Microtonal Music Burleigh, Ian George Burleigh, I. G. (2013). An Application of Calculated Consonance in Computer-Assisted Microtonal Music (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/24833 http://hdl.handle.net/11023/1225 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY An Application of Calculated Consonance in Computer-Assisted Microtonal Music by Ian George Burleigh A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE INTERDISCIPLINARY DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF COMPUTER SCIENCE and SCHOOL OF CREATIVE AND PERFORMING ARTS | MUSIC CALGARY, ALBERTA DECEMBER, 2013 © Ian George Burleigh 2013 Abstract Harmony (the audible result of varied combinations of simultaneously sounding tones) ought to, for the most part, sound pleasing to the ear. The result depends, among other factors, on a proper choice of the pitches for the tones that form harmonious chords, and on their correct intonation during musical performance. This thesis proposes a computational method for calculation of relative consonance among groups of tones, and its possible practical applications in machine-assisted arrangement of tones, namely the choice of tone pitches and their microtonal adjustment. The consonance of tone groups is calculated using a model that is based on the physiological theory of tone con- sonance that was published by Hermann Helmholtz in the middle of the 19th century. Given a group of tones that have fixed pitches, changes in the aggregate dissonance caused by adding another \probe" tone of a variable pitch can be represented as a \dissonance landscape". Local minima in the \height" of the landscape correspond to local minima of the aggregate dissonance as a function of the pitch of the probe tone. Finding a local dissonance minimum simulates the actions of a musician who is \tuning by ear". The set of all local minima within a given pitch range is a collection of potentially good pitch choices from which a composer (a human, or an algorithmic process) can fashion melodies that sound in harmony with the fixed tones. Several practical examples, realized in an experimental software, demonstrate applications of the method for: 1) computer-assisted microtonal tone arrangement (music composition), 2) algorithmic (machine-generated) music, and 3) musical interplay between a human and a machine. The just intonation aspect of the tuning method naturally leads to more than twelve, poten- tially to many, pitches in an octave. Without some restrictions that limit the complexity of the process, handling of so many possibilities by a human composer and their precise rendi- tion as sound by a performing musician would be very difficult. Restricting the continuum of possible pitches to the discrete 53-division of the octave, and employing machine-assistance in their arrangement and in sound synthesis make applications of the method feasible. ii Preface There was Eru, the One, who in Arda is called Il´uvatar;and he made first the Ainur, the Holy Ones, that were the offspring of his thought, and they were with him before aught else was made. And he spoke to them, propounding to them themes of music. And it came to pass that he declared to them a mighty theme, unfolding to them things greater and more wonderful that he had yet revealed: \Of the theme that I have declared to you, I will now that ye make in harmony together a Great Music. Ye shall show forth your powers in adorning this theme, each with his own thoughts and devices." And a sound arose of endless interchanging melodies woven in a harmony that passed beyond hearing into the depths and into the heights, and the music and the echo of the music went out into the Void, and it was not void. J.R.R.Tolkien, Ainulindal¨e(The Music of the Ainur), The Silmarillion, 1977. Music is made from melodious strands of tones (voices) that are \woven in a harmony" into greater patterns and structures. The weaving and interplay of melodic strands (counter- point) bring into existence chords (combinations of simultaneously sounding tones) and thus harmony. The composer may deal with all the voices as equally important, or choose one voice as the primary one that carries the main melody and make the rest to function as an accompaniment. In any case, the proper combination of tones that sound together is a most essential factor in making music.1 Weaving of musical patterns is not unlike solving a combinatorial puzzle: a task to organize a large number of items so that they fit well together. There are many possible combinations of the items; most of the combinations have to be outright rejected since they do not lead to any potential solution. Somewhere among the remaining combinations may lie possible answers; there could be several or perhaps many of those. Some may be but acceptable, some may be good, and occasionally there are some that are exquisite. 1\Harmony". Oxford Music Online. iii A common musical puzzle is the problem of creating a melody that fits a given harmonic progression. (This text proposes a computational method that can be used to assist in solving such puzzles.) A famous example is Charles Gounod's \Ave Maria",2 superposed over J.S. Bach's Prelude in C.3 The beautifully clear structure of the Prelude with a mobile, yet firmly grounded harmonic progression makes it a great foundational material for composition of musical variations. In Chapter 4 we shall discuss several melodies and other musical structures that were fitted over the chord progression of the Prelude, to demonstrate the feasibility of our method and the practicability of the experimental software in which the method has been implemented. Weaving musical patterns is a craft and an art, practised mainly by music composers and performing musicians. Music composers create musical compositions (that include solutions of various musical puzzles) and write them down using musical notation in the form of musical scores. Performing musicians interpret the scores, in a live performance or during a studio recording, turning them into sound. It takes talent and many years of training for both music composers and performing musicians to acquire necessary skills and insight. The composer and the musician can be the same person: some top performers of classical music and many songwriters of popular music write and perform their own compositions and songs. Improvising musicians, in particular the players of Renaissance, Baroque, Eastern, and jazz music, invent musical themes (or create them from prepared and practised melodic fragments) at the time of their performance. Fitting numerous composed or improvised (that is, invented on the spot in \real" time) melodies over an existing harmonic progression is one of the essential aspects of jazz music. Jazz musicians do often borrow chord progressions from other sources, but almost always create their own original melodic themes. Some of such newly created themes even have become a part of the \jazz songbook", a corpus of \standard" jazz songs. For example, Miles Davis's song \Donna Lee"4 is a bebop melody written over the more traditional harmonic progression of the song \Back Home Again in Indiana".5 The chord progression of George Gershwin's song \I Got Rhythm"6 became known as \rhythm changes"7 and was used in 2M´editationsur le premier pr´eludede S. Bach, 1853. 3Prelude and Fugue No.1 in C major, BWV 846. 4\Donna Lee (1947)". Wilson et al., JazzStandards.com | the first and only centralized information source for the songs and instrumentals jazz musicians play most frequently. 5\Indiana (Back Home Again in Indiana) (1917)". ibid. 6\I Got Rhythm (1930)". ibid. 7\Jazz Theory: Rhythm Changes". ibid. iv so many jazz songs, that it is very frequently used as one of the most common background accompaniments for improvisation at jam sessions.8 Chapter 5 describes an experimental real-time system for a musical interplay of a human and a machine, as if they were two improvising jazz musicians. Music theorists analyze existing compositions, attempt to discover inner principles and rules that guided their weaving, and then construct theories that attempt to explain how the compositions were built and why their tone patterns do (or do not) sound in harmony. Many musical works can be then subsequently created following the rules of a given music theory, within the limits of the musical genre for which the theory was constructed. Great composers, however, often in their work stretch or even break the boundaries of established theories and thus advance musical practice. And then there are engineers. Engineers may not have the creative talent or feelings of artists, nor the insight of music theorists; but engineers recognize structured patterns and with that ability they build machines. Computers are the ultimately flexible and adaptable machines brought to action by computer programs, machines that can with remarkable success assist composers and musicians to solve musical puzzles, write musical scores, and render them as sound. This text describes one such attempt to build a suite of software applications that assist composers in creating music with higher level of tuning complexity and precision than otherwise possible.
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