Exploration of an Adaptable Just Intonation System Jeff Snyder Submitted in partial fulfillment of the requirements of the degree of Doctor of Musical Arts in the Graduate School of Arts and Sciences Columbia University 2010 ABSTRACT Exploration of an Adaptable Just Intonation System Jeff Snyder In this paper, I describe my recent work, which is primarily focused around a dynamic tuning system, and the construction of new electro-acoustic instruments using this system. I provide an overview of my aesthetic and theoretical influences, in order to give some idea of the path that led me to my current project. I then explain the tuning system itself, which is a type of dynamically tuned just intonation, realized through electronics. The third section of this paper gives details on the design and construction of the instruments I have invented for my own compositional purposes. The final section of this paper gives an analysis of the first large-scale piece to be written for my instruments using my tuning system, Concerning the Nature of Things. Exploration of an Adaptable Just Intonation System Jeff Snyder I. Why Adaptable Just Intonation on Invented Instruments? 1.1 - Influences 1.1.1 - Inspiration from Medieval and Renaissance music 1.1.2 - Inspiration from Harry Partch 1.1.3 - Inspiration from American country music 1.2 - Tuning systems 1.2.1 - Why just? 1.2.1.1 – Non-prescriptive pitch systems 1.2.1.2 – Just pitch systems 1.2.1.3 – Tempered pitch systems 1.2.1.4 – Rationale for choice of Just tunings 1.2.1.4.1 – Consideration of non-prescriptive tunings 1.2.1.4.2 – Consideration of twelve-tone equal temperament 1.2.1.4.3 – Consideration of non-twelve equal temperaments 1.2.1.4.4 – Consideration of unequal temperaments 1.2.1.4.5 – Consideration of Just tuning systems 1.2.2 - The developments of Harry Partch 1.2.2.1 – Partch’s 43-tone scale 1.2.2.2 – Partch’s otonality and utonality 1.2.2.3 – Consideration of Partch’s system 1.2.3 - The developments of Ben Johnston 1.2.3.1 – Johnston’s use of traditional instruments 1.2.3.2 – Johnston’s notation system 1.2.4 - Other tuning theory research 1.3 - Invented instruments 1.3.1 - Early experimentation 1.3.1.1 - The Anolé 1.3.1.1.1 – Advantages of the Anolé 1.3.1.1.2 – Disadvantages of the Anolé 1.3.1.2 - Computer-controlled cymbals 1.3.2 - Intentions for new instruments II. The Pitch System 2.1 - General features of the pitch system 2.2 - The 12-note ratio scales i 2.2.1 - The normal scale: standard 5-limit just intonation 2.2.2 - The otonal scale: 19-limit just intonation with only otonal ratios 2.2.3 - the utonal scale: 19-limit just intonation with only utonal ratios 2.3 - Movable reference pitches 2.3.1 - Objections to a fixed reference pitch 2.3.2 - Objections to a wide range of reference pitches 2.3.3 - Objection to the use of equal tempered pitches as reference pitches 2.3.4 - Objections to dynamic or automatically-configured reference pitches 2.3.5 - Justification for the use of the “normal scale” as a generator for reference pitches. 2.3.6 - Avoidance of gaps in the full gamut 2.4 - Performer navigation through the scale system 2.4.1 - Selection of the reference pitch 2.4.2 - Selection of the ratio scale 2.4.3 - Notation of tuning adjustments III. The Instruments 3.1 - General features of all the instruments 3.1.1 - Electronic or acoustic? 3.1.2 - Electronic made acoustic 3.1.3 - Traditional interface models 3.1.4 - Instruments vs. controllers 3.1.5 - Traditional design features 3.1.6 - Continuous control over amplitude 3.1.7 - Acoustic construction techniques 3.2 - Individual instruments: design construction and performer interface 3.2.1 - The Bass Manta and the Resophonic Manta 3.2.1.1 - The Manta keyboard 3.2.1.1.1 - Capacitive touch sensing 3.2.1.1.2 - Keyboard layout 3.2.1.1.3 - Manta performance methods 3.2.1.1.4 - Computer interface for the Manta 3.2.1.1.5 - Tuning procedure for the Manta 3.2.1.1.6 - Pitch mapping on the Manta 3.2.1.2 - The resonators for the Manta keyboard 3.2.1.2.1 - The Bass Manta 3.2.1.2.2 - The Resophonic Manta 3.2.2 - The Contravielles 3.2.2.1 - Contravielle visual and structural design features ii 3.2.2.2 - Contravielle left-hand buttons 3.2.2.3 - Contravielle right-hand controls 3.2.2.4 - Treble and Tenor Contravielles 3.2.3 - The Birl 3.2.3.1 - The Birl controller 3.2.3.1.1 - The Birl controller keying system 3.2.3.1.2 - The Birl controller breath sensor 3.2.3.2 - The electromechanical oscillator 3.2.3.3 - The Birl resonator 3.2.3.4 - Future development of the Birl IV. The Composition 4.1 - Structure of “Concerning the Nature of Things” 4.1.1 - Origin of the text, and philosophical reasons for its selection 4.1.2 - Major formal divisions in the piece 4.2 - Vocal writing in “Concerning the Nature of Things” 4.2.1 - American country music vocal harmony rules 4.2.1.1 - Hierarchy of voices 4.2.1.2 - “Close” harmony 4.2.1.3 - Avoidance of contrary motion 4.2.1.4 - Voices should be in rhythmic unison, or homophony 4.2.1.5 - Examples of American country music theory in practice 4.2.2 - Use of false relations 4.2.3 - Complex melismas 4.2.4 - Phrases in text setting, and acceptable cadential consonances 4.2.5 - Middle section hocket 4.2.6 - Rhythmic language of the vocal writing 4.2.6.1 - Speech rhythms and even declamation 4.2.6.2 - Rational metric divisions 4.2.7 - Last line repetition 4.3 - Instrumental writing in “Concerning the Nature of Things” 4.3.1 - The role of the Bass Manta: continuo 4.3.2 - The role of the Resophonic Manta: pedal steel 4.3.3 - The role of the Contravielles and the Birls: strings and winds 4.4. - Adaptable Just Intonation in “Concerning the Nature of Things” 4.4.1 - Large-scale harmonic progression in the piece 4.4.2 - Beatless consonances 4.4.3 - Unusual harmonic structures 4.4.4 - Just intonation false relations 4.4.6 - Intonation and the voice parts 4.4.7 - Resources for further exploration iii 1 I. Why Adaptable Just Intonation on Invented Instruments? This paper has three main goals: to explain the tuning system which I call Adaptable Just Intonation, to examine the instruments I have built to realize this tuning system and my music, and to analyze a particular composition I have written for my instruments using this tuning system. To make clear the reasoning behind the choices I have made in my work, the initial section will explore the prior art that has influenced my work most significantly. At the end of the first chapter, I will describe some of my earlier artistic works, to more accurately show the course of development toward the current state of my music and instruments. 1.1 - Influences 1.1.1 - Inspiration from Medieval and Renaissance music For a long time, I have found the art music of the late medieval period and the Renaissance period in European history to be particularly fascinating. I am attracted to the complicated melismatic lines of the Ars Subtilior composers, the strange false relations in British keyboard music in the 16th century, and the gradual transition of harmonic and melodic thinking from a modal and horizontal mindset toward a more tonal and vertical one. I also find the mysterious nature of many of the less- documented features of this music intriguing, such as the practice of musica ficta and some of the instruments which only survive as visual representations in paintings, not to mention the more subtle details of performance practice which have been lost to 2 time. For many years I have found myself continually seeking out recordings of music made with historical instruments tuned to historical temperaments like ¼- comma meantone or one of the many unequal well-temperaments of the Baroque period. These interests have inspired me to conceive of a musical sound-world that imagines improbable or impossible answers to the more mysterious aspects of this music. In some ways, I view my current art as a kind of “alternate universe” Early music, in which electricity was discovered before tonality. 1.1.2 - Inspiration from Harry Partch Ever since I became aware of the work of Harry Partch, I have been in awe of his accomplishments. At the age of twenty, I first read Genesis of a Music; it influenced my thinking greatly in the years to follow. I was studying music composition at the University of Wisconsin-Madison, where Partch had briefly settled in the mid-1940s while he completed the manuscript for the book. While his music was stylistically very removed from the aesthetics I was pursuing at the time, I found his individualism and inventiveness extremely stimulating. The fact that he had imagined an entirely original genre of music, influenced by diverse sources like Ancient Greek music theory and hobo songs, and then almost single-handedly managed to build an entire ensemble of instruments for its performance was incredibly impressive. The fact that his music had a theatrical and visual element as well was equally interesting.