An Algorithm for Real-Time Harmonic Microtuning
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An Adaptive Tuning System for MIDI Pianos
David Løberg Code Groven.Max: School of Music Western Michigan University Kalamazoo, MI 49008 USA An Adaptive Tuning [email protected] System for MIDI Pianos Groven.Max is a real-time program for mapping a renstemningsautomat, an electronic interface be- performance on a standard keyboard instrument to tween the manual and the pipes with a kind of arti- a nonstandard dynamic tuning system. It was origi- ficial intelligence that automatically adjusts the nally conceived for use with acoustic MIDI pianos, tuning dynamically during performance. This fea- but it is applicable to any tunable instrument that ture overcomes the historic limitation of the stan- accepts MIDI input. Written as a patch in the MIDI dard piano keyboard by allowing free modulation programming environment Max (available from while still preserving just-tuned intervals in www.cycling74.com), the adaptive tuning logic is all keys. modeled after a system developed by Norwegian Keyboard tunings are compromises arising from composer Eivind Groven as part of a series of just the intersection of multiple—sometimes oppos- intonation keyboard instruments begun in the ing—influences: acoustic ideals, harmonic flexibil- 1930s (Groven 1968). The patch was first used as ity, and physical constraints (to name but three). part of the Groven Piano, a digital network of Ya- Using a standard twelve-key piano keyboard, the maha Disklavier pianos, which premiered in Oslo, historical problem has been that any fixed tuning Norway, as part of the Groven Centennial in 2001 in just intonation (i.e., with acoustically pure tri- (see Figure 1). The present version of Groven.Max ads) will be limited to essentially one key. -
The Group-Theoretic Description of Musical Pitch Systems
The Group-theoretic Description of Musical Pitch Systems Marcus Pearce [email protected] 1 Introduction Balzano (1980, 1982, 1986a,b) addresses the question of finding an appropriate level for describing the resources of a pitch system (e.g., the 12-fold or some microtonal division of the octave). His motivation for doing so is twofold: “On the one hand, I am interested as a psychologist who is not overly impressed with the progress we have made since Helmholtz in understanding music perception. On the other hand, I am interested as a computer musician who is trying to find ways of using our pow- erful computational tools to extend the musical [domain] of pitch . ” (Balzano, 1986b, p. 297) Since the resources of a pitch system ultimately depend on the pairwise relations between pitches, the question is one of how to conceive of pitch intervals. In contrast to the prevailing approach which de- scribes intervals in terms of frequency ratios, Balzano presents a description of pitch sets as mathematical groups and describes how the resources of any pitch system may be assessed using this description. Thus he is concerned with presenting an algebraic description of pitch systems as a competitive alternative to the existing acoustic description. In these notes, I shall first give a brief description of the ratio based approach (§2) followed by an equally brief exposition of some necessary concepts from the theory of groups (§3). The following three sections concern the description of the 12-fold division of the octave as a group: §4 presents the nature of the group C12; §5 describes three perceptually relevant properties of pitch-sets in C12; and §6 describes three musically relevant isomorphic representations of C12. -
Thursday, April 03, 2014 the Winter 2014
The BYU-Idaho Research and Creative Works Council Is Pleased to Sponsor The Winter 2014 Thursday, April 03, 2014 Conference Staff Hayden Coombs Conference Manager Caroline Baker Conference Logistics Michael Stoll Faculty Support Meagan Pruden Faculty Support Cory Daley Faculty Support Blair Adams Graphic Design Kyle Whittle Assessment Jordan Hunter Assessment Jarek Smith Outreach Blaine Murray Outreach Advisory Committee Hector A. Becerril Conference Chair Jack Harrell Faculty Advisor Jason Hunt Faculty Advisor Tammy Collins Administrative Support Greg Roach Faculty Advisor Brian Schmidt Instructional Development Jared Williams Faculty Advisor Alan K. Young Administrative Support Brady Wiggins Faculty Advisor Lane Williams Faculty Advisor Agricultural and Biological Sciences Biological & Health Sciences, Oral Presentations SMI 240, 04:30 PM to 06:30 PM Comparison of Embryonic Development and the Association of Aeration on Rate of Growth in Pacific Northeastern Nudibranchs Elysa Curtis, Daniel Hope, Mackenzie Tietjen, Alan Holyoak (Mentor) Egg masses of six species of nudibranchs were kept and observed in a laboratory saltwater table with a constant flow of water directly from the ocean, from the time the eggs were laid to the time they hatched. The egg masses were kept in the same relative place in which they were laid, and protected by plastic containers with two mesh sides to let the water flow freely past the eggs. Samples of the egg masses were collected and observed under a microscope at regular intervals while temperature, salinity, width of eggs and stage of development were recorded. It was found that each embryo developed significantly faster compared to previous studies conducted on the respective species’ egg masses, including studies with higher water temperatures. -
Unified Music Theories for General Equal-Temperament Systems
Unified Music Theories for General Equal-Temperament Systems Brandon Tingyeh Wu Research Assistant, Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan ABSTRACT Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems. Without confining the study to the twelve-tone equal-temperament (12-TET) system, we propose a set of basic axioms based on musical observations. The axioms may lead to scales that are reasonable both mathematically and musically in any equal- temperament system. We reexamine the mathematical understandings and interpretations of ideas in classical music theory, such as the circle of fifths, enharmonic equivalent, degrees such as the dominant and the subdominant, and the leading tone, and endow them with meaning outside of the 12-TET system. In the process of deriving scales, we create various kinds of sequences to describe facts in music theory, and we name these sequences systematically and unambiguously with the aim to facilitate future research. - 1 - 1. INTRODUCTION Keyboard configuration and combinatorics The concept of key signatures is based on keyboard-like instruments, such as the piano. If all twelve keys in an octave were white, accidentals and key signatures would be meaningless. Therefore, the arrangement of black and white keys is of crucial importance, and keyboard configuration directly affects scales, degrees, key signatures, and even music theory. To debate the key configuration of the twelve- tone equal-temperament (12-TET) system is of little value because the piano keyboard arrangement is considered the foundation of almost all classical music theories. -
Models of Octatonic and Whole-Tone Interaction: George Crumb and His Predecessors
Models of Octatonic and Whole-Tone Interaction: George Crumb and His Predecessors Richard Bass Journal of Music Theory, Vol. 38, No. 2. (Autumn, 1994), pp. 155-186. Stable URL: http://links.jstor.org/sici?sici=0022-2909%28199423%2938%3A2%3C155%3AMOOAWI%3E2.0.CO%3B2-X Journal of Music Theory is currently published by Yale University Department of Music. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/yudm.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Mon Jul 30 09:19:06 2007 MODELS OF OCTATONIC AND WHOLE-TONE INTERACTION: GEORGE CRUMB AND HIS PREDECESSORS Richard Bass A bifurcated view of pitch structure in early twentieth-century music has become more explicit in recent analytic writings. -
2012 02 20 Programme Booklet FIN
COMPOSITION - EXPERIMENT - TRADITION: An experimental tradition. A compositional experiment. A traditional composition. An experimental composition. A traditional experiment. A compositional tradition. Orpheus Research Centre in Music [ORCiM] 22-23 February 2012, Orpheus Institute, Ghent Belgium The fourth International ORCiM Seminar organised at the Orpheus Institute offers an opportunity for an international group of contributors to explore specific aspects of ORCiM's research focus: Artistic Experimentation in Music. The theme of the conference is: Composition – Experiment – Tradition. This two-day international seminar aims at exploring the complex role of experimentation in the context of compositional practice and the artistic possibilities that its different approaches yield for practitioners and audiences. How these practices inform, or are informed by, historical, cultural, material and geographical contexts will be a recurring theme of this seminar. The seminar is particularly directed at composers and music practitioners working in areas of research linked to artistic experimentation. Organising Committee ORCiM Seminar 2012: William Brooks (U.K.), Kathleen Coessens (Belgium), Stefan Östersjö (Sweden), Juan Parra (Chile/Belgium) Orpheus Research Centre in Music [ORCiM] The Orpheus Research Centre in Music is based at the Orpheus Institute in Ghent, Belgium. ORCiM's mission is to produce and promote the highest quality research into music, and in particular into the processes of music- making and our understanding of them. ORCiM -
The Ten String Quartets of Ben Johnston, Written Between 1951 and 1995, Constitute No Less Than an Attempt to Revolutionize the Medium
The ten string quartets of Ben Johnston, written between 1951 and 1995, constitute no less than an attempt to revolutionize the medium. Of them, only the First Quartet limits itself to conventional tuning. The others, climaxing in the astonishing Seventh Quartet of 1984, add in further microtones from the harmonic series to the point that the music seems to float in a free pitch space, unmoored from the grid of the common twelve-pitch scale. In a way, this is a return to an older conception of string quartet practice, since players used to (and often still do) intuitively adjust their tuning for maximum sonority while listening to each other’s intonation. But Johnston has extended this practice in two dimensions: Rather than leave intonation to the performer’s ear and intuition, he has developed his own way to specify it in notation; and he has moved beyond the intervals of normal musical practice to incorporate increasingly fine distinctions, up to the 11th, 13th, and even 31st partials in the harmonic series. This recording by the indomitable Kepler Quartet completes the series of Johnston’s quartets, finally all recorded at last for the first time. Volume One presented Quartets 2, 3, 4, and 9; Volume Two 1, 5, and 10; and here we have Nos. 6, 7, and 8, plus a small piece for narrator and quartet titled Quietness. As Timothy Ernest Johnson has documented in his exhaustive dissertation on Johnston’s Seventh Quartet, Johnston’s string quartets explore extended tunings in three phases.1 Skipping over the more conventional (though serialist) First Quartet, the Second and Third expand the pitch spectrum merely by adding in so-called five-limit intervals (thirds, fourths, and fifths) perfectly in tune (which means unlike the imperfect, compromised way we tune them on the modern piano). -
MTO 20.2: Wild, Vicentino's 31-Tone Compositional Theory
Volume 20, Number 2, June 2014 Copyright © 2014 Society for Music Theory Genus, Species and Mode in Vicentino’s 31-tone Compositional Theory Jonathan Wild NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.14.20.2/mto.14.20.2.wild.php KEYWORDS: Vicentino, enharmonicism, chromaticism, sixteenth century, tuning, genus, species, mode ABSTRACT: This article explores the pitch structures developed by Nicola Vicentino in his 1555 treatise L’Antica musica ridotta alla moderna prattica . I examine the rationale for his background gamut of 31 pitch classes, and document the relationships among his accounts of the genera, species, and modes, and between his and earlier accounts. Specially recorded and retuned audio examples illustrate some of the surviving enharmonic and chromatic musical passages. Received February 2014 Table of Contents Introduction [1] Tuning [4] The Archicembalo [8] Genus [10] Enharmonic division of the whole tone [13] Species [15] Mode [28] Composing in the genera [32] Conclusion [35] Introduction [1] In his treatise of 1555, L’Antica musica ridotta alla moderna prattica (henceforth L’Antica musica ), the theorist and composer Nicola Vicentino describes a tuning system comprising thirty-one tones to the octave, and presents several excerpts from compositions intended to be sung in that tuning. (1) The rich compositional theory he develops in the treatise, in concert with the few surviving musical passages, offers a tantalizing glimpse of an alternative pathway for musical development, one whose radically augmented pitch materials make possible a vast range of novel melodic gestures and harmonic successions. -
Intervals and Transposition
CHAPTER 3 Intervals and Transposition Interval Augmented and Simple Intervals TOPICS Octave Diminished Intervals Tuning Systems Unison Enharmonic Intervals Melodic Intervals Perfect, Major, and Minor Tritone Harmonic Intervals Intervals Inversion of Intervals Transposition Consonance and Dissonance Compound Intervals IMPORTANT Tone combinations are classifi ed in music with names that identify the pitch relationships. CONCEPTS Learning to recognize these combinations by both eye and ear is a skill fundamental to basic musicianship. Although many different tone combinations occur in music, the most basic pairing of pitches is the interval. An interval is the relationship in pitch between two tones. Intervals are named by the Intervals number of diatonic notes (notes with different letter names) that can be contained within them. For example, the whole step G to A contains only two diatonic notes (G and A) and is called a second. Figure 3.1 & ww w w Second 1 – 2 The following fi gure shows all the numbers within an octave used to identify intervals: Figure 3.2 w w & w w w w 1ww w2w w3 w4 w5 w6 w7 w8 Notice that the interval numbers shown in Figure 3.2 correspond to the scale degree numbers for the major scale. 55 3711_ben01877_Ch03pp55-72.indd 55 4/10/08 3:57:29 PM The term octave refers to the number 8, its interval number. Figure 3.3 w œ œ w & œ œ œ œ Octavew =2345678=œ1 œ w8 The interval numbered “1” (two notes of the same pitch) is called a unison. Figure 3.4 & 1 =w Unisonw The intervals that include the tonic (keynote) and the fourth and fi fth scale degrees of a Perfect, Major, and major scale are called perfect. -
The Devil's Interval by Jerry Tachoir
Sound Enhanced Hear the music example in the Members Only section of the PAS Web site at www.pas.org The Devil’s Interval BY JERRY TACHOIR he natural progression from consonance to dissonance and ii7 chords. In other words, Dm7 to G7 can now be A-flat m7 to resolution helps make music interesting and satisfying. G7, and both can resolve to either a C or a G-flat. Using the TMusic would be extremely bland without the use of disso- other dominant chord, D-flat (with the basic ii7 to V7 of A-flat nance. Imagine a world of parallel thirds and sixths and no dis- m7 to D-flat 7), we can substitute the other relative ii7 chord, sonance/resolution. creating the progression Dm7 to D-flat 7 which, again, can re- The prime interval requiring resolution is the tritone—an solve to either a C or a G-flat. augmented 4th or diminished 5th. Known in the early church Here are all the possibilities (Note: enharmonic spellings as the “Devil’s interval,” tritones were actually prohibited in of- were used to simplify the spelling of some chords—e.g., B in- ficial church music. Imagine Bach’s struggle to take music stead of C-flat): through its normal progression of tonic, subdominant, domi- nant, and back to tonic without the use of this interval. Dm7 G7 C Dm7 G7 Gb The tritone is the characteristic interval of all dominant bw chords, created by the “guide tones,” or the 3rd and 7th. The 4 ˙ ˙ w ˙ ˙ tritone interval can be resolved in two types of contrary motion: &4˙ ˙ w ˙ ˙ bbw one in which both notes move in by half steps, and one in which ˙ ˙ w ˙ ˙ b w both notes move out by half steps. -
Curriculum Vitae
Curriculum Vitae Nathan E. Nabb, D.M. Associate Professor of Music – Saxophone Stephen F. Austin State University www.nathannabbmusic.com Contact Information: 274 Wright Music Building College of Fine Arts - School of Music Stephen F. Austin State University TEACHING EXPERIENCE Associate Professor of Saxophone Stephen F. Austin State University 2010 to present Nacogdoches, Texas Maintain and recruit private studio averaging 20+ music majors Applied saxophone instruction to saxophone majors (music education and performance) Saxophone quartets (number depending on enrollment) Private Applied Pedagogy and Repertoire for graduate saxophone students Recruitment tour performances and master classes with other wind faculty Saxophone studio class Assistant Professor of Saxophone Morehead State University 2005 to 2010 Morehead, Kentucky Maintain and recruit private studio averaging 17-22 music majors Applied saxophone instruction to saxophone majors (education, performance and jazz) Saxophone quartets (three or four depending on enrollment) Woodwind methods course (flute, clarinet and saxophone) Saxophone segment of Advanced Woodwind Methods Course Private Applied Pedagogy and Performance Practice for graduate saxophone students Guided independent study courses for graduate saxophone students Present annual clinics for Kentucky high-school saxophonists for the MSU Concert Band Clinic Present annual All-State audition preparation clinics Academic advisor for undergraduate private applied saxophonists Saxophone studio class Nathan E. Nabb Curriculum -
Harmonic Dualism and the Origin of the Minor Triad
45 Harmonic Dualism and the Origin of the Minor Triad JOHN L. SNYDER "Harmonic Dualism" may be defined as a school of musical theoretical thought which holds that the minor triad has a natural origin different from that of the major triad, but of equal validity. Specifically, the term is associated with a group of nineteenth and early twentieth century theo rists, nearly all Germans, who believed that the minor harmony is constructed in a downward ("negative") fashion, while the major is an upward ("positive") construction. Al though some of these writers extended the dualistic approach to great lengths, applying it even to functional harmony, this article will be concerned primarily with the problem of the minor sonority, examining not only the premises and con clusions of the principal dualists, but also those of their followers and their critics. Prior to the rise of Romanticism, the minor triad had al ready been the subject of some theoretical speculation. Zarlino first considered the major and minor triads as en tities, finding them to be the result of harmonic and arith metic division of the fifth, respectively. Later, Giuseppe Tartini advanced his own novel explanation: he found that if one located a series of fundamentals such that a given pitch would appear successively as first, second, third •.• and sixth partial, the fundamentals of these harmonic series would outline a minor triad. l Tartini's discussion of combination tones is interesting in that, to put a root un der his minor triad outline, he proceeds as far as the 7:6 ratio, for the musical notation of which he had to invent a new accidental, the three-quarter-tone flat: IG.