5-Limit Counterpoint for Violin and Viola (2018)
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On the True Principles of Harmony As Presented
ON THE TRUE PRINCIPLES OF HARMONY AS PRESENTED THROUGH THE SPECULUM MUSICUM* By L. Euler Translated by Larry Blaine and Douglas Kendall 1 All harmony, and, what is more, all music, rests upon four or five simple consonances which novices in the art should be taught to accustom their ears to, and to produce, whether by voice or by instruments, as exactly as possible. These consonances are the following: I. Unison; II. Octave,or Diapason; III. Fifth,or Diapente; IV. Major Third; on which four consonances music of previous ages was built up; more recently an additional consonance, usually signified by the name seventh, seems to have been adopted. Let us, then, investigate these five consonances with considerable care as the pillars of harmony, since many who have attempted to treat of this science have dealt with these elements too negligently. 2 Let us thus begin with the unison, which consists of perfect equality of two or more musical tones. Since indeed every sound is produced by a vibratory motion, or tremor, agitated in the air, whether that tremor be regular or irregular, no tones are admitted in music except when all vibrations are isochronous among themselves, that is to say, completed in identical small intervals of time. Thus we will have an adequate notion of some musical tone when we have learned how many vibrations are produced in a given time, that is, within a small span; two or more tones which in the same span give forth the same number of vibrations will be unisons; and because tones are customarily characterized by the number of vibrations they give forth in a given time, the nature of the unison will lie in a relationship of equality. -
JI Primer Ed.3
THE JUST INTONATION PPRIRIMMEERR An Introduction to the Theory and Practice of Just Intonation by David B. Doty Third Edtion, December 2002 ISBN 0-9726810-0-0 ©1993, 1994, 2002 The Just Intonation Network A Project of Other Music, Inc. 535 Stevenson Street San Francisco, CA 94103 Phone: (415) 864-8123 Fax: (415) 864-8726 www.justintonation.net [email protected] iii Contents The Harmonic Series and the Subharmonic Series Preface to the Third Edition (2002).................... iv ........................................................................... 28 Preface to the Second Edition (1994)................. iv Converting Ratios to a Harmonic or Introduction .....................................1 Subharmonic Series Segment ..................... 28 Identities...................................................... 30 What is Just Intonation? ...................................... 1 Prime Numbers, Primary Intervals, A Little History.................................................... 2 and Prime Limits ............................................... 30 Antiquity ....................................................... 2 What is a Chord? ............................................... 30 The Middle Ages and the Renaissance ......... 2 Interval Names .................................................. 32 The Common-Practice Period Notation............................................................. 32 and the Rise of Temperament ....................... 3 Anomalies.......................................................... 33 The End of -
Tones and Intervals of Hindu Classical Music
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Papers from the University Studies series (The University of Nebraska) University Studies of the University of Nebraska 1-1961 Tones and Intervals of Hindu Classical Music Donald A. Lentz Follow this and additional works at: https://digitalcommons.unl.edu/univstudiespapers Part of the Arts and Humanities Commons This Article is brought to you for free and open access by the University Studies of the University of Nebraska at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Papers from the University Studies series (The University of Nebraska) by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. · . ....., ." - -. "-. ,.~ ... I A .~ 1l6.J ~~c IV·3 DONALD A. LENTZ .. .... .•. .-..~ Tones and Intervals of Hindu Classical Music new senes no. 24 University of Nebraska Studies January 1961 TONES AND INTERVALS OF HINDU CLASSICAL MUSIC DONALD A. LENTZ TONES AND INTERVALS OF HINDU CLASSICAL MUSIC A Discussion and Comparison for the Western Musician of the Basic Tones and Interuals of the Hindu Classical Music with Those of Western Music university of nebraska studies new series no. 24 published by the university at lincoln : january 1961 The University of Nebraska The Board of Regents RICHARD E. ADKINS J. G. ELUOTI', president FRANK FOOTE JOHN KENT SELLECK, corporation secretary B. N. GREENBERG, M.D. CLARENCE E. SWANSON J. LEROY WELSH The Chancellor CUFFORD M. HARDIN Contents 1. Prelude 2. Tones and Intervals 5 3. Comparative Chart of Intervals 10 4. A Physical Analysis of Basic Tones and Intervals from the Comparative Chart 12 5. -
Plainsound Music Edition
Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space by Marc Sabat P L A I N S O U N D M U S I C E D I T I O N 2 Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space by Marc Sabat after JAMES TENNEY for Jim with love – thank you The following three tables of 190 pitches develop some ideas suggested in James Tenney’s paper “On ‘Crystal Growth’ in Harmonic Space” (1993-98). To generate my crystals I began by looking at his computer programs, written in BASIC, and then coded an extension of his algorithm in C++. The starting premises remained the same – to be chosen each new point must (1.) be directly connected to a point of the crystal and (2.) produce the least possible HD-sum (sum of harmonic distances to all other points of the crystal). In harmonic space (HS), each pitch is represented by co-ordinates, which are exponents of the prime factors of its frequency ratio. As the number of primes is infinite, HS theoretically has infinite dimension; for musical applications, it is constrained by specifying a finite number of prime axes. For example, the classical Riemann tone- lattice is a subset of (2,3,5)-HS, in which the frequency ratio 3/2 (= 2-1·31·50) is represented by the pitch-point (-1,1,0). As Tenney’s crystals show (see Figure 10a/b), any HS includes points outside the range of musical perception. This suggests the possibility to add an additional constraint – pitch-height range. -
L'intonation Juste, Un Renouveau Esthétique Et Théorique
L’intonation juste, un renouveau esthétique et théorique (Just intonation: an aesthetic and theoretical renewal) In Théorie et composition musicales au vingtième siècle, ed. Nicolas Donin and Laurent Feneyrou (Lyon: Symétrie, 2013), 1499–1531. Translated by Gilles Rico. Robert Hasegawa (Schulich School of Music of McGill University) Introduction: Precursors of extended just intonation Of all the neglected chapters of music theory, just intonation seems at first glance the least likely to resurface in the century of serialism and chance composition. The essential principle of just intonation is that simple ratios between numbers produce the ideal, pure tunings for intervals in tonal music; with the standardization of equal temperament and the advent of atonality, just intonation seemed fated to obscurity and irrelevance. What use could composers have for an ancient tuning system, designed for simple tonal structures, that lacked the ease and flexibility of equal temperament? For Harry Partch (1901-1974), the most influential figure in the just intonation revival in America, the appeal of this antiquated practice was thoroughly modern: the desire to build a rational musical world from strict rational principles, rather than simply accepting an established practice now alienated from its origins. For Partch, the music theory of a thriving culture would be built on a solid bedrock of “Archean granite” instead of on the inherited instruments, forms, and tunings of eighteenth-century Europe.1 Just intonation reflected the natural preferences of the listening ear: on this solid foundation, he saw the possibility for an controlled, logical expansion of musical resources, eventually breaking free of the “prison bars” of the twelve-tone keyboard.2 By turning to ratios as the basis for his theories, Partch placed himself in a tradition with a long history, which we can divide into three basic stages: Pythagorean, just, and extended just intonation. -
Musical Scale
Musical Scale Musical scale consists of series of notes having certain relation to one an- other as regards the frequency of vibration . The human ear can distinguish a number of notes of definite frequencies between a note and its octave.The note of lowest frequency at such a series called key note or tonic. The building up of a musical scale is based on two assumptions about the human hearing process: • The ear is sensitive to ratios of frequencies (pitches) rather than to differ- ences in establishing musical intervals. • The intervals which are perceived to be most consonant are composed of small integer ratios of frequency. Musical Interval: The ratio of frequencies between two notes in the musical scale is known as musical intervals.The term musical interval refers to a step up or down in pitch which is specified by the ratio of the frequencies involved. For example, an octave is a music interval defined by the ratio 2:1 regardless of the starting frequency. From 100 Hz to 200 Hz is an octave, as is the in- terval from 2000 Hz to 4000 Hz. The intervals which are generally the most consonant to the human ear are intervals represented by small integer ratios. Intervals represented by exact integer ratios are said to be Just intervals, and the temperament which keeps all intervals at exact whole number ratios is Just temperament. For example, in the buildup of a pentatonic scale by a circle of fifths, a nat- ural whole tone of ratio 9/8 emerges, satisfying the condition for consonance. -
Nicola Vicentino and the Enharmonic Diesis: an Analytical and Empirical Study
Nicola Vicentino and the Enharmonic Diesis: An Analytical and Empirical Study Mikaela Miller Degree of Masters of Arts (Music Theory) Department of Music Research, Schulich School of Music A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Masters of Arts McGill University Montréal, Québec, Canada January, 2011 © Copyright 2011 All rights reserved iii ABSTRACT Nicola Vicentino is recognized as a sixteenth-century musical revolutionary; a wealth of scholarly work has been devoted to his theories and philosophies. Attempts to analyze Vicentino’s compositions are limited in number, however, and empirical studies of the perception of his music are non-existent. In his treatise, Ancient Music Adapted to Modern Practice, Vicentino illustrates the practical application of his theories with compositional examples that employ the microtonal interval of the minor enharmonic diesis, and novel 31-tone tuning system that he developed himself. The first two chapters of this thesis review Vicentino’s theories and philosophies of music, and undertake an analytical survey of the extant enharmonic compositions. This analysis explores the possibilities available in Vicentino’s tuning system, and characterizes the voice-leading and harmonic patterns found in Vicentino’s enharmonic compositions in terms of the use of the microtonal interval, the minor enharmonic diesis. I show that Vicentino uses only a handful of possibilities at his disposal, and that the voice-leading and harmonic patterns involving the minor enharmonic diesis are used in systematic ways depending on the musical context. The final two chapters of this thesis develop and test the hypothesis that trained musicians can hear the nuances of Vicentino’s music when the enharmonic diesis is involved (as Vicentino claims). -
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UC Santa Barbara Electronic Theses and Dissertations
UC Santa Barbara UC Santa Barbara Electronic Theses and Dissertations Title Musicological Writings from the Modern Arab “Renaissance” in Nineteenth and Early- Twentieth-Century Syria and Egypt Permalink https://escholarship.org/uc/item/80x2c647 Author Popper, Tess Publication Date 2019 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Santa Barbara Musicological Writings from the Modern Arab “Renaissance” in Nineteenth and Early-Twentieth-Century Syria and Egypt A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Music by Tess Judith Popper Committee in Charge: Professor Scott Marcus, Chair Professor Dwight Reynolds Professor Timothy Cooley December 2019 The dissertation of Tess Judith Popper is approved _______________________________________________ Dwight Reynolds _______________________________________________ Timothy J. Cooley _______________________________________________ Scott Marcus, Committee Chair September 2019 ACKNOWLEDGEMENTS In my work with this dissertation I have had considerable guidance, instruction, and mentoring from Professor Scott Marcus of the Department of Music, Ethnomusicology Program at UC Santa Barbara. Of especial help to me has been his dissertation Arab Music Theory in the Modern Period (UCLA 1989) along with his 2007 publication Music in Egypt: Experiencing Music, Expressing Culture. Numerous articles of his are among my secondary sources as well, assisting -
The Forms of Tonality a Preview
The Forms of Tonality a preview © 2001 Paul Erlich This paper briefly illustrates the concepts of tone-lattices, scales, periodicity and notational systems for 5-limit and 7-limit music. These concepts will be explored in much greater detail in a future work. Consonance and Dissonance (optional) Using the harmonic entropy model,1 one obtains general-purpose dyadic dissonance curves such as the example in FIGURE 1. For the simplest ratios, remarkable agreement is found with Tenney’s Harmonic Distance function,2 i.e., the exponential of the dissonance measure is directly proportional to the product of the ratio’s numerator and denominator. Between these ratios, we see a continuous curve, similar to those obtained by Helmholtz,3 Sethares,4 and others. However, we may wish to think of intervals in an octave-invariant sense, so that we may construct music theories like that of Partch:5 the field of pitches to consider is reduced to within one octave. This move reflects many composers’ use of techniques relying on the phenomenon of octave- equivalence in pitch perception, and offers great theoretical simplification by obviating the need to evaluate separately many intervals in a given interval-class. Partch classed interval-ratios by an odd number (“Ratios of 3”, “Ratios of 5”, “of 7”, “of 9” . .) which is defined as the largest odd factor found in either the numerator or the denominator of the ratio. Unlike Partch, we will use these terms to describe ratios when they represent interval classes (dyads –- for which consonance is relevant), but never pitch classes (for which it isn’t).