Transposition of Notations in Just Intonation
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Consonance and Dissonance in Visual Music Bill Alves Harvey Mudd College
Claremont Colleges Scholarship @ Claremont All HMC Faculty Publications and Research HMC Faculty Scholarship 8-1-2012 Consonance and Dissonance in Visual Music Bill Alves Harvey Mudd College Recommended Citation Bill Alves (2012). Consonance and Dissonance in Visual Music. Organised Sound, 17, pp 114-119 doi:10.1017/ S1355771812000039 This Article is brought to you for free and open access by the HMC Faculty Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in All HMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Organised Sound http://journals.cambridge.org/OSO Additional services for Organised Sound: Email alerts: Click here Subscriptions: Click here Commercial reprints: Click here Terms of use : Click here Consonance and Dissonance in Visual Music Bill Alves Organised Sound / Volume 17 / Issue 02 / August 2012, pp 114 - 119 DOI: 10.1017/S1355771812000039, Published online: 19 July 2012 Link to this article: http://journals.cambridge.org/abstract_S1355771812000039 How to cite this article: Bill Alves (2012). Consonance and Dissonance in Visual Music. Organised Sound, 17, pp 114-119 doi:10.1017/ S1355771812000039 Request Permissions : Click here Downloaded from http://journals.cambridge.org/OSO, IP address: 134.173.130.244 on 24 Jul 2014 Consonance and Dissonance in Visual Music BILL ALVES Harvey Mudd College, The Claremont Colleges, 301 Platt Blvd, Claremont CA 91711 USA E-mail: [email protected] The concepts of consonance and dissonance broadly Plato found the harmony of the world in the Pythag- understood can provide structural models for creators of orean whole numbers and their ratios, abstract ideals visual music. -
The Unexpected Number Theory and Algebra of Musical Tuning Systems Or, Several Ways to Compute the Numbers 5,7,12,19,22,31,41,53, and 72
The Unexpected Number Theory and Algebra of Musical Tuning Systems or, Several Ways to Compute the Numbers 5,7,12,19,22,31,41,53, and 72 Matthew Hawthorn \Music is the pleasure the human soul experiences from counting without being aware that it is counting." -Gottfried Wilhelm von Leibniz (1646-1716) \All musicians are subconsciously mathematicians." -Thelonius Monk (1917-1982) 1 Physics In order to have music, we must have sound. In order to have sound, we must have something vibrating. Wherever there is something virbrating, there is the wave equation, be it in 1, 2, or more dimensions. The solutions to the wave equation for any given object (string, reed, metal bar, drumhead, vocal cords, etc.) with given boundary conditions can be expressed as a superposition of discrete partials, modes of vibration of which there are generally infinitely many, each with a characteristic frequency. The partials and their frequencies can be found as eigenvectors, resp. eigenvalues of the Laplace operator acting on the space of displacement functions on the object. Taken together, these frequen- cies comprise the spectrum of the object, and their relative intensities determine what in musical terms we call timbre. Something very nice occurs when our object is roughly one-dimensional (e.g. a string): the partial frequencies become harmonic. This is where, aptly, the better part of harmony traditionally takes place. For a spectrum to be harmonic means that it is comprised of a fundamental frequency, say f, and all whole number multiples of that frequency: f; 2f; 3f; 4f; : : : It is here also that number theory slips in the back door. -
Musical Tuning Systems As a Form of Expression
Musical Tuning Systems as a Form of Expression Project Team: Lewis Cook [email protected] Benjamin M’Sadoques [email protected] Project Advisor Professor Wilson Wong Department of Computer Science This report represents the work of WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review. For more information about the projects program at WPI, please see http://www.wpi.edu/academics/ugradstudies/project- learning.html Abstract Many cultures and time periods throughout history have used a myriad of different practices to tune their instruments, perform, and create music. However, most musicians in the western world will only experience 12-tone equal temperament a represented by the keys on a piano. We want musicians to recognize that choosing a tuning system is a form of musical expression. The goal of this project was to help musicians of any skill-level experience, perform, and create music involving tuning systems. We created software to allow musicians to experiment and implement alternative tuning systems into their own music. ii Table of Contents Abstract ................................................................................................................................... ii Table of Figures .................................................................................................................... vii 1 Introduction ........................................................................................................................ -
The Foundations of Scientific Musical Tuning by Jonathan Tennenbaum
Click here for Full Issue of Fidelio Volume 1, Number 1, Winter 1992 The Foundations of Scientific Musical Tuning by Jonathan Tennenbaum want to demonstrate why, from a scientific stand teenth-century physicist and physiologist whose 1863 point, no musical tuning is acceptable which is not book, Die Lehre von den Tonempfindungen als physiolo I based on a pitch value fo r middle C of 256Hz (cycles gische Grundlage fu r die Theorie der Musik (The Theory per second), corresponding to A no higher than 432Hz. of the Sensations of Tone as a Foundation of Music Theory) In view of present scientificknowl edge, all other tunings became the standard reference work on the scientific including A =440 must be rejected as invalid and arbi bases of music, and remains so up to this very day. trary. Unfortunately, every essential assertion in Helmholtz's Those in fa vor of constantly raising the pitch typically book has been proven to be fa lse. argue, "What diffe rence does it make what basic pitch Helmholtz's basic fallacy-still taught in most music we choose, as long as the other notes are properly tuned conservatories and universities today-was to claim that relative to that pitch? After all, musical tones are just the scientificbasis of music is to be fo und in the properties frequencies, they are all essentially alike. So, why choose of vibrating, inert bodies, such as strings, tuning fo rks, one pitch rather than another?" To these people, musical pipes, and membranes. Helmholtz definedmusical tones tones are like paper money, whose value can be inflated merely as periodic vibrations of the air. -
Foundations in Music Psychology
Foundations in Music Psy chol ogy Theory and Research edited by Peter Jason Rentfrow and Daniel J. Levitin The MIT Press Cambridge, Mas sa chu setts London, England © 2019 Mas sa chu setts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Stone Serif by Westchester Publishing Ser vices. Printed and bound in the United States of Amer i ca. Library of Congress Cataloging- in- Publication Data Names: Rentfrow, Peter J. | Levitin, Daniel J. Title: Foundations in music psy chol ogy : theory and research / edited by Peter Jason Rentfrow and Daniel J. Levitin. Description: Cambridge, MA : The MIT Press, 2019. | Includes bibliographical references and index. Identifiers: LCCN 2018018401 | ISBN 9780262039277 (hardcover : alk. paper) Subjects: LCSH: Music— Psychological aspects. | Musical perception. | Musical ability. Classification: LCC ML3830 .F7 2019 | DDC 781.1/1— dc23 LC rec ord available at https:// lccn . loc . gov / 2018018401 10 9 8 7 6 5 4 3 2 1 Contents I Music Perception 1 Pitch: Perception and Neural Coding 3 Andrew J. Oxenham 2 Rhythm 33 Henkjan Honing and Fleur L. Bouwer 3 Perception and Cognition of Musical Timbre 71 Stephen McAdams and Kai Siedenburg 4 Pitch Combinations and Grouping 121 Frank A. Russo 5 Musical Intervals, Scales, and Tunings: Auditory Repre sen ta tions and Neural Codes 149 Peter Cariani II Music Cognition 6 Musical Expectancy 221 Edward W. Large and Ji Chul Kim 7 Musicality across the Lifespan 265 Sandra E. -
Euler's Theories of Musical Tuning
Euler’s Theories of Musical Tuning With an English Translation of Du Véritable Caractère de la Musique Moderne Larry G. Blaine Plymouth State University, MSC 29 Plymouth NH 03264 [email protected] Susan Ferré Independent Scholar [email protected] Originally published as: Blaine, Larry G. and Ferré, Susan (2021) "Euler’s Theories of Musical Tuning With an English Translation of Du Véritable Caractère de la Musique Moderne," Euleriana: Vol. 1: Iss. 1, Article 8. Available at: https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/8 Introduction Euler and Music Here is a passage from the oration delivered at Euler’s funeral by his son-in-law Nicholas Fuss. It is worth quoting at length: Euler’s chief relaxation was music, but even here his mathematical spirit was active. Yielding to the pleasant sensation of consonance, he immersed himself in the search for its cause and during musical performances would calculate the proportions of tones. One may say that his Attempt at a New Theory of Music was the fruit of his relaxation. This deeply pondered work, full of new or newly presented ideas, did not meet with the success anticipated, perhaps because it contains too much mathematics for a musician or too much music for a mathematician. [7] It is surprising, then, that nothing seems to be known about Euler’s musical education or tastes. Did he sing? Play an instrument? Were any particular composers, contemporary or not, favorites of his? Any particular forms or styles? It is rather a mystery. Be this as it may, Euler left a substantial body of work on the theory of music, including the book- length work Tentamen Novae Theoriae Musicae [6], Du Véritable Charactère de la Musique Moderne [3], De Harmoniae Veris Principiis [4], a number of shorter works, including [5], and a large body of unpublished material in his notebooks.1 [12] None of this can be said to have been very influential in the course of development of Western art music, though the Tentamen has aroused a certain amount of controversy over the years. -
Infants' and Adults' Perception of Scale Structure
Journal of Experimental Psychology: Copyright 1999 by the American Psychological Association, Inc. Human Perception and Performance 0096-1523/99/S3.00 1999, Vol. 25, No. 4,965-975 Infants' and Adults' Perception of Scale Structure Sandra E. Trehub, E. Glenn Schellenberg, and Stuart B. Kamenetsky University of Toronto Adults and 9-month-old infants were required to detect mistuned tones in multitone sequences. When 7-tone versions of a common nursery tune were generated from the Western major scale (unequal scale steps) or from an alternative scale (equal steps), infants detected the mistuned tones more accurately in the unequal-step context than in the equal-step context (Experiment 1). Infants and adults were subsequently tested with 1 of 3 ascending-descending scales (15 tones): (a) a potentially familiar scale (major) with unequal steps, (b) an unfamiliar scale with unequal steps, and (c) an unfamiliar scale with equal steps. Infants detected mistuned tones only in the scales with unequal steps (Experiment 2). Adults performed better on the familiar (major) unequal-step scale and equally poorly on both unfamiliar scales (Experiments 3 and 4). These findings are indicative of an inherent processing bias favoring unequal-step scales. The diversity of musical forms across cultures (e.g., perceive each pitch as being distinct from others. Note, Western, Indian, Chinese, African) and even within a culture however, that scales are abstractions or formalizations of the (e.g., pop, jazz, Baroque) implies that there are few defining collection of pitches in style-specific compositions. Thus, features of music. Accordingly, definitions of music are melodies that conform to particular scales may predate necessarily general, as can be seen in the following ex- formal descriptions of those scales. -
Music Theory Contents
Music theory Contents 1 Music theory 1 1.1 History of music theory ........................................ 1 1.2 Fundamentals of music ........................................ 3 1.2.1 Pitch ............................................. 3 1.2.2 Scales and modes ....................................... 4 1.2.3 Consonance and dissonance .................................. 4 1.2.4 Rhythm ............................................ 5 1.2.5 Chord ............................................. 5 1.2.6 Melody ............................................ 5 1.2.7 Harmony ........................................... 6 1.2.8 Texture ............................................ 6 1.2.9 Timbre ............................................ 6 1.2.10 Expression .......................................... 7 1.2.11 Form or structure ....................................... 7 1.2.12 Performance and style ..................................... 8 1.2.13 Music perception and cognition ................................ 8 1.2.14 Serial composition and set theory ............................... 8 1.2.15 Musical semiotics ....................................... 8 1.3 Music subjects ............................................. 8 1.3.1 Notation ............................................ 8 1.3.2 Mathematics ......................................... 8 1.3.3 Analysis ............................................ 9 1.3.4 Ear training .......................................... 9 1.4 See also ................................................ 9 1.5 Notes ................................................ -
The Perfect Fifth: the Basis of All Harmony? | Hub Guitar
FREE PERFECT FIFTHS PDF Megan McCafferty | 258 pages | 02 Mar 2010 | Three Rivers Press (CA) | 9780307346537 | English | New York, NY, United States The Perfect Fifth: The Basis of All Harmony? | Hub Guitar By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. It only takes a minute to sign up. I Perfect Fifths gone through many documents, but don't understand what a perfect fifth is. Can somebody please explain with an example? An example is important! In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio ofor very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of five consecutive notes in a diatonic scale. The perfect fifth often abbreviated P5 spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones. Perfect Fifths example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C. An interval is just the distance between two notes. The name perfect 5th comes from the idea of a scale. For example the C major scale consists of the following notes:. The 5th note of the scale is G hence the 5th of the C major scale is G. The interval is perfect because if we flip the interval we would get a 4th which exist in the G major scale. Thus C to G is a perfect 5th. The ratio is the ratio of the distance between the notes in hertz. -
Enculturation Effects of Musical Training on Pitch Discrimination
Enculturation Effects of Musical Training on Pitch Discrimination Greta D. Grannan-Rubenstein ([email protected]) William L. Grannan-Rubenstein ([email protected]) Paul H. Thibodeau ([email protected]) Oberlin College Department of Psychology 120 West Lorain St; Oberlin, OH 44074 Abstract facilitate the emergence of an innate faculty for discrimination of domain-specific communicative categories Research on the acquisition and use of communicative (Chomsky, 1965; Lerdahl, 1992), or does it facilitate categories in domains such as language and music is largely selective perception of learned communicative categories divided between approaches suggesting innate cognitive (Cutting & Rosner, 1974; Tomasello, 2008)? constraints on domain-specific communicative forms, and Existing research on pitch perception suggests that people approaches suggesting domain-general mechanisms through with extensive professional musical training recognize and which specific communicative forms are learned. The present study investigates the effect of greater or lesser enculturation reproduce culturally familiar pitch-class sets better than in the communicative system of Western tonal music on people without such training (Smith et al., 1994). That is, peoples’ ability to discriminate culturally familiar and musical training has been shown to facilitate discrimination culturally unfamiliar pitch categories. The results indicate that between a prototypical pitch and a pitch that deviates while prior musical training affects peoples’ overall approach slightly from this prototype. While this finding supports the to pitch discrimination, the advantage is dependent on the hypothesis that musical training tunes people to familiar familiarity (in both pitch and timbre) of the aural stimulus, prototypical pitches, it does not rule out the possibility that and is negligible under conditions of maximal musical musical training facilitates unfamiliar pitch discrimination unfamiliarity. -
Challenging Equal Temperament: Perceived Differences Between Twelve-Tone Equal Temperament and Twelve Fifth-Tones Tuning
CHALLENGING EQUAL TEMPERAMENT: PERCEIVED DIFFERENCES BETWEEN TWELVE-TONE EQUAL TEMPERAMENT AND TWELVE FIFTH-TONES TUNING Mikko Leimu Master’s Thesis Music, Mind & Technology Department of Music 5 January 2017 University of Jyväskylä JYVÄSKYLÄN YLIOPISTO Tiedekunta – Faculty Laitos – Department Faculty of Humanities Department of Music Tekijä – Author Mikko Leimu Työn nimi – Title Challenging equal temperament: Perceived differences between twelve-tone equal temperament and twelve fifth-tones tuning. Oppiaine – Subject Työn laji – Level Music, Mind & Technology Master’s Thesis Aika – Month and year Sivumäärä – Number of pages December 2016 90+7 Tiivistelmä – Abstract A listening experiment was arranged to evaluate perceptual preferences between two musical tuning systems: twelve-tone equal temperament (i.e. the current international standard) and twelve fifth-tones tuning. The latter being a system that, according to its author Maria Renold, provides a more accurate and aurally genuine reproduction of musical harmonics. Hence, it is considered a superior tuning method compared to the equal temperament tuning. 34 participants (mainly experienced musicians) evaluated realistic musical stimuli consisting of intervals, chords and simple musical sequences using a grand piano timbre. Results showed that the standard twelve-tone equal temperament system was found overall more in-tune, with ca. 68% of the participants preferred it over the twelve fifth-tones tuning. This is considered to be most likely due to enculturation affects, i.e. people have preferred the tonality that is more familiar to them. No evidence for the supposed aural genuineness of the Renold’s tuning systems was found. Instead, it may be concluded that intonation preferences in perceptual context are subject to high amounts of individual variation and clear definition of tonality preferences is often a difficult task. -
A Study of Perceptual Development for Musical Tuning
Perception & Psychophysics /992. 52 (6). 599-608 A study of perceptual development for musical tuning MICHAEL P. LYNCH Purdue University, West Lafayette, Indiana and REBECCA E. EILERS University of Miami, Coral Gables, Florida Musical tuning perception in infancy and adulthood was explored in three experiments. In Ex periment 1, Western adults were tested in detection of randomly located mistunings in a melody based on musical interval patterns from native and nonnative musical scales. Subjects performed better in a Western major scale context than in either a Western augmented or a Javanese pelog scale context. Because the major scale is used frequently in Western music and, therefore, is more perceptually familiar than either the augmented scale or the pelog scale are, the adults' pattern of performance is suggestive of musical acculturation. Experiments 2 and 3 were designed to ex plore the onset of culturally specific perceptual reorganization for music in the age period that has been found to be important in linguistically specific perceptual reorganization for speech. In Experiment 2, 1-year-oIds had a pattern of performance similar to that of the adults, but 6 month-olds could not detect mistunings reliably better than chance. In Experiment 3, another group of 6-month-olds was tested, and a larger degree of mistuning was used 80 that floor effects might be avoided. These 6-month-olds performed better in the major and augmented scale con texts than in the pelog context, without a reliable performance difference between the major and augmented contexts. Comparison of the results obtained with 6-month-olds and 1-year-olds sug gests that culturally specific perceptual reorganization for musical tuning begins to affect per ception between these ages, but the 6-month-olds' pattern of results considered alone is not as clear.