A Composition Procedure for Digitally Synthesized Music on Logarithmic Scales of the Harmonic Series
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Exploring the Symbiosis of Western and Non-Western Music: a Study
7/11/13 17:44 To Ti Ta Thijmen, mini Mauro, and an amazing Anna Promotoren Prof. dr. Marc Leman Vakgroep Kunst-, Muziek- en Theaterwetenschappen Lucien Posman Vakgroep Muziekcreatie, School of Arts, Hogeschool Gent Decaan Prof. dr. Marc Boone Rector Prof. dr. Anne De Paepe Leescommissie Dr. Micheline Lesaffre Prof. Dr. Francis Maes Dr. Godfried-Willem Raes Peter Vermeersch Dr. Frans Wiering Aanvullende examencommissie Prof. Dr. Jean Bourgeois (voorzitter) Prof. Dr. Maximiliaan Martens Prof. Dr. Dirk Moelants Prof. Dr. Katharina Pewny Prof. Dr. Linda Van Santvoort Kaftinformatie: Art work by Noel Cornelis, cover by Inge Ketelers ISBN: 978-94-6197-256-9 Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd, opgeslagen in een geautomatiseerd gegevensbestand, of openbaar gemaakt, in enige vorm of op enige wijze, hetzij elektronisch, mechanisch, door fotokopieën, opnamen, of enige andere manier, zonder voorafgaande toestemming van de uitgever. Olmo Cornelis has been affiliated as an artistic researcher to the Royal Conservatory, School of Arts Ghent since February 2008. His research project was funded by the Research Fund University College Ghent. Faculteit Letteren & Wijsbegeerte Olmo Cornelis Exploring the symbiosis of Western and non-Western music a study based on computational ethnomusicology and contemporary music composition Part I Proefschrift voorgelegd tot het behalen van de graad van Doctor in de kunsten: muziek 2013 Dankwoord Een dankwoord lokt menig oog, en dient een erg persoonlijke rol. Daarom schrijf ik dit deel liever in het Nederlands. Een onderzoek dat je gedurende zes jaar voert, is geen individueel verhaal. Het komt slechts tot stand door de hulp, adviezen en meningen van velen. -
Mto.95.1.4.Cuciurean
Volume 1, Number 4, July 1995 Copyright © 1995 Society for Music Theory John D. Cuciurean KEYWORDS: scale, interval, equal temperament, mean-tone temperament, Pythagorean tuning, group theory, diatonic scale, music cognition ABSTRACT: In Mathematical Models of Musical Scales, Mark Lindley and Ronald Turner-Smith attempt to model scales by rejecting traditional Pythagorean ideas and applying modern algebraic techniques of group theory. In a recent MTO collaboration, the same authors summarize their work with less emphasis on the mathematical apparatus. This review complements that article, discussing sections of the book the article ignores and examining unique aspects of their models. [1] From the earliest known music-theoretical writings of the ancient Greeks, mathematics has played a crucial role in the development of our understanding of the mechanics of music. Mathematics not only proves useful as a tool for defining the physical characteristics of sound, but abstractly underlies many of the current methods of analysis. Following Pythagorean models, theorists from the middle ages to the present day who are concerned with intonation and tuning use proportions and ratios as the primary language in their music-theoretic discourse. However, few theorists in dealing with scales have incorporated abstract algebraic concepts in as systematic a manner as the recent collaboration between music scholar Mark Lindley and mathematician Ronald Turner-Smith.(1) In their new treatise, Mathematical Models of Musical Scales: A New Approach, the authors “reject the ancient Pythagorean idea that music somehow &lsquois’ number, and . show how to design mathematical models for musical scales and systems according to some more modern principles” (7). -
Lucytuning - Chapter One of Pitch, Pi, and Other Musical Paradoxes an Extract From
LucyTuning - Chapter One of Pitch, Pi, and other Musical Paradoxes an extract from: Pitch, Pi, and Other Musical Paradoxes (A Practical Guide to Natural Microtonality) by Charles E. H. Lucy copyright 1986-2001 LucyScaleDevelopments ISBN 0-9512879-0-7 Chapter One. (First published in Music Teacher magazine, January 1988, London) IS THIS THE LOST MUSIC OF THE SPHERES? After twenty five years of playing, I realised that I was still unable to tune any guitar so that it sounded in tune for both an open G major and an open E major. I tried tuning forks, pitch pipes, electronic tuners and harmonics at the seventh, fifth and twelfth frets. I sampled the best guitars I could find, but none would "sing" for both chords. At the risk of appearing tone deaf, I confessed my incompetence to a few trusted musical friends, secretly hoping that someone would initiate me into the secret of tuning guitars, so that they would "sing" for all chords. A few admitted that they had the same problem, but none would reveal the secret. I had read how the position of the frets was calculated from the twelfth root of two, so that each of the twelve semitones in an octave had equal intervals of 100 cents. It is the equality of these intervals, which allows us to easily modulate or transpose into any of the twelve keys. Without realising it, I had begun a quest for the lost music of the spheres. I still secretly doubted my musical ear, but rationalised my search by professing an interest in microtonal music, and claimed to be searching for the next step in the evolution of music. -
Frequency-And-Music-1.34.Pdf
Frequency and Music By: Douglas L. Jones Catherine Schmidt-Jones Frequency and Music By: Douglas L. Jones Catherine Schmidt-Jones Online: < http://cnx.org/content/col10338/1.1/ > This selection and arrangement of content as a collection is copyrighted by Douglas L. Jones, Catherine Schmidt-Jones. It is licensed under the Creative Commons Attribution License 2.0 (http://creativecommons.org/licenses/by/2.0/). Collection structure revised: February 21, 2006 PDF generated: August 7, 2020 For copyright and attribution information for the modules contained in this collection, see p. 51. Table of Contents 1 Acoustics for Music Theory ......................................................................1 2 Standing Waves and Musical Instruments ......................................................7 3 Harmonic Series ..................................................................................17 4 Octaves and the Major-Minor Tonal System ..................................................29 5 Tuning Systems ..................................................................................37 Index ................................................................................................49 Attributions .........................................................................................51 iv Available for free at Connexions <http://cnx.org/content/col10338/1.1> Chapter 1 Acoustics for Music Theory1 1.1 Music is Organized Sound Waves Music is sound that's organized by people on purpose, to dance to, to tell a story, to make other people -
Musical Techniques
Musical Techniques Musical Techniques Frequencies and Harmony Dominique Paret Serge Sibony First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA www.iste.co.uk www.wiley.com © ISTE Ltd 2017 The rights of Dominique Paret and Serge Sibony to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2016960997 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-058-4 Contents Preface ........................................... xiii Introduction ........................................ xv Part 1. Laying the Foundations ............................ 1 Introduction to Part 1 .................................. 3 Chapter 1. Sounds, Creation and Generation of Notes ................................... 5 1.1. Physical and physiological notions of a sound .................. 5 1.1.1. Auditory apparatus ............................... 5 1.1.2. Physical concepts of a sound .......................... 7 1.1.3. -
The Mathematics of Electronic Music
The Mathematics of Electronic Music One of the difficult aspects of the study of electronic music is the accurate description of the sounds used. With traditional music, there is a general understanding of what the instruments sound like, so a simple notation of 'violin', or 'steel guitar' will convey enough of an aural image for study or performance. In electronic music, the sounds are usually unfamiliar, and a composition may involve some very delicate variations in those sounds. In order to discuss and study such sounds with the required accuracy, we must use the tools of mathematics. There will be no proofs or rigorous developments, but many concepts will be illustrated with graphs and a few simple functions. Here is a review of the concepts you will encounter: Hertz In dealing with sound, we are constantly concered with frequency, the number of times some event occurs within a second. In old literature, you will find this parameter measured in c.p.s., standing for cycles per second. In modern usage, the unit of frequency is the Hertz, (abbr. hz) which is officially defined as the reciprocal of one second. This makes sense if you remember that the period of a cyclical process, which is a time measured in seconds, is equal to one over the frequency. (P=1/f) Since we often discuss frequencies in the thousands of Hertz, the unit kiloHertz (1000hz=1khz) is very useful. Exponential functions Many concepts in electronic music involve logarithmic or exponential relationships. A relationship between two parameters is linear if a constant ratio exists between the two, in other words, if one is increased, the other is increased a proportianal amount, or in math expression: Y=kX where k is a number that does not change (a constant). -
The Math Behind the Music Leon Harkleroad Cambridge University
The Math behind the Music Leon Harkleroad Cambridge University Press, 2006 142 pages, CD included review by Ehrhard Behrends Department of Mathematics and Computer Science of the Free University of Berlin Arnimallee 2 – 6 D14195 Berlin Mathematics and Music: there are several interesting connections, and a number of books which deal with various aspects of this interplay have been published during the last years. Whereas [1] and [2] are collections of articles written by different people the book under review is the author’s summary of a number of courses he has given at Cornell University. As a natural starting point the problem of how to construct scales is chosen. How is the Pythogerean scale definied, what are just intonations, what is the equal temperament and how comes the twelfth root of two into play? Harkleroad uses the opportunity to explain also some fundamental facts on Fourier analysis. In the next chapter some elementary procedures how to vary a musical theme are explained in the language of group theory. T “, the transposition of 7 semitones, has ” 7 T−7 as its inverse etc. Here one has to calculate modulo 12, and the reader can learn how arithmetic modulo a fixed integer is defined. As illustrations of these theoretical facts many examples are included. E.g., in Pomp and Circumstance (by E. Elgar) the main theme is varied by using transpositions whereas inversion plays a crucial role in The muscal offering (by J.S. Bach). It is very helpful that a compact disc is included which allows one to compare the theoretical facts with the real sound. -
Musical Notes and Scales Glen Bull, Jo Watts, and Joe Garofalo
8. Musical Notes and Scales Glen Bull, Jo Watts, and Joe Garofalo A music note is associated with a rate of vibration or frequency. For example, when a piano key is struck, a lever causes a padded hammer to strike a piano string. When struck, the piano string vibrates a specific number of times per second. A standard piano keyboard has 88 keys. Notes on the left end of the keyboard play notes that correspond to the lower frequencies, while notes on the higher end of the keyboard play notes that correspond to the higher frequencies. The frequency of the lowest note on a standard piano keyboard is 27.5 Hz. The highest note on a piano keyboard is slightly more than 4,000 Hz. The piano key for the note “C” that is in the middle of the keyboard is known as “Middle C.” Middle C has a frequency of 262 Hz. The frequency of the next C on the keyboard (above middle C) is 524 Hz. In other words, it is double the frequency of middle C. Topic 8.1 Musical Scales As noted above, each music note is associated with a frequency. The term musical scale refers to the relationships among the frequencies of different notes. Many different musical scales have been developed throughout history. The modern western musical scale consists of twelve notes. A span of seven white notes and five black notes on a piano keyboard is known as an octave. The octave that begins with middle C is the fourth octave (counting from the left) on the keyboard. -
Kingkorg Parameter Guide
English Parameter guide Contents Parameters . 3 1. Program parameters ................................................................................... 3 2. Timbre parameters..................................................................................... 4 3. Vocoder parameters ..................................................................................13 4. Arpeggio parameters .................................................................................14 5. Edit utility parameters.................................................................................16 6. GLOBAL parameters...................................................................................16 7. MIDI parameters ......................................................................................18 8. CV&Gate parameters..................................................................................20 9. Foot parameters ......................................................................................20 10. UserKeyTune parameters ............................................................................21 11. EQ parameters.......................................................................................22 12. Tube parameters.....................................................................................22 13. Global utility.........................................................................................22 Effects . .23 . 1. What are effects.......................................................................................23 -
List of Numbers
List of numbers This is a list of articles aboutnumbers (not about numerals). Contents Rational numbers Natural numbers Powers of ten (scientific notation) Integers Notable integers Named numbers Prime numbers Highly composite numbers Perfect numbers Cardinal numbers Small numbers English names for powers of 10 SI prefixes for powers of 10 Fractional numbers Irrational and suspected irrational numbers Algebraic numbers Transcendental numbers Suspected transcendentals Numbers not known with high precision Hypercomplex numbers Algebraic complex numbers Other hypercomplex numbers Transfinite numbers Numbers representing measured quantities Numbers representing physical quantities Numbers without specific values See also Notes Further reading External links Rational numbers A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.[1] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or blackboard bold , Unicode ℚ);[2] it was thus denoted in 1895 byGiuseppe Peano after quoziente, Italian for "quotient". Natural numbers Natural numbers are those used for counting (as in "there are six (6) coins on the table") and ordering (as in "this is the third (3rd) largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are -
Microkorg XL+ Synthesizer / Ulate These Parameters and Create Sounds with a High Degree of Freedom
E 1 Precautions THE FCC REGULATION WARNING (for USA) Data handling Location NOTE: This equipment has been tested and found to com- Unexpected malfunctions can result in the loss of memory Using the unit in the following locations can result in a ply with the limits for a Class B digital device, pursuant to contents. Please be sure to save important data on an malfunction. Part 15 of the FCC Rules. These limits are designed to external data filer (storage device). Korg cannot accept • In direct sunlight provide reasonable protection against harmful interference any responsibility for any loss or damage which you may • Locations of extreme temperature or humidity in a residential installation. This equipment generates, incur as a result of data loss. • Excessively dusty or dirty locations uses, and can radiate radio frequency energy and, if not • Locations of excessive vibration installed and used in accordance with the instructions, may • Close to magnetic fields cause harmful interference to radio communications. How- * All product names and company names are the trademarks ever, there is no guarantee that interference will not occur or registered trademarks of their respective owners. Power supply in a particular installation. If this equipment does cause Please connect the designated AC adapter to an AC out- harmful interference to radio or television reception, which let of the correct voltage. Do not connect it to an AC outlet can be determined by turning the equipment off and on, of voltage other than that for which your unit is intended. the user is encouraged to try to correct the interference by one or more of the following measures: Interference with other electrical devices • Reorient or relocate the receiving antenna. -
Introduction to Chern-Simons Theories
Preprint typeset in JHEP style - HYPER VERSION Introduction To Chern-Simons Theories Gregory W. Moore Abstract: These are lecture notes for a series of talks at the 2019 TASI school. They contain introductory material to the general subject of Chern-Simons theory. They are meant to be elementary and pedagogical. ************* THESE NOTES ARE STILL IN PREPARATION. CONSTRUCTIVE COMMENTS ARE VERY WELCOME. (In par- ticular, I have not been systematic about trying to include references. The literature is huge and I know my own work best. I will certainly be interested if people bring reference omissions to my attention.) **************** June 7, 2019 Contents 1. Introduction: The Grand Overview 5 1.1 Assumed Prerequisites 8 2. Chern-Simons Theories For Abelian Gauge Fields 9 2.1 Topological Terms Matter 9 2.1.1 Charged Particle On A Circle Surrounding A Solenoid: Hamiltonian Quantization 9 2.1.2 Charged Particle On A Circle Surrounding A Solenoid: Path Integrals 14 2.1.3 Gauging The Global SO(2) Symmetry And Chern-Simons Terms 16 2.2 U(1) Chern-Simons Theory In 3 Dimensions 19 2.2.1 Some U(1) Gauge Theory Preliminaries 19 2.2.2 From θ-term To Chern-Simons 20 2.2.3 3D Maxwell-Chern-Simons For U(1) 22 2.2.4 The Formal Path Integral Of The U(1) Chern-Simons Theory 24 2.2.5 First Steps To The Hilbert Space Of States 25 2.2.6 General Remarks On Quantization Of Phase Space And Hamiltonian Reduction 27 2.2.7 The Space Of Flat Gauge Fields On A Surface 31 2.2.8 Quantization Of Flat Connections On The Torus: The Real Story 39 2.2.9 Quantization Of Flat