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The 17-Tone Puzzle — and the Neo-Medieval Key That Unlocks It
The 17-tone Puzzle — And the Neo-medieval Key That Unlocks It by George Secor A Grave Misunderstanding The 17 division of the octave has to be one of the most misunderstood alternative tuning systems available to the microtonal experimenter. In comparison with divisions such as 19, 22, and 31, it has two major advantages: not only are its fifths better in tune, but it is also more manageable, considering its very reasonable number of tones per octave. A third advantage becomes apparent immediately upon hearing diatonic melodies played in it, one note at a time: 17 is wonderful for melody, outshining both the twelve-tone equal temperament (12-ET) and the Pythagorean tuning in this respect. The most serious problem becomes apparent when we discover that diatonic harmony in this system sounds highly dissonant, considerably more so than is the case with either 12-ET or the Pythagorean tuning, on which we were hoping to improve. Without any further thought, most experimenters thus consign the 17-tone system to the discard pile, confident in the knowledge that there are, after all, much better alternatives available. My own thinking about 17 started in exactly this way. In 1976, having been a microtonal experimenter for thirteen years, I went on record, dismissing 17-ET in only a couple of sentences: The 17-tone equal temperament is of questionable harmonic utility. If you try it, I doubt you’ll stay with it for long.1 Since that time I have become aware of some things which have caused me to change my opinion completely. -
Download the Just Intonation Primer
THE JUST INTONATION PPRIRIMMEERR An introduction to the theory and practice of Just Intonation by David B. Doty Uncommon Practice — a CD of original music in Just Intonation by David B. Doty This CD contains seven compositions in Just Intonation in diverse styles — ranging from short “fractured pop tunes” to extended orchestral movements — realized by means of MIDI technology. My principal objectives in creating this music were twofold: to explore some of the novel possibilities offered by Just Intonation and to make emotionally and intellectually satisfying music. I believe I have achieved both of these goals to a significant degree. ——David B. Doty The selections on this CD process—about synthesis, decisions. This is definitely detected in certain struc- were composed between sampling, and MIDI, about not experimental music, in tures and styles of elabora- approximately 1984 and Just Intonation, and about the Cageian sense—I am tion. More prominent are 1995 and recorded in 1998. what compositional styles more interested in result styles of polyphony from the All of them use some form and techniques are suited (aesthetic response) than Western European Middle of Just Intonation. This to various just tunings. process. Ages and Renaissance, method of tuning is com- Taken collectively, there It is tonal music (with a garage rock from the 1960s, mendable for its inherent is no conventional name lowercase t), music in which Balkan instrumental dance beauty, its variety, and its for the music that resulted hierarchic relations of tones music, the ancient Japanese long history (it is as old from this process, other are important and in which court music gagaku, Greek as civilization). -
ASR-X Pro 3.00
9ÑSupplemental Information 9 Suppll ementttall II nffformatttii on Lii sttt offf ROM Waves KEYBOARD ELEC PIANO JAMM SNARE CONGA LOW PERC ORGAN LIVE SNARE CONGA MUTE DRAWBAR LUDWIG SNARE CONGA SLAP ORGAN MUTT SNARE CUICA PAD SYNTH REAL SNARE ETHNO COWBELL STRII NG-SOUND STRING HIT RIMSHOT GUIRO MUTE GUITAR SLANG SNARE MARACAS MUTE GUITARWF SPAK SNARE SHAKER GTR-SLIDE WOLF SNARE SHEKERE DN BRASS+HORNS HORN HIT ZEE SNARE SHEKERE UP WII ND+REEDS BARI SAX HIT BRUSH SLAP SLAP CLAP BASS-SOUND UPRIGHT BASS SIDE STICK 1 TAMBOURINE DN BS HARMONICS SIDE STICK 2 TAMBOURINE UP FM BASS STICKS TIMBALE HI ANALOG BASS 1 STUDIO TOM TIMBALE LO ANALOG BASS 2 ROCK TOM TIMBALE RIM FRETLESS BASS 909 TOM TRIANGLE HIT MUTE BASS SYNTH DRUM VIBRASLAP SLAP BASS CYMBALS 808 CLOSED HT WHISTLE DRUM-SOUND 2001 KICK 808 OPEN HAT WOODBLOCK 808 KICK 909 CLOSED HT TUNED-PERCUS BIG BELL AMBIENT KICK 909 OPEN HAT SMALL BELL BAM KICK HOUSE CL HAT GAMELAN BELL BANG KICK PEDAL HAT MARIMBA BBM KICK PZ CL HAT MARIMBA WF BOOM KICK R&B CL HAT SOUND-EFFECT SCRATCH 1 COSMO KICK SMACK CL HAT SCRATCH 2 ELECTRO KICK SNICK CL HAT SCRATCH 3 MUFF KICK STUDIO CL HAT SCRATCH 4 PZ KICK STUDIO OPHAT1 SCRATCH 5 SNICK KICK STUDIO OPHAT2 SCRATCH 6 THUMP KICK TECHNO HAT SCRATCH LOOP TITE KICK TIGHT CL HAT WAVEFORM SAWTOOTH WILD KICK TRANCE CL HAT SQUARE WAVE WOLF KICK CR78 OPENHAT TRIANGLE WAV WOO BOX KICK COMPRESS OPHT SQR+SAW WF 808 SNARE CRASH CYMBAL SINE WAVE 808 RIMSHOT CRASH LOOP ESQ BELL WF 909 SNARE RIDE CYMBAL BELL WF BANG SNARE RIDE BELL DIGITAL WF BIG ROCK SNAR CHINA CRASH E PIANO WF -
Different Ecological Processes Determined the Alpha and Beta Components of Taxonomic, Functional, and Phylogenetic Diversity
Different ecological processes determined the alpha and beta components of taxonomic, functional, and phylogenetic diversity for plant communities in dryland regions of Northwest China Jianming Wang1, Chen Chen1, Jingwen Li1, Yiming Feng2 and Qi Lu2 1 College of Forestry, Beijing Forestry University, Beijing, China 2 Institute of Desertification Studies, Chinese Academy of Forestry, Beijing, China ABSTRACT Drylands account for more than 30% of China’s terrestrial area, while the ecological drivers of taxonomic (TD), functional (FD) and phylogenetic (PD) diversity in dryland regions have not been explored simultaneously. Therefore, we selected 36 plots of desert and 32 plots of grassland (10 Â 10 m) from a typical dryland region of northwest China. We calculated the alpha and beta components of TD, FD and PD for 68 dryland plant communities using Rao quadratic entropy index, which included 233 plant species. Redundancy analyses and variation partitioning analyses were used to explore the relative influence of environmental and spatial factors on the above three facets of diversity, at the alpha and beta scales. We found that soil, climate, topography and spatial structures (principal coordinates of neighbor matrices) were significantly correlated with TD, FD and PD at both alpha and beta scales, implying that these diversity patterns are shaped by contemporary environment and spatial processes together. However, we also found that alpha diversity was predominantly regulated by spatial structure, whereas beta diversity was largely determined by environmental variables. Among environmental factors, TD was Submitted 10 June 2018 most strongly correlated with climatic factors at the alpha scale, while 5 December 2018 Accepted with soil factors at the beta scale. -
IALL2017): Law, Language and Justice
Proceedings of The Fifteenth International Conference on Law and Language of the International Academy of Linguistic Law (IALL2017): Law, Language and Justice May, 16-18, 2017 Hangzhou, China and Montréal, Québec, Canada Chief Editors: Ye Ning, Joseph-G. Turi, and Cheng Le Editors: Lisa Hale, and Jin Zhang Cover Designer: Lu Xi Published by The American Scholars Press, Inc. The Proceedings of The Fifteenth International Conference on Law, Language of the International Academy of Linguistic Law (IALL2017): Law, Language, and Justice is published by the American Scholars Press, Inc., Marietta, Georgia, USA. No part of this book may be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems, without permission in writing from the publisher. Copyright © 2017 by the American Scholars Press All rights reserved. ISBN: 978-0-9721479-7-2 Printed in the United States of America 2 Foreword In this sunny and green early summer, you, experts and delegates from different parts of the world, come together beside the Qiantang River in Hangzhou, to participate in The Fifteenth International Conference on Law and Language of the International Academy of Linguistic Law. On the occasion of the opening ceremony, it gives me such great pleasure on behalf of Zhejiang Police College, and also on my own part, to extend a warm welcome to all the distinguished experts and delegates. At the same time, thanks for giving so much trust and support to Zhejiang Police College. Currently, the law-based governance of the country is comprehensively promoted in China. As Xi Jinping, Chinese president, said, “during the entire reform process, we should attach great importance to applying the idea of rule of law and the way of rule of law to play the leading and driving role of rule of law”. -
Pietro Aaron on Musica Plana: a Translation and Commentary on Book I of the Libri Tres De Institutione Harmonica (1516)
Pietro Aaron on musica plana: A Translation and Commentary on Book I of the Libri tres de institutione harmonica (1516) Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Matthew Joseph Bester, B.A., M.A. Graduate Program in Music The Ohio State University 2013 Dissertation Committee: Graeme M. Boone, Advisor Charles Atkinson Burdette Green Copyright by Matthew Joseph Bester 2013 Abstract Historians of music theory long have recognized the importance of the sixteenth- century Florentine theorist Pietro Aaron for his influential vernacular treatises on practical matters concerning polyphony, most notably his Toscanello in musica (Venice, 1523) and his Trattato della natura et cognitione de tutti gli tuoni di canto figurato (Venice, 1525). Less often discussed is Aaron’s treatment of plainsong, the most complete statement of which occurs in the opening book of his first published treatise, the Libri tres de institutione harmonica (Bologna, 1516). The present dissertation aims to assess and contextualize Aaron’s perspective on the subject with a translation and commentary on the first book of the De institutione harmonica. The extensive commentary endeavors to situate Aaron’s treatment of plainsong more concretely within the history of music theory, with particular focus on some of the most prominent treatises that were circulating in the decades prior to the publication of the De institutione harmonica. This includes works by such well-known theorists as Marchetto da Padova, Johannes Tinctoris, and Franchinus Gaffurius, but equally significant are certain lesser-known practical works on the topic of plainsong from around the turn of the century, some of which are in the vernacular Italian, including Bonaventura da Brescia’s Breviloquium musicale (1497), the anonymous Compendium musices (1499), and the anonymous Quaestiones et solutiones (c.1500). -
A Study of Microtones in Pop Music
University of Huddersfield Repository Chadwin, Daniel James Applying microtonality to pop songwriting: A study of microtones in pop music Original Citation Chadwin, Daniel James (2019) Applying microtonality to pop songwriting: A study of microtones in pop music. Masters thesis, University of Huddersfield. This version is available at http://eprints.hud.ac.uk/id/eprint/34977/ The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or not-for-profit purposes without prior permission or charge, provided: • The authors, title and full bibliographic details is credited in any copy; • A hyperlink and/or URL is included for the original metadata page; and • The content is not changed in any way. For more information, including our policy and submission procedure, please contact the Repository Team at: [email protected]. http://eprints.hud.ac.uk/ Applying microtonality to pop songwriting A study of microtones in pop music Daniel James Chadwin Student number: 1568815 A thesis submitted to the University of Huddersfield in partial fulfilment of the requirements for the degree of Master of Arts University of Huddersfield May 2019 1 Abstract While temperament and expanded tunings have not been widely adopted by pop and rock musicians historically speaking, there has recently been an increased interest in microtones from modern artists and in online discussion. -
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). -
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. -
Tuning: at the Grcssroads
WendyGarloo ?O. Box1024 Tuning:At the New YorkCit, New York 10276USA Grcssroads lntrodrciion planned the construction of instruments that per- formed within the new "tunitrg of choice," and all The arena o{ musical scales and tuning has cer_ publishedpapers or books demonstretingthe supe- tainly not been a quiet place to be for the past thlee dority of their new scales in at least some way over hundred yeals. But it might iust as well have beenif €qual temperament.The tradition has continued we iudge by the results: the same 12V2 equally with Yunik and Swi{t {1980),Blackwood (1982),and temperedscale established then as the best avail- the presentauthor (Milano 1986),and shows no able tuning compromise, by J. S. Bach and many sign of slowing down despite the apparent apathy otheis lHelrnholtz 1954j Apel 1972),remains to with which the musical mainstream has regularly this day essentially the only scale heard in Westem grceted eech new proposal. music. That monopoly crossesall musical styles, of course therc's a perf€ctly reasonable explana- {rom the most contemporary of jazz and av^rf,t' tion lor the mainstream's evident preferetrce to rc- "rut-bound" gardeclassical, and musical masteeieces from the main when by now there are at least past, to the latest technopop rock with fancy s)'n- a dozen clearly better-sounding ways to tune our thesizers,and everwvherein between.Instruments scales,i{ only for at least part of the time: it re' ol the symphonyorchestra a((empr with varyirrg quires a lot of effort ol several kinds. I'm typing this deSreesof successto live up ro lhe 100-centsemi manuscript using a Dvorak keyboard (lor the ffrst tone, even though many would find it inherently far time!), and I assureyou it's not easyto unlearn the easierto do otherwise: the stdngs to "lapse" into QWERTY habits of a lifetime, even though I can Pythagoieen tuning, the brass into several keys of akeady feel the actual superiodty of this unloved lust irtonation lBarbour 1953).And th€se easily but demonstrablv better kevboard. -
Tuning, Timbre, Spectrum, Scale William A
Tuning, Timbre, Spectrum, Scale William A. Sethares Tuning, Timbre, Spectrum, Scale Second Edition With 149 Figures William A. Sethares, Ph.D. Department of Electrical and Computer Engineering University of Wisconsin–Madison 1415 Johnson Drive Madison, WI 53706-1691 USA British Library Cataloguing in Publication Data Sethares, William A., 1955– Tuning, timbre, spectrum, scale.—2nd ed. 1. Sound 2. Tuning 3. Tone color (Music) 4. Musical intervals and scales 5. Psychoacoustics 6. Music—Acoustics and physics I. Title 781.2′3 ISBN 1852337974 Library of Congress Cataloging-in-Publication Data Sethares, William A., 1955– Tuning, timbre, spectrum, scale / William A. Sethares. p. cm. Includes bibliographical references and index. ISBN 1-85233-797-4 (alk. paper) 1. Sound. 2. Tuning. 3. Tone color (Music) 4. Musical intervals and scales. 5. Psychoacoustics. 6. Music—Acoustics and physics. I. Title. QC225.7.S48 2004 534—dc22 2004049190 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 of licences issued by the Copyright Licensing Agency. Enquiries con- cerning reproduction outside those terms should be sent to the publishers. ISBN 1-85233-797-4 2nd edition Springer-Verlag London Berlin Heidelberg ISBN 3-540-76173-X 1st edition Springer-Verlag Berlin Heidelberg New York Springer Science+Business Media springeronline.com © Springer-Verlag London Limited 2005 Printed in the United States of America First published 1999 Second edition 2005 The software disk accompanying this book and all material contained on it is supplied without any warranty of any kind. -
Encyclopedia of the History of Arabic Science. Volume 2, Mathematics
Encyclopedia of the History of Arabic Science Encyclopedia of the History of Arabic Science Volume 2 Edited by ROSHDI RASHED in collaboration with RÉGIS MORELON LONDON AND NEW YORK First published in 1996 by Routledge 11 New Fetter Lane, London EC4P 4EE 29 West 35th Street, New York, NY 10001 This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. Structure and editorial matter © 1996 Routledge The chapters © 1996 Routledge All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloguing-in-Publication Data A catalogue record for this book is available on request. ISBN 0-203-40360-6 Master e-book ISBN ISBN 0-203-71184-X (Adobe ebook Reader Format) ISBN 0-415-12411-5 (Print Edition) 3 volume set ISBN 0-415-02063-8 Contents VOLUME 1 Contents v Preface ix 1 General survey of Arabic astronomy Régis Morelon 1 2 Eastern Arabic astronomy between the eighth and the eleventh centuries 20 Régis Morelon 3 Arabic planetary theories after the eleventh century AD 58 George Saliba 4 Astronomy and