Functional Organization for Musical Consonance and Tonal Pitch Hierarchy in Human Auditory Cortex
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Perceptual Interactions of Pitch and Timbre: an Experimental Study on Pitch-Interval Recognition with Analytical Applications
Perceptual interactions of pitch and timbre: An experimental study on pitch-interval recognition with analytical applications SARAH GATES Music Theory Area Department of Music Research Schulich School of Music McGill University Montréal • Quebec • Canada August 2015 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Arts. Copyright © 2015 • Sarah Gates Contents List of Figures v List of Tables vi List of Examples vii Abstract ix Résumé xi Acknowledgements xiii Author Contributions xiv Introduction 1 Pitch, Timbre and their Interaction • Klangfarbenmelodie • Goals of the Current Project 1 Literature Review 7 Pitch-Timbre Interactions • Unanswered Questions • Resulting Goals and Hypotheses • Pitch-Interval Recognition 2 Experimental Investigation 19 2.1 Aims and Hypotheses of Current Experiment 19 2.2 Experiment 1: Timbre Selection on the Basis of Dissimilarity 20 A. Rationale 20 B. Methods 21 Participants • Stimuli • Apparatus • Procedure C. Results 23 2.3 Experiment 2: Interval Identification 26 A. Rationale 26 i B. Method 26 Participants • Stimuli • Apparatus • Procedure • Evaluation of Trials • Speech Errors and Evaluation Method C. Results 37 Accuracy • Response Time D. Discussion 51 2.4 Conclusions and Future Directions 55 3 Theoretical Investigation 58 3.1 Introduction 58 3.2 Auditory Scene Analysis 59 3.3 Carter Duets and Klangfarbenmelodie 62 Esprit Rude/Esprit Doux • Carter and Klangfarbenmelodie: Examples with Timbral Dissimilarity • Conclusions about Carter 3.4 Webern and Klangfarbenmelodie in Quartet op. 22 and Concerto op 24 83 Quartet op. 22 • Klangfarbenmelodie in Webern’s Concerto op. 24, mvt II: Timbre’s effect on Motivic and Formal Boundaries 3.5 Closing Remarks 110 4 Conclusions and Future Directions 112 Appendix 117 A.1,3,5,7,9,11,13 Confusion Matrices for each Timbre Pair A.2,4,6,8,10,12,14 Confusion Matrices by Direction for each Timbre Pair B.1 Response Times for Unisons by Timbre Pair References 122 ii List of Figures Fig. -
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. -
MTO 19.3: Nobile, Interval Permutations
Volume 19, Number 3, September 2013 Copyright © 2013 Society for Music Theory Interval Permutations Drew F. Nobile NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.13.19.3/mto.13.19.3.nobile.php KEYWORDS: Interval permutations, intervals, post-tonal analysis, mathematical modeling, set-class, space, Schoenberg, The Book of the Hanging Gardens ABSTRACT: This paper presents a framework for analyzing the interval structure of pitch-class segments (ordered pitch-class sets). An “interval permutation” is a reordering of the intervals that arise between adjacent members of these pitch-class segments. Because pitch-class segments related by interval permutation are not necessarily members of the same set-class, this theory has the capability to demonstrate aurally significant relationships between sets that are not related by transposition or inversion. I begin with a theoretical investigation of interval permutations followed by a discussion of the relationship of interval permutations to traditional pitch-class set theory, specifically focusing on how various set-classes may be related by interval permutation. A final section applies these theories to analyses of several songs from Schoenberg’s op. 15 song cycle The Book of the Hanging Gardens. Received May 2013 [1] Example 1 shows the score to the opening measures of “Sprich nicht immer von dem Laub,” the fourteenth song from Schoenberg’s Book of the Hanging Gardens, op. 15. Upon first listen, one is drawn to the relationship between the piano’s gesture in the first measure and the vocal line in the second. -
An Exploration of the Relationship Between Mathematics and Music
An Exploration of the Relationship between Mathematics and Music Shah, Saloni 2010 MIMS EPrint: 2010.103 Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester Reports available from: http://eprints.maths.manchester.ac.uk/ And by contacting: The MIMS Secretary School of Mathematics The University of Manchester Manchester, M13 9PL, UK ISSN 1749-9097 An Exploration of ! Relation"ip Between Ma#ematics and Music MATH30000, 3rd Year Project Saloni Shah, ID 7177223 University of Manchester May 2010 Project Supervisor: Professor Roger Plymen ! 1 TABLE OF CONTENTS Preface! 3 1.0 Music and Mathematics: An Introduction to their Relationship! 6 2.0 Historical Connections Between Mathematics and Music! 9 2.1 Music Theorists and Mathematicians: Are they one in the same?! 9 2.2 Why are mathematicians so fascinated by music theory?! 15 3.0 The Mathematics of Music! 19 3.1 Pythagoras and the Theory of Music Intervals! 19 3.2 The Move Away From Pythagorean Scales! 29 3.3 Rameau Adds to the Discovery of Pythagoras! 32 3.4 Music and Fibonacci! 36 3.5 Circle of Fifths! 42 4.0 Messiaen: The Mathematics of his Musical Language! 45 4.1 Modes of Limited Transposition! 51 4.2 Non-retrogradable Rhythms! 58 5.0 Religious Symbolism and Mathematics in Music! 64 5.1 Numbers are God"s Tools! 65 5.2 Religious Symbolism and Numbers in Bach"s Music! 67 5.3 Messiaen"s Use of Mathematical Ideas to Convey Religious Ones! 73 6.0 Musical Mathematics: The Artistic Aspect of Mathematics! 76 6.1 Mathematics as Art! 78 6.2 Mathematical Periods! 81 6.3 Mathematics Periods vs. -
How to Read Music Notation in JUST 30 MINUTES! C D E F G a B C D E F G a B C D E F G a B C D E F G a B C D E F G a B C D E
The New School of American Music How to Read Music Notation IN JUST 30 MINUTES! C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E 1. MELODIES 2. THE PIANO KEYBOARD The first thing to learn about reading music A typical piano has 88 keys total (including all is that you can ignore most of the informa- white keys and black keys). Most electronic tion that’s written on the page. The only part keyboards and organ manuals have fewer. you really need to learn is called the “treble However, there are only twelve different clef.” This is the symbol for treble clef: notes—seven white and five black—on the keyboard. This twelve note pattern repeats several times up and down the piano keyboard. In our culture the white notes are named after the first seven letters of the alphabet: & A B C D E F G The bass clef You can learn to recognize all the notes by is for classical sight by looking at their patterns relative to the pianists only. It is totally useless for our black keys. Notice the black keys are arranged purposes. At least for now. ? in patterns of two and three. The piano universe tends to revolve around the C note which you The notes ( ) placed within the treble clef can identify as the white key found just to the represent the melody of the song. -
Music Is Made up of Many Different Things Called Elements. They Are the “I Feel Like My Kind Building Bricks of Music
SECONDARY/KEY STAGE 3 MUSIC – BUILDING BRICKS 5 MINUTES READING #1 Music is made up of many different things called elements. They are the “I feel like my kind building bricks of music. When you compose a piece of music, you use the of music is a big pot elements of music to build it, just like a builder uses bricks to build a house. If of different spices. the piece of music is to sound right, then you have to use the elements of It’s a soup with all kinds of ingredients music correctly. in it.” - Abigail Washburn What are the Elements of Music? PITCH means the highness or lowness of the sound. Some pieces need high sounds and some need low, deep sounds. Some have sounds that are in the middle. Most pieces use a mixture of pitches. TEMPO means the fastness or slowness of the music. Sometimes this is called the speed or pace of the music. A piece might be at a moderate tempo, or even change its tempo part-way through. DYNAMICS means the loudness or softness of the music. Sometimes this is called the volume. Music often changes volume gradually, and goes from loud to soft or soft to loud. Questions to think about: 1. Think about your DURATION means the length of each sound. Some sounds or notes are long, favourite piece of some are short. Sometimes composers combine long sounds with short music – it could be a song or a piece of sounds to get a good effect. instrumental music. How have the TEXTURE – if all the instruments are playing at once, the texture is thick. -
Automatic Music Transcription Using Sequence to Sequence Learning
Automatic music transcription using sequence to sequence learning Master’s thesis of B.Sc. Maximilian Awiszus At the faculty of Computer Science Institute for Anthropomatics and Robotics Reviewer: Prof. Dr. Alexander Waibel Second reviewer: Prof. Dr. Advisor: M.Sc. Thai-Son Nguyen Duration: 25. Mai 2019 – 25. November 2019 KIT – University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association www.kit.edu Interactive Systems Labs Institute for Anthropomatics and Robotics Karlsruhe Institute of Technology Title: Automatic music transcription using sequence to sequence learning Author: B.Sc. Maximilian Awiszus Maximilian Awiszus Kronenstraße 12 76133 Karlsruhe [email protected] ii Statement of Authorship I hereby declare that this thesis is my own original work which I created without illegitimate help by others, that I have not used any other sources or resources than the ones indicated and that due acknowledgement is given where reference is made to the work of others. Karlsruhe, 15. M¨arz 2017 ............................................ (B.Sc. Maximilian Awiszus) Contents 1 Introduction 3 1.1 Acoustic music . .4 1.2 Musical note and sheet music . .5 1.3 Musical Instrument Digital Interface . .6 1.4 Instruments and inference . .7 1.5 Fourier analysis . .8 1.6 Sequence to sequence learning . 10 1.6.1 LSTM based S2S learning . 11 2 Related work 13 2.1 Music transcription . 13 2.1.1 Non-negative matrix factorization . 13 2.1.2 Neural networks . 14 2.2 Datasets . 18 2.2.1 MusicNet . 18 2.2.2 MAPS . 18 2.3 Natural Language Processing . 19 2.4 Music modelling . -
Musical Elements in the Discrete-Time Representation of Sound
0 Musical elements in the discrete-time representation of sound RENATO FABBRI, University of Sao˜ Paulo VILSON VIEIRA DA SILVA JUNIOR, Cod.ai ANTONIOˆ CARLOS SILVANO PESSOTTI, Universidade Metodista de Piracicaba DEBORA´ CRISTINA CORREA,ˆ University of Western Australia OSVALDO N. OLIVEIRA JR., University of Sao˜ Paulo e representation of basic elements of music in terms of discrete audio signals is oen used in soware for musical creation and design. Nevertheless, there is no unied approach that relates these elements to the discrete samples of digitized sound. In this article, each musical element is related by equations and algorithms to the discrete-time samples of sounds, and each of these relations are implemented in scripts within a soware toolbox, referred to as MASS (Music and Audio in Sample Sequences). e fundamental element, the musical note with duration, volume, pitch and timbre, is related quantitatively to characteristics of the digital signal. Internal variations of a note, such as tremolos, vibratos and spectral uctuations, are also considered, which enables the synthesis of notes inspired by real instruments and new sonorities. With this representation of notes, resources are provided for the generation of higher scale musical structures, such as rhythmic meter, pitch intervals and cycles. is framework enables precise and trustful scientic experiments, data sonication and is useful for education and art. e ecacy of MASS is conrmed by the synthesis of small musical pieces using basic notes, elaborated notes and notes in music, which reects the organization of the toolbox and thus of this article. It is possible to synthesize whole albums through collage of the scripts and seings specied by the user. -
Understanding Music Past and Present
Understanding Music Past and Present N. Alan Clark, PhD Thomas Heflin, DMA Jeffrey Kluball, EdD Elizabeth Kramer, PhD Understanding Music Past and Present N. Alan Clark, PhD Thomas Heflin, DMA Jeffrey Kluball, EdD Elizabeth Kramer, PhD Dahlonega, GA Understanding Music: Past and Present is licensed under a Creative Commons Attribu- tion-ShareAlike 4.0 International License. This license allows you to remix, tweak, and build upon this work, even commercially, as long as you credit this original source for the creation and license the new creation under identical terms. If you reuse this content elsewhere, in order to comply with the attribution requirements of the license please attribute the original source to the University System of Georgia. NOTE: The above copyright license which University System of Georgia uses for their original content does not extend to or include content which was accessed and incorpo- rated, and which is licensed under various other CC Licenses, such as ND licenses. Nor does it extend to or include any Special Permissions which were granted to us by the rightsholders for our use of their content. Image Disclaimer: All images and figures in this book are believed to be (after a rea- sonable investigation) either public domain or carry a compatible Creative Commons license. If you are the copyright owner of images in this book and you have not authorized the use of your work under these terms, please contact the University of North Georgia Press at [email protected] to have the content removed. ISBN: 978-1-940771-33-5 Produced by: University System of Georgia Published by: University of North Georgia Press Dahlonega, Georgia Cover Design and Layout Design: Corey Parson For more information, please visit http://ung.edu/university-press Or email [email protected] TABLE OF C ONTENTS MUSIC FUNDAMENTALS 1 N. -
How to Play the Musical
' '[! . .. ' 1 II HOW TO PLAY THE MUSI CAL SAW by RENE ' BOGART INTRODUCTION TO PLAYING THE MUSICA L SAW: It is unknown just when nor where THE MUSICAL SAW had it's origin and was first played. It ~s believed among some MUSICAL SAW players, however, that i t originated in South America in the 1800's and some believe the idea was imported into the U. S. from Europe . I well remember the fi r st time I heard it played. It wa s in Buffalo, N.Y. and played at the Ebrwood M!L6,£.c..Ha..U about 1910 when I was a boy. It has been used extensively in the ho me, on stage at private cl ubs, church fun ctions, social gatherings , hospita l s and nursing homes, in vaudevi l le and theaters for years, and more recently on Radio and Televisi on Programs in the enter tainmentfield. The late Cf.alte.nc..e.MM ~e.ht , of Fort Atkinson, Wi sconsin, was the first to introduce and suppl y Musical Saw Kits to the field under the name of M!L6 ~e. ht&Wutpha1.,** and did a great deal to develop the best line of SAWS suitable for this use, after considerable research. Before taking up the MUSICAL SAW and going into the detail s of there quired proceedure for playing it wel l , it is important to understand some of the basic rudiments and techniques involved for it's proper manipu l ation. While the MUSICAL SAW is essential l y a typi cal carpenter's or craftsman's saw, it' s use as a very unique musical instrument has gained in popu larity, and has recently become a means of expressing a very distinctive qua l ity of music. -
Elementary Music Synthesis
Elementary Music Synthesis This lab is by Professor Virginia Stonick of Oregon State University. The purp ose of this lab is to construct physically meaningful signals math- ematically in MATLAB using your knowledge of signals. You will gain some understanding of the physical meaning of the signals you construct by using audio playback. Also, we hop e you have fun! 1 Background In this section, we explore how to use simple tones to comp ose a segment of music. By using tones of various frequencies, you will construct the rst few bars of Beethoven's famous piece \Symphony No. 5 in C-Minor." In addition, you will get to construct a simple scale and then play it backwards. IMPORTANT: Eachmusical note can b e simply represented by a sinusoid whose frequency dep ends on the note pitch. Assume a sampling rate of 8KHz and that an eighth note = 1000 samples. Musical notes are arranged in groups of twelve notes called octaves. The notes that we'll be using for Beethoven's Fifth are in the o ctave containing frequencies from 220 Hz to 440 Hz. When we construct our scale, we'll include notes from the o ctave containing frequencies from 440 Hz to 880 Hz. The twelve notes in each o ctave are logarithmically spaced in frequency, 1=12 with each note b eing of a frequency 2 times the frequency of the note of lower frequency. Thus, a 1-o ctave pitch shift corresp onds to a doubling of the frequencies of the notes in the original o ctave. -
Interval Cycles and the Emergence of Major-Minor Tonality
Empirical Musicology Review Vol. 5, No. 3, 2010 Modes on the Move: Interval Cycles and the Emergence of Major-Minor Tonality MATTHEW WOOLHOUSE Centre for Music and Science, Faculty of Music, University of Cambridge, United Kingdom ABSTRACT: The issue of the emergence of major-minor tonality is addressed by recourse to a novel pitch grouping process, referred to as interval cycle proximity (ICP). An interval cycle is the minimum number of (additive) iterations of an interval that are required for octave-related pitches to be re-stated, a property conjectured to be responsible for tonal attraction. It is hypothesised that the actuation of ICP in cognition, possibly in the latter part of the sixteenth century, led to a hierarchy of tonal attraction which favoured certain pitches over others, ostensibly the tonics of the modern major and minor system. An ICP model is described that calculates the level of tonal attraction between adjacent musical elements. The predictions of the model are shown to be consistent with music-theoretic accounts of common practice period tonality, including Piston’s Table of Usual Root Progressions. The development of tonality is illustrated with the historical quotations of commentators from the sixteenth to the eighteenth centuries, and can be characterised as follows. At the beginning of the seventeenth century multiple ‘finals’ were possible, each associated with a different interval configuration (mode). By the end of the seventeenth century, however, only two interval configurations were in regular use: those pertaining to the modern major- minor key system. The implications of this development are discussed with respect interval cycles and their hypothesised effect within music.