3 Manual Microtonal Organ Ruben Sverre Gjertsen 2013
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Chords and Scales 30/09/18 3:21 PM
Chords and Scales 30/09/18 3:21 PM Chords Charts written by Mal Webb 2014-18 http://malwebb.com Name Symbol Alt. Symbol (best first) Notes Note numbers Scales (in order of fit). C major (triad) C Cmaj, CM (not good) C E G 1 3 5 Ion, Mix, Lyd, MajPent, MajBlu, DoHar, HarmMaj, RagPD, DomPent C 6 C6 C E G A 1 3 5 6 Ion, MajPent, MajBlu, Lyd, Mix C major 7 C∆ Cmaj7, CM7 (not good) C E G B 1 3 5 7 Ion, Lyd, DoHar, RagPD, MajPent C major 9 C∆9 Cmaj9 C E G B D 1 3 5 7 9 Ion, Lyd, MajPent C 7 (or dominant 7th) C7 CM7 (not good) C E G Bb 1 3 5 b7 Mix, LyDom, PhrDom, DomPent, RagCha, ComDim, MajPent, MajBlu, Blues C 9 C9 C E G Bb D 1 3 5 b7 9 Mix, LyDom, RagCha, DomPent, MajPent, MajBlu, Blues C 7 sharp 9 C7#9 C7+9, C7alt. C E G Bb D# 1 3 5 b7 #9 ComDim, Blues C 7 flat 9 C7b9 C7alt. C E G Bb Db 1 3 5 b7 b9 ComDim, PhrDom C 7 flat 5 C7b5 C E Gb Bb 1 3 b5 b7 Whole, LyDom, SupLoc, Blues C 7 sharp 11 C7#11 Bb+/C C E G Bb D F# 1 3 5 b7 9 #11 LyDom C 13 C 13 C9 add 13 C E G Bb D A 1 3 5 b7 9 13 Mix, LyDom, DomPent, MajBlu, Blues C minor (triad) Cm C-, Cmin C Eb G 1 b3 5 Dor, Aeo, Phr, HarmMin, MelMin, DoHarMin, MinPent, Ukdom, Blues, Pelog C minor 7 Cm7 Cmin7, C-7 C Eb G Bb 1 b3 5 b7 Dor, Aeo, Phr, MinPent, UkDom, Blues C minor major 7 Cm∆ Cm maj7, C- maj7 C Eb G B 1 b3 5 7 HarmMin, MelMin, DoHarMin C minor 6 Cm6 C-6 C Eb G A 1 b3 5 6 Dor, MelMin C minor 9 Cm9 C-9 C Eb G Bb D 1 b3 5 b7 9 Dor, Aeo, MinPent C diminished (triad) Cº Cdim C Eb Gb 1 b3 b5 Loc, Dim, ComDim, SupLoc C diminished 7 Cº7 Cdim7 C Eb Gb A(Bbb) 1 b3 b5 6(bb7) Dim C half diminished Cø -
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. -
The Science of String Instruments
The Science of String Instruments Thomas D. Rossing Editor The Science of String Instruments Editor Thomas D. Rossing Stanford University Center for Computer Research in Music and Acoustics (CCRMA) Stanford, CA 94302-8180, USA [email protected] ISBN 978-1-4419-7109-8 e-ISBN 978-1-4419-7110-4 DOI 10.1007/978-1-4419-7110-4 Springer New York Dordrecht Heidelberg London # Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer ScienceþBusiness Media (www.springer.com) Contents 1 Introduction............................................................... 1 Thomas D. Rossing 2 Plucked Strings ........................................................... 11 Thomas D. Rossing 3 Guitars and Lutes ........................................................ 19 Thomas D. Rossing and Graham Caldersmith 4 Portuguese Guitar ........................................................ 47 Octavio Inacio 5 Banjo ...................................................................... 59 James Rae 6 Mandolin Family Instruments........................................... 77 David J. Cohen and Thomas D. Rossing 7 Psalteries and Zithers .................................................... 99 Andres Peekna and Thomas D. -
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. -
Nora-Louise Müller the Bohlen-Pierce Clarinet An
Nora-Louise Müller The Bohlen-Pierce Clarinet An Introduction to Acoustics and Playing Technique The Bohlen-Pierce scale was discovered in the 1970s and 1980s by Heinz Bohlen and John R. Pierce respectively. Due to a lack of instruments which were able to play the scale, hardly any compositions in Bohlen-Pierce could be found in the past. Just a few composers who work in electronic music used the scale – until the Canadian woodwind maker Stephen Fox created a Bohlen-Pierce clarinet, instigated by Georg Hajdu, professor of multimedia composition at Hochschule für Musik und Theater Hamburg. Hence the number of Bohlen- Pierce compositions using the new instrument is increasing constantly. This article gives a short introduction to the characteristics of the Bohlen-Pierce scale and an overview about Bohlen-Pierce clarinets and their playing technique. The Bohlen-Pierce scale Unlike the scales of most tone systems, it is not the octave that forms the repeating frame of the Bohlen-Pierce scale, but the perfect twelfth (octave plus fifth), dividing it into 13 steps, according to various mathematical considerations. The result is an alternative harmonic system that opens new possibilities to contemporary and future music. Acoustically speaking, the octave's frequency ratio 1:2 is replaced by the ratio 1:3 in the Bohlen-Pierce scale, making the perfect twelfth an analogy to the octave. This interval is defined as the point of reference to which the scale aligns. The perfect twelfth, or as Pierce named it, the tritave (due to the 1:3 ratio) is achieved with 13 tone steps. -
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). -
Shifting Exercises with Double Stops to Test Intonation
VERY ROUGH AND PRELIMINARY DRAFT!!! Shifting Exercises with Double Stops to Test Intonation These exercises were inspired by lessons I had from 1968 to 1970 with David Smiley of the San Francisco Symphony. I don’t have the book he used, but I believe it was one those written by Dounis on the scientific or artist's technique of violin playing. The exercises were difficult and frustrating, and involved shifting and double stops. Smiley also emphasized routine testing notes against other strings, and I also found some of his tasks frustrating because I couldn’t hear intervals that apparently seemed so familiar to a professional musician. When I found myself giving violin lessons in 2011, I had a mathematical understanding of why it was so difficult to hear certain musical intervals, and decided not to focus on them in my teaching. By then I had also developed some exercises to develop my own intonation. These exercises focus entirely on what is called the just scale. Pianos use the equal tempered scale, which is the predominate choice of intonation in orchestras and symphonies (I NEED VERIFICATION THAT THIS IS TRUE). It takes many years and many types of exercises and activities to become a good violinist. But I contend that everyone should start by mastering the following double stops in “just” intonation: 1. Practice the intervals shown above for all possible pairs of strings on your violin or viola. Learn the first two first, then add one interval at a time. They get harder to hear as you go down the list for reasons having to do with the fractions: 1/2, 2/3, 3/4, 3/5, 4/5, 5/6. -
Helmholtz's Dissonance Curve
Tuning and Timbre: A Perceptual Synthesis Bill Sethares IDEA: Exploit psychoacoustic studies on the perception of consonance and dissonance. The talk begins by showing how to build a device that can measure the “sensory” consonance and/or dissonance of a sound in its musical context. Such a “dissonance meter” has implications in music theory, in synthesizer design, in the con- struction of musical scales and tunings, and in the design of musical instruments. ...the legacy of Helmholtz continues... 1 Some Observations. Why do we tune our instruments the way we do? Some tunings are easier to play in than others. Some timbres work well in certain scales, but not in others. What makes a sound easy in 19-tet but hard in 10-tet? “The timbre of an instrument strongly affects what tuning and scale sound best on that instrument.” – W. Carlos 2 What are Tuning and Timbre? 196 384 589 amplitude 787 magnitude sample: 0 10000 20000 30000 0 1000 2000 3000 4000 time: 0 0.23 0.45 0.68 frequency in Hz Tuning = pitch of the fundamental (in this case 196 Hz) Timbre involves (a) pattern of overtones (Helmholtz) (b) temporal features 3 Some intervals “harmonious” and others “discordant.” Why? X X X X 1.06:1 2:1 X X X X 1.89:1 3:2 X X X X 1.414:1 4:3 4 Theory #1:(Pythagoras ) Humans naturally like the sound of intervals de- fined by small integer ratios. small ratios imply short period of repetition short = simple = sweet Theory #2:(Helmholtz ) Partials of a sound that are close in frequency cause beats that are perceived as “roughness” or dissonance. -
Microtonality As an Expressive Device: an Approach for the Contemporary Saxophonist
Technological University Dublin ARROW@TU Dublin Dissertations Conservatory of Music and Drama 2009 Microtonality as an Expressive Device: an Approach for the Contemporary Saxophonist Seán Mac Erlaine Technological University Dublin, [email protected] Follow this and additional works at: https://arrow.tudublin.ie/aaconmusdiss Part of the Composition Commons, Musicology Commons, Music Pedagogy Commons, Music Performance Commons, and the Music Theory Commons Recommended Citation Mac Erlaine, S.: Microtonality as an Expressive Device: an Approach for the Contemporary Saxophonist. Masters Dissertation. Technological University Dublin, 2009. This Dissertation is brought to you for free and open access by the Conservatory of Music and Drama at ARROW@TU Dublin. It has been accepted for inclusion in Dissertations by an authorized administrator of ARROW@TU Dublin. For more information, please contact [email protected], [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License Microtonality as an expressive device: An approach for the contemporary saxophonist September 2009 Seán Mac Erlaine www.sean-og.com Table of Contents Abstract i Introduction ii CHAPTER ONE 1 1.1 Tuning Theory 1 1.1.1 Tuning Discrepancies 1 1.2 Temperament for Keyboard Instruments 2 1.3 Non‐fixed Intonation Instruments 5 1.4 Dominance of Equal Temperament 7 1.5 The Evolution of Equal Temperament: Microtonality 9 CHAPTER TWO 11 2.1 Twentieth Century Tradition of Microtonality 11 2.2 Use of Microtonality -
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. -
Tuning and Intervals
CHAPTER 4 Tuning and Intervals Sitting on the riverbank, Pan noticed the bed of reeds was swaying in the wind, making a mournful moaning sound, for the wind had broken the tops of some of the reeds. Pulling the reeds up, Pan cut them into pieces and bound them together to create a musical instrument, which he named “Syrinx”, in memory of his lost love Ovid (Roman Poet; 43 BC - AD 18/19) Have you ever watched someone tune a guitar? Or maybe even a piano? The lengths of the strings have to be adjusted by hand to exactly the right sound,bymakingthestringstighteror looser. Bue how does the tuner know which sound is the right one? This question has been asked throughout history and different cultures at different times have found different answers. Many cultures tune their instruments differently than we do. Listen for instance to the Indian instrument sarod in http://www.youtube.com/watch?v=hobK_8bIDvk.Also,2000yearsago,theGreekwere using different tuning ideas than we do today. Of course the Greek did not have guitars or pianos at that time, but they were still thinking about tuning for theinstrumentstheyhadandaboutthe structure of music in general. The pan flute,oneoftheoldestmusicalinstrumentsintheworld, was used by the ancient Greeks and is still being played today.Itconsistsofseveralpipesofbamboo of increasing lengths. The name is a reference to the Greek godPanwhoisshownplayingtheflute in Figure 1. Figure 1. Pan playing the pan flute. For the following investigations you need to make your own “pan flute” out of straws. Straws for bubble tea1,workbetterthanregularstrawssincetheyhaveawiderdiameter. You need to plug the bottom with a finger to get a clear pitch. -
Playing Music in Just Intonation: a Dynamically Adaptive Tuning Scheme
Karolin Stange,∗ Christoph Wick,† Playing Music in Just and Haye Hinrichsen∗∗ ∗Hochschule fur¨ Musik, Intonation: A Dynamically Hofstallstraße 6-8, 97070 Wurzburg,¨ Germany Adaptive Tuning Scheme †Fakultat¨ fur¨ Mathematik und Informatik ∗∗Fakultat¨ fur¨ Physik und Astronomie †∗∗Universitat¨ Wurzburg¨ Am Hubland, Campus Sud,¨ 97074 Wurzburg,¨ Germany Web: www.just-intonation.org [email protected] [email protected] [email protected] Abstract: We investigate a dynamically adaptive tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the chordal structure, our tuning scheme continually solves a system of linear equations, rather than relying on sequences of conditional if-then clauses. In complex situations, where not all intervals of a chord can be tuned according to the frequency ratios of just intonation, the method automatically yields a tempered compromise. We outline the implementation of the algorithm in an open-source software project that we have provided to demonstrate the feasibility of the tuning method. The first attempts to mathematically characterize is particularly pronounced if m and n are small. musical intervals date back to Pythagoras, who Examples include the perfect octave (m:n = 2:1), noted that the consonance of two tones played on the perfect fifth (3:2), and the perfect fourth (4:3). a monochord can be related to simple fractions Larger values of mand n tend to correspond to more of the corresponding string lengths (for a general dissonant intervals. If a normally consonant interval introduction see, e.g., Geller 1997; White and White is sufficiently detuned from just intonation (i.e., the 2014).