Tuning by Spectra: Computer Tools for Crafting Tuning Systems from Korean Musical Timbres and Other Sounds
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Chapter 1 Geometric Generalizations of the Tonnetz and Their Relation To
November 22, 2017 12:45 ws-rv9x6 Book Title yustTonnetzSub page 1 Chapter 1 Geometric Generalizations of the Tonnetz and their Relation to Fourier Phases Spaces Jason Yust Boston University School of Music, 855 Comm. Ave., Boston, MA, 02215 [email protected] Some recent work on generalized Tonnetze has examined the topologies resulting from Richard Cohn's common-tone based formulation, while Tymoczko has reformulated the Tonnetz as a network of voice-leading re- lationships and investigated the resulting geometries. This paper adopts the original common-tone based formulation and takes a geometrical ap- proach, showing that Tonnetze can always be realized in toroidal spaces, and that the resulting spaces always correspond to one of the possible Fourier phase spaces. We can therefore use the DFT to optimize the given Tonnetz to the space (or vice-versa). I interpret two-dimensional Tonnetze as triangulations of the 2-torus into regions associated with the representatives of a single trichord type. The natural generalization to three dimensions is therefore a triangulation of the 3-torus. This means that a three-dimensional Tonnetze is, in the general case, a network of three tetrachord-types related by shared trichordal subsets. Other Ton- netze that have been proposed with bounded or otherwise non-toroidal topologies, including Tymoczko's voice-leading Tonnetze, can be under- stood as the embedding of the toroidal Tonnetze in other spaces, or as foldings of toroidal Tonnetze with duplicated interval types. 1. Formulations of the Tonnetz The Tonnetz originated in nineteenth-century German harmonic theory as a network of pitch classes connected by consonant intervals. -
Echo-Enabled Harmonics up to the 75Th Order from Precisely Tailored Electron Beams E
LETTERS PUBLISHED ONLINE: 6 JUNE 2016 | DOI: 10.1038/NPHOTON.2016.101 Echo-enabled harmonics up to the 75th order from precisely tailored electron beams E. Hemsing1*,M.Dunning1,B.Garcia1,C.Hast1, T. Raubenheimer1,G.Stupakov1 and D. Xiang2,3* The production of coherent radiation at ever shorter wave- phase-mixing transformation turns the sinusoidal modulation into lengths has been a long-standing challenge since the invention a filamentary distribution with multiple energy bands (Fig. 1b). 1,2 λ of lasers and the subsequent demonstration of frequency A second laser ( 2 = 2,400 nm) then produces an energy modulation 3 ΔE fi doubling . Modern X-ray free-electron lasers (FELs) use relati- ( 2) in the nely striated beam in the U2 undulator (Fig. 1c). vistic electrons to produce intense X-ray pulses on few-femto- Finally, the beam travels through the C2 chicane where a smaller 4–6 R(2) second timescales . However, the shot noise that seeds the dispersion 56 brings the energy bands upright (Fig. 1d). amplification produces pulses with a noisy spectrum and Projected into the longitudinal space, the echo signal appears as a λ λ h limited temporal coherence. To produce stable transform- series of narrow current peaks (bunching) with separation = 2/ limited pulses, a seeding scheme called echo-enabled harmonic (Fig. 1e), where h is a harmonic of the second laser that determines generation (EEHG) has been proposed7,8, which harnesses the character of the harmonic echo signal. the highly nonlinear phase mixing of the celebrated echo EEHG has been examined experimentally only recently and phenomenon9 to generate coherent harmonic density modu- at modest harmonic orders, starting with the 3rd and 4th lations in the electron beam with conventional lasers. -
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). -
HSK 6 Vocabulary List
HSK 6 Vocabulary List No Chinese Pinyin English HSK 1 呵 ā to scold in a loud voice; to yawn HSK6 to suffer from; to endure; to tide over (a 2 挨 āi HSK6 difficult period); to delay to love sth too much to part with it (idiom); 3 爱不释手 àibùshìshǒu HSK6 to fondle admiringly 4 爱戴 àidài to love and respect; love and respect HSK6 5 暧昧 àimèi vague; ambiguous; equivocal; dubious HSK6 hey; ow; ouch; interjection of pain or 6 哎哟 āiyō HSK6 surprise 7 癌症 áizhèng cancer HSK6 8 昂贵 ángguì expensive; costly HSK6 law case; legal case; judicial case; 9 案件 ànjiàn HSK6 CL:宗[zong1],樁|桩[zhuang1],起[qi3] 10 安居乐业 ānjūlèyè live in peace and work happily (idiom) HSK6 11 案例 ànlì case (law); CL:個|个[ge4] HSK6 12 按摩 ànmó massage HSK6 13 安宁 ānníng peaceful; tranquil; calm; composed HSK6 14 暗示 ànshì to hint; to suggest; suggestion; a hint HSK6 15 安详 ānxiáng serene HSK6 find a place for; help settle down; arrange 16 安置 ānzhì HSK6 for; to get into bed; placement (of cooking) to boil for a long time; to 17 熬 áo HSK6 endure; to suffer 18 奥秘 àomì profound; deep; a mystery HSK6 bumpy; uneven; slotted and tabbed joint; 19 凹凸 āotú HSK6 crenelation to hold on to; to cling to; to dig up; to rake; 20 扒 bā to push aside; to climb; to pull out; to strip HSK6 off 21 疤 bā scar HSK6 to be eager for; to long for; to look forward 22 巴不得 bābudé HSK6 to the Way of the Hegemon, abbr. -
Andrián Pertout
Andrián Pertout Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition Volume 1 Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy Produced on acid-free paper Faculty of Music The University of Melbourne March, 2007 Abstract Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition encompasses the work undertaken by Lou Harrison (widely regarded as one of America’s most influential and original composers) with regards to just intonation, and tuning and scale systems from around the globe – also taking into account the influential work of Alain Daniélou (Introduction to the Study of Musical Scales), Harry Partch (Genesis of a Music), and Ben Johnston (Scalar Order as a Compositional Resource). The essence of the project being to reveal the compositional applications of a selection of Persian, Indonesian, and Japanese musical scales utilized in three very distinct systems: theory versus performance practice and the ‘Scale of Fifths’, or cyclic division of the octave; the equally-tempered division of the octave; and the ‘Scale of Proportions’, or harmonic division of the octave championed by Harrison, among others – outlining their theoretical and aesthetic rationale, as well as their historical foundations. The project begins with the creation of three new microtonal works tailored to address some of the compositional issues of each system, and ending with an articulated exposition; obtained via the investigation of written sources, disclosure -
Generation of Attosecond Light Pulses from Gas and Solid State Media
hv photonics Review Generation of Attosecond Light Pulses from Gas and Solid State Media Stefanos Chatziathanasiou 1, Subhendu Kahaly 2, Emmanouil Skantzakis 1, Giuseppe Sansone 2,3,4, Rodrigo Lopez-Martens 2,5, Stefan Haessler 5, Katalin Varju 2,6, George D. Tsakiris 7, Dimitris Charalambidis 1,2 and Paraskevas Tzallas 1,2,* 1 Foundation for Research and Technology—Hellas, Institute of Electronic Structure & Laser, PO Box 1527, GR71110 Heraklion (Crete), Greece; [email protected] (S.C.); [email protected] (E.S.); [email protected] (D.C.) 2 ELI-ALPS, ELI-Hu Kft., Dugonics ter 13, 6720 Szeged, Hungary; [email protected] (S.K.); [email protected] (G.S.); [email protected] (R.L.-M.); [email protected] (K.V.) 3 Physikalisches Institut der Albert-Ludwigs-Universität, Freiburg, Stefan-Meier-Str. 19, 79104 Freiburg, Germany 4 Dipartimento di Fisica Politecnico, Piazza Leonardo da Vinci 32, 20133 Milano, Italy 5 Laboratoire d’Optique Appliquée, ENSTA-ParisTech, Ecole Polytechnique, CNRS UMR 7639, Université Paris-Saclay, 91761 Palaiseau CEDEX, France; [email protected] 6 Department of Optics and Quantum Electronics, University of Szeged, Dóm tér 9., 6720 Szeged, Hungary 7 Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany; [email protected] * Correspondence: [email protected] Received: 25 February 2017; Accepted: 27 March 2017; Published: 31 March 2017 Abstract: Real-time observation of ultrafast dynamics in the microcosm is a fundamental approach for understanding the internal evolution of physical, chemical and biological systems. Tools for tracing such dynamics are flashes of light with duration comparable to or shorter than the characteristic evolution times of the system under investigation. -
Boris's Bells, by Way of Schubert and Others
Boris's Bells, By Way of Schubert and Others Mark DeVoto We define "bell chords" as different dominant-seventh chords whose roots are separated by multiples of interval 3, the minor third. The sobriquet derives from the most famous such pair of harmonies, the alternating D7 and AI? that constitute the entire harmonic substance of the first thirty-eight measures of scene 2 of the Prologue in Musorgsky's opera Boris Godunov (1874) (example O. Example 1: Paradigm of the Boris Godunov bell succession: AJ,7-D7. A~7 D7 '~~&gl n'IO D>: y 7 G: y7 The Boris bell chords are an early milestone in the history of nonfunctional harmony; yet the two harmonies, considered individually, are ofcourse abso lutely functional in classical contexts. This essay traces some ofthe historical antecedents of the bell chords as well as their developing descendants. Dominant Harmony The dominant-seventh chord is rightly recognized as the most unambiguous of the essential tonal resources in classical harmonic progression, and the V7-1 progression is the strongest means of moving harmony forward in immediate musical time. To put it another way, the expectation of tonic harmony to follow a dominant-seventh sonority is a principal component of forehearing; we assume, in our ordinary and long-tested experience oftonal music, that the tonic function will follow the dominant-seventh function and be fortified by it. So familiar is this everyday phenomenon that it hardly needs to be stated; we need mention it here only to assert the contrary case, namely, that the dominant-seventh function followed by something else introduces the element of the unexpected. -
Frequency Spectrum Generated by Thyristor Control J
Electrocomponent Science and Technology (C) Gordon and Breach Science Publishers Ltd. 1974, Vol. 1, pp. 43-49 Printed in Great Britain FREQUENCY SPECTRUM GENERATED BY THYRISTOR CONTROL J. K. HALL and N. C. JONES Loughborough University of Technology, Loughborough, Leics. U.K. (Received October 30, 1973; in final form December 19, 1973) This paper describes the measured harmonics in the load currents of thyristor circuits and shows that with firing angle control the harmonic amplitudes decrease sharply with increasing harmonic frequency, but that they extend to very high harmonic orders of around 6000. The amplitudes of the harmonics are a maximum for a firing delay angle of around 90 Integral cycle control produces only low order harmonics and sub-harmonics. It is also shown that with firing angle control apparently random inter-harmonic noise is present and that the harmonics fall below this noise level at frequencies of approximately 250 KHz for a switched 50 Hz waveform and for the resistive load used. The noise amplitude decreases with increasing frequency and is a maximum with 90 firing delay. INTRODUCTION inductance. 6,7 Literature on the subject tends to assume that noise is due to the high frequency Thyristors are now widely used for control of power harmonics generated by thyristor switch-on and the in both d.c. and a.c. circuits. The advantages of design of suppression components is based on this. relatively small size, low losses and fast switching This investigation has been performed in order to speeds have contributed to the vast growth in establish the validity of this assumption, since it is application since their introduction, when they were believed that there may be a number of perhaps basically a solid-state replacement for mercury-arc separate sources of noise in thyristor circuits. -
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). -
Partch 43 Tone Scale © Copyright Juhan Puhm 2016 Puhm Juhan Copyright © Scale Tone 43 Partch N Our Door with Our Common Scales
! "#$!%&'()#! *+!",-$!.)&/$! ! ! ! 01#&-!%1#2 !!! "#$!%&'()#!*+!",-$!.)&/$"#$!%&'()#!*+!",-$!.)&/$!!!! One can only imagine the years Harry Partch spent formulating his 43 tone scale and then the lifetime spent realizing it. A pinnacle of Just Intonation, a fair bit of time can be spent unraveling the intricacies of the 43 tone scale and coming to terms with the choices Partch made. What are some of the features of this scale? For starters the scale is a pure Just Intonation scale, no tempering of any intervals whatsoever. All pitches are given exact ratios and so all intervals are exact as well. For the most part all the music we listen to is constructed of up to 5 limit ratios. Partch expanded our common tonality to include 7 and 11 limit ratios. It can be argued that 2, 3 and 5 limit ratios are the language of harmony and any higher limit ratios are not harmonic in the least bit, regardless of what people would like to pretend. Possibly some 7 limit ratios can be said to push the bounds of what can be considered harmonic. Since our current 12 note scale and instruments do not even remotely support or approximate any 7 or 11 limit ratios, 7 and 11 limit ratios are completely outside the realm of our listening and composing experience. The equal tempered tritone and minor seventh intervals do not approximate 7 limit ratios. It would be incorrect to think of the minor seventh approximating the 7 limit ratio of 7/4, which is almost one-third of a semitone lower (969 cents). Our tempered minor seventh (1000 cents) is firmly in the realm of two perfect fourths (4/3 * 4/3 = 16/9, (996 cents)) or further removed, a minor third above the dominant (3/2 * 6/5 = 9/5 (1018 cents)). -
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INFORMATION TO USERS This manuscript has been reproduced from the microfihn master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI University Microfilms International A Bell & Howell Information Company 3 0 0 North Z eeb Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9401386 Enharmonicism in theory and practice in 18 th-century music Telesco, Paula Jean, Ph.D. The Ohio State University, 1993 Copyright ©1993 by Telesco, Paula Jean. -
Generalized Tonnetze and Zeitnetz, and the Topology of Music Concepts
June 25, 2019 Journal of Mathematics and Music tonnetzTopologyRev Submitted exclusively to the Journal of Mathematics and Music Last compiled on June 25, 2019 Generalized Tonnetze and Zeitnetz, and the Topology of Music Concepts Jason Yust∗ School of Music, Boston University () The music-theoretic idea of a Tonnetz can be generalized at different levels: as a network of chords relating by maximal intersection, a simplicial complex in which vertices represent notes and simplices represent chords, and as a triangulation of a manifold or other geomet- rical space. The geometrical construct is of particular interest, in that allows us to represent inherently topological aspects to important musical concepts. Two kinds of music-theoretical geometry have been proposed that can house Tonnetze: geometrical duals of voice-leading spaces, and Fourier phase spaces. Fourier phase spaces are particularly appropriate for Ton- netze in that their objects are pitch-class distributions (real-valued weightings of the twelve pitch classes) and proximity in these space relates to shared pitch-class content. They admit of a particularly general method of constructing a geometrical Tonnetz that allows for interval and chord duplications in a toroidal geometry. The present article examines how these du- plications can relate to important musical concepts such as key or pitch-height, and details a method of removing such redundancies and the resulting changes to the homology the space. The method also transfers to the rhythmic domain, defining Zeitnetze for cyclic rhythms. A number of possible Tonnetze are illustrated: on triads, seventh chords, ninth-chords, scalar tetrachords, scales, etc., as well as Zeitnetze on a common types of cyclic rhythms or time- lines.