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MTO 10.1: Wibberley, Syntonic Tuning
Volume 10, Number 1, February 2004 Copyright © 2004 Society for Music Theory Roger Wibberley KEYWORDS: Aristoxenus, comma, Ganassi, Jachet, Josquin, Ptolemy, Rore, tetrachord, Vesper-Psalms, Willaert, Zarlino ABSTRACT: This Essay makes at the outset an important (if somewhat controversial) assumption. This is that Syntonic tuning (Just Intonation) is not—though often presumed to be so—primarily what might be termed “a performer’s art.” On the contrary it is a composer’s art. As with the work of any composer from any period, it is the performer’s duty to render the music according to the composer’s wishes as shown through the evidence. Such evidence may be indirect (perhaps documentary) or it may be explicitly structural (to be revealed through analysis). What will be clear is the fallacy of assuming that Just Intonation can (or should) be applied to any music rather than only to that which was specifically designed by the composer for the purpose. How one can deduce whether a particular composer did, or did not, have the sound world of Just Intonation (henceforward referred to as “JI”) in mind when composing will also be explored together with a supporting analytical rationale. Musical soundscape (especially where voices are concerned) means, of course, incalculably more than mere “accurate intonation of pitches” (which alone is the focus of this essay): its color derives not only from pitch combination, but more importantly from the interplay of vocal timbres. These arise from the diverse vowel sounds and consonants that give life, color and expression. The audio examples provided here are therefore to be regarded as “playbacks” and no claim is being implied or intended that they in any way stand up as “performances.” Some care, nonetheless, has been taken to make them as acceptable as is possible with computer-generated sounds. -
Construction and Verification of the Scale Detection Method for Traditional Japanese Music – a Method Based on Pitch Sequence of Musical Scales –
International Journal of Affective Engineering Vol.12 No.2 pp.309-315 (2013) Special Issue on KEER 2012 ORIGINAL ARTICLE Construction and Verification of the Scale Detection Method for Traditional Japanese Music – A Method Based on Pitch Sequence of Musical Scales – Akihiro KAWASE Department of Corpus Studies, National Institute for Japanese Language and Linguistics, 10-2 Midori-cho, Tachikawa City, Tokyo 190-8561, Japan Abstract: In this study, we propose a method for automatically detecting musical scales from Japanese musical pieces. A scale is a series of musical notes in ascending or descending order, which is an important element for describing the tonal system (Tonesystem) and capturing the characteristics of the music. The study of scale theory has a long history. Many scale theories for Japanese music have been designed up until this point. Out of these, we chose to formulate a scale detection method based on Seiichi Tokawa’s scale theories for traditional Japanese music, because Tokawa’s scale theories provide a versatile system that covers various conventional scale theories. Since Tokawa did not describe any of his scale detection procedures in detail, we started by analyzing his theories and understanding their characteristics. Based on the findings, we constructed the scale detection method and implemented it in the Java Runtime Environment. Specifically, we sampled 1,794 works from the Nihon Min-yo Taikan (Anthology of Japanese Folk Songs, 1944-1993), and performed the method. We compared the detection results with traditional research results in order to verify the detection method. If the various scales of Japanese music can be automatically detected, it will facilitate the work of specifying scales, which promotes the humanities analysis of Japanese music. -
The Order of Numbers in the Second Viennese School of Music
The order of numbers in the Second Viennese School of Music Carlota Sim˜oes Department of Mathematics University of Coimbra Portugal Mathematics and Music seem nowadays independent areas of knowledge. Nevertheless, strong connections exist between them since ancient times. Twentieth-century music is no exception, since in many aspects it admits an obvious mathematical formalization. In this article some twelve-tone music rules, as created by Schoenberg, are presented and translated into math- ematics. The representation obtained is used as a tool in the analysis of some compositions by Schoenberg, Berg, Webern (the Second Viennese School) and also by Milton Babbitt (a contemporary composer born in 1916). The Second Viennese School of Music The 12-tone music was condemned by the Nazis (and forbidden in the occupied Europe) because its author was a Jew; by the Stalinists for having a bourgeois cosmopolitan formalism; by the public for being different from everything else. Roland de Cand´e[2] Arnold Schoenberg (1874-1951) was born in Vienna, in a Jewish family. He lived several years in Vienna and in Berlin. In 1933, forced to leave the Academy of Arts of Berlin, he moved to Paris and short after to the United States. He lived in Los Angeles from 1934 until the end of his life. In 1923 Schoenberg presented the twelve-tone music together with a new composition method, also adopted by Alban Berg (1885-1935) and Anton Webern (1883-1945), his students since 1904. The three composers were so closely associated that they became known as the Second Viennese School of Music. -
Kostka, Stefan
TEN Classical Serialism INTRODUCTION When Schoenberg composed the first twelve-tone piece in the summer of 192 1, I the "Pre- lude" to what would eventually become his Suite, Op. 25 (1923), he carried to a conclusion the developments in chromaticism that had begun many decades earlier. The assault of chromaticism on the tonal system had led to the nonsystem of free atonality, and now Schoenberg had developed a "method [he insisted it was not a "system"] of composing with twelve tones that are related only with one another." Free atonality achieved some of its effect through the use of aggregates, as we have seen, and many atonal composers seemed to have been convinced that atonality could best be achieved through some sort of regular recycling of the twelve pitch class- es. But it was Schoenberg who came up with the idea of arranging the twelve pitch classes into a particular series, or row, th at would remain essentially constant through- out a composition. Various twelve-tone melodies that predate 1921 are often cited as precursors of Schoenberg's tone row, a famous example being the fugue theme from Richard Strauss's Thus Spake Zararhustra (1895). A less famous example, but one closer than Strauss's theme to Schoenberg'S method, is seen in Example IO-\. Notice that Ives holds off the last pitch class, C, for measures until its dramatic entrance in m. 68. Tn the music of Strauss and rves th e twelve-note theme is a curiosity, but in the mu sic of Schoenberg and his fo ll owers the twelve-note row is a basic shape that can be presented in four well-defined ways, thereby assuring a certain unity in the pitch domain of a composition. -
MTO 20.2: Wild, Vicentino's 31-Tone Compositional Theory
Volume 20, Number 2, June 2014 Copyright © 2014 Society for Music Theory Genus, Species and Mode in Vicentino’s 31-tone Compositional Theory Jonathan Wild NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.14.20.2/mto.14.20.2.wild.php KEYWORDS: Vicentino, enharmonicism, chromaticism, sixteenth century, tuning, genus, species, mode ABSTRACT: This article explores the pitch structures developed by Nicola Vicentino in his 1555 treatise L’Antica musica ridotta alla moderna prattica . I examine the rationale for his background gamut of 31 pitch classes, and document the relationships among his accounts of the genera, species, and modes, and between his and earlier accounts. Specially recorded and retuned audio examples illustrate some of the surviving enharmonic and chromatic musical passages. Received February 2014 Table of Contents Introduction [1] Tuning [4] The Archicembalo [8] Genus [10] Enharmonic division of the whole tone [13] Species [15] Mode [28] Composing in the genera [32] Conclusion [35] Introduction [1] In his treatise of 1555, L’Antica musica ridotta alla moderna prattica (henceforth L’Antica musica ), the theorist and composer Nicola Vicentino describes a tuning system comprising thirty-one tones to the octave, and presents several excerpts from compositions intended to be sung in that tuning. (1) The rich compositional theory he develops in the treatise, in concert with the few surviving musical passages, offers a tantalizing glimpse of an alternative pathway for musical development, one whose radically augmented pitch materials make possible a vast range of novel melodic gestures and harmonic successions. -
INVARIANCE PROPERTIES of SCHOENBERG's TONE ROW SYSTEM by James A. Fill and Alan J. Izenman Technical·Report No. 328 Department
INVARIANCE PROPERTIES OF SCHOENBERG'S TONE ROW SYSTEM by James A. Fill and Alan J. Izenman Technical·Report No. 328 Department of Applied Statistics School of Statistics University of Minnesota Saint Paul, MN 55108 October 1978 ~ 'It -: -·, ........ .t .. ,.. SUMMARY -~ This paper organizes in a ~ystematic manner the major features of a general theory of m-tone rows. A special case of this development is the twelve-tone row system of musical composition as introduced by Arnold Schoenberg and his Viennese school. The theory as outlined here applies to tone rows of arbitrary length, and can be applied to microtonal composition for electronic media. Key words: 12-tone rows, m-tone rows, inversion, retrograde, retrograde-inversion, transposition, set-complex, permutations. Short title: Schoenberg's Tone .Row System. , - , -.-· 1. Introduction. Musical composition in the twentieth century has been ~ enlivened by Arnold Schoenberg's introduction of a structured system which em phasizes.its serial and atonal nature. Schoenberg called his system "A Method of Composing with Twelve Tones which are Related Only with One Another" (12, p. 107]. Although Schoenberg himself regarded his work as the logical outgrowth of tendencies inherent in the development of Austro-German music during the previous one hundred years, it has been criticized as purely "abstract and mathematical cerebration" and a certain amount of controversy still surrounds the method. The fundamental building-block in Schoenberg's system is the twelve-tone !2!!, a specific linear ordering of all twelve notes--C, CU, D, Eb, E, F, FU, G, G#, A, Bb, and B--of the equally tempered chromatic scale, each note appearing once and only once within the row. -
Major and Minor Scales Half and Whole Steps
Dr. Barbara Murphy University of Tennessee School of Music MAJOR AND MINOR SCALES HALF AND WHOLE STEPS: half-step - two keys (and therefore notes/pitches) that are adjacent on the piano keyboard whole-step - two keys (and therefore notes/pitches) that have another key in between chromatic half-step -- a half step written as two of the same note with different accidentals (e.g., F-F#) diatonic half-step -- a half step that uses two different note names (e.g., F#-G) chromatic half step diatonic half step SCALES: A scale is a stepwise arrangement of notes/pitches contained within an octave. Major and minor scales contain seven notes or scale degrees. A scale degree is designated by an Arabic numeral with a cap (^) which indicate the position of the note within the scale. Each scale degree has a name and solfege syllable: SCALE DEGREE NAME SOLFEGE 1 tonic do 2 supertonic re 3 mediant mi 4 subdominant fa 5 dominant sol 6 submediant la 7 leading tone ti MAJOR SCALES: A major scale is a scale that has half steps (H) between scale degrees 3-4 and 7-8 and whole steps between all other pairs of notes. 1 2 3 4 5 6 7 8 W W H W W W H TETRACHORDS: A tetrachord is a group of four notes in a scale. There are two tetrachords in the major scale, each with the same order half- and whole-steps (W-W-H). Therefore, a tetrachord consisting of W-W-H can be the top tetrachord or the bottom tetrachord of a major scale. -
The Computational Attitude in Music Theory
The Computational Attitude in Music Theory Eamonn Bell Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2019 © 2019 Eamonn Bell All rights reserved ABSTRACT The Computational Attitude in Music Theory Eamonn Bell Music studies’s turn to computation during the twentieth century has engendered particular habits of thought about music, habits that remain in operation long after the music scholar has stepped away from the computer. The computational attitude is a way of thinking about music that is learned at the computer but can be applied away from it. It may be manifest in actual computer use, or in invocations of computationalism, a theory of mind whose influence on twentieth-century music theory is palpable. It may also be manifest in more informal discussions about music, which make liberal use of computational metaphors. In Chapter 1, I describe this attitude, the stakes for considering the computer as one of its instruments, and the kinds of historical sources and methodologies we might draw on to chart its ascendance. The remainder of this dissertation considers distinct and varied cases from the mid-twentieth century in which computers or computationalist musical ideas were used to pursue new musical objects, to quantify and classify musical scores as data, and to instantiate a generally music-structuralist mode of analysis. I present an account of the decades-long effort to prepare an exhaustive and accurate catalog of the all-interval twelve-tone series (Chapter 2). This problem was first posed in the 1920s but was not solved until 1959, when the composer Hanns Jelinek collaborated with the computer engineer Heinz Zemanek to jointly develop and run a computer program. -
Modern Art Music Terms
Modern Art Music Terms Aria: A lyrical type of singing with a steady beat, accompanied by orchestra; a songful monologue or duet in an opera or other dramatic vocal work. Atonality: In modern music, the absence (intentional avoidance) of a tonal center. Avant Garde: (French for "at the forefront") Modern music that is on the cutting edge of innovation.. Counterpoint: Combining two or more independent melodies to make an intricate polyphonic texture. Form: The musical design or shape of a movement or complete work. Expressionism: A style in modern painting and music that projects the inner fear or turmoil of the artist, using abrasive colors/sounds and distortions (begun in music by Schoenberg, Webern and Berg). Impressionism: A term borrowed from 19th-century French art (Claude Monet) to loosely describe early 20th- century French music that focuses on blurred atmosphere and suggestion. Debussy "Nuages" from Trois Nocturnes (1899) Indeterminacy: (also called "Chance Music") A generic term applied to any situation where the performer is given freedom from a composer's notational prescription (when some aspect of the piece is left to chance or the choices of the performer). Metric Modulation: A technique used by Elliott Carter and others to precisely change tempo by using a note value in the original tempo as a metrical time-pivot into the new tempo. Carter String Quartet No. 5 (1995) Minimalism: An avant garde compositional approach that reiterates and slowly transforms small musical motives to create expansive and mesmerizing works. Glass Glassworks (1982); other minimalist composers are Steve Reich and John Adams. Neo-Classicism: Modern music that uses Classic gestures or forms (such as Theme and Variation Form, Rondo Form, Sonata Form, etc.) but still has modern harmonies and instrumentation. -
An Examination of Jerry Goldsmith's
THE FORBIDDEN ZONE, ESCAPING EARTH AND TONALITY: AN EXAMINATION OF JERRY GOLDSMITH’S TWELVE-TONE SCORE FOR PLANET OF THE APES VINCENT GASSI A DISSERTATION SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN MUSIC YORK UNIVERSITY TORONTO, ONTARIO MAY 2019 © VINCENT GASSI, 2019 ii ABSTRACT Jerry GoldsMith’s twelve-tone score for Planet of the Apes (1968) stands apart in Hollywood’s long history of tonal scores. His extensive use of tone rows and permutations throughout the entire score helped to create the diegetic world so integral to the success of the filM. GoldsMith’s formative years prior to 1967–his training and day to day experience of writing Music for draMatic situations—were critical factors in preparing hiM to meet this challenge. A review of the research on music and eMotion, together with an analysis of GoldsMith’s methods, shows how, in 1967, he was able to create an expressive twelve-tone score which supported the narrative of the filM. The score for Planet of the Apes Marks a pivotal moment in an industry with a long-standing bias toward modernist music. iii For Mary and Bruno Gassi. The gift of music you passed on was a game-changer. iv ACKNOWLEDGEMENTS Heartfelt thanks and much love go to my aMazing wife Alison and our awesome children, Daniela, Vince Jr., and Shira, without whose unending patience and encourageMent I could do nothing. I aM ever grateful to my brother Carmen Gassi, not only for introducing me to the music of Jerry GoldsMith, but also for our ongoing conversations over the years about filM music, composers, and composition in general; I’ve learned so much. -
Specifying Spectra for Musical Scales William A
Specifying spectra for musical scales William A. Setharesa) Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706-1691 ~Received 5 July 1996; accepted for publication 3 June 1997! The sensory consonance and dissonance of musical intervals is dependent on the spectrum of the tones. The dissonance curve gives a measure of this perception over a range of intervals, and a musical scale is said to be related to a sound with a given spectrum if minima of the dissonance curve occur at the scale steps. While it is straightforward to calculate the dissonance curve for a given sound, it is not obvious how to find related spectra for a given scale. This paper introduces a ‘‘symbolic method’’ for constructing related spectra that is applicable to scales built from a small number of successive intervals. The method is applied to specify related spectra for several different tetrachordal scales, including the well-known Pythagorean scale. Mathematical properties of the symbolic system are investigated, and the strengths and weaknesses of the approach are discussed. © 1997 Acoustical Society of America. @S0001-4966~97!05509-4# PACS numbers: 43.75.Bc, 43.75.Cd @WJS# INTRODUCTION turn closely related to Helmholtz’8 ‘‘beat theory’’ of disso- nance in which the beating between higher harmonics causes The motion from consonance to dissonance and back a roughness that is perceived as dissonance. again is a standard feature of most Western music, and sev- Nonharmonic sounds can have dissonance curves that eral attempts have been made to explain, define, and quantify differ dramatically from Fig. -
Theory IV – Study Guide Dr. Amy Dunker Clarke College Dubuque, IA 52001 Classical Serialism Arnold Schoenb
Theory IV – Study Guide Dr. Amy Dunker Clarke College Dubuque, IA 52001 www.amydunker.com Classical Serialism Arnold Schoenberg composed the first twelve-tone piece in the summer of 1921 (Suite, Op. 25 (completed in 1923). Schoenberg had developed a method of composing with twelve tones that are related only with one another. He saw twelve-tone or serial composition as the natural extension of chromaticism on the tonal system. Anton Webern and Alban Berg: Schoenberg’s two pupils who composed in the twelve- tone method. Tone Row (also called , Row, Set, Basic Set, Series): an arrangement of the twelve pitches of the chromatic scale so that no notes repeat (except immediately after it is heard and trills/tremolos) until all pitches of the row have sounded in order. Dodecaphonic Scale: Twelve tone scale Four Forms of the Tone Row: Prime: The original set (do not confuse this with the terms use in Non-Serial Atonality) Retrograde: The original set in reverse order (i.e. backwards) Inversion: The mirror inversion of the original set Retrograde Inversion: The inversion in reverse order Abbreviations: P=Prime R=Retrograde I=Inversion RI=Retrograde Inversion *In addition, each of the four basic forms has twelve transpositions Order Numbers: numbers assigned to the row which indicate each notes intervallic distance from the first note of the row. The first note of the row is assigned the number zero (0). Twelve-Tone Matrix (“Magic Square”): a method of determining all 48 possible versions of the tone row. To construct a Twelve-Tone Matrix do the following: 1.) Fill in the Prime or Original row across the top ( from left to right) using the row’s order numbers.