George Perle Research Articles

Изучение и практика применения серийной техники в Китае

At the turn of the 1970s and the 1980s, after the cessation of the Cultural Revolution Chinese composers began intensive study of the 20th century European musical classics, including the compositions of the Second Viennese School, as well as the European and American postwar avant-garde, including serialism. The result of this was an adaptation of serial technique on the Chinese cultural soil, a synthesis of the method with national traditions – modal, timbral, metro-rhythmic, philosophical and aesthetical. Mastery of the technique took place in two mutually conditioned directions – the theoretical-methodological, connected with expounding the chief principles of Schoenberg’s compositional method, and the practical, which led to the creation of dodecaphonic works by Chinese composers. The first to demonstrate interest in the 20th century Western classics was Luo Zhongrong. As the result of his translations of musical texts, the theoretical works of Arnold Schoenberg and Paul Hindemith became well-known, the ideas of the American apologists of serialism, George Perle and Allen Forte, began to be disseminated. A major researcher of serial technique in China is musicologist Zheng Yinglie. From the late 1970s he developed original courses devoted to twelve-tone music for students and aspirants, and in 1989 he published his own tutorial materials as a monograph “Courses of Composition of Serial Music.” Special interest for Chinese musicians was aroused by the figure of Arnold Schoenberg. At the present time analysis of chosen works carried out by Chinese music scholars has firmly entered into tutorial material for students of higher musical educational institutions in the People’s Republic of China. The greater part of articles about Schoenberg written in China is devoted to his pedagogical, theoretical and conducting activities. In the domain of Chinese scholarship all of the crucial works by Schoenberg pertaining to different periods of his work have been examined. In recent years there have appeared articles elucidating the history of study of the legacy of Schoenberg in China. Keywords: Chinese serial technique, Arnold Schoenberg, Zheng Yinglie, Luo Zhongrong, Chinese musicology.

Aligned-Cycle Spaces

In this article I investigate aligned cycles. First identified by Alban Berg in a letter to Arnold Schoenberg and later discussed by George Perle and David Headlam, an aligned cycle is when two (or more) interval cycles unfold in the same direction in a note-against-note alignment, for instance, a rising whole-tone scale (an interval 2-cycle) simultaneously with a rising chromatic scale (an interval 1-cycle). This article extends beyond prior discussions of aligned cycles by exploring the different combinations and rotations of these cyclic structures and investigates how these permutations create different families of harmonies. In particular, this article focuses on three-voice aligned cycles. I show how the different combinations, alignments, and rotations of the individual voices of an aligned cycle create a unique collection of aligned-cycle classes and, at a more large-scale level, aligned-cycle families. To conclude, I reexamine a three-voice aligned cycle from the second movement of Berg's String Quartet, op. 3, and investigate cyclic progressions in Thomas Adès's Piano Quintet, Lieux retrouvés, and The Tempest.

In Defense of Theory and Analysis: A Critical Evaluation of the Discipline and Its Application to Bartók’s Musical Language

This paper defends an evaluation of Bartók’s music based on analytical procedures that use abstract theoretical concepts instead of, as advocate some scholars like László Somfai, restrict it to the scrutiny of compositional sketches and ethnomusicological influences. The analytical contributions of Roy Travis, Malcolm Gillies, Erno Lendvai, János Kárpáti, Colin Mason, Allen Forte and Richard Cohn, among others, are evaluated in order to introduce an original model that proposes a nontraditional tonal system based on the interval cycles and inversional symmetry, following some of George Perle’s propositions.

Narratives of Identity in Alban Berg’s Lulu by Silvio J. dos Santos

Reviewed by: Narratives of Identity in Alban Berg’s Lulu by Silvio J. dos Santos Lyle Barkhymer Silvio J. dos Santos, Narratives of Identity in Alban Berg’s Lulu. Rochester: U of Rochester P, 2014. 226 pp. This fascinating and excellent study is an important addition to the field of Alban Berg scholarship. It might be pointed out, in no way negatively, that the reader interested generally in the culture surrounding the music of the “Second Vienna School” or the knowledgeable amateur opera lover will encounter some frustration approaching this book. Dos Santos’s target audience is a professional one; it is a book written by a musicologist for musicologists, or at the least not only for those with a serious background and knowledge in [End Page 97] the music of Wagner and Berg but also for those who can read musical notation and scores. The reader who understands the process of using all twelve chromatic tones equally and serially, usually referred to as dodecaphonic or serial music, will get the most from this book. It is written above all for those who know the theory, practice, and nomenclature of music composed by Schoenberg, Webern, and Berg. The central concept explored in dos Santos’s book is that there is a conflict in Berg’s art between his forward-looking aesthetic and his backward-looking impulse to compose in the traditions of the past, and that the music of Wagner is the source of this conflict. Berg’s opera Lulu, composed 1928–1935, is the material of the study, chosen because of its place of maturity in Berg’s opus, and because, in dos Santos’s view, it represents a return to Berg’s developmental years in fin-de-siècle Vienna. The author uses the idea of narrative identity as a way to increase understanding of Berg and his work both from Berg’s writing, sketches, and composition and also in the sense of a more comprehensive concept of identity. He warns the reader at the outset that narrative identity is a complex idea and that there is little agreement among scholars about it. The book is divided into five chapters grouped into two sections. The first three chapters, Part I, address narratives of the composer as one who made an identity as a modernist and strove at the same time to continue musical tradition. The influence of Wagner on Berg and the role of that influence on his growing separation from his teacher and mentor, Schoenberg, are explored in chapter 1. By using good evidence, the author succeeds in his attempt to provide a nuanced view of this crisis in Berg’s development. Chapter 2 looks at the affair between Berg and Hannah Fuchs and draws a parallel with the liaison between Wagner and Mathilde Wesendonck. To the proposal that Berg drew heavily on the Wagnerian concept of Erlösung durch Liebe, the author brings convincing arguments. Might it be going too far to say that Berg actually “modeled” his affair after Wagner’s? That speculation opens a possibility, but seems less substantial. In any case, building on George Perle’s identification of structures on “H” (German “B-natural”) and “F-natural” as “Hanna Fuchs,” in Berg compositions, the author makes a strong case for the importance of Hannah Fuchs to Berg to the end of his life and in the opera Lulu. Berg’s use of Wagner’s “Tristan Chord” and love motif in Lulu form the core of chapter 3. The author brings into play theories about three stages of [End Page 98] love from a book widely read in Berg’s time, Die Drei Stufen der Erotik by Viennese philosopher and poet Emil Lucka. Part Two of dos Santos’s work, “Personal and Cultural Identities,” begins in chapter 4 with a fascinating and highly original analysis of the methods and motifs that Berg uses to represent Lulu’s portrait in the opera. He forcefully points out the importance of the portrait as an illustration of Lulu’s character at turning points in the opera. In this effort Berg’s concept sketches found in the Austrian National Library play an important role. Chapter 5, “Marriage as...

George Perle - GEORGE PERLE: String Quartet No. 2; String Quartet No. 5; Windows of Order (String Quartet No. 8); Molto Adagio. Daedalus Quartet. Bridge 9398.

George Perle - GEORGE PERLE: String Quartet No. 2; String Quartet No. 5; <i>Windows of Order</i> (String Quartet No. 8); <i>Molto Adagio</i>. Daedalus Quartet. Bridge 9398.

George Perle’s Twelve–Tone Tonality: Some Developments for CAC using PWGL

This paper presents a description and some developments on Perle’s theory and compositional system known as Twelve-Tone Tonality, a system that, because of its characteristics and fundamentals, is currently associated with Schoenberg dodecaphonic system. Some research has been made in the last few decades in order to develop his model in a Computer Assisted Composition (CAC) environment. After some efforts in order to analyse these prototypes, we realize that in general they were discontinued or outdated. A three-scope proposal is so outlined: Firstly, to simplify the grasp of a system that presents an easily understandable starting premise but afterwards enters a world of unending lists and arrays of letters and numbers; Secondly, to present the implementation process already started using PWGL [1] (see Laurson, 1996; Laurson, 2003; Laurson, 2009). Finally, the model is applied in a short original compositional work, and it is presented and analysed emphasizing the standpoints properties of the system. Some further considerations were made regarding the continuity of this project where the construction of a dedicated PWGL library of Perle’s model reveals a pre-compositional necessary tool. PWGL software was selected due to its specific fitting features: it is based on Common Lisp - perfectly powerful and suitable to process lists of integers — and it is specialized in CAC.

Aligned Cycles in Thomas Adès's Piano Quintet

AbstractIn this article I investigate aligned cycles in Thomas Adès's Piano Quintet, Op. 20. First identified by Berg in a letter to Schoenberg and later discussed by George Perle and Dave Headlam, an aligned cycle is the result of two or more interval cycles unfolding in the same direction in a note‐against‐note alignment – for example, a rising whole‐tone scale (an interval‐2 cycle) simultaneously with a rising chromatic scale (an interval‐1 cycle). I begin by exploring in more detail the theoretical properties of three‐voice aligned cycles and use concentric circles to show how these cyclic structures generate a closed, tight‐knit family of harmonies. I then reveal how Adès uses aligned cycles to provide harmonic, melodic and motivic material throughout his Quintet. These cyclic structures are combined not only with other kinds of cycles (one‐, two‐ and five‐voice, and multi‐aggregate) but also with the non‐cyclic material in the piece. Finally, I discuss how all the transformations of the different cycles function within the large‐scale formal design of the piece.

Review of Patricia Hall,Berg’s “Wozzeck”(Oxford University Press, 2011)

[1] The release of Patricia Hall's sketch-based study of composer Alban Berg's first opera Wozzeck, fifteen years after her earlier parallel study of Berg's second opera Lulu (Hall 1996, awarded the ASCAP Deems Taylor Award), is a seminal event in Berg scholarship. I have previously defined three stages in Berg research (Headlam 1993). The first encompasses writings of Berg himself and his circle of students and correspondents, notably Willi Reich and Theodor W. Adorno. The second stage begins with the writings of Hans Redlich in the 1950s and extends through seminal studies of individual works and overviews of Berg's oeuvre by writers such as George Perle, Mark DeVoto, and Douglas Jarman in the 1970s and 80s. This stage also includes the onset of comprehensive studies of sketches and other materials, and the revelations of the secret programs in Berg's music. The third stage is a continuation and expansion of the directions in the second; it includes my own book (Headlam 1996), Hall's Lulu book (Hall 1996), exegeses of further secret programs in the Chamber Concerto, Violin Concerto and other works, and a number of collected and individual volumes on Berg's music.(1) Hall's present book and the passing of George Perle (January 2009) may turn out to mark the completion of this third stage. In this review, I will consider Hall's book in this context and try to frame some questions that might set the stage for the next generation, which should properly provide a complete biography of Berg as well as new directions for analysis.[2] In her Wozzeck study, Patricia Hall deploys the exemplary sketch and analytical techniques evident in her earlier book. Hall is the undisputed English-language expert on the Berg sketch and biographical material, and this welcome second volume offers the same high level of scholarship and insight into the working methods of this fascinating composer familiar from the first study on Lulu. Readers will come away impressed by the detailed analytical nature of Berg's compositional method, and by the thorough and self-conscious way in which he approached musical and related dramatic questions. Berg was a careful analyst of his own and others' music, and the notes and letters surrounding his first opera confirm that he was sensitive to subtle dramatic and formal points and all aspects of musical and text combinations; his notations characterizing the psychological aspects of Schoenberg's orchestration in Erwartung provide further evidence of this propensity (see pages 103-7). Berg's analytical and communicative abilities are exemplified in the famous lecture presented before some performances of Wozzeck in the 1920s, as well as in several analytical letters to Schoenberg.[3] As in her earlier book, Hall expertly takes us through not only the immediate sketches, but also through other surrounding sketch and biographical material to support her narrative. Hall's assessment allows us to extrapolate a provocative parallel with Lulu. As early as 1985 Hall pointed out a two-part compositional structure for Lulu: measures 85-528 in Act I are, with a few exceptions, based on the original sketch material (1927), and the Prologue (written last) and remaining sections of the opera follow from correspondence between Berg and Willi Reich and the composition of Der Wein (1929). This in turn leads to an expanded set of materials derived from the row, most notably the order position cycles creating most of the character rows of the opera (Hall 1985). We can detect an analogous two-part compositional process for Wozzeck, based on the increased use of permutational alignments of intervals cycles (described by Berg in a letter to Schoenberg of 1920) and his general implementation of serial ordering, but in a more comprehensive fashion than before (110, identified in sketches from 1919). The notable increase in these algorithmic procedures-some foreshadowing the coming twelve-tone techniques-suggests an analogous bifurcation in the composition of Wozzeck, which Hall divides into three phases: 1914-18, 1919-22, and 1923-25 (the latter more concerned with arranging and preparing for the premiere in 1925). …

Interviewer's Reflections

RACHEL S. VANDAGRIFF IKE MOST of the people I interviewed for this project, I first came across Perspectives of New Music as an undergraduate student. I read a few PNM articles during those years when they were assigned to me, but I now do not recall which ones, nor which professors led me to them. I became acquainted with a number of the “classic” texts from the early years of PNM through work I did in graduate school. But a deeper relationship to the journal began when I commenced primary source research for my dissertation, provisionally titled “The History and Impact of the Fromm Music Foundation, 1952–1983.” Persuaded in part by Milton Babbitt, Paul Fromm pledged support for the journal in 1961, believing the venture would help fulfill his Foundation ’s goal to further communication among composers, performers, theorists, and listeners. Fromm, who had promised to “remain in the background,” did often involve himself in the journal’s operations. Yet as Ben and others I interviewed for this project discuss, Ben had the idea for Perspectives of New Music long before he met Paul Fromm. L Rachel S. Vandagriff 245 Fromm wanted to popularize contemporary American music. His definition of what kind of contemporary music he wanted his Foundation to promote was informed by his German background. He wanted to support what he took to be new music of the highest quality and prestige . The American compositional practices that he championed early were those most clearly related to and informed by the contemporary music to which he was first attracted: that of the Second Viennese School. Later, his desire for public recognition, together with shifting trends in contemporary music, led him to abandon his loyalty to the American composers in the Schoenberg tradition in favor of composers such as Earle Brown, John Adams, Steve Reich, Alvin Lucier, James Tenney, Morton Subotnik, Lee Hyla, Steve Mackey, Bernard Rands, David Finko, Barbara Kolb, Stephen Paulus, Sheila Silver, and Ramon Zupko, and to support compositional approaches that became more prominent during the 1970s. Ironically, when the Fromm Music Foundation, Princeton University Press, and Perspectives parted ways in 1972, those involved with the journal felt more free to expand their horizons, too. The Fromm Music Foundation supported the first ten years of the journal’s operation during which PNM published seminal articles by Milton Babbitt, Arthur Berger, Ben Boretz, Herbert Brün, Ernst Krenek, Lukas Foss, Billy Jim Layton, J. K. Randall, Seymour Shifrin, Claudio Spies, and Peter Westergaard; debates between David Lewin and Edward T. Cone, between Babbitt, David Lewin, and George Perle, and between Charles Rosen and Joseph Kerman, among others; and the “Some Younger American Composers” series. Many of these early articles continue to evoke discussions and disagreements, particularly about the practicality or perceptibility of novel compositional systems. As someone studying PNM in relation to its founder (and in the larger context of American private foundational patronage), I was struck by the fact that some of the aspects of the journal Fromm resisted in its earliest years are still controversial. He did not think it was appropriate for composers to write about their own music: he thought that was merely “self-promotion.” Fromm opposed what he saw as the narrowness of the journal’s scope and the high degree of “science in music.” He opposed PNM becoming a “scholarly journal” in which many articles would be inaccessible to someone unacquainted with a highly technical branch of American music theory. Fromm was uneasy about specialization, a tendency that he felt ran counter to the goals of his Foundation. In the interviews that I conducted, many of the people involved in PNM noted that the journal has long been a space hospitable to all kinds of musical practitioners: composers, theorists, performers, and critics. 246 History of Perspectives (In fact, it very much began as a vehicle for the writing of composertheorists .) At the same time, PNM has sometimes been viewed from the outside as a closed shop. On this matter the interviewees will express their varying opinions. The letters I found in the Fromm Music Foundation archive provided a great deal of information about the beginnings of the journal, but the story...

I&lt;span class="small-caps"&gt;nterview&lt;/span&gt;

ELEANOR CORY ELEANOR CORY: This is a lovely occasion. Many names are coming to mind as I have been thinking about Perspectives. I wish we could all see each other. RACHEL VANDAGRIFF: Yes, I can imagine. It has been fun and interesting talking to everyone, and then corresponding about our conversations afterward. So many people keep thinking of things; people or articles pop into their minds after our conversations. . . . It has also been nice to hear that the actual conversing about PNM has brought out new thoughts and ideas about the journal for some people. CORY: I have been jotting down people and ideas that I had not thought about in a long time. VANDAGRIFF: Would you be willing to share with me when and how you first encountered Perspectives of New Music? 148 History of Perspectives CORY: Sure. It started in graduate school in the early 70s. I was in the Columbia DMA program where Charles Wuorinen was my composition teacher, and Ben Boretz was one of my teachers for theory and analysis. Both were writing articles in Perspectives. My fellow students and I looked forward to new issues of Perspectives which connected with what we were learning in class. I felt like we were part of a very serious conversation about music. At New England Conservatory I had studied Schenker analysis with Ernst Oster, Schoenberg String Quartets with Rudolf Kolisch, and taken an in-depth course on Stravinsky taught by John Heiss, all of which had made me very excited about analyzing music. I read Perspectives articles, went to class, and studied scores. I was interested in how music theory was elucidating atonal music, and how that process was changing a larger musical climate. The work was completely new to me and very interesting. Perspectives was also very important for my own music. As I searched for a compositional language, I began to write some articles. In Perspectives I wrote an analysis of a Martin Boykan String Quartet. There were two views of the piece; the other was by John Harbison (Harbison and Cory 1973). In the Musical Quarterly I wrote analyses of string quartets by Martin Boykan and Elaine Barkin and a record review of solo piano music including pieces by Wuorinen, Wolpe, Wyner, Perle, Moss, and others (These articles appeared respectively in vol. 61, no.2 (1975) and vol. 62, no.4 (1976)). I also wrote a book review of George Perle’s Twelve-Tone Tonality in Theory and Practice (vol. 4, no. 1 (1979): 30–36). The common motivation was my fascination with compositional processes. I also assumed I was going to graduate and get a teaching job. Articles were part of what composers were ‘supposed to do’ in order to get and keep jobs. They also helped me think through ideas for my own music. I went to Music Theory conferences and became part of the academic music world. VANDAGRIFF: It sounds like something happened next, or you ended up not staying a part of that world. . . . CORY: Yes, it was interesting. Perspectives went in other directions, and I went in other directions. One of the directions I went was totally personal: I got married (to another composer, Joel Gressel) and eventually had two children. After teaching full-time at Baruch College, CUNY, and Yale (a non-tenure track) for ten years, I taught part-time at Manhattan School of Music, Sarah Lawrence, Hofstra, Brooklyn College , and the New School (not all at the same time). I didn’t have time to do anything but write music, teach, and raise my children. VANDAGRIFF: And you probably did not have time to do all of that! Eleanor Cory 149 CORY: Yes, and I did not have time to do all of that! That was sort of a startling chapter in my life, actually. . . . I did not read or write articles. Also, at around that time, it seemed to me, Perspectives was going in a more experimental direction, and I did not subscribe after a while. Sometimes I would see individual articles. Later there was Open Space. I read some of the articles and listened to the CDs while following the scores, some of which were...

Interview

ELEANOR CORY ELEANOR CORY: This is a lovely occasion. Many names are coming to mind as I have been thinking about Perspectives. I wish we could all see each other. RACHEL VANDAGRIFF: Yes, I can imagine. It has been fun and interesting talking to everyone, and then corresponding about our conversations afterward. So many people keep thinking of things; people or articles pop into their minds after our conversations. . . . It has also been nice to hear that the actual conversing about PNM has brought out new thoughts and ideas about the journal for some people. CORY: I have been jotting down people and ideas that I had not thought about in a long time. VANDAGRIFF: Would you be willing to share with me when and how you first encountered Perspectives of New Music? 148 History of Perspectives CORY: Sure. It started in graduate school in the early 70s. I was in the Columbia DMA program where Charles Wuorinen was my composition teacher, and Ben Boretz was one of my teachers for theory and analysis. Both were writing articles in Perspectives. My fellow students and I looked forward to new issues of Perspectives which connected with what we were learning in class. I felt like we were part of a very serious conversation about music. At New England Conservatory I had studied Schenker analysis with Ernst Oster, Schoenberg String Quartets with Rudolf Kolisch, and taken an in-depth course on Stravinsky taught by John Heiss, all of which had made me very excited about analyzing music. I read Perspectives articles, went to class, and studied scores. I was interested in how music theory was elucidating atonal music, and how that process was changing a larger musical climate. The work was completely new to me and very interesting. Perspectives was also very important for my own music. As I searched for a compositional language, I began to write some articles. In Perspectives I wrote an analysis of a Martin Boykan String Quartet. There were two views of the piece; the other was by John Harbison (Harbison and Cory 1973). In the Musical Quarterly I wrote analyses of string quartets by Martin Boykan and Elaine Barkin and a record review of solo piano music including pieces by Wuorinen, Wolpe, Wyner, Perle, Moss, and others (These articles appeared respectively in vol. 61, no.2 (1975) and vol. 62, no.4 (1976)). I also wrote a book review of George Perle’s Twelve-Tone Tonality in Theory and Practice (vol. 4, no. 1 (1979): 30–36). The common motivation was my fascination with compositional processes. I also assumed I was going to graduate and get a teaching job. Articles were part of what composers were ‘supposed to do’ in order to get and keep jobs. They also helped me think through ideas for my own music. I went to Music Theory conferences and became part of the academic music world. VANDAGRIFF: It sounds like something happened next, or you ended up not staying a part of that world. . . . CORY: Yes, it was interesting. Perspectives went in other directions, and I went in other directions. One of the directions I went was totally personal: I got married (to another composer, Joel Gressel) and eventually had two children. After teaching full-time at Baruch College, CUNY, and Yale (a non-tenure track) for ten years, I taught part-time at Manhattan School of Music, Sarah Lawrence, Hofstra, Brooklyn College , and the New School (not all at the same time). I didn’t have time to do anything but write music, teach, and raise my children. VANDAGRIFF: And you probably did not have time to do all of that! Eleanor Cory 149 CORY: Yes, and I did not have time to do all of that! That was sort of a startling chapter in my life, actually. . . . I did not read or write articles. Also, at around that time, it seemed to me, Perspectives was going in a more experimental direction, and I did not subscribe after a while. Sometimes I would see individual articles. Later there was Open Space. I read some of the articles and listened to the CDs while following the scores, some of which were...

More MOF and Mallalieu-related Rows

More MOF and Mallalieu related rows Caleb Morgan and Michael Davis IN POLYPHONIC MUSIC, SEPARATE MELODIC STRANDS combine to form a meaningful whole. No matter what the style, the combina tion is controlled and deliberate. In the history of 12-tone music, there have been many efforts to control the "harmonies" created by multiple rows sounding at once. How to create amusic inwhich vertical combi nations relate to the original series in some way?so that the harmonies are made from the same cloth as the lines?seems to be an enduring problem. Multiple-order-function series (MOF rows) are one solution to thisproblem. They also have a number of other uses. As we will see, themost impressiveMOF row is theMallalieu series. Because it is unique?to within multiplicative transforms?we are motivated to find other series that have a good deal of theMallalieu row's MOF properties. By approaching the generation of MOF rows from several angles, we can produce a number of different lists of series ?large and varied enough to satisfydifferent composer's sensibilities. MOF and Mallalieu-Related Rows 101 We extend previous work of music theorists such as Babbitt, Morris, and others in fiveways: 1) a handy algorithm for generating MOF rows; 2) a list of 73+ "limited-interval" series for use in creation and expansion of series; 3) software which performs brute-force generate and -test techniques to findMOF rows; 4) a "ranking" technique for generating "fuzzy" MOF rows from the discrete logarithms of power residue series; 5) another simple technique for deriving MOF rows from any power-residue series. Starting with the Mallalieu series?named after its discoverer, Pohlman Mallalieu?we will examine various MOF rows and their methods for generation. (We will also consider some self-similar pitch class sequences that are not 12-tone rows.) Definitions ofMOF row A succinct definition seems difficult.Morris does not produce a defini tion per se, but he implies that a MOF row X has a certain series of successive contiguous segments that are found in another transformation of the row, FX, such that each segment fromX occurs in either forward or retrograde order and the segments are merged contiguously or non contiguously in FX. Philip Batstone attempts no definition, but gives a technique for generating MOF rows. Andrew Mead has this to say about theMallalieu row: The row has the property that when it is divided into chains of equally spaced order numbers and the resulting partition isproperly concatenated, the ordered aggregate so produced is itself some transposition of the row.1 In an article by Brian Alegant, we find thisdefinition of the properties of theMallalieu row: ". . .the cyclic-interval patterns of this row generate its own transpositions."2 George Perle, in a mention of the series of Schoenberg's Quintet for Wind Instruments, Op. 26?a very early 12 tone composition perhaps employing the first MOF row?says "(it) is based upon a set that is cyclically permuted to produce an approximate transposition of the theme originally derived from the set."3 Our defini tion here is slightly broader and more pragmatic. For our purposes, a MOF row is any 12-tone series containing embedded sequences of pcs? especially sequences formed by skipping some pcs?which clearly resem ble another related series (usually in the same row-class). The 102 PerspectivesofNew Music resemblance can be imprecise and may involve sequences or motifs that are shorter than twelve notes. We are concerned with two kinds ofMOF rows: 1) Exact sequences of pcs that are found multiple times in the other related rows in the row-class with variable or irregular patterns of intervening pcs. 2) Inexact sequences of pcs (altered by small intervals) that are found multiple times in other related rows in the row-class with regular patterns of intervening pcs (or permutation). The self-similar patterns desired involve either imperfect resemblances or irregular patterns of permutation, but not both at once. Both kinds of pattern may be found in the same series, however, in different parts of the series. Both kinds of self-similarity at once is beyond the scope of thispaper. Illustration ofMOF concept with Mallalieu matrix The basic concept isperhaps more...

The Efficacy of K-Nets in Perlean Theory

[1] This response addresses two topics in Michael Buchler's article "Reconsidering Klumpenhouwer Networks," namely relational abundance and the issue of hierarchy and recursion. In the abstract preceding his essay Buchler states that "K-nets also enable us to relate sets and networks that are neither transpositionally nor inversionally equivalent, but this is another double-edged sword: as nice as it is to associate similar sets that are not simple canonical transforms of one another, the manner in which K-nets accomplish this arguably lifts the lid off a Pandora's Box of relational permissiveness." I will confine my remarks to K-nets and their applicability to George Perle's compositional theory of twelve-tone tonality. In so doing, I hope to demonstrate that not only are K-nets "nice" to use in associating similar sets, they are highly efficient tools in a Perlean context.K-nets and Cyclic Sets[2] In order to establish the efficacy of K-nets in Perlean theory, we must first define cyclic sets, arrays, and axis-dyad chords. A cyclic set combines two inversionally related interval cycles, such as interval 7 and interval 5. When the members of the two cycles are placed in alternation, every pair of alternating pcs shows a consistent difference, representing the formative interval cycle. In Figure 1 the pcs in open noteheads show the cyclic interval 7, and the alternating pcs in closed noteheads show the inversionally related cycle 5.Figure 1. Cyclic set 2,9 generated by alternating inversionally related interval cycles 7 and 5Additionally, every pair of adjacent pcs forms a sum. Three adjacent pcs form two so-called tonic sums, which repeat throughout the cyclic set. In Figure 1 the three bracketed pcs 0-2-7 yield the tonic sums 2 and 9, which repeat with every trichordal segment. The second bracketed pcs 9-5-4 also sum to 2 and 9. The recurring pair of tonic sums provides the cyclic set its name; the cyclic set in Figure 1 is thus identified as 2,9. Finally, the difference between the tonic sums provides the underlying interval cycle (9-2=7).[3] The trichordal segments in Figure 1 belong to two different set classes, 3-9 (027) and 3-4 (015). As such, they are neither transpositionally nor inversionally equivalent. Yet a declaration of non-equivalence seems counterintuitive, since both sets derive from the same symmetrical cyclic set and thus share the same internal structure. The K-nets in Figure 2a clearly display this relationship. These networks are strongly isographic; that is, they have identical arrow configurations and associated T and I transformations. Moreover, all trichords in the 2,9 cyclic set are strongly isographic since they arise from the same source, the 2,9 cyclic set. Any three adjacent pcs from this set can be fitted into the nodes of the more abstract K-graph in Figure 2b. This K-graph efficiently displays the recursion inherent in the 2,9 cyclic set.Figure 2a. Strongly isographic K-nets of trichordal segments of cyclic set 2,9Figure 2b. K-graph of any trichordal segment of cyclic set 2,9[4] A different alignment of the ascending and descending interval 7 cycles from Figure 1 produces a new pair of repeating tonic sums, as shown in the 0,7 cyclic set of Figure 3.Figure 3. Cyclic set 0,7 generated by rotating cyclic set 2,9Although all trichordal segments within this cyclic set will be strongly isographic, they will not share this relationship with trichordal segments from the 2,9 cyclic set of Figure 1. Instead, the bracketed segments drawn from the two cyclic sets are positively isographic; that is, they share identical T-values between corresponding nodes but a consistent difference between their I-values, as shown in Figure 4. In these two K-graphs the identical T-values represent the interval 7 cycle underlying both cyclic sets, while the difference of ten (t) in both of their corresponding I-values represents the difference between the tonic sums in the two cyclic sets. …

Computer-Assisted Analysis of Music in George Perle's System of Twelve-Tone Tonality

53 Music theorists face many challenges when analyzing music written according to George Perle’s compositional theory of twelve-tone tonality, a system based on inversional symmetry. Analysts focusing on Mr. Perle’s music seek relationships among collections of notes in an effort to discover connections within and across a specific work. It is often possible to rely solely on the analytical tools of twelve-tone tonality when working with Mr. Perle’s music, but in many instances other tools have proven rather useful, such as can be found in pitchclass set theory and transformational theory. The interested reader may refer to a number of excellent resources to acquire a working knowledge of these theories (Forte 1973; Rahn 1980; Lewin 1987; Straus 2005). However, in some cases even these theories do not assist the analyst in generating meaningful results from the pitch material in a twelve-tone tonal composition. Because Mr. Perle’s music is non-tonal, it lends itself particularly well to computer-assisted mathematical anlysis. We have developed a simple computer application, Twelve-Tone Tonality Reverse Engineer, or T3RevEng, that helps determine the organization and context of the material, based on the input of pitch classes expressed as integers. In all tests thus far, T3RevEng has proven to be an essential tool for the Perlean analyst owing to its comprehensive, efficient, and accurate manipulation of data.

Isographies and Some Klumpenhouwer Networks They Involve

This study explores musical and methodological aspects of isographic Klumpenhouwer networks. It gives particular attention to strong isographies and their connections to set-class formation and relevance for music of Schoenberg and Webern. The paper also suggests ways in which positive and negative isographies can be considered, and some affinities between this methodology and George Perle's compositional system.

Thoughts on Klumpenhouwer Networks and Perle-Lansky Cycles

As strongly suggested by George Perle, every Klumpenhouwer network (K-net) can indeed (essentially) be embedded in a “Perle-Lansky Cycle” (or, simply, “Lansky Cycle”), a generalization of the Perle cycles basic to Perle's theories of Twelve-Tone Tonality. This enables the K-nets to be transformed by certain spatial operations idiomatic to the nature of Perle's cycles. On the other hand, PL-cycles can be themselves regarded as certain species of K-nets, and that enables their graphs to be interrelated and organized, in certain contexts, by operations of “isography,” operations idiomatic to K-net theory that are particularly well adapted both to building and examining transformational structures at various hierarchic levels and to exploring in particular any recursive features of such structuring. By way of approach to these theoretical topics, analytic observations are made about passages from Webern and Schoenberg. The analyses demonstrate sorts of observations idiomatic to K-net theory as well as observations idiomatic to Perle-cycle theory.

Perle's Cyclic Sets and Klumpenhouwer Networks: A Response

Each of the papers in this issue addresses how elements of George Perle’s compositional system and analytical methodology intersect with features of Klumpenhouwer networks (K-nets), drawing on Perle’s own communication on the subject as well as his writings.1 This commentary is intended both to clarify Perle’s position and to provide additional context from his writings. Lewin and Lambert directly refer to Perle’s materials. Lewin compares K-nets and “Perle cycles” (Perle calls them cyclic sets) as models for compositional events, and Lambert describes his K-net families in terms of Perle’s cyclic sets.2 Perle was initially in uenced by Berg’s Lyric Suite, where the row is comprised of two interlocking inversionally-related interval5 or -7 cycles and thus is comprised of adjacent dyads from two sums, 9 and 4, as shown in Example 1, where sums of 9 are bracketed on top, and those of 4 on bottom. Perle calls such a construct a “cyclic set.” A cyclic set is identiŽ ed by its interval cycles and its sums; the cyclic interval is the difference of the sums (9– 4 = 5 or 4–9 = 7; either 5 or 7 may be used). Each imbricated trichord in the set is comprised of a middle “axis note” with surrounding “neighbor notes.” The trichord is the smallest unit that can identify a cyclic set, as it contains the two sums and the cyclic interval. In K-net terms, these trichords are all related by strong isography, with the same conŽ guration of Ts and Is.3 For instance, {8,1,3}, {6,A,B} and {4,0,9} can all be interpreted as T5/7, I9/I4 K-nets. The given row-form of P5 (rows in Example 1 are rotated by one hexachord to create continuous cyclic sets) shares one sum with related forms at sum 9 (row-form I4), and sum 4 (row-form IB). These three rows vertically create the same group of K-nets related by strong isography when aligned. Cyclic sets that share one sum, such as the sums-9/2 and -9/4 sets, are called “cognate sets” by Perle. Cyclic sets are part of a “cyclic set complex” that includes all alignments of the two interlocking interval cycles. Example 2(a) reproduces Lewin’s Example 1.1, with T1 and TB cycles in an offset alignment and sums 6,7 found on the diagonals. In later examples, Lewin maintains this offset arrangement, showing trichords as triangles between the two sets, and does not represent them in one line, as Perle does in his cyclic sets. This example is rewritten as a cyclic set of sums 6/7 in Example 2(b). It is placed within a cyclic set complex, where the sets are based on interval cycles 1/B. The interval-B cycle in boldface shifts one to the right in 1See the citation list for pertinent material. 2Lewin writes that Perle suggests that K-nets “can best be viewed” in terms of cycles, but Perle only notes that they “may be deŽ ned and efŽ ciently and economically represented in this way.” Perle 1993, 300. 3Tracing this type of row would open a twelve-tone component to K-nets.

Style and Idea in the Lyric Suite of Alban Berg

Review Article| October 01 1999 Style and Idea in the Lyric Suite of Alban Berg Style and Idea in the Lyric Suite of Alban Berg by George Perle Stuyvesant, NY: Pendragon Press, 1995 68 pp. Dave Headlam Dave Headlam Search for other works by this author on: This Site Google Journal of Music Theory (1999) 43 (2): 349–358. https://doi.org/10.2307/3090665 Cite Icon Cite Share Icon Share Facebook Twitter LinkedIn MailTo Permissions Search Site Citation Dave Headlam; Style and Idea in the Lyric Suite of Alban Berg. Journal of Music Theory 1 October 1999; 43 (2): 349–358. doi: https://doi.org/10.2307/3090665 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search Books & JournalsAll JournalsJournal of Music Theory Search Advanced Search The text of this article is only available as a PDF. 1999 © Yale University, New Haven, Connecticut 065201999 Article PDF first page preview Close Modal You do not currently have access to this content.

The Music of Alban Berg

Austrian composer Alban Berg (1855-1935), along with his contemporaries Arnold Schoenberg and Anton von Webern, altered the musical landscape of the Western world. Dave Headlam offers a comprehensive analysis of Berg's music in this book. He examines each of the composer's works - including the Piano Sonata, Opus I, the operas Wozzeck and Lulu, and the Violin Concerto - and defines the main components of his musical language. Charting Berg's development as he progressed from late-romantic tonality to atonality and finally to his own distinctive dodecaphonic language, Headlam demonstrates the compositional continuity that underlies all of Berg's music. Headlam closely analyses Berg's compositional technique and the use of symmetry and cycles throughout his oeuvre. He brings into the discussion Berg's own writings as well as those of composer and musicologist George Perle; the techniques of Schoenberg, Webern and other serialists; and aspects of pitch-class set and twelve-tone theory. Headlam contends that in his treatment of all musical elements - pitch, rhythmic, formal and even orchestrational techniques - Berg achieved a synthesis that transcends the surface distinctions of his tonal, atonal, and twelve-tone period and that the cyclic basis of these chronological periods differs in degree rather than in kind. Berg's achievement of this synthesis foreshadows later developments in the work of his many musical heirs.

BOOK REVIEWS

Journal Article BOOK REVIEWS Get access Twelve-Tone Tonality(2nd edn) By GEORGE PERLE University of California Press pp 256 No price given TIM HOWELL TIM HOWELL University of York Search for other works by this author on: Oxford Academic Google Scholar The British Journal of Aesthetics, Volume 38, Issue 3, July 1998, Pages 348–349, https://doi.org/10.1093/bjaesthetics/38.3.348 Published: 01 July 1998