schoenberg composition with twelve tones schoenberg composition with twelve tones

Schoenberg's music from 1908 onward experiments in a variety of ways with the absence of traditional keys or tonal centers. [12], World War I brought a crisis in his development. "Arnold Schoenberg: The Composer as Jew". Ringer, Alexander. Covach, John. In addition to publishing its own journals, the division also provides traditional and digital publishing services to many client scholarly societies and associations. It is in no way identical wiith the chromatic scale..[The method involves ordering the twelve tones of the chromatic scale into a row, known as the Basic Set, and using that row and its properties exclusively throughout the composition in question.] [42] This stunned and depressed the composer, for up to that point he had only been wary of multiples of 13 and never considered adding the digits of his age. His father Samuel, a native of Szcsny, Hungary,[3] later moved to Pozsony (Pressburg, at that time part of the Kingdom of Hungary, now Bratislava, Slovakia) and then to Vienna, was a shoe-shopkeeper, and his mother Pauline Schoenberg (ne Nachod), a native of Prague, was a piano teacher. XII II Taborstrae 4. Untransposed, it is notated as P0. Though most sources will say it was invented by Austrian composer Arnold Schoenberg in 1921 and first described privately to his associates in 1923, in fact Josef Matthias Hauer published his "law of the twelve tones" in 1919, requiring that all twelve chromatic notes sound before any note is repeated. [58], In the 1920s, Ernst Krenek criticized a certain unnamed brand of contemporary music (presumably Schoenberg and his disciples) as "the self-gratification of an individual who sits in his studio and invents rules according to which he then writes down his notes". "Set Structure as a Compositional Determinant". Schoenberg was dismissed from his post at the academy. It may also be transposed up or down to any pitch level. [7][8], In 1898 Schoenberg converted to Christianity in the Lutheran church. The Schoenbergs were able to employ domestic help and began holding Sunday afternoon gatherings that were known for excellent coffee and Viennese pastries. Schoenbergs earlier music was by that time beginning to find recognition. Closer acquaintance with the more remote consonances - the dissonances, that is, - gradually eliminated the difficulty of comprehension and finally admitted not only the emancipation of dominant and other seventh chords, dimished sevenths and augmented triads, but also the emancipation of Wagner's, Strauss's, Moussorgky's, Debussy's, Mahler's, Puccini's, and Reger's more remote dissonances. His often polemical views of music history and aesthetics were crucial to many significant 20th-century musicologists and critics, including Theodor W. Adorno, Charles Rosen, and Carl Dahlhaus, as well as the pianists Artur Schnabel, Rudolf Serkin, Eduard Steuermann, and Glenn Gould. This technique was taken up by many of his students, who constituted the so-called Second Viennese School. [37], He lived there the rest of his life, but at first he was not settled. The tone row chosen as the basis of the piece is called the prime series (P). This page was last edited on 23 February 2023, at 20:54. About the author (1984) An American of Austrian birth, Arnold Schoenberg composed initially in a highly developed romantic style but eventually turned to painting and expressionism. 33a & b (1931), and the Piano Concerto, Op. He would self-identify as a member of the Jewish religion later in life. That work is innovative in another respect, too: it is the first string quartet to include a vocal part. [26] This happened after his attempts to move to Britain came to nothing. Founded in 1948, the Journal of the American Musicological Society welcomes topics from all fields of musical inquiry, including historical musicology, critical theory, music analysis, iconography and organology, performance practice, aesthetics and hermeneutics, ethnomusicology, gender and sexuality, popular music and cultural studies. This was the first composition without any reference at all to a key.[11]. He spent brief periods in the Austrian Army in 1916 and 1917, until he was finally discharged on medical grounds. Thus the parts were differentiated as clearly as they had formerly been by the tonal and structural functions of harmony. He regarded it as the equivalent in music of Albert Einstein's discoveries in physics. The differences in size and shape of the parts and the change in character and mood were mirrored in the shape and size of the composition, in its dynamics and tempo, figuration and accentuation, instrumentation and orchestration. Weber's ideal type can help to move the discussion away from scientistic ideas of problem solving and overly abstract invocations of the twelve-tone idea, and toward what Weber would call the cultural significance of twelve-tone methodologies (a move in line with influential revisions to the historiography of scientific problem solving proposed by Thomas Kuhn and Imre Lakatos).Differences of perspective between Arnold Schoenberg and the young Pierre Boulez, at about the time the latter first arrived at Darmstadt, highlight the difficulty in establishing a coherent history of twelve-tone compositional practice (as opposed to a heuristic ideal type). Nevertheless, the desire for a conscious control of the new means and forms will arise in every artist's mind; and he will wish to know consciously the laws and rules which govern the forms which he has conceived 'as in a dream'. Jack Boss takes a unique approach to analyzing Arnold Schoenberg's twelve-tone music, adapting the composer's notion of a 'musical idea' - problem, elaboration, solution - as a framework and focusing on the large-scale coherence of the whole piece. [66], Adrian Leverkhn, the protagonist of Thomas Mann's novel Doctor Faustus (1947), is a composer whose use of twelve-tone technique parallels the innovations of Arnold Schoenberg. 41 (1942), the haunting Piano Concerto, Op. 42 (1942); and the Fantasia for violin with piano accompaniment, Op. He was associated with the expressionist movement in German poetry and art . Trio (1921-1923) 3. Schnberg's Reorganization of Music March 15 - December 22, 2023 Oxford: Clarendon Press; New York: Oxford University Press. [i.e. [27][28] He was appointed visiting professor at UCLA in 1935 on the recommendation of Otto Klemperer, music director and conductor of the Los Angeles Philharmonic Orchestra;[citation needed] and the next year was promoted to professor at a salary of $5,100 per year, which enabled him in either May 1936 or 1937 to buy a Spanish Revival house at 116 North Rockingham in Brentwood Park, near the UCLA campus, for $18,000. [41] This possibly began in 1908 with the composition of the thirteenth song of the song cycle Das Buch der Hngenden Grten Op. 28. 39, for chorus and orchestra (1938), the Ode to Napoleon Buonaparte, Op. Unentrinnbar [Inescapable] (Arnold Schnberg), 2. During the summer of 1910, Schoenberg wrote his Harmonielehre (Theory of Harmony, Schoenberg 1922), which remains one of the most influential music-theory books. He seriously considered the offer, but he declined. Composition With Twelve Tones Explore Arnold Schoenberg Please Note EnglishFranaisItalianoPolski Composition With Twelve Tones Schoenberg 12-tone Lecture My Evolution Listen to Schoenberg's 12-Tone Works Copyright 2023 Arnold Schnberg Center & Belmont Music Publishers In my Harmonielehre, [a harmony textbook written by Schoenberg] I presented the theory that dissonant tones appear later among the overtones, for which reason the ear is less intimately acquainted with them. Jontow. These give rise to a set-complex of forty-eight forms of the set, 12 transpositions of the four basic forms: P, R, I, RI. Arved Ashby, Schoenberg, Boulez, and Twelve-Tone Composition as "Ideal Type", Journal of the American Musicological Society, Vol. He wanted to find a new principle of unification that would help him to control the rich harmonic and melodic resources now at his disposal. Musicians associated with Schoenberg have had a profound influence upon contemporary music performance practice in the US (e.g., Louis Krasner, Eugene Lehner and Rudolf Kolisch at the New England Conservatory of Music; Eduard Steuermann and Felix Galimir at the Juilliard School). 40 (1940), and the Theme and Variations for Band, Op. Wright, James and Alan Gillmor (eds.). Such pieces, in which no one tonal centre exists and in which any harmonic or melodic combination of tones may be sounded without restrictions of any kind, are usually called atonal, although Schoenberg preferred pantonal. Atonal instrumental compositions are usually quite short; in longer vocal compositions, the text serves as a means of unification. Marsch (1921) 2. Schoenberg's students have been influential teachers at major American universities: Leonard Stein at USC, UCLA and CalArts; Richard Hoffmann at Oberlin; Patricia Carpenter at Columbia; and Leon Kirchner and Earl Kim at Harvard. Landsknechte (Arnold Schnberg) [Trooper] (1930), 6. VII 34 (192930; Accompaniment to a Film Scene). [16] Instead, audiences at the Society's concerts heard difficult contemporary compositions by Scriabin, Debussy, Mahler, Webern, Berg, Reger, and other leading figures of early 20th-century music.[17]. In this way, tonality was already dethroned in practice, if not in theory. Hill, Richard S. 1936. The second, 19081922, is typified by the abandonment of key centers, a move often described (though not by Schoenberg) as "free atonality". However, the songs also explore unusually bold incidental chromaticism and seem to aspire to a Wagnerian "representational" approach to motivic identity. A derived set can be generated by choosing appropriate transformations of any trichord except 0,3,6, the diminished triad[citation needed]. 30 (1927); the opera Von Heute auf Morgen, Op. [17] Apart from his work in cartoon scores, Bradley also composed tone poems that were performed in concert in California. 10, The New Grove Dictionary of Music and Musicians, Book of a Lifetime: Doktor Faustus, by Thomas Mann, Baker's Biographical Dictionary of Musicians, University of Southern California Thornton School of Music, "The Test Pressings of Schoenberg Conducting, The First Moderns: Profiles in the Origins of Twentieth-Century Thought, Les Fonctions structurelles de l'harmonie d'Arnold Schoenberg, Arnold Schoenberg and the Ideology of Progress in Twentieth-Century Musical Thinking, "Schoenberg's Chordal Experimentalism Revealed through Representational Hierarchy Association (RHA), Contour Motives, and Binary State Switching", International Music Score Library Project, Archival records: Arnold Schoenberg collection, 19001951. Arnold Schoenberg (13 September 1874 13 July 1951) was an Austrian and later American composer . From its inception through 1921, when it ended because of economic reasons, the Society presented 353 performances to paying members, sometimes at the rate of one per week. They are the natural forerunners of my later works, and only those who understand and comprehend these will be able to gain an understanding of the later works that goes beyond a fashionable bare minimum. Schoenberg's significant compositions in the repertory of modern art music extend over a period of more than 50 years. Arnold Schoenberg came up with his twelve-tone composition system in 1921. [39] Here he was the first composer in residence at the Music Academy of the West summer conservatory.[40]. [4] It is commonly considered a form of serialism. Motivic development can be driven by such internal consistency. If Schoenberg really believed what he said (and it is hard to be quite sure about this), then it represents one of the most poignant moments in the history of music. 9 (1906), a work remarkable for its tonal development of whole-tone and quartal harmony, and its initiation of dynamic and unusual ensemble relationships, involving dramatic interruption and unpredictable instrumental allegiances; many of these features would typify the timbre-oriented chamber music aesthetic of the coming century. 217 von Petrarca (1922-1923) 5. Frequent guests included Otto Klemperer (who studied composition privately with Schoenberg beginning in April 1936), Edgard Varse, Joseph Achron, Louis Gruenberg, Ernst Toch, and, on occasion, well-known actors such as Harpo Marx and Peter Lorre. [A version of this article originally appeared in Nineteenth-Century Music 19/3 (Spring 1996): 252-62.] This resulted in the "method of composing with twelve tones which are related only with one another",[49] in which the twelve pitches of the octave (unrealized compositionally) are regarded as equal, and no one note or tonality is given the emphasis it occupied in classical harmony. Starr, Daniel. The twelve tone technique was preceded by "freely" atonal pieces of 19081923 which, though "free", often have as an "integrative element a minute intervallic cell" which in addition to expansion may be transformed as with a tone row, and in which individual notes may "function as pivotal elements, to permit overlapping statements of a basic cell or the linking of two or more basic cells". In November 1933 he took a position at the Malkin Conservatory in Boston, and in 1934 he moved to California, where he spent the remainder of his life, becoming a citizen of the United States in 1941. Personally, I refuse to believe that in the great masterworks [of opera, such as Don Giovanni, or Orfeo] pieces are connected only by the superficial coherence of the dramatic proceedings. Twelve-tone techniquealso known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note compositionis a method of musical composition devised by Austrian composer Arnold Schoenberg (1874-1951).. What is 12 tone scale technique? However, such a change became necessary when there occurred simultaneously a development which ended in what I call the emancipation of the dissonance. The only motivic elements that persist throughout the work are those that are perpetually dissolved, varied, and re-combined, in a technique, identified primarily in Brahms's music, that Schoenberg called "developing variation". 10, with soprano. This address was directly across the street from Shirley Temple's house, and there he befriended fellow composer (and tennis partner) George Gershwin. There are 9,985,920 classes of twelve-tone rows up to equivalence (where two rows are equivalent if one is a transformation of the other).[23]. [44], Schoenberg's ashes were later interred at the Zentralfriedhof in Vienna on 6 June 1974.[45]. Beginning with songs and string quartets written around the turn of the century, Schoenberg's concerns as a composer positioned him uniquely among his peers, in that his procedures exhibited characteristics of both Brahms and Wagner, who for most contemporary listeners, were considered polar opposites, representing mutually exclusive directions in the legacy of German music. 38 (begun in 1906, completed in 1939), the Variations on a Recitative in D minor, Op. Free shipping for many products! The last movement of this piece has no key signature, marking Schoenberg's formal divorce from diatonic harmonies. Copyright 2023 Arnold Schnberg Center & Belmont Music Publishers, 4. Invariance is defined as the "properties of a set that are preserved under [any given] operation, as well as those relationships between a set and the so-operationally transformed set that inhere in the operation",[26] a definition very close to that of mathematical invariance. Schoenbergs major American works show ever-increasing mastery and freedom in the handling of the 12-tone method. 2 in E minor, Op. At a time when music became open to sounds outside of traditional tonal harmony, the twelve-tone method provided a secure foundation upon which his compositional thinking could develop freely. [10] Oliver Neighbour argues that Bartk was "the first composer to use a group of twelve notes consciously for a structural purpose", in 1908 with the third of his fourteen bagatelles. "Sets, Invariance and Partitions". The combination of the retrograde and inversion transformations is known as the retrograde inversion (RI). His Chamber Symphony No. For Richard Wagner, operas consisted almost exclusively of independent pieces, whose mutual relation did not seem to be a musical one. But political events proved his undoing. I contend that historians and theorists have neglected a heuristic perspective of twelve-tone composition. [1][2] He emigrated to the United States in 1933, becoming an American citizen in 1941. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Formerly the use of the fundamental harmony had been thoeretically regulated through recognition of the effects of root progressions. His wife Gertrud reported in a telegram to her sister-in-law Ottilie the next day that Arnold died at 11:45pm, 15 minutes before midnight. Suppose the prime form of the row is as follows: Then the retrograde is the prime form in reverse order: The inversion is the prime form with the intervals inverted (so that a rising minor third becomes a falling minor third, or equivalently, a rising major sixth): And the retrograde inversion is the inverted row in retrograde: P, R, I and RI can each be started on any of the twelve notes of the chromatic scale, meaning that 47 permutations of the initial tone row can be used, giving a maximum of 48 possible tone rows. 2000. A cross partition is an often monophonic or homophonic technique which, "arranges the pitch classes of an aggregate (or a row) into a rectangular design", in which the vertical columns (harmonies) of the rectangle are derived from the adjacent segments of the row and the horizontal columns (melodies) are not (and thus may contain non-adjacencies). Later I discovered that our sense of form was right when it forced us to counterbalance extreme emotionality with extraordinary shortness. " Some Aspects of Twelve-Tone Composition," The Score and IMA Magazine 12 (1955): 53 . Arnold Schoenberg or Schnberg (/rnbr/, US also /on-/; German: [nbk] (listen); 13 September 1874 13 July 1951) was an Austrian-American composer, music theorist, teacher, writer, and painter. The Director, Edgar Bainton, rejected him for being Jewish and for having "modernist ideas and dangerous tendencies." [50] This period included the Variations for Orchestra, Op. I contend that historians and theorists have neglected a heuristic perspective of twelve-tone composition. 36 (193436); the Fourth String Quartet, Op. This method consists primarily of the constant and exclusive use of a set of twelve different tones. Schoenberg's archival legacy is collected at the Arnold Schnberg Center in Vienna. After many unsuccessful attempts during a period of apporximately twelve years, I laid the foundations for a new procedure in musical construction which seemed fitted to replace those structural differentiations provided formerly by tonal harmonies. Schoenberg had just begun working on his Piano Suite, Op. "[13], Rudolph Reti, an early proponent, says: "To replace one structural force (tonality) by another (increased thematic oneness) is indeed the fundamental idea behind the twelve-tone technique", arguing it arose out of Schoenberg's frustrations with free atonality,[14][pageneeded] providing a "positive premise" for atonality. 15, based on the collection of the same name by the German mystical poet Stefan George. An extensive music composition and analysis tool. Schoenberg announced it characteristically, during a walk with his friend Josef Rufer, when he said, "I have made a discovery which will ensure the supremacy of German music for the next hundred years". This alone would perhaps not have caused a radical change in compositional technique. Mrz 1872. In a scene where the mouse, wearing a dog mask, runs across a yard of dogs "in disguise", a chromatic scale represents both the mouse's movements, and the approach of a suspicious dog, mirrored octaves lower. His pupil and assistant Max Deutsch, who later became a professor of music, was also a conductor. A couple of months later he wrote to Schreker suggesting that it might have been a bad idea for him as well to accept the teaching position. 3 (18991903), for example, exhibit a conservative clarity of tonal organization typical of Brahms and Mahler, reflecting an interest in balanced phrases and an undisturbed hierarchy of key relationships. For instance, only a consonance was suitable for an ending. The anonymous typescript Komposition mit zwlf Tnen, linked with Schoenberg's Viennese circle of the early 1920s, reveals how the early twelve-tone discovery described by Schoenberg is, no less than the later descriptions by Boulez, an a posteriori constructor, as Kuhn and Lakatos might say, an ideological colonization of past practice. Each issue includes articles, book reviews, and communications. Schoenberg's best-known students, Hanns Eisler, Alban Berg, and Anton Webern, followed Schoenberg faithfully through each of these intellectual and aesthetic transitions, though not without considerable experimentation and variety of approach. Variation: Listesso tempo; aber etwas langsamer, Frau Ihr habt euch also ber mich unterhalten?, Frau Nun werde ich mir auch die Haare frben, Frau Glaubst Du wirklich, du kannst mich erwrmen, Frau Aber wirklich: verstndest du mich,, Frau Baby, lies, was auf dieser Schachtel steht, Freundin und Snger Oho, oho, oho, was seh ich da?, 1. He talks about the relationship to the text, new and outmoded music, composition in twelve tones, entertaining through composing, the relationship of heart and mind in music, evaluation of music, and other essays. The twelve-tone techniquealso known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note compositionis a method of musical composition first devised by Austrian composer Josef Matthias Hauer,[not verified in body] who published his "law of the twelve tones" in 1919. Deeply beholden to musical tradition, Schnberg took up the search for compositional logic amidst a freedom and diversity of expression. His widely circulated comment that he found something that will ensure the supremacy of German music for the next hundred years reflected ideological positions of the early 20th century. . Many important composers who had originally not subscribed to or actively opposed the technique, such as Aaron Copland and Igor Stravinsky,[clarification needed] eventually adopted it in their music. Diese Angaben divergieren vom Aufgebot, das die Kultusgemeinde verffentlichte: 17. Schoenberg was a painter of considerable ability, whose works were considered good enough to exhibit alongside those of Franz Marc and Wassily Kandinsky. As a Jewish composer, Schoenberg was targeted by the Nazi Party, which labeled his works as degenerate music and forbade them from being published. At the time Schoenberg lived in Berlin. Utilizing the technique of Sprechstimme, or melodramatically spoken recitation, the work pairs a female vocalist with a small ensemble of five musicians. 25, the first 12-tone piece. It is composed of a contrapuntal combination of two melodic parts, using some tones of INV6 in the upper and others in the lower voice. What distinguishes dissonances from consonances is not a greater or a lesser degree of beauty, but a greater or lesser degree of comprehensibility. Journal of the American Musicological Society Having considered many candidates, he offered teaching positions to Schoenberg and Franz Schreker in 1912. ", Last edited on 23 February 2023, at 20:54, List of compositions by Arnold Schoenberg, University of Southern California Thornton School of Music 2008, "New German Archive Focuses on Music Silenced by the Nazis", Mahler's Musical Idea: A Schenkerian-Schoenbergian Analysis of the Adagio from Symphony No. [24], Schoenberg continued in his post until the Nazi regime Machtergreifung came to power in 1933. [60] Richard Taruskin asserted that Schoenberg committed what he terms a "poietic fallacy", the conviction that what matters most (or all that matters) in a work of art is the making of it, the maker's input, and that the listener's pleasure must not be the composer's primary objective. Copyright 2023 Arnold Schnberg Center & Belmont Music Publishers Both Richard Strauss and Gustav Mahler recognized Schoenberg's significance as a composer; Strauss when he encountered Schoenberg's Gurre-Lieder, and Mahler after hearing several of Schoenberg's early works. Linking two continents in sound. Solomon, Larry. Along with his twelve-tone works, 1930 marks Schoenberg's return to tonality, with numbers 4 and 6 of the Six Pieces for Male Chorus Op. For serialism did not achieve popularity; the process of familiarization for which he and his contemporaries were waiting never occurred. 8. This book is full of essays which Arnold Schoenberg wrote on style and idea. Many composers from at least three generations have consciously extended his thinking, whereas others have passionately reacted against it. VI A simple case is the ascending chromatic scale, the retrograde inversion of which is identical to the prime form, and the retrograde of which is identical to the inversion (thus, only 24 forms of this tone row are available). Schoenberg's text on his twelve-tone technique During the first year and a half, Schoenberg did not let any of his own works be performed. Schoenberg had just begun working on his Piano Suite, Op. Given the twelve pitch classes of the chromatic scale, there are 12 factorial[22] (479,001,600[13]) tone rows, although this is far higher than the number of unique tone rows (after taking transformations into account). 2009. Until that period all of Schoenbergs works had been strictly tonal; that is, each of them had been in a specific key, centred upon a specific tone. However, not all prime series will yield so many variations because transposed transformations may be identical to each other. [13] According to Norman, this is a reference to Schoenberg's apparent "destiny" as the "Emancipator of Dissonance". Hence, it seemed at first impossible to compose pieces of complicated organization or of great length. 21 (1912), as well as his dramatic Erwartung, Op. The rise of National Socialism in Germany in 1933 led to the extirpation of Jewish influence in all spheres of German cultural life. .. The method of composing with twelve tones grew out of a necessity. Twelve-tone music as a declared artform: By the 1920s, Schoenberg had created his own method for organizing music, which fell well outside the conventions of diatonic harmony. 1992. On February 23, 1913, his Gurrelieder (begun in 1900) was first performed in Vienna. Strongly convincing as this dream may have been, the conviction that these new sounds obey the laws of nature and our manner of thinking - the conviction that order, logic, comprehensibility and form cannot be present without obedience to such laws - forces the composer along the road of exploration. While on vacation in France, he was warned that returning to Germany would be dangerous. Sample of "Sehr langsam" from String Trio Op. Another of his most important works from this atonal or pantonal period is the highly influential Pierrot lunaire, Op. [10][21] They had three children: Nuria Dorothea (born 1932), Ronald Rudolf (born 1937), and Lawrence Adam (born 1941). From the very beginning such compositions differed from all preceding music, not harmonically but also melodically, thematically and motivally. Arnold Schoenberg or Schnberg (/ r n b r /, US also / o n-/; German: [nbk] (); 13 September 1874 - 13 July 1951) was an Austrian-American composer, music theorist, teacher, writer, and painter.He is widely considered one of the most influential composers of the 20th century. Listen to Schoenberg's 12-Tone Works. 39 (1938)the Kol Nidre is a prayer sung in synagogues at the beginning of the service on the eve of Yom Kippur (Day of Atonement)and the Prelude to the Genesis Suite for orchestra and mixed chorus, Op. Babbitt, Milton. Theresia geb Lwy 15. What is another term for 12 tone music? Appearances of P can be transformed from the original in three basic ways: The various transformations can be combined. 18 (1924; The Hand of Fate), drama with music; and the unfinished oratorio Die Jakobsleiter (begun 1917; Jacobs Ladder). Gertrud would marry Schoenberg's pupil Felix Greissle in 1921. 15. 585-625. On this Wikipedia the language links are at the top of the page across from the article title. During his life, he was "subjected to a range of criticism and abuse that is shocking even in hindsight". what made a tonic a tonic] Richard Wagner's harmony had promoted a change in the logic and the constructive power of harmony. This means, of course, that no tone is repeated within the series and that it uses all twelve tones of the chromatic scale, though in a different order. [32], Ten features of Schoenberg's mature twelve-tone practice are characteristic, interdependent, and interactive:[33]. Combinatoriality is a side-effect of derived rows where combining different segments or sets such that the pitch class content of the result fulfills certain criteria, usually the combination of hexachords which complete the full chromatic.