The terms twelve-tone technique and series technique or dodecaphony (Greek dodeka = 12, phone = voice) and twelve-tone music are used to summarize compositional processes that were carried out by a circle of Viennese composers around Arnold Schönberg , the so-called "Schönberg School" or " Viennese School ", were developed around 1920.
The basis of the twelve-tone technique is the method of composing with twelve tones that are only related to one another . The twelve-tone row and its downright modifications became the new ordering principle of the musical material and subsequently replaced the free atonality, which was not subject to any specific rules .
The "totality of twelve-tone technique" as understood by Schönberg was expanded many times in the music-theoretical discourse that followed. As a “row technique” or “serial technique”, it also dealt with not twelve-tone rows. The extension of the series principle to all parameters of the tone expanded the twelve-tone technique to the serial technique , which spread in the French, Italian and German-speaking areas in the early 1950s.
The invention of the twelve-tone technique Arnold Schoenberg has been attributed solely to itself. Like him, composers such as Josef Matthias Hauer , Herbert Eimert , Anton Webern , Josef Rufer and Alban Berg made important contributions to the development of twelve-tone technology in the early years. Josef Matthias Hauer was the first of all to compose in this system in 1919 with his 12-note composition Nomos , op.19 .
The twelve-tone technique has had diverse and profound effects on modern and avant-garde music in both compositional practice and analytical thinking. It is one of the most influential music history developments in Western music of the 20th century. Since it has branched out into a wide variety of schools and individual styles from the earliest beginning, discussions and aftermaths are not placed at the end in this article, but discussed in connection with their respective triggers.
In his first lecture, Composition With Twelve Tones , given in 1935, Arnold Schönberg gave a simple introduction to the twelve-tone technique.
“This method consists [...] of the constant and exclusive use of a series of twelve different tones. This means, of course, that no tone is repeated within the series and that it uses all twelve tones of the chromatic scale, although in a different order [from the chromatic scale]. "
Octave registers and enharmonic mix-ups are not taken into account in this initially abstract formulation of the series; for example, c sharp 1 represents all other notes c sharp / c sharp or des / db.
A basic row therefore contains every note exactly once. The attempt is made to mirror the individual tone series or to use them in ascending and descending order. The basic series from Schönberg's piano piece op.33a reads:
To be derived from a basic row (G)
- the inversion (U) or mirroring: every interval that was directed upwards in the basic row is now directed downwards, and vice versa. The descending quart b 1 -f 1 becomes the ascending quart b 1 -es 2 .
- the cancer (K): The basic row backwards.
- the cancer reversal (KU): the reversal of the cancer or the cancer of the reversal.
For Schönberg's op.33a:
In the compositional implementation, the octaves of the individual tones can be freely selected. The descending fourth b 1 -f 1 at the beginning of the basic row can become the ascending fifth b 1 -f 2 as well as any other combination of octaves.
Each of these four series forms can be transposed to any of the twelve chromatic levels. This means that the composition has a total of 48 different series forms available, which are usually summarized in a series table.
In his compositional sketches, Schönberg used interval symbols to denote the series forms: K + 2 means cancer transposed upwards by a major second (+2); K − 3 correspondingly a minor third (−3) lower. Other composers number from 1 to 12; or the respective starting note is used for the designation: basic row on f sharp; or KU (e) = reversal of cancer with the initial tone / on e.
The 48 series forms are the material for horizontal (melodic) sequences as well as for vertical formations (chords). Several different series forms can run simultaneously; from a series that forms a melody, parts can also be outsourced to accompanying chords. Immediate tone repetitions are allowed, but neither octave jumps nor octave coherences, not even if two chromatically identical tones in different octave positions belong to different series forms running at the same time. Interpolations are also possible: A section of a different row shape is stored in a row sequence; the remainder of this other series form appears elsewhere in the composition.
Style and thought
The first time in 1950, published in New York collection Style and Idea (1976 German Style and Idea) includes Schoenberg's most important writings on the twelve-tone technique. It is a collection of essays and lectures, the original versions of which Schönberg had mostly written in English after his emigration to the USA. They deal with various musical as well as political issues.
The following texts are particularly important for the twelve-tone technique:
- Composition With Twelve Tones : A lecture first given in 1935 at the University of Southern California, which gives an introduction to technology and, along with various other technical and aesthetic reflections, explains the concept of "developing variation".
- Brahms the Progressive: Typescript, dated October 28, 1947. It contains reflections on “form” and “comprehensibility” that are essential for Schönberg's twelve-tone technique, as well as the controversial attempt to create Brahms' compositional structures in the sense of a forerunner to the twelve-tone technique to analyze at intervals.
It is also essential:
- Composition With Twelve Tones : A typescript with the same title only as the 1935 lecture; the text was not included in Style and Idea .
The theses of these writings are discussed in the following chapter in connection with the presentation of the compositional technique.
The twelve-tone row in the composition
The piano piece op.33a
In the note examples, the tones of the row shapes are indicated by numbers next to the noteheads. As in the table of rows above , the base sequence and the inversion are numbered 1 to 12, the cancer forms 12 to 1.
Measure 1 brings the basic row beginning with b, grouped into groups of four as four-part chords; Measure 2 proceeds accordingly with the reversal of cancer beginning with a. Bars 3 to 5 are layered in two rows, KU (a) in the right hand and K (e) in the left. The decisive factor in the assignment is not the playing hand or the system in which the note is written, but rather the instrumentation: D-flat 3 in bar 5 is played by the left hand (originally notated with treble clef in the lower system), but belongs in the row KU (a) and is therefore placed in the tonally upper range, while the fourth f 1 -b 1 of the right hand lies lowest within the overall sound and belongs to the lower level K (e).
The basic row runs completely and correctly in the first bar, but cannot be derived from it alone. Since the row is indifferent to the octave position, i.e. only defines a temporal sequence of the tones, but not their spatial overlap, it cannot be clearly reconstructed from simultaneously occurring tones. In the first chord the first four row tones are consistently arranged from top to bottom, in the second the arrangement has already been changed: the earliest tone according to the series, the 5th (a), is the lowest, the following 6th (f sharp) is the highest ; the other two in this group of four are in the middle. From the beginning bar it can only be deduced which four tones form the beginning of the series, which four are the continuation and which four are the end, but not which order applies within the groups of four. In many twelve-tone compositions, the sequence intended by the composer has to be reconstructed from different places.
From bar 3, the series forms in principle run as melodic formations (especially the beginning of bar 4, the beginning of bar 5; right hand in each case), but are pushed together several times as harmonies: in bar 3, the notes 12 to 9 are played in the right hand struck in succession but held so that they form a chord; in the left the notes 12 and 11 appear immediately as a harmony.
Bars 14 to 18 show a more free use of the order of the notes:
The lower layer U (es) is consistently unanimous; the upper G (b) (which in bars 17 and 18 in the original score is partly notated in the lower system and is to be played by the left hand) has been pushed together to form three and two-part structures. In bar 14 the basic row runs in the right hand up to the 5th and 6th note and then back to the beginning; Bar 15 is an almost literal repetition. The strict sequence of the notes is therefore entirely up to us. The lower layer from the last quarter of bar 16 to the beginning of bar 18 is similar: The notes 7 and 8 are introduced in the normal order, after going back to 7 and again 8 appears 9. After the 10th note F begins with the transition to Bar 18 again the sequence 7-8-9. - Note the crossing of voices between the rows in bar 15: The 3rd tone of the lower level of the 1 is above the b of the upper level. The difference in articulation is clear enough, however, to leave no doubt about the connections; also the pianist will presumably emphasize the lower level slightly.
In these bars the problem of the statement becomes clear, the series organizes both the horizontal (melodic) references and the vertical (chordal). The more precise version reads: The series organizes either one or the other; both at the same time is not possible. The small seventh e-flat 1 -des² in the right hand in bar 16 is formed from the 7th and 8th row notes, similar to the major seventh a-flat 1 -g 2 in the following bar from 9 and 10 . and 9th tone, i.e. two tones in the series that are not intended to be adjacent, a very noticeable melodic movement of the²-g 2 . Similarly, in bar 14, the chord c 1 -f 1 -b 1 of the right hand is formed by moving the first three tones of the basic row closer together (of course, three eighth notes later, the non- row composition 1-6-5 is created by holding over the tone b 1 ), but when the note es occurs in the left hand, the layering of two different series forms creates a chord that does not come from any series form.
The twelve-tone row as an avoidance of tonality
“The construction of a basic series of twelve tones goes back to the intention to postpone the repetition of each tone as long as possible. In my theory of harmony I have shown that the stress which a tone receives through premature repetition can raise it to the rank of a tonic. On the other hand, the regular use of a series of twelve tones emphasizes all other tones in the same way, thereby depriving the individual tone of the privilege of predominance. "
When Schoenberg wrote this, avoiding tonality was still a virulent problem. The listening styles not only of the listener but also of the composer were shaped by a traditional musical language; the atonality that has become common today in musical listening seemed strange and frightening for many listeners. It is true that the American composers Henry Cowell and Charles Ives had already advanced to atonal structures before Schönberg's arrival in the USA ; a broad impact, at least in musical circles, such as that which would then proceed from Schönberg's twelve-tone technique, was denied to them. In this respect, Schönberg's attempt to stabilize a new musical language initially by distinguishing it from an old, firmly established one was probably not only obvious, but inevitable.
However, with his appeal to his theory of harmony from 1911, Schönberg made a revealing memory error. His argument in the book, which is decades older, actually deals with repetitions of notes in pure musical notation exercises for traditional tonal music (i.e. short chord progressions without artistic claim)
“And that brings us to a second requirement that comes into consideration when designing good sentences: the desire for variety. It is difficult to deal with this without also speaking of the opposite requirement of repetition. For if the first manifold produces, the second gives the first connection, meaning, system. And system can only be based on repetition. We will find little opportunity to make use of the repetition [...] "
There follows a number of cases in which tone repetition within a set exercise is little or no problem. Then:
“The worst form of repetition will be that which sets the highest or lowest note of a line twice. […] In particular, the climax is unlikely to be repeated. […] If, for example, it should be proven in a Schubert song that the highest note occurs more often in a melody (for example: 'With the green lute band'), then this is of course a different case, because other means provide the necessary variety here . "
In fact, an analysis of Schubert's Mit dem grün Lautenbande shows that the highest note of the melody is the subject of a conscious dramaturgy: it is initially the goal of a consistent melodic upward development, then appears even more pronounced as a conspicuous dissonance, and finally becomes when the melody changes to another Direction developed, playfully released into the casualness. At the same time, however, the analysis of a tone other than the high tone - which comes from inside the tone space - shows that not all tones react so sensitively to repetition, and therefore cannot be made the subject of a targeted dramaturgy.
A composer of tonal music can thus play with a few exposed notes in his melodic lines. For all other tones the fact of repetition is mostly of no consequence; The structures of meaning that are primarily set by harmony are far too strong. The situation is completely different in music, which renounces the meaning structures of tonality. Béla Bartók builds large parts of his fourth string quartet (1928) on a motif that appears for the first time in bar 7 of the first movement in the cello:
The 4th and 5th tone are repetitions of the 2nd and 1. How much their effect is weakened is shown by the dramatic effect of the final tone b, which is new and through this novelty - after the weakness of the previous one - receives a dynamically driving effect . However, if you add the notes preceding this motif from bar 7, the effect changes fundamentally:
The b has already expanded in bar 6, and it was reached in a similar way to the final note, via c 1 and b. The final note of the motif, which was new in the first musical example, is now a repeated one. In this version the motif returns to itself, it loses its dynamic, propulsive effect, it closes, acts like a summary of the preceding. That has nothing to do with a keynote in the traditional sense; no one who has ever heard this quartet will doubt that it is thoroughly atonal. Nevertheless there is a strong weighting effect on the tones; the final b in the first note sample is completely different from the final b in the second. Since the superimposition by the strong sense structures of the functional harmonic no longer exists, the fact of novelty or repetition in an atonal context fundamentally changes the effect of a tone - and indeed every tone, not just a few peak tones . The results of this phenomenon are unpredictable for a composer used to tonal language - they are made more complicated by the use of different intervals - and of intimidating power. A pathetically staged target tone, for example, has an unbearably banal effect (because the fact that it had already sounded shortly before is not covered by a corresponding harmony); or it does not act as a target tone at all, but as a starting point for something new that the composer did not intend; or it sounds - horribile dictu in atonal music - simply wrong. Atonality is anything but a land of lawlessness, and a composer who has just freed himself from the constraints of tonality and is still half and half in it, and who now believes he can do whatever he likes, can have nasty surprises experience.
In the quotation at the beginning of this chapter, Schönberg clearly does not speak of the tonic effect within an unquestionably tonal, function-harmonic context - in any case, this does not come about through tone repetition - but of tone repetitions in an atonal context. These are not discussed in harmony . Nevertheless, Schönberg's reference to the book has a meaning, albeit an unintentional one. For when the theory of harmony arose - it first appeared in 1911 - Schönberg was just taking his first steps in the then completely new field of atonality; their first compositional problems and the work on the book, which in other places definitely reflects the new developments, may have mixed up in his memory. Even in the much later statement about the twelve-tone technique, the exorbitant effort which, despite all the joy of discovery, undoubtedly required the first steps into atonality, as well as perhaps the frustration that a myriad of committed attempts ended in sonic changelings, which the ideas of the Composers did not reproduce in any way. What Schönberg describes as a method of avoiding tonality is actually the reaction to a genuinely atonal problem. A comparison with Bartók, which is characteristic for both composer personalities, seems to be offered here: Bartók, who saw a great opportunity in the unforeseen effects of the tones and devoted whole string quartets to their concentrated research and experimentation; Schönberg, who had learned to fear these effects and devised a system to avoid them.
But this formulation does not match the facts. If only because the system doesn't work.
"The use of more than one row was ruled out because in each subsequent row one or more tones would have been repeated too soon."
For example, if in the first row c sharp is the 10th tone, in the following row, which changes the order, but the 3rd, then c sharp is repeated before the remaining eleven tones run through, and is therefore inappropriately preferred. But that also excludes the use of different series forms. The premature repetition of a tone is prevented only as long as one and the same series form is running one after the other; as soon as one row shape is followed by another, repetitions of tones move irregularly together and apart. Compare with this in bar 2 of op.33a (note example above ) the top note d 1 of the last chord (4th note of KU (a)), which is repeated an octave lower than the first note of the left hand in the following bar (11th tone of K (e)). Likewise in bar 3 the last note of the left hand G (9th note of K (e)), which is only separated by two notes from g 1 (bar 4, right hand, third note; 6th note of KU (a)) is. Such cases are common. Only over longer distances does the use of increasingly complete series forms result in a statistical equal distribution of the tones, unless the composer prevents it by compositional means.
The equality of tones
That is exactly what Schönberg did over and over again. The most spectacular example is the musette from the Suite for Piano, Op. 25, in the opening and closing sections of which a note (g) is separated from the series and continuously plays as the organ point . But beyond that, the formation of long surfaces from a few series of tones is one of Schönberg's most frequent compositional means. At the beginning of the 3rd String Quartet, Op. 30, the second violin and viola alternately repeat a motif made up of five notes for twelve bars, above which the main part of the first violin stands from the 5th bar. Bars 19 and 20 of the piano piece op.33a read as follows:
From the end of bar 19, constant repetitions and recursions of 4 notes each from K (e) and KU (a), which are fixed in their octave positions, create a harmoniously standing surface that is strongly moved by sharply defined rhythms. Such surfaces are among the most common compositional means of Schönberg's twelve-tone works. They conspicuously approach Bartók's compositional techniques: The set of notes shoots itself into a few notes, which, combined with very specific, recurring rhythms, are recorded over a longer distance, so that the notes that then appear have a strong renewal effect. In using these remedies, however, Schönberg appears generally more nervous than Bartók; his stretches are shorter, and often their continuation does not appear as a logical consequence, as with Bartók, but as a break in affect.
Within such passages, the order of the notes becomes fundamentally questionable; but they also regularly lead to a strong predominance of a certain group of tones over the rest, at least for a certain period of time.
“You will find that the sequence of the notes has always been strictly observed according to their arrangement in the row [namely in the music examples given in the continuation of Schönberg's text]. Perhaps in the later part of the work, if the ear had already become familiar with the series, one could tolerate a slight deviation from this sequence (according to the same principle that allowed a distant variant in earlier styles). At the beginning of a piece, however, you wouldn't deviate that much. "
There is no need to refuse this statement; a little generosity is sufficient in interpreting it. In 1935, Schönberg was probably still too interested in establishing the form-creating, logic behind the twelve-tone row to the outside world to want to explain to an audience that was new to twelve-tone technology what degree of freedom he had already gained at this point . If one takes the “maybe” and the “slight deviation” in the second sentence of this quotation as strong diminutions, then one comes to a thoroughly accurate description: At the beginning (and, as the table for op. 33a shows, at the end) of the piece Maintain the sequence and completeness of the series notes more or less precisely, in the middle of the piece profound deviations sometimes occur.
The twelve-tone row as a substitute for tonality
Schönberg did not see the renunciation of tonality as just progress.
“In the past, harmony served not only as a source of beauty, but, more importantly, as a means of distinguishing between features of form. For example, only one consonance at the end was deemed appropriate. Fastening functions required different harmony sequences than wandering ones; a preparation, a transition required other consequences than a final thought [...] "
Schönberg worked on a book on the form-forming tendencies of [tonal] harmony until 1948. The fact that with the transition to atonality that took place around 1909 these form-forming tendencies had ceased led to the composition of only short pieces at first; longer pieces had to rely on a text that seemed to take over the form.
"After many unsuccessful attempts over a period of almost twelve years, I laid the foundation for a new musical construction method that seemed suitable to replace the structural differentiations that had previously been provided by the tonal harmonies."
A table shows the use of the series in Schönberg's piano piece op.33a:
|Time signature, tempo||4/4 Moderate||- poco rit||a tempo||- poco rit -|
|right hand||G (b)||KU (a)||KU (a)||...||...||G (b)||KU (a)||G (b) 1, 3, 4 in two octaves||...||G (b)||KU (a)||U (it)|
|left hand||K (e)||...||...||U (es) 1, 4 in two octaves||...||U (it)||K (e)||G (b)|
|T, T||2/4 molto rit||4/4 a tempo||more violent||- poco rit||calmer||- rit -|
|D.||f||p||p cantabile||f martellato||p||- p -|
|r H||...||G (b)||...||...||...||...||K (e) 12-3||...||G (b) 7-9, 5, 11-12||...||G (b) 1-6||...|
|l H||...||U (it)||...||...||...||...||KU (a) 12-3||...||G (b) 3, 1/6, 2, 4 (missing 10)||...||U (es) 1-6||...|
|T, T||a tempo||increasing|
|D.||f energetically, ff, - p||- scherzando -||- p martellato, cresc||f||- f||dim - mp - cresc|
|r H||G (b)||...||K (e) 12-7; KU (a) 6-1||G (c) 1-6; U (b) 1-6; G (c)||...; U (b)||...; U (b)||...; K (h)|
|l H||KU (a)||...||KU (es) 7-12 (!); K (e) 6-1; U (f) 1-6||...; G (f) 1-6; U (f)||...; G (f)||...; G (f)||...; KU (e)|
|Tact||32||32 after a general break with a fermata||33||34||35||36||37||38||39||40|
|T, T||5/4||9/8||6/8 - rit||4/4 quiet||- increasing -||3/4 rit|
|D.||ff||p||p dolce||p cresc||f||ff|
|r H||...||G (b)||...; KU (a)||...||K (e)||...||G (b); KU (a)||U (es); K (e)||G (b)||...|
|l H||...||U (it)||...; K (e)||...||KU (a)||...||U (it)||...|
Notes: The list is simplified; individual closing notes at the beginning of the bar and upbeats as well as sforzati are not taken into account.
- Three points: The row beginning in the previous measure is continued. (In the case of incomplete rows, the total available notes are immediately after the abbreviation).
- Arabic numerals denote series tones.
- Dash in front of a tempo or dynamic rule: stands at the end of the measure;
- Dash on both sides of a tempo or dynamic rule: stands in the middle of the measure.
So there are only two really different series that run either forwards or backwards. As soon as two series forms run simultaneously, these are always the combinations G (b) -U (es) and K (e) -KU (a). Schönberg wrote:
"Later [d. H. after the wind quintet op. 26] […] I changed my idea, if necessary, so that it met the following conditions […]: The inversion of the first six notes […] on the lower quine should not produce a repetition of one of these six notes, but result in the previously unused six tones of the chromatic scale. "
The first six tones of the basic row on b and the inversion on eb (the starting tone is a fifth lower) result in all twelve chromatic tones without repeating a tone (which automatically also applies to the respective tones 7 to 12). Schoenberg was able to run these two series forms simultaneously without having to fear an early repetition of a tone belonging to two different series forms within the halves of the series: bars 14 to 16 (second note) result in a complete twelve-tone field without repetition; likewise measure 16 (use of the right hand) up to the end of measure 18, although the series are incomplete in and of themselves (see the note example above ).
Schönberg only uses additional series forms in measure 27 end to measure 32 start:
|G (f)||K (h)|
|U (b)||KU (e)|
Here, too, the starting notes of the row shapes are spaced a fifth apart, so that they can be layered on top of each other. G (f) -K (h) and U (b) -KU (e) in turn relate to one another as forms of cancer.
In style and thought, Schönberg wrote:
“While a piece usually begins with the basic row itself, the mirror forms and other derivations such as the eleven transpositions of all four basic forms are only used later; Especially the transpositions, like the modulations in earlier styles, serve to form secondary ideas. "
The basic row - in op.33a more likely the four main rows exposed in the first bars - thus functions roughly like the main key of traditional tonal music: it forms a starting point from which the piece first modulates away into other keys - into other series forms - and then modulated back to the starting point. This formation can be clearly seen from the arrangement of the series forms in op. 33a. Bars 27 to 32 thus correspond to a middle section in different keys in tonal music.
"[...] every tone [appears] always in the vicinity of two other tones in an unchangeable combination, which creates a close relationship that is extremely similar to the relationship of a third and a fifth to the fundamental. It is just a relationship, of course, but its repeated occurrence can produce psychological effects very similar to closer relationships [within a triad]. "
Discussion and criticism
Theodor W. Adorno
The German philosopher Theodor W. Adorno (1903–1969) should be mentioned for the music-aesthetic and historical-philosophical underpinning of the twelve-tone technique , who interpreted the twelve-tone technique as the progressive answer to what he saw as the reactionary tonality and composed pieces himself using the twelve-tone technique. However, his handling of the twelve-tone rows was never as strict as, for example, Schoenberg's, but he defended, also theoretically, a certain artistic freedom that he saw endangered by an overly orthodox use of the twelve-tone technique. So he extended z. B. for the setting of the Trakl poem Entlang (op. 5, no. 4) the tone row to 98 tones. In addition, Adorno provided Thomas Mann with musical advice for his novel Doctor Faustus , especially with regard to the music-theoretical reflections on twelve-tone music and technique.
The regular twelve-tone technique
A regular codification of the twelve-tone technique, which originated around 1920, cannot be grasped before the forties. Of the “classical” composers of the twelve-tone technique (Schönberg, Berg, Webern) only Schönberg made a theoretical contribution to the explanation of the technique. His lecture Composition With Twelve Tones , given for the first time in 1935 at the University of Southern California, is, however, perceived by representatives of the regular twelve-tone technique as "at least disappointing". After Schönberg emigrated in 1933 and began teaching in the USA, the twelve-tone technique spread at American universities, where it soon seems to have become a highly trained typesetting technique. In addition, in the last two years of his life, Schönberg advised Josef Rufer on the composition of his book The Composition with Twelve Tones , which was published in 1952, one year after Schönberg's death - to an extent that could not be precisely determined; Schönberg did not return to Europe after the war, while Rufer never emigrated. In addition to Rufer's book, it was the writings of René Leibowitz ( Schönberg et son école 1946, Introduction à la musique de douze sons 1949) and, secondarily, the textbooks by Herbert Eimert and Hanns Jelinek , which have spread this to this day in general music studies and reference works Image of the twelve-tone technique as a primarily regular instruction for arranging notes.
The weaknesses of these sets of rules are obvious even without an analytical consideration of significant twelve-tone compositions: They say nothing in the least about the functioning of the row technique in a composition; rather, they tend to isolate the pitch organization from other parameters of the musical movement. The consideration of the historically formative twelve-tone compositions - which by and large originated earlier than the set of rules - shows that none of the rules and instructions in these textbooks have been followed with any reliability by the composers, that the rules do not even begin to reflect the variety of approaches able to capture. Nonetheless, the rule systems have become the starting point for an academic way of composing which, apart from countless successors in Europe after 1945, was particularly widespread in the universities of North America around the middle of the 20th century. Glenn Gould characterized this atmosphere of twelve-tone orthodoxy in an essay written in 1974. In 1953 Ernst Krenek , who emigrated to the USA - as an Austrian and a well-known composer in the field of twelve-tone composition - came to hold a master class at the Toronto Conservatory , where Gould studied.
“I remember once before him the score of Schönberg's Piano Concerto, for which I had prepared a list of mistakes - a compilation of deviations from the series form used in each case. 'Could any of this be more than a careless mistake?' I asked. 'I mean, could any of this possibly (blushes... Stutter ... well , that was 1953, and most of us were screwed up constructivists) the result of (gulp) inspiration?'
'I don't know either what went on in Schönberg's head,' replied Krenek, 'but I don't see why it shouldn't have been an inspiration.' "
Gould leaves no doubt that even minor deviations from the norm caused a stir at a North American conservatoire in the 1950s.
In 1966 the essay on the theory of some series combinations by Eberhardt Klemm appeared . In the basic series from Schönberg's Violin Concerto op.36, Klemm replaces the notes with numbers: the initial note a with the 0, the other notes with the number of semitones that stand above the initial note (the following b with a 1, the third note it through a 6 etc.).
"This row of numbers is a different arrangement, expressed algebraically a permutation of the numbers 0, 1, ..., 11, which are to be seen as the 'reduced representatives after module 12'."
A series of algebraic transformations follows . Klemm only sporadically relates them to actually composed structures, and the reference to artistic statements possibly intended by the composer remains loose. "The present study is less about the description of compositional facts than about theoretical insights into the structure of the twelve-tone rows."
Klemm's approach is related to a strong interest in mathematical analysis methods that persisted through the second half of the 20th century and dealt with the entire available musical repertoire not only in the western world. However, the theory of pitch class sets established by Allen Forte in the mid-sixties , which was applied several times to works of the Vienna School, has prevailed .
Due to its affinity for algebra, the regular twelve-tone technique is the earliest example of modern composition methods, in which compositional decisions are made not by hearing, but using mathematical processes. To what extent individual composers who used more or less complicated mathematical, but therefore not necessarily serial, methods to define pitch sequences - especially Iannis Xenakis , but (partly) also György Ligeti - followed a stimulus from the twelve-tone technique, or rather one from ascension The zeitgeist , influenced by scientific thinking , will often not be able to be decided because none of these composers could do without an examination of both modern natural science and twelve-tone technique. The best-known direct successor to the regular twelve-tone technique is serial music in Europe in the fifties. Its representatives ( Pierre Boulez , Karlheinz Stockhausen , Henri Pousseur and many others) relied on Anton Webern, not on Schönberg. Your Webern analyzes have, however, been sharply criticized from various quarters since the 1970s. In serial music, not only the pitches, but also all other parameters of the musical set, such as tone duration, volume, articulation, etc., are organized in mutually independent rows. The number twelve only plays a role in the order of the chromatic tones. Above all, the rhythmic relationships, due to intricate numerical relationships, often run the risk of being completely inexecutable and not verifiable by the composer. For the United States, Milton Babbitt pioneered serial music. For the first time, Babbitt systematically described the phenomenon of hexachord complementarity, which was also valid for the series of op. 33a , and which he established under the term combinatoriality as a constructive principle of a serial composition.
- Arnold Schönberg: Harmony. Vienna 1911.
- Anton Webern: The Way to New Music (16 lectures 1932). Universal Edition, Vienna 1960.
- Arnold Schönberg: Style and Thought. In: Gesammelte Schriften 1. Style and Thought, Essays on Music. Edited by Ivan Vojtech. Frankfurt am Main 1976. (Also as a Fischer paperback, 1992) Mainly:
- Brahms the progressive. Lecture of February 12, 1933 in Frankfurter Rundfunk (no longer available), English version dated October 28, 1947 (Brahms the Progressive) .
- Composition with twelve notes. Lecture first given in 1935 at the University of Southern California (Composition With Twelve Tones) .
- René Leibowitz: Schoenberg et son école (1947). Janin, Paris 1947.
- René Leibowitz: Introduction a la musique de douze sons (1949). L'Arche, Paris 1949.
- Theodor W. Adorno: Philosophy of the new music. Tübingen 1949.
- Ernst Krenek: Studies in Counterpoint (1940), German: twelve-tone counterpoint studies. Schott, Mainz 1952.
- Herbert Eimert: Textbook of the twelve-tone technique . Breitkopf & Härtel, Wiesbaden 1952.
- Josef Rufer: The composition with twelve notes. Berlin / Wunsiedel 1952.
- Luigi Nono: The development of serial technology. In: Darmstadt Contributions to New Music. Mainz 1958.
- György Ligeti: The composition with rows. In: Austrian music magazine. No. XVI, Vienna 1961.
- Eberhard Klemm: On the theory of some row combinations. In: Archives for Musicology . XXIII, 1966 pp. 170-212.
- Hanns Jelinek: Instructions for twelve-tone composition (1952–58), 2 parts in 4 volumes. Vienna 1967 (= UE. 1967 2teA).
- Michael Beiche: Article twelve-tone music in the pocket dictionary of musical terminology , edited by Hans Heinrich Eggebrecht (now Albrecht Riethmüller). Steiner, Wiesbaden 1971 ff. ( Digitized version ).
- Eberhard Friday: Schönberg . Rowohlt, Reinbek near Hamburg 1973.
- Arnold Schoenberg. Memorial exhibition 1974 (catalog, editorial staff Ernst Hilmar) Universal Edition, Vienna 1974.
- Christian Möllers: Series technique and musical form with Arnold Schönberg. An investigation into the III. String quartet op. 30 (= supplements to the archive for musicology , volume XVIII). Wiesbaden 1977.
- Rudolf Stephan: twelve-tone music. In: Ludwig Finscher (Hrsg.): The music in past and present . Second edition, factual part, Volume 9 (Sydney - Cyprus). Bärenreiter / Metzler, Kassel et al. 1998, ISBN 3-7618-1128-4 ( online edition , subscription required for full access)
- On the history of the development of twelve-tone music
- Technical terms on the topic of sound series music / dodecaphony
- A row square for the automatic calculation of all transpositions in a twelve-tone row
- Database of tone series and tropes
For a breakdown of the short titles cf. the reading list
- Arnold Schönberg: Style and Thought. Fischer, Frankfurt a. M. 1995 p. 75.
- Joseph Matthias Hauer . In: Riemann Musiklexikon . Schott-Mainz, 2012, Volume 4, p. 343.
- quoted from the paperback edition: Stil und Gedanke , p. 110
- cf. the facsimile of Schönberg's series table for the 4th string quartet in: Arnold Schönberg. 1974 memorial exhibition (catalog, editorial staff Ernst Hilmar) Universal Edition, Vienna 1974, p. 150 (explanation p. 339).
- Arnold Schönberg: Style and Thought. Essays on music ed. by Ivan Vojtech, S. Fischer-Verlag Frankfurt 1976 (= Collected Writings 1). In addition to Style and Thought under the heading Essays on Music , the edition contains other texts from the area of the original collection. The volume Stil und Gedanke , published in 1992 by Fischer Taschenbuch Verlag , which only reproduces the original collection as a reprint of the Gesammelte Schriften , tacitly corrects a number of errors, unfortunately without evidence that the original was consulted again.
- The original German version, presumably broadcast on Frankfurter Rundfunk in 1933, was only found after the publication of the Gesammelte Schriften and printed in 1990 in: Festschrift Rudolf Stephan zum 65th Birthday , Laaber-Verlag, Laaber 1990; as well as in: Albrecht Dümling: Defense of musical progress. Brahms and Schönberg , Argument Verlag, Hamburg 1990 (after the note in the paperback edition of Style and Thought ).
- It is accordingly missing in the German paperback edition, but is contained in the collected writings , volume 1.
- Composition with twelve tones (typescript) Gesammelte Schriften , Volume 1, p. 380
- Josef Rufer (Ed.): Harmonielehre . 7th edition. 1966, p. 142 f.
- The Enharmonik has been changed to make it easier to read .
- Composition with twelve notes (lecture) paperback edition p. 111
- Composition with twelve notes (lecture) paperback edition p. 118 f.
- Composition with twelve notes (lecture). Paperback p. 108
- Structural Functions of Harmony , published posthumously in 1954.
- Composition with twelve notes (lecture). Paperback p. 109 f.
- Composition with twelve notes (lecture). Paperback p. 117
- Composition with twelve notes (lecture). Paperback p. 119
- Composition with twelve notes (typescript). In: Collected Writings Volume 1 p. 381
- Stefan Müller-Doohm: Adorno. A biography .
- Gerhard Schweppenhäuser : Theodor W. Adorno for an introduction .
- Klemm p. 171.
- translated to: A Festschrift for “Ernst Who ???” . In: Tim Page (Ed.): The Glenn Gould Reader . New York 1984, p. 189
- Klemm, p. 173. The abbreviation points are in the original.
- Klemm p. 170.
- Andrew Mead : An Introduction to the Music of Milton Babbitt. Princeton University Press, Princeton 1994 pp. 20-38.