Introduction

As a result of my experiments with music composition, Suite for Virtual Pipe Organ, Op. 1 has been written. It might be quite incomprehensible to some listeners, because it is based upon principles of the twelve-tone technique and counterpoint. To provide some clues, I discussed the history of the latter earlier. Now, it is the time to look at the twelve-tone technique (also known as dodecaphony).

Limitations of tonality

It is a common place to seek roots of the tonal music crisis that occurred during the late Romantic period, in the opera Tristan and Isolde (1857–1859) by Richard Wagner (1813–1883). Its prelude opens up with the phrase the first chord of which consists of the notes F3, B3, D#4, and G#4. The set of intervals between these notes is not something groundbreaking by itself. The same set of intervals had been used many times before Wagner. However, there are debates on proper interpretation of the chord given its surroundings. An explanation exists that Tristan chord is the half-diminished seventh chord, but some musicologists criticize this view. The absence of a generally accepted position witnesses that the role of the chord in functional harmony is not well-defined. Sonic qualities of the set of pitches become more prominent than functions of the chord.

Sonorities that can be compiled from notes found in major or minor scale, are limited. To add more colors to the music, all 12 pitches in the octave must be used. Actually, the 5 pitches that are outside diatonic scale are called chromatic (from Greek: χρῶμα “color”) for this reason. An interest in expressive and intense sounding was growing after Tristan and Isolde and this led to more active usage of chromatic pitches.

Though, it became clear that chromatic pitches cannot be used without any restrictions. The more dense their concentration is, the harder it is to figure out the current key. Besides potential awkwardness at local level, there is also a damage to musical form. To organize a tonal piece, modulations are often used for parts separation, but if chromaticism makes the list of notes used before a modulation equal to the list of notes used after this modulation, the boundary between parts is diluted. The risk of getting a poorly structured piece arises.

At the end of the 19th century and at the beginning of the 20th century, the above-mentioned difficulties in combining tonality with highly chromatic sound brought the Romantic era to an end. Atonal directions in music started to develop, but although further discussion is focused on them, it is worth noting that tonal music also continued to evolve and yielded, say, counterpoint of Hindemith (1895–1963), neoclassicism of Stravinsky (1882–1971), and modalism of Shostakovich (1906–1975).

Free atonality

There are numerous alternatives to major and minor scales. For example, Debussy (1862–1918), after Mussorgsky (1839–1881), used whole-tone scale (it includes 6 pitches out of 12 and an interval between any two adjacent pitches is equal to the whole tone). Since time immemorial, various nations have used pentatonic scales (5 pitches out of 12; they are arranged so that there are no strong melodic gravities between them). In blues, some degrees of diatonic scales can be altered or an extra degree can be added to pentatonic scale.

This way or that, the twelve-tone technique is derived from another approach — the scale must include all 12 pitches and they must be used uniformly. Here, it is convenient to introduce the notion of pitch class — a pitch with discarded information about its octave and enharmonically equivalent spelling. For example, C3 and C4 belong to the same pitch class which can be denoted as C, whereas C#3 and D♭3 belong to the same pitch class which can be denoted as C#. Coming back to uniform usage, let us formalize it as the requirement that no one pitch class can be neither more salient than others (like tonic) nor more foreign than others (like chromatic pitches in diatonic scale). According to a popular explanation, more frequent usage of a pitch class can create the illusion that this pitch class is the tonic and so the listeners end up with false expectations. However, there is a more general explanation — aesthetics associated with the full scale demands continuous recirculation of all 12 pitch classes in order to constantly maintain maximum level of chromaticism. This argument can also shed light on the twelve-tone music rule that prohibits octave intervals (but not unisons) as well as so-called false octaves, i.e., situations in which pitch class is used immediately after another voice has stopped using it.

The above considerations are not very restrictive and they define musical direction which, for historical reasons, is called free atonality. Free atonality emerged around 1910, but in the 1920s it was superseded by the twelve-tone technique and regained public interest only in the second half of the 20th century. The main problem with free atonality is that it does not provide any means for structuring long pieces. On the contrary, dodecaphony grants them.

Second Viennese School

The key figure in the establishment of the twelve-tone technique was Arnold Schoenberg (1874–1951). He and his students Alban Berg (1885–1935) and Anton Webern (1883–1945) formed the core of the Second Viennese School which is often compared to the First Viennese School (Haydn, Mozart, Beethoven).

Schoenberg suggested to back a piece by a tone row (also known as series), i.e., an ordered sequence of all 12 pitch classes. Tone row is a building block and a piece is made of its instances. Tone row can enter the piece in several forms:

  • being entirely within a single voice, from its first pitch class to the twelfth pitch class,
  • being distributed among two or more voices so that the earlier a note starts, the earlier its pitch class is in the series,
  • being split into two groups so that the upper voice (the melody) uses all pitch classes from the first group (keeping their ordering) and the second group is distributed among lower voices (the accompaniment).

On par with a tone row, its transformed versions can be used. Usually, the list of transformations is as follows:

  • inversion (new tone row starts with the same pitch class as the original one, but then upward intervals between adjacent pitch classes are replaced with downward ones of the same size and vice versa; i.e., the series is reflected over horizontal axis),
  • reversion (the series becomes its retrograde version),
  • transposition (the same interval is added to all pitch classes),
  • rotation (the first pitch class becomes the second one, the second pitch class is now the third one, …, the twelfth pitch class becomes the first one; this transformation is not used by Schoenberg).

More than one transformation can be applied to get a new tone row instance — for example, both inversion and reversion, or multiple rotations.

The twelve-tone technique assumes that the whole piece consists of instances of the same tone row and its transformed versions. Compared to free atonality, dodecaphony makes it easier to write large works due to the following properties:

  • greater unity, because everything is derived from the series;
  • a rich set of tools for motivic development (inversion of the motif and reversion of the motif can be achieved trivially; rhythm of the motif can be changed given repeated series; elision is possible if the pitch class to be excluded from the motif is distributed to another voice);
  • native support of writing in the musical form of the theme and variations; atonal analogues of sonata form can be created.

At the same time, dodecaphony alone does not guarantee an even recirculation of the 12 pitch classes needed to get totally chromatic music. For example, if a series is played by a voice and then this voice plays its reversion, the last pitch class of the original series is duplicated. If there are multiple voices, octaves or false octaves are possible. It is up to the composer to avoid these flaws.

Similarly, the twelve-tone technique by itself does not prevent tonal associations. Say, C-major chord can occur in an arbitrary place. If the goal is to write a totally chromatic piece, such situations must be avoided. However, Berg intentionally introduced tonal elements in his dodecaphonic pieces such as Violin Concerto (1935), because he tried to combine the two worlds. This shows that, in general, there is no contradiction between tonality and serialism.

Outside Second Viennese School

Actually, the idea of writing pieces that can be decomposed into groups derived from a set of 12 pitch classes, was not first proposed by Schoenberg. A few years before him, Josef Hauer (1883–1959) suggested his own variant of dodecaphony, but it was largely based on mystical arguments far from music, so this technique did not become widespread. As for essential differences, the most important one is that Hauer used rotation and, even more, sometimes did not fix the order of pitch classes. In particular, Hauer developed an approach that looks like this. The piece opens with instances of the original tone row and no transformed versions are involved. At any time, composer can shuffle the first 6 pitch classes in the series or the last 6 pitch classes in the series. Then, only instances of the new tone row are used. The tone row can be replaced in the above manner as many times as needed.

Ernst Krenek (1900–1991), while working on Lamentatio Jeremiae Prophetae (1941–1942), came to the conclusion that it is not mandatory to show the series explicitly. The tone row can affect the piece implicitly leaving its imprint on the material from which the work is constructed. Besides the initial tone row, there are 5 other tone rows created with simultaneous rotation of the first 6 pitch classes and the last 6 pitch classes. One of these 6 tone rows is selected, its instances (both in prime form and in inverted/reverted/transposed form) are used, and at any moment the tone row can be replaced with one of the 5 remaining alternatives. Krenek likened this tone row switch to mode switch in the Renaissance music. The above 6 “modes” of the tone row are called diatonic modes by Krenek. He also introduced 6 chromatic “modes” obtained from the diatonic ones by transposing the first 6 pitch classes so that the first pitch class is equal to that of the original series and transposing the last 6 pitch classes so that the first of them (i.e., the seventh in the whole tone row) is equal to that of the original series too. After this transformation, some of the 12 pitch classes may be missed in the resulting tone row. This is the reason why these “modes” are called chromatic — an absence of a tone in a palette changes overall color.

In 1924, Herbert Eimert (1897–1972) described an idea that a piece can be composed from blocks inside of which every voice uses every pitch class exactly once and also every block can be divided into segments where each pitch class occurs exactly once (now, in total by all voices). Milton Babbitt (1916–2011) combined this idea with Schoenberg’s tweve-tone technique by imposing an extra requirement that, within a block, every voice must be an instance of original or transformed tone row. Of course, not every tone row is suitable for creating such blocks. Babbitt defined hexachordal combinatoriality as a property of a tone row to have a transformed version such that its last 6 pitch classes are equal to the first 6 pitch classes of this tone row (therefore, the first 6 pitch classes of the transformed series are equal to the last 6 pitch classes of the prime series, and the first 6 pitch classes of both series together cover all 12 pitch classes, and the last 6 pitch classes of both series together cover all 12 pitch classes). Similarly, Babbitt defined tetrachordal combinatoriality as a property of a tone row to have two transformed versions such that all of them can be split into 3 segments with 4 pitch classes in each so that each segment contains all 12 pitch classes in total by the three series. Finally, Babbitt defined trichordal combinatoriality as a property of a tone row to have three transformed versions such that all of them can be split into 4 segments with 3 pitch classes in each so that each segment contains all 12 pitch classes in total by the four series. If the selected tone row is combinatorial, it is by design easier to achieve totally chromatic sound (however, there is no built-in defense against false octaves at segment junctions).

The European avant-garde of the 1950s generalized dodecaphony to integral serialism. Pitch domain is not the only one, there is also rhythm, dynamics, timbre, and so on. It is possible to increase overall coherence of the piece by repeating the same rhythmic patterns or the same dynamics contour. Serial regulation of some domains allows relaxing form-building constraints imposed on other domains and makes these domains more flexible.

Prospects for the twelve-tone technique

When expressionism was the main artistic movement at the beginning of the 20th century, totally chromatic music and arbitrary sequences of dissonant sonorities reflected its aesthetics. The ability of the twelve-tone technique to fit other stylistic preferences might be questionable. However, lyrical twelve-tone pieces have been successfully created by composers such as Luigi Dallapiccola (1904–1975), so the limits of dodecaphony has not been reached yet.

Finally, it is important to figure out which ideas and techniques have audible effects and how strong these effects are. Arguably, some suggestions are merely formal prescriptions that, at best, can be seen in sheet music, but can not add anything to listener’s experience. For example, if a voice repeats in the retrograde form the melody of another voice simultaneously with it, chances are that the listener is not able to parse this connection between the voices. Composers and music theorists still face the problem of revision and systematization of the dodecaphonic tools and approaches.