Off Topic – Serial Music

Another Austrian invention

there is another field pioneered by Austrians, one perhaps even better known than their contribution to economics – namely serial, or dodecaphonic music, a.k.a. 12-tone music.

The most famous composers of such music were Arnold Schoenberg, the inventor of the 12-tone technique, and his contemporaries Anton von Webern and Alban Berg. In modern times Karl-Heinz Stockhausen, Luigi Nono, Milton Babbitt et al. became well known proponents of this type of music.

Lesser known, but no less interesting, is Josef Matthias Hauer, who made his own contribution to serial music theory by introducing the so-called 'tropes' – a method for constructing chords in music without a specific key that allows for the composition of less 'dissonant sounding' 12-tone music. This method was developed independently of Schoenberg's theoretical work.

Take a look at this interview with classical pianist Mitsuko Uchida on Schoenberg and his piano concerto op. 42; she is one of the foremost interpreters of this work, which is extremely difficult to play (as she explains in the interview, this partly owes to Schoenberg not playing the piano very well, so he didn't consider the technical troubles a pianist would encounter when trying to play this composition, perhaps unwittingly making it a real tour-de-force for the interpreter).


Mitsuko Uchida on Schoenberg's piano concerto, opus 42

Note her mentions of the original 'tone row' (P0), the retrogrades, inversions, etc. - an explanation of these terms follows below.

A little bit of theory

Serial music favors a seemingly very 'mathematical' approach to composition, as it has certain specific rules, that govern the order in which different pitches can be used. At the core of the theory is Schoenberg's idea that 'no note should be accorded more importance than any other'; this is achieved by the rule that once a note of a '12-tone row' has been sounded, it may not be heard again until all other 11 notes of the row have been sounded. A tonal democracy so to speak, or rather, an atonal democracy.

Serial composers do not really think in terms of 'notes' – rather, they refer to them as 'pitch classes', that are typically numbered. For instance, if one were to write down a 12-tone row consisting simply of a chromatic scale beginning with 'C' , then the note 'C' would be termed pitch class 0, C# would be pitch class 1, D would be pitch class 2, etc.
Note also, in terms of notation, accidentals (#,b) are only valid for the pitch immediately following them, not for all subsequent appearances of the pitch, and enharmonic spellings of the same (well-tempered) pitch , like e.g. C# and Db are used indiscriminately.

At the beginning of every serial composition is the initial, or prime tone row, P0. This could for instance be:

D, G, F#(Gb), D#(Eb), C, B, A, E, G#(Ab), A#(Bb), F, C#(Db)

(this is the basic tone row that was used in the composition 'Matrix' that is available for free download at the bottom of this post).
If we were to write down this tone row in numbered pitch classes, it would look thusly:

0, 5, 4, 1, 10, 9, 7, 2, 6, 8, 3, 11


The above 12-tone row in normal musical notation - below the notes the respective pitch class numbers click on image to see larger version

Next one constructs from this original tone row P0 a number of additional tone rows, that are all derived from the original with a simple mathematical method. These basic transformations of the tone row are referred to as transposition, inversion, retrograde, and retrograde inversion. One thus arrives at 48 tone rows (P0 transposed 12 times, inverted 12 times, mirrored 12 times, and inverse-mirrored 12 times).

This can be done using a matrix. First one writes down the original tone row at the top, from left to right, then one constructs the inversion I0, writing it down in the first column to the left. The inversion is constructed by finding the complements to the pitch classes of P0, which are given by the number that when added to the pitch class number will equal 12.
Thus the inversion I0 of the above tone row P0 will be:

D, A, A#(Bb), C#(Db), E, F, G, C, G#(Ab), F#(Gb), B, D#(Eb) ,

or in pitch class numbers:

0, 7, 8, 11, 2, 3, 5, 10, 6, 4, 9, 1

from the pitch class numbers in the top row (P0) and left-most column (I0), all the other transformations are easily deduced. The numbers of the first row are at the same time the index numbers of the inversion columns, while the numbers of the first column give us the index numbers of the transposed rows. Thus the second row in this example will be P7, or P0 transposed by 7 half-tones, the third row P8, the forth row P11, and so forth. The second pitch class of P7 is determined by adding the second pitch class number of I0 to the second pitch class number of P0 modulus 12, the third by adding the second number of I0 to the third number of P0 mod 12, etc.
The rows when read from right to left give us the retrogrades (mirroring the intervals), the inversions when read from bottom to top give us the retrograde inversions (mirrored intervals of the inverted tone rows).

The entire matrix then looks like this:


The 12-tone matrix in numbers click on image to see larger version

or in terms of notes:


The 12-tone matrix in notes; P 0-11 are the original tone row plus its transpositions; I0-11 the inversions of the tone row and its transpositions, R0-11 the retrogrades and RI0-11 the retrograde inversions.
This matrix is the 'raw material' from which a 12-tone composition is made. click on image to see larger version

Josef M. Hauer , whom I mentioned earlier, developed methods that retained some of the features described above, while introducing new ones, especially w.r.t. construction of chords. Below a handwritten sheet of chords constructed with Hauer's method. (note: the letter 'H' is how the note 'B' is referred to in German). The main difference: it doesn't sound quite as 'dissonant'.


A picture of chords constructed with Hauer's method; the 12-tone rows (circled in red) are the only thing that changes – all other notes remain the same as one progresses; the notes are taken from the groups of 3 notes in the immediate vicinity of each other – whereby one starts with the ones next to the first note in the tone row. The 12-tone row moves like a snake through the chords. click on image to see larger version

This is only a very basic overview over the theory – if you wish to learn more, further introductory material can be found here: 12-tone composition

A labyrinth worth exploring

If one is not familiar with 12-tone music, it may seem a bit difficult to swallow at first, so to speak.
Milton Babbitt famously declared that he didn't care if anyone liked his music.
His argument went like this: most people don't understand it, but that is not an indicator of its worth. If a layman were to walk into a congress of nuclear physicists he wouldn't understand a word either – and so presumably would the majority of people, but that does not mean nuclear physics is not a worthy endeavor.

The infamous Babbitt essay 'Who cares if you listen?' is where these thoughts were formulated. Advanced music is for advanced listeners, so Babbitt. The rest have no basis by which to judge this type of music, just as a radio repairman has no basis to criticize the work of a nuclear physicist.
To some extent i'm sympathetic to this argument – as long as some people find enjoyment from dodecaphony, there is sufficient proof of its worth.

Popularity may count in pecuniary terms, but it is hardly the main criterion by which to judge art. Naturally, Babbitt put off a lot of people with his elitist essay, but he probably reckoned, so what? Those were the people who wouldn't listen to his music anyway! Here you find btw. an interesting early 80's article by Greg Sandow on the 'fine madness' of Milton Babbitt.

This elitist argument was carried even further by a German composer: Karl-Heinz Stockhausen. When asked by a student in the 1970's if the use of electronic instruments like synthesizer modules in his compositions would not risk losing a valuable and very important component of music as artistic expression , namely human emotion, he answered that he thought people were simply afraid.
Afraid of what? Afraid of not belonging to the newly evolving species of man that could relate to this type of music. He regarded modern music as accompanying the next step in human evolution - to truly grasp it, you had to have 'evolved' , or at least be in the process of evolving, to the next stage of human consciousness.

Oh well, what can one say to that. :) A recording of Stockhausen's 1972 lecture is below:


Stockhausen on human evolution and music, 1972

My experience is as follows: most people are rather taken aback when hearing serial music for the first time – chances are, after all, that they will hear a 'difficult' piece , since by their very nature, most pieces are difficult , and often dissonant.
In spite of its 'mathematical construction' aspect 12-tone music often gives the initial impression of being chaotic and disorganized - which of course it is not, but few people will realize it at first. It certainly is what one would call 'uncompromising' – it doesn't exactly cater to popular tastes.

You might ask, how does the composer actually introduce emotion when he works with tone rows that have been calculated beforehand? This is done by making use of all other aspects of musical expression. Rhythm, the way the various tone rows are interlaced, the timing of musical events, textures and tone colors, the type of instrumentation used – all can be and are used to create an individual artistic expression within the confines of the system. Naturally, great masters like Schoenberg and others occasionally would break their own rules. Once you know the rules well, you also know how to break them effectively after all.

It is generally unlikely that the untrained listener will immediately find his way to enjoying serial music. For one thing, it lacks the patterned, repetitive elements we are used to hearing in most tonal music; in addition, it frequently sounds dissonant, although as J.M. Hauer's work proves, this does not always have to be the case. Here is a rare recording of a Hauer piano piece as an example:


Josef Matthias Hauer's Klavierstuecke, opus 25

Nevertheless, it is a labyrinth well worth exploring – as Ms. Uchida remarks in her interview, there are a number of composers such as Debussy who did not use the 12-tone technique, but still left tonality largely behind in many of their compositions. Debussy is probably a good way of approaching atonal music 'painlessly' initially, before one takes the next step of exploring Schoenberg and the modern age composers.
I for one disagree with both Babbitt and Stockhausen – neither do I think it doesn't matter whether anyone listens to the music, nor do it think you need to climb the next step on the evolutionary ladder in order to find enjoyment from this type of music as opposed to being 'afraid' of it.
To be sure, it is not for everyone. If your idea of aural fulfillment is the next Britney Spears hit single, then forget it. Even if you like classical (a.k.a. 'serious') music it does not follow automatically that you will like 12-tone music. There's a pretty wide gulf between Mozart and Schoenberg after all.

A tip for getting acquainted with Schoenberg: his 'Variations for Orchestra', opus 31.

The Electronic Primitivism Project is a loose association of musicians that plays mostly my compositions. Below you find for free download a serial music composition for synthesizer and orchestra. It uses both Schoenberg's and Hauer's methodologies , as a result it sounds alternately tonal and atonal – furthermore, there is some rule-breaking trickery involved in several passages, whereby a 12 tone row was sent through sequencer combined with a so-called voltage quantizer; the quantizer takes incoming pitches and then picks the most nearby pitches conforming to a scale (in this case, minor scale) that has the incoming pitch as its tonic keynote. Thus, every time a new pitch class is received by the quantizer it will begin transposing to a new minor scale; in this way the 12-tone row is serialized in a new manner – as a series of different tonal scales.
It's probably best to download the mp3 file and listen to it over a system resp. headphones with good stereo imaging. By the way, the gentleman who unwittingly lent his hacked-to-pieces voice to the final vocoded part is Shimon Peres.

Please note: even though this is for free download, I retain the copyright – no commercial use without my consent (as unlikely as commercial use of this stuff is) and if reproduced for private use, the EPP must be identified as the author.

Matrix (P0: D, G, F#(Gb), D#(Eb), C, B, A, E, G#(Ab), A#(Bb), F, C#(Db)) - 58,6 mb