Serialism is the systematic organization of one or more musical parameters during composition.

The serialism most people identify with involves pitch; as a result, pitch serialism employs twelve-tone techniques: the use of all twelve equal-tempered tones equally without preference for any particular pitch or pitches. Such an austere principle in composition dictates that no pitch shall repeat until most (if not all) of the other pitches have sounded.

This robs the compositional process of a tonal center and dictates that this process must be carefully maintained throughout the entirety of the work in order for it to have any consistency.

This music is also sometimes called atonal (meaning without a tonal center, or key, as it were), or pantonal (meaning that each tone is treated equally).

It is easy to think of this kind of music as directionless or unlistenable, but chromaticism and diatonicism both have pitfalls - if either principle is clung to with veracity, the music will be boring, or indeed directionless. Hence, it is generally acceptable for notes to be repeated, to be phrased, or to be played harmonically (at the same time) as long as the general twelve-tone structure continues to develop.

Twelve-tone mehtods can give composers a fairly unrestricted chromatic procedure which allows him/her to explore greater complexity in orchestration, timbre, rhythm, and melodic development. Although traditional diatonicism is normally avoided, this is still an important concept for any good composer to have a firm grasp of.

The Tone Row
Before actual composition can begin, the composer must establish a row of twelve tones which incorporates every pitch in an octave. For a good piece to result from such organization, the original row must have strong logic, consitency in intervallic placement, and a certain amount of creative inventiveness.


The Matrix
The original ordered row (called P for Prime) can be transposed eleven times: the numeral 0 is used to describe the original pitch level and the numbers 1-11 to describe the transpositions in accordance with the distance in half steps away from the original pitch the transposition is. The different ways to arrange the original row are called Inversion or I (upside down), Retrograde or R (backwards), and Inversion Retrograde or IR (backwards and upside down). The Matrix is a visual tool for organizing your row and making its variations easily accessable.

The original row (P0) begins our matrix, being placed at the very top and from left to right.


P0  |A |E  |Eb |Ab |Bb |F  |B  |C  |G  |Db |D  | G  
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |  |   |   |   |   |   |   |   |   |   |   |    

The inversion of P0 (called I0) is placed down the left hand side of the matrix and is a mirror-image of the original row, with each interval being exactly inverted.
    |I0 |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
P0  |A  |E  |Eb |Ab |Bb |F  |B  |C  |G  |Db |D  | G  
-----------------------------------------------------
    |D  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |Eb |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |Bb |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |Ab |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |Db |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |G  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |Gb |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |B  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |F  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |E  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |C  |   |   |   |   |   |   |   |   |   |   |    
-----------------------------------------------------
    |   |   |   |   |   |   |   |   |   |   |   |    
When done correctly, the I0 row will contain all twelve chromatic pitches. The matrix is then completed by filling the horizontal rows keeping the intervallic distance between the current row and the row directly above constant, or by any number of other transpositional methods.
    |I0 |I7 |I6 |I11|I1 |I8 |I2 |I3 |I10|I4 |I5 |I9    
-----------------------------------------------------
P0  |A  |E  |Eb |Ab |Bb |F  |B  |C  |G  |Db |D  |G  
-----------------------------------------------------
P5  |D  |A  |Ab |Db |Eb |Bb |E  |F  |C  |Gb |G  |B    
-----------------------------------------------------
P6  |Eb |Bb |A  |D  |E  |B  |F  |Gb |Db |G  |Ab |C    
-----------------------------------------------------
P1  |Bb |F  |E  |A  |B  |Gb |C  |Db |Ab |D  |Eb |G    
-----------------------------------------------------
P11 |Ab |Eb |D  |G  |A  |E  |Bb |B  |Gb |C  |Db |F    
-----------------------------------------------------
P4  |Db |Ab |B  |C  |D  |A  |Eb |E  |B  |F  |Gb |Bb    
-----------------------------------------------------
P10 |G  |D  |Db |Gb |Ab |Eb |A  |Bb |F  |B  |C  |E    
-----------------------------------------------------
P9  |Gb |Db |C  |F  |G  |D  |Ab |A  |E  |Bb |B  |Eb    
-----------------------------------------------------
P2  |B  |Gb |F  |Bb |C  |G  |Db |D  |A  |Eb |E  |Ab    
-----------------------------------------------------
P8  |F  |C  |B  |E  |Gb |Db |G  |Ab |Eb |A  |Bb |D    
-----------------------------------------------------
P7  |E  |B  |Bb |Eb |F  |Ab |Gb |G  |D  |Ab |A  |Db    
-----------------------------------------------------
P3  |C  |G  |Gb |B  |Db |Ab |D  |Eb |Bb |E  |F  |A    
-----------------------------------------------------
      
The complete matrix includes all four forms of the row starting on all twelve available notes, adding up to 48 forms in all. The original row and its transpositions run from left to right, the inversion and all of its transpositions from top to bottom, the retrograde from right to left and the retrograde inversions from bottom to top. The numbers outside the matrix indicate the level of transposition.

The matrix may seem like a pain in the ass but it really, really helps in the analysis and compositions of twelve-tone music. At this point the twelve-tone material is ready to use in composition.

Categorization
Pieces of music in which only one version of the twelve-tone row occur at any given time are known as Category 1. All of the harmonic and melodic materials of a Category 1 work are generated from a given row before another version of that row is utilized.

Category 2 make use of more than one version of the row at the same time. This method seems freer but actually requires more control in order to remain effective musically, as contextual dissonances can occur in the form of triadic implications in a non-triadic row or consonant intervals in a primarily dissonant row formation. With enough skill and craftsmanship these anti-musical blunders can be controlled: in fact, many composers prefer to work within this category as it represents the opportunity for restrictive creativity in composition, much the same way that traditional counterpoint does.

When its all said and done, however, the composer's skill will dictate how musical the end product is, regardless of which process used or adhered to. A severe pre-occupation with intervallic relationships and obsessive note-counting will lead to creative sterility and a fialed project.

More extreme forms of serialism exist, including applying these intervallic relationship theories to rhythms, articulations, and dynamics, among other things. Pointilism is the systematic serial separation of intervals by way of octave displacements, rests, contrasting articulations, contrasting dynamics, or any combination of these in a systematic manner. Klangfarbenmelodie (literally "sound color melody") further extends pointilism by way of applying a different timbre or instrument voicing to each pitch, further establishing its uniqueness. Many of these techniques lead to constant variety which has the habit of making the music it is applied to uninteresting, unlistenable, and inaccessable, so major or significantly long works utilizing strict pointilism or Klangfarbenmelodie are very hard if not impossible to produce.

In summary, every composer with concern for his craft should learn about, experiment with, and compose using serialistic techniques. However, care should be used when applying these concepts to an extreme level in a piece of any sort. Twelve-tone techniques give your brain a work out and can be used to add interest or color to a piece; pointilism can be striking if used sparingly, as can be Klangfarbenmelodie. The composer should always keep his listener in mind and know when to say when and what, if anything, is too much.

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