A system of musical composition developed by Arnold Schoenberg between 1911 and 1922.
The method assumes absolutely equal harmonic and tonal relationships among all 12 notes of the 12-ET tuning system.
Generally, a note used once is not to be used again until all of the 11 others have been used. A prime row is set up, containing each of the 12 notes in turn, in an order chosen by the composer.
A row may undergo 4 different permutations, as follows:
In addition, any of these 4 permutations may be transposed in pitch to any of the 12 tonal regions; thus there are altogether 48 different rows based on the original.
An interesting fact about 12-edo, simply because of numerical properties of the number 12, is that it may be divided into many smaller sub-sections, speaking here either about the notes themselves or the intervallic structure of the row-order. Serial composers often take advantage of this by cleverly devising a 12-tone row composed of 3 tetrachords or 2 hexachords with identical, reverse, or inverted intervallic structures. When the rows are subjected to different permutations and transpositions, these smaller units are repeated intact in the different versions of the row, allowing serial composers to employ a technique akin to "common-chord" modulation in tonal music. Schoenberg's pupil Webern was probably the first to explore this procedure in depth.
While evidently enshrining 12-edo tuning, serialism has been applied with some success to other tunings. Ben Johnston has used serial technique with 11-limit JI tuning, notably in his 6th Quartet.
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