Twelve-note piece of February 19, 1953 Josef (Matthias) Hauer

Origin of a twelve-note piece 
(from the example of "the twelve-note piece of February 19, 1953)

This twelve-note piece bears the subtitle: 

This crystallic combination of harmony, melody and rhythm arises in the following way:
Hauer subdivides the chromatic scale into four three-note groups:

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Now he chooses a twelve-note row that flows again into the beginning (the 13th note = the first note) and writes each note into the line where it appears in the three-note group:

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In every line the note is sustained as a harmonic sound until he can step by step modulate into the next note.

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The 13th chord is: C - E - G - B. As Hauer considers the 12-note row a closed texture that flows back into the beginning (12-note cycle), the same applies to the newly gained chords. Consequently the 13th chord C - E - G - B is also used as the first chord and by suspension the following chords also become four-note chords.

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In this way a series has arisen, a twelve-note row with chords.

In Hauer's twelve-note piece of February 19, 1953 these four-note chords are played in the right hand in syncopated quavers. The left hand plays a melody that has been devised according to rules, consisting of the notes of the chords.

Origin of the melodic line 

Further information:
Steinbauer: Josef Matthias Hauers Zwölftonspiel
Zwölftonreihe
Dreitongruppe
Klangreihe