Fritz Heinrich Klein
Klein's twelve-tone theories appear to originate independently of Schoenberg's as with Josef Matthias Hauer's, and these claims as well as frequent stylistic changes helped to exclude him from the Second Viennese School, though Klein's theories where highly influential on Alban Berg. Klein considered his piece, Die Maschine: Eine extonale Selbstsatire, Op. 1 (1921) the first in which a twelve-tone row appears along with its retrograde, inversion, and transposed forms.
An all-interval row is a tone row arranged so that it contains one instance of each interval within the octave, 0 through 11. For example, the first all-interval row, by Klein: F, E, C, A, G, D, A♭, D♭, E♭, G♭, B♭, C♭.
In integers this row is represented as
0 e 7 4 2 9 3 8 t 1 5 6
with the interval between each note being
e 8 9 t 7 6 5 2 3 4 1
Klein died in Linz, aged 85.
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