Review TC and CSEG 1 transpositional combination A
Review TC and CSEG 1
transpositional combination ‣ A dyad often combines with its own transposition, resulting in a tetrachord ‣ For example, [C D] and [E F#], could be united to form the whole-tone tetrachord [C D E F#]and repeated ‣ [C D E F#], could be combined with the transposition [F G A B], to form an eight-note diatonic collection.
transpositional combination ‣ Every transpositional combination may be reversed by “de-combination" ‣ Only a small number of octachords can be ‣ created or de-combined by transpositional combination from dyads Any octachord capable of being produced by TC can de-combine in a several ways. ‣ [C D E F F# G A B] = ‣ ([F A C E] and [G B D F#]) = ([FA], [C E], [G B], [DF#];
George Perle’s Bartók chords 1. X = (0123) = the chromatic tetrachord 2. Y = (0246) = the whole-tone tetrachord 3. Z = (0167) = two tritones at T 1
Transpositional combination 1. X = (0123) = the chromatic tetrachord • • (01) at T 2 (02) at T 1
Transpositional combination 1. Y = (0246) = the whole-tone tetrachord • • (02) at T 4 (04) at T 2
Transpositional combination 1. Z = (0167) = two tritones at T 1 • • (01) at T 6 (06) at T 1
XX==(0123) Eb-E-F-F#
Y = (0246) Bb-C-D-E
CSEG Class Two trichordal 3 -1 <012>, 3 -2 <021> Eight tetrachordal 4 -1 <0123> 4 -2 <0132> 4 -3 <0213> 4 -4 <0231> 4 -5 <0312> 4 -6 <0321> 4 -7 <1032> 4 -8 <1302> 11
Which is the “prime form”? I <2013> <1320> RI R R RI <3102> I <0231> 12
Which is the “prime form”? I <0123> <3210> RI R R RI <3210> I <0123> 13
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