Derived row

In music using the twelve tone technique a derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. Anton Webern often used derived rows in his pieces.

Related Topics:
Music - Twelve tone technique - Tone row - Generator - Anton Webern - Derived

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Rows may derived from a sub-set of any number of pitch classes that is a divisor of 12, the most common being the first three pitches or a trichord. This segment may then undergo transposed, inversion, retrograde, or any combination to produce the other parts of the row (in this case, the other three segments).

Related Topics:
Set - Pitch class - Divisor - Trichord - Transposed - Inversion - Retrograde

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One of the side effects of derived rows is invariance. For example, since a segment may be equivalent to the generating segment inverted and transposed, say, 6 semitones, when the entire row is inverted and transposed six semitones the generating segment will now consist of the pitch classes of the derived segment.

Related Topics:
Invariance - Equivalent - Semitone

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Here is a row derived from a trichord taken from Webern's Concerto:

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O represents the original trichord, RI, retrograde and inversion, R retrograde, and I inversion.

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The entire row, if B=0, is:

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• 0, 11, 3, 4, 8, 7, 9, 5, 6, 1, 2, 10.

For instance, the third trichord:

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• 9, 5, 6

is the first trichord:

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• 0, 11, 3

backwards:

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• 3, 11, 0

and transposed 6

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• 3+6, 11+6, 0+6 = 9, 5, 6 mod 12.

The opposite is partitioning, the use of methods to create segments from entire sets, most often through registral difference.

Related Topics:
Partition - Registral

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See musical set theory.

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