Tone-row music and serialism III

"Anton Webern - Variations for piano, Op. 27". The tone-row used in this piece is:

	E - F - C# - Eb - C -  D - G# - A - Bb - F# - G - B
	0 - 1 - 9  - 11 - 8 - 10 - 4  - 5 - 6  - 2  - 3 - 7
The first 7 bars present both P0 and R 7 at the same time:
	Right hand	0  1  9  11  8  10  |  10  8  11  9  1  0
	Left hand	7  3  2   6  5  4   |   4  5  6   2  3  7
P0 starts in the right hand (first six sounds) and continues in the left hand (last six sounds) while R 7, starts in the left hand (first six sounds) and continues in the right hand (last six sounds). The result is a a complex symmetry where the first three and a half bars of the piece are presented in retrograde starting in bar 4. The crossing of the hands seems to be a constant feature in this work and the tone-row also crosses from one hand to the other.

I2 (starting in the right hand) and RI7 (starting in the left hand) are used between bar line 8 and bar line 11 with the same kind of crossing and sharing of sounds in the middle. RI7 does not include the sound B or 7 which it is found immediately preceding and immediately after this statement. Bar 11-15 repeat the first seven bars without the crossing from hand to hand and bars 16-19 are a more concentrated (some rests are omitted) version of 8-11.

With only 2 set forms, P0 and I2 and their retrogrades, Webern creates the entire first page of this piece.

The second movement has a very intricate structure.

This piece and a few other similar works by Webern were influential in triggering a new school of thought (composition) after WWII in Europe. Following his example, these European composers (Boulez, Stockhausen, Berio, Nono, etc.) and Milton Babbitt in the USA, started to apply strict control over all musical parameters and not only over pitch and duration. The most obvious such parameters are:

	Duration 		Time interval
	Pitch			Frequency
	Dynamics (loudness)	Amplitude
	Timbre			Waveform
	Articulations		Envelope
The first column above includes terms used by musicians; the second, their correspondent description in acoustics. Although widely accepted, this chart is not without flaw since it represents a rather crude description of the qualities of a sound as it was proposed in late 19th century by Helmholtz. More about this to follow soon.

It is interesting to observe that, in the Western musical culture, pitch and rhythm were practically the only ingredients in the music written before the 16-17th centuries. The Baroque period introduced dynamics as an important element of music while only in the 19th century composers started paying serious attention to timbre (orchestration). A strong interest in composing the way articulations are applied is very recent. Historically, the list of parameters has increased from 2 to at least 5 in the last millenium.

More on sound parameters.

A riddle Webern liked

			S  A  T  O  R
			A  R  E  P  O
			T  E  N  E  T
			O  P  E  R  A
			R  O  T  A  S
The Creator keeps the world together, a stoic saying.

A brief look at the row used in his Op.24:

	B - Bb - D | Eb - G - F# | G# - E - F | C - C# - A
or                 |             |            |
        0   11   3 | 4    8   7  |  9   5   6 | 1   2    10
          -1   4   |    4   -1   |   -4   1   |   1   -4


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