I have started reading an article, called “Mosaic Polyphony: Formal Balance, Imbalance, and Phrase Formation in the Prelude of Schoenberg’s Suite, Op. 25”, by Richard B. Kurth. He suggests “mosaic isomorphism” as a method of analysis by Donald Martino and Andrew Mead for this piece, that is applicable to any work composed in the twelve-tone system. Isomorphism is a concept in mathematics that means “a one-to-one correspondence between two sets that preserves binary relationships between elements of the sets.” (Britannica, Academic Edition)
Through isomorphism, in music, first each passage is separately analyzed in terms of intervallic and rhythmic relations. In the next step, through a more fundamental division, the smaller, yet independent group of two tones are observed. This leads us to a precise and detailed understanding of the relations between the two pitches of each cell (dyad: a two-member group) and later in the passages. The result would be perception of the logic that the composer has chosen and followed in order to achieve balance or even imbalance throughout the piece in terms of pitch and rhythm. Concerning pitch, the result of analysis will be finding the intervallic relation between each two pitches, where and how often do they appear, whether there is a relation between the dyads containing pitches with the same interval and if yes, do they complete, follow or oppose each other. Moreover during the process of analysis we might even notice the probable modifications executed to the pitches of similar dyads by the composer.
The explanation of author about how the method approaches the rhythm of music is: “The form-producing aspect of these rhythmic relationships between subunits must be conceived analytically twofold. It must be considered on the one hand with regard to specific ‘quantitative’ relations between duration and rhythmic alignments and, on the other, with regard to more abstract ‘qualitative’ relations- that is, allowing for the fact that one subunit may precede, follow, or overlap another in temporal progressions.” (Kurth, 192)
For the coming week I will continue with summarizing this article as well as presenting some examples taken from the Prelude of Op. 25 Suite.
- Kurth, Richard B. Mosaic Polyphony: Formal Balance, Imbalance, and Phrase Formation in the Prelude of Schoenberg’s Suite, Op. 25. Theory Spectrum, Vol. 14, No. 2 (Autumn, 1992), pp. 188-208. http://www.jstor.org/stable/746107. Web.
- “isomorphism.” Encyclopædia Britannica. Encyclopædia Britannica Online Academic Edition. Encyclopædia Britannica Inc., 2012. Web. 15 Nov. 2012. <http://www.britannica.com/EBchecked/topic/296410/isomorphism>.