Born in Philadelphia and growing up with a love for music and mathematics alike, composer and theorist Milton Babbitt found a way to incorporate the two together. He, through his studies and compositions, became one of the biggest contributors to serialist music of 20th century. He did more than just extend the practice and understanding of 12-tone music in itself, though. Milton Babbitt was one of the forerunners in “total” serialism, the application of serialist concepts to aspects of composition such as dynamics and rhythm in addition to pitch; in fact, his *Three Compositions for Piano* is often credited as being the first total serialist work.

When taking an analytical eye to Babbitt’s *Three Compositions for Piano*, movement I, one can clearly see his systematic approach to the piece. To comprehend Babbitt’s compositional decisions, though, one should begin by constructing a full matrix (see photo) based on the first twelve pitch classes stated in the left hand.

From this point, it is easy to see the basis from which *Three Compositions for Piano* was constructed. Beginning with P0 in the left hand and, shortly after, P6 in the right hand, Babbitt then makes use of an RI1 row in the left hand which is followed by the occurrence of R0 in the right hand (mm. 3-4).

Just by observing this small portion of the piece, several observations can immediately be made. The first interesting fact to note is Babbitt’s use of combinatoriality in this work, a technique that he essentially brought to serialist music. This is evident upon first employment of P0 in the left hand and P6 in the right: two seemingly unconnected row choices which actually serve to unify the piece through their similar content. As can be seen through the following diagram, these two pieces are *hexachordally combinatorial*, as the first six pitch classes in R0 are the same (though ordered differently) as the last six of row P6, and the reverse is true for the following six pitches.

This is seen again immediately in measures 3-4, with the use of row RI1 in the left hand and R0 in the right hand. Though the row choices do not seem to correspond with one another, they actually contain combinatorial hexachords. Through use of this technique, Babbitt was able to combine the similar pitch material to unify the piece.

This is not the only unique technique found in this short passage we’ve analyzed thus far. In just these first four measures, we can see this combinatoriality along with the other notable feature of this piece: serialism as applied to dynamics, that which makes this piece truly the first work of “total serialism.”

Taking note of these dynamic markings in this short passage, we see that the first two rows (mm.1-2 in both the left and right hand) are marked *mp*. Measures 3-4, however, employ different dynamic levels: *p* in the left hand and *mf* in the right hand. Observing Babbitt’s row choices in these measures that correspond with the dynamic changes will reveal that *mp* is used at the onset of both occurrences of P rows. Similarly, *mf* appears to correspond with R and *p* with RI.

Continuing the analysis of both of these new techniques used by Babbitt (dynamic serialism and use of combinatorial hexachords) will confirm that this, his *Three Compositions for Piano*, truly broke new ground for serial music by employing these tactics throughout. At measure 5, we see the first occurrence of an I row (I7) in the left hand, marked with the first use of the dynamic *f*, rounding out and confirming the system of dynamic serialism: P – *mp*, R – *mf*, RI – *p*, I – *f*. This is followed by RI7 in the right hand; these two rows contain hexachordal combinatoriality, as the row is in fact the same one in retrograde. Beginning at measure 7, we see R6 assumed in the left hand followed by I1 in the right; these rows are also hexachordally combinatorial. Measure 9 only contains P0. Measure 10, however, contains R0 (in the right hand) and RI1( in the left hand) simultaneously, followed by I1 (right hand) and RI1 (left hand) in measure 11. Both of these make use of the same combinatoriality we’ve seen thus far. Just as in measure 9, measure 12 only uses one row, and the combinatoriality is not present as a result. The next two measures, on the other hand, both use this technique: through use of R0 (right hand) and I7 (left hand), in measure 13, and RI7 (right hand) and P0 (left hand) in measure 14. This pattern repeats again in measures 15-17: one measure of a single, non-combinatorial row, followed by two measures of hexachordal combinatoriality. Measure 15 makes use of R6 by itself, while combinatoriality is employed in measure 16’s R6 (right) and I7 (left) and measure 17’s P6 (right) and R6 (left).

One should not overlook, when examining the pitch class complexity in these measures, the serialism of the dynamic markings as well. As previously discussed, every use of a prime (P) row (mm.1-2, m.9, m.14, m.16, m.17) is accompanied by a mezzopiano dynamic marking. Each retrograde (R) row, on the other hand, is marked mezzoforte (mm.3-4, mm.7-8, m.10, m.13, m.15, m.17). The rows of retrograde inversion (RI) use the piano dynamic (mm.3-4, mm.5-6, m.10, m.11, m.14), and the inverted rows (I) are marked forte (mm.5-6, mm.7-8, m.11, m.12, m.13, m.16).