*sesquiCENtennial* was composed to commemorate the New England Conservatory’s 150th anniversary. In writing the piece and to connect the composition to NEC specifically, I wanted somehow to incorporate not only the number 150, but also the years 1867 and 2017, which span NEC’s first hundred fifty years. The musical representations of these numbers are achieved through some applications of set theory.

If we assign the number 0 to the pitch C and count one higher for every semitone ascended (1 corresponds to C-sharp / D-flat, 2 to D-natural, and so on), then the digits of the number 150 can be represented with the notes D-flat, F, and C. This melodic fragment is repeated and layered throughout the first several measures and also forms the beginning of the longer melody that follows shortly thereafter. It is sprinkled throughout the rest of piece as well, sometimes starting at times on different pitches and in different places of any given scale (but maintaining the same melodic intervals). The fragment also appears, appropriately, in the one-hundred-fiftieth measure.

In exploring how I might incorporate 1867 and 2017 into the piece, I uncovered a connection between the musical representations of these two numbers that, to put it aptly, is quite noteworthy. Translating both these numbers into pitches yields the following two sets:

If we ‘rotate’ the first of these two sets—that is, if we move the first note to the last position—we will arrive with the following:

This set can then be transposed down—or up—a tritone (six semitones) to produce the second set: A-flat becomes D (2), F-sharp becomes C (0), G becomes C-sharp (1), and D-flat becomes G (7). [2,0,1,7]. In other words, these two ‘musical years’ are actually very closely related (quite a remarkable feat for the founders of NEC, especially because the music for which this approach to music theory is most closely associated would not be written for another half century or so after the school opened its doors).

While the melodic fragments for 1867 and 2017 (which, as shown above, are really one and the same) are incorporated into the music much like the fragment for 150 is, the overlapping nature of the two tetrachords is also reflected in the structure of the piece. Broadly speaking, the music passes through five different tonal centers: D-flat, A-flat, F-sharp, G, and finally back to D-flat. Thus, 1867 circles back on itself—much as we are now looking back to that year—and in doing so references 2017:

Although it is numerically inspired, *sesquiCENtennial* is also driven by a love for music that transcends set theory or any other particular method of composition. The piece is, at its core, a celebration of music and all who devote time to creating it.