Prelude & Fugue & Postlude Numerical Associations

for Solo Cello

“Numerical Associations” is a collection of three pieces for solo cello. They are a Prelude: “5ths by 3rds”, a Fugue: “1 Less”, and a Postlude: “Odds and Squares”. Each piece uses a numerical association as the basis for its composition. The performer does not need to know about the following in order to perform the piece. The Prelude, “5ths by 3rds”, uses a collection of three notes a fifth apart. Three groupings of these collections, transposed by a major third, are used in all. The three three-note collections are A-E-B, D

!

-A

!

-E

!

, and F-C-G. The melody uses only these notes, and is in 11-measure phrases. After completion of the phrase, the whole melody is transposed by a major third. The only constant, non-transposed element of the melody is open C. This is because C is zero. The third statement of the melody cuts off where A-E- B would be played, this is because A-E-B is a collection from the prelude that is used as the first half of the subject of the Fugue, “1 Less”. The second half of the subject is an inversion of the F-C-G collection. A fugue for solo cello can be somewhat limiting, as opposed to a keyboard instrument or ensemble of instruments, because most counterpoint is impossible with a solo instrument. The subject had to be deliberately chosen as a melody that is recognizable, yet adaptable and interesting in the context of where the fugue goes musically. Including a countersubject with a defined set of pitches would have been very difficult, and probably would have made the fugue very mechanical and predictable. The phrase “1 Less” refers to the relationship between the tonic key and the leading tone key. The leading tone key is one half step less than the tonic. The recurrence of this “1 Less” key serves as the countersubject. The Postlude, “Odds and Squares”, is based off the association of odd and square numbers. The sum of N sequential odd numbers will equal N

2

, which, also, is equal to the sum of N sequential integers and the N-1 sequential integers. An integer corresponds to one half step of pitch. C2 is equal to 0 in this piece. The pitches rise from C as N sequential odd numbers, and fall as pitches that are

!

(N

2

) apart. For example, if N = 3, the first sequence of pitches is [(C+1), (C+1+3), (C+1+3+5)], which corresponds to the pitches [C#, E, A]. The second sequence of pitches are [C+3, C+3+3, C+3+3+3], which correspond to the pitches [D#, F#, A]. Each section lasts 12 quarter note beats, and is divided by the ration of N:(N-1). The sequence of N odd numbers sustain for (N/12) quarter note beats, and the sequence of

!

(N

2