Thursday, September 26, 2013

19.) Refresh September 24, 2013


This week I took a break from the modes of limited transposition and decided to focus on another technique that Messiaen used.  It was nice to take a break from the modes and take a different approach.  In The Technique of My Musical Language, Messiaen writes a lot about prime numbers, mainly in regard to phrase length - phrases with a total rhythmic length that is a prime number are preferred.

I decided to use primes in a different way here.  I constructed a sequence of intervals that used exclusively prime numbers, that was non-retrogradable, and that had a total number of thirteen intervals (also a prime number).  Basically, I had to use these intervals like a row, using each one before the next, following their order.  I didn't repeat the intervals within the sequence.   The sequence is the following: [-3,11,5,1,7,2,13,2,7,1,5,11,-3].  I made the thirds minor to avoid a diatonic situation.  All other intervals are major or perfect.

After I finished, I was looking up prime numbers on the internet, mainly to find a title for a piece.  I noticed on the Wikipedia that 1 is not considered a prime number.  My relationship to prime numbers mainly consists of them helping me with stage fright in public restrooms, so I wasn't really aware of this.  But my use of 1 turned out to be one of the most important decisions I made.  It really defined the character of the piece because it was realized with repeated notes.  It was actually annoying to deal with in the composing process, but, along with the juxtaposed perfect fifth, it gave the piece a specific vibe.

The title, Refresh, not only refers to a refreshing break from the modes of limited transposition, but also the September weather in New York City (it's the best), and the refreshment allowed by my recently acquired means of surfing into the cooler months (it's also the best).


  1. This comment has been removed by the author.

  2. You were actually in good company! Until the 20th century, many mathematicians did consider the number "one" to be prime. Goldbach and Euler disagreed about this in the mid-18th century . . . . Only by the early 20th century was there finally some general agreement -- mainly for semantic reasons -- that "one" was not prime.

    1. Thank you Willis! Let's bring back 1 as a prime! Just for the sake of interval sequence generation at least.