## Score and MP3 of Sigma X

As promised, here’s an MP3 of Sigma X (generated, not a recording), my piece for concert band for assignment 3 of the music composition course I took last term.  Unfortunately, the balance isn’t very realistic, and I couldn’t get the suspended cymbal and anvil to sound like they’re supposed to, so the percussion is absent from the MP3.  It’s really too bad, since the suspended cymbal rolls would add a lot.  😦

Here’s the score in case people are interested.  In order to fill out the parts to make it a full concert band piece, I still need to write parts for 3rd Clarinet, 3rd Trumpet, 3rd Trombone, Oboe, Bass Clarinet, Bassoon, 2nd Alto Sax., and Euphonium.  It’s easy to see how it’s a lot of work writing for full concert band, but oh well, it’s fun.  🙂

In case people are wondering about the name, sigma x ($\sigma_x$) is one of the Pauli matrices, namely:

$\sigma_x = \begin{bmatrix} 0&1\\ 1&0 \end{bmatrix}$

As an operator, it acts like a NOT gate:

$\sigma_x |0\rangle = \begin{bmatrix} 0&1\\ 1&0 \end{bmatrix} \begin{bmatrix} 1\\ 0 \end{bmatrix} = \begin{bmatrix} 0\\ 1 \end{bmatrix} = |1\rangle$

$\sigma_x |1\rangle = \begin{bmatrix} 0&1\\ 1&0 \end{bmatrix} \begin{bmatrix} 0\\ 1 \end{bmatrix} = \begin{bmatrix} 1\\ 0 \end{bmatrix} = |0\rangle$

It also represents an observable in quantum mechanics, and as part of a Hamiltonian (energy landscape), it effectively represents the “amount of quantum superposition” (I know that isn’t exactly correct, so please don’t flame me) in a quantum system.