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Western music is based on a division of 12 distinct frequencies per \textit{octave}. An octave is an \textit{interval}, or distance between two frequencies, that corresponds to a power of 2 multiplication. Musical pitch is perceived in a logarithmic scale---one octave above a given perceived frequency is double that frequency; one octave below is half that frequency. The progression of notes containing all 12 pitches in succession in an octave is called a \textit{chromatic scale}. A \textit{semitone}, or \textit{half-step}, is the smallest interval, equal to $1/12$ of an octave. $n$ semitones above a given frequency $f_0$ or $-n$ below can be calculated as $f_0 \cdot 2^{n/12}$.  \textit{Note names} are used to classify the pitches in the chromatic scale. Note names consist of a base name and 0 or more \textit{accidentals}. The base names of a note correspond to the white keys on a piano---in any one given octave there are the following names: $C$, $D$, $E$, $F$, $G$, $A$, and $B$. A base note name can optionally be decorated with an indefinite number of sharps ($\#$) ($\sharp$)  or flats ($b$), ($\flat$),  but not both, in the note name. This can be illustrated with the following context-free grammar (figure~\ref{fig:cfgnote}): \begin{figure}[h!]  \centering  \begin{align*}