Comparing Harmonic Similarity Measures Using Extracted Chord Features and Ground-Truth Data


Overview of Music and Computation


A Primer on Western Music Theory

Notes: The Basic Building Block

In music, a note is the most basic element. A note is based on pitch, a subjective and perceptual property. Though the pitch of a note is closely related and usually resembles its objective physical frequency (as measured in Hertz, or cycles per second, of a waveform), pitch differs in that its semantic meaning is derived from the listener. This distinction can be demonstrated with a visual analogy used by Terheardt(Terhardt 1974) in figure \ref{fig:virtualpitch2} in which the word aureplacedverbatimaa is apparent even though the visual information suggests only shadow – a pitch can be heard even if its perceived frequency is not physically present. A note also consists of a duration.

[Terheardt’s visual pitch analogy]Terheardt’s visual pitch analogy. In this illusion, the eye perceives contours not present. Pitch describes the information received by a listener even if physical frequencies are not present.

Western music is based on a division of 12 distinct frequencies per octave. An octave is an 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 chromatic scale. A semitone, or 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 \(f_0 \cdot 2^{n/12}\).

Note names are used to classify the pitches in the chromatic scale. Note names consist of a base name and 0 or more 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 (\(\flat\)), but not both, in the note name. Th