Harmonic pitch class profiles - AbsoluteAstronomy.com

Harmonic pitch class profiles (HPCP) is a vector of features extracted from an audio signal

Audio signal

An audio signal is an analog representation of sound, typically as an electrical voltage. Audio signals may be synthesized directly, or may originate at a transducer such as a microphone, musical instrument pickup, phonograph cartridge, or tape head. Loudspeakers or headphones convert an electrical...

, based on the Pitch Class Profile descriptor proposed by Fujishima in the context of a chord recognition system. HPCP is an enhanced pitch distribution feature which are sequences of feature vectors describing tonality

Tonality

Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

measuring the intensity of each of the 12 pitch classes of the temperate scale within an analysis frame. It is also called Chroma. By doing some process on musical signals, HPCP feature can be found and be used to measure pitch similarity by computed in a frame-by-frame basis, and only uses the local maxima of the spectrum

Spectrum

A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

within a certain frequency band. The process is related to time-frequency analysis

Time-frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations...

. In general, chroma features is robust to noise (e.g., ambient noise or percussive sounds), independent of timbre and played instruments and independent of loudness and dynamics.
HPCPs are tuning independent and consider the presence of harmonic frequencies, so that the reference frequency can be different from the standard A 440 Hz. The result of HPCP computation is a 12, 24, or 36-bin octave-independent histogram

Histogram

In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...

depending on the desired resolution, representing the relative intensity of each 1, 1/2, or 1/3 of the 12 semitones

Semitone

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....

of the equal tempered scale.

General HPCP feature extraction procedure

The block diagram of the procedure is shown in Fig.1.
The General HPCP feature extraction procedure is summarized as follows:

Input musical signal.
Do spectral analysis to know the frequency components of the music signal.
Use constant Q transform
Constant Q transform
In mathematics and signal processing, the Constant Q Transform transforms a data series to the frequency domain, and is related to the Fourier Transform ....

to convert the signal into a spectrogram. (The constant-Q transform is a type of time-frequency analysis
Time-frequency analysis
In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations...

.)
Do frequency filtering
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

. Only a frequency band between 100 and 5000 Hz is used.
Do peak detection. Only the local maximum values of spectrum are considered.
Do reference frequency computation procedure. Estimate the deviation with respect to 440Hz.
Normalize the feature frame by frame dividing through the maximum value in order to eliminate dependency on global loudness. And then we can get a result HPCP sequence like Fig.2.

Pitch class mapping is a procedure for determining the pitch class value from frequency values. A weighting scheme with cosine function is used. It considers the presence of harmonic frequency, taking account a total of 8 harmonics for each frequency. In order to map the value on a one-third of a semitone

Semitone

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....

, the size of the pitch class distribution vectors has to be equal to 36.

System of measuring similarity between two songs

After getting the HPCP feature, the pitch of the signal in a time section is known. The HPCP feature has been used to compute similarity between two songs in many research. A system of measuring similarity between two songs is shown in Fig.3. First, time-frequency analysis is needed to extract the HPCP feature. And then set two songs’ HPCP feature to a global HPCP, so there is a standard of comparing. The next step is to use the two features to construct a binary similarity matrix. Smith–Waterman algorithm is used to construct a local alignment matrix H in the Dynamic Programming Local Alignment. Finally, after doing post processing, the distance between two songs can be computed.

General HPCP feature extraction procedure

System of measuring similarity between two songs

See also