# Overview

This analyser implements the virtual pitch algrorithm of Ernst Terhardt et al (1982), followed by analysis parameters described in part by Richard Parncutt (1989). It is very similar to the pitch analysis in PsySound2.

The term ‘pitch’ is used in here the psychoacoustical sense - the analyser is concerned with modelling perceived pitch. This is different to both physical frequency analysis, and automatic music notation (voice tracking).

# Outputs

## Virtual Pitch Pattern

This time-spectrum represents the strength of virtual pitches (using Terhardt's algorithm).

## Spectral Pitch Pattern

This time-spectrum represents the strength of spectral pitches (using Terhardt's algorithm).

## Chroma Pattern

Chroma salience is calculated following Parncutt (1989), with the following qualification.

It is assumed that a pitch that is perfectly in tune to an equal temperament pitch category will always be heard only as the corresponding chroma. If a pitch is halfway between two pitch categories (50 cents out of tune) then there is a 0.5 chance of either of the two corresponding chromata being heard. Thus a linear interpolation is made so that deviations from equal temperament contribute to the tallies and probabilities of two adjacent chromata. Clearly these assumptions are simplistic (just intonation is more in-tune than equal temperament, and the distribution of probability may be context sensitive).

## Pure Tonalness and Complex Tonalness

Pure Tonalness and complex tonalness are calculated using the algorithms given by Parncutt (1989, pp.91-2). Pure tonalness reflects the audibility of spectral pitches. Complex tonalness reflects the audibility of virtual pitch, and might be thought of a measure of how similar the spectrum is to a harmonic (or complex) tone.

## Multiplicity

Multiplicity is an estimation of the number of tones simultaneously noticed in a sound. The algorithm is given by Parncutt (1989, p.92).

# Code Authors

Terhardt's virtual pitch algorithm implementation was supplied by him, and adapted for the program by Matt Flax and the PsySound3 team.

# Key References

Parncutt, R. (1989). Harmony: A Psychoacoustical Approach. Berlin, Springer-Verlag.

Terhardt, E., G. Stoll and M. Seewann (1982). “Algorithm for Extraction of Pitch and Pitch Salience from Complex Tonal Signals.” Journal of the Acoustical Society of America 71(3): 679-688.