Tristimulus (audio)

The concept of tristimulus originates in the world of colour, describing the way three primary colours can be mixed together to create a given colour. By analogy, the musical tristimulus measures the mixture of harmonics in a given sound, grouped into three sections. The first tristimulus measures the relative weight of the first harmonic; the second tristimulus measures the relative weight of the 2nd, 3rd, and 4th harmonics taken together; and the third tristimulus measures the relative weight of all the remaining harmonics.

:$T1\; =\; frac\{a\_1\}\{sum\_\{h=1\}^\{H\}\{a\_h$

:$T2\; =\; frac\{a\_2\; +\; a\_3\; +\; a\_4\}\{sum\_\{h=1\}^\{H\}\{a\_h$

:$T3\; =\; frac\{sum\_\{h=5\}^\{H\}\{a\_h\{sum\_\{h=1\}^\{H\}\{a\_h$

References

* G. Peeters (2003) “ [http://www.ircam.fr/anasyn/peeters/ARTICLES/Peeters_2003_cuidadoaudiofeatures.pdf A large set of audio features for sound description (similarity and classification) in the CUIDADO project] ”
* HF Pollard, EV Jansson (1982) "A Tristimulus Method for the Specification of Musical Timbre". Acustica.