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Re: Detection of harmonics and rhythmic structure

Dear Brian and List

An algorithm that has some physiological and psychophysical plausibility
is to compute the modulation power spectrum (see refs below).

(a) harmonic structure

For the extraction of harmonic structure the most recent version of this has the
following components

(i)   outer-middle ear,         standard table
(ii)  gammatone filter bank
(iii) hair-cell
(iv)  low-pass                  40 Hz
(v)   onset-cells
(vi)  modulation band-pass filter bank,         approx. 0.5 - 16 Hz

(b) beat induction

If you wish to extract a beat you also need a preferred tempo mechanism, which we have argued
can only be accounted for by the addition a motor component, since a sense of beat has a quite narrow
existence region,  much narrower that our range of temporal discriminability. This shouldn't be
controversial if you consider that most music that has a beat is dance music.

(c) rhythmic structure

Note that rhythmic structure can exist is the absense of a clear beat or harmonic structure. Rhythm
involves the interaction of both temporal grouping and metre. We have argued that temporal grouping
can be extracted by a modulation low-pass filter system. Thus a complete description of rhythm
requires both the band-pass and low-pass represenations and a motor representation.


Neil Todd

Todd, N.P.McAngus (1994) The auditory primal sketch: A multi-scale model of rhythmic grouping.
 J. New Music Research  23(1), 25-70.

Todd, N.P.McAngus (1995) The kinematics of musical expression. J. Acoust. Soc. Am. 97(3), 1940-1949.

Todd, N.P.McAngus (1996) An auditory cortical theory of auditory stream segregation. Network :
Computation in Neural Systems. 7, 349-356.

Todd, N.P.McAngus and Brown, G.J. (1996) Visualization of rhythm, time and metre. Artificial
Intelligence Review   10, 253-273.

Todd, N.P.McAngus, Lee, C.S. and O'Boyle, D.J. (1999) A sensory-motor theory of rhythm, time
perception and beat induction. J. New Music Research. 28(1), 5-29.

Todd, N.P.McAngus (1999) Motion in Music: A neurobiological perspective. Music Perception. 17(1),

Todd, N.P.McAngus et al (2000) A sensory-motor theory of beat induction. Human vs. Machine
Performance. Proceedings of the Sixth International Conference on Music Perception and Cognition.