Robert Ferguson
Feb 13, 2003
Melody and Bass Tracking by Masataka Goto

	One of the long standing problem in music information retrieval is how to extract pitch data from a dense audio signal.  Researchers have achieved moderate success in approaching the problem of polyphonic transcription but usually only under strict conditions.  There are, however, stringent conditions that characterize much of the genre of popular music.  Models that adhere to general musicological conditions may already be capable of extracting much of the desired pitch content.

	Japanese researcher, Masataka Goto, has taken a unique approach to the polyphonic transcription problem (Masataka 1999, 31-32).  Goto limited his search by creating a set of rules based on scene analysis principles and music theory that applied to the majority of popular music.  He sought to identify the melody and baseline of a CD track as, for most listeners, melody is essential in the identity of a musical piece and the bass is closely related with the tonality of the tune.

	Prior pitch estimation methods often relied on determining the fundamental frequency of a audio signal, as the fundamental often sounds as the perceived pitch  (Masataka 2000, 757).  Many of these estimation methods assumed that the audio signal contained only a single-pitch sound with aperiodic noises.  In popular music, however, part of the melody's harmonic structure is often overlapped by harmonic elements of accompanying instruments.  As this is often the case, tracing a single frequency component in dense harmonics is neither stable or reliable for fundamental approximation.

	The other danger presented in pitch estimation is the phenomenon of "the missing fundamental" (Masataka 2000, 757).  In this case the audio signal sounds the pitch of the fundamental without its presence.  Even the most sophisticated fundamental estimation methods generally rely on the existence of a frequency component corresponding to the fundamental.   Not only does this approach ignore "the missing fundamental" but also it is unreliable when the frequency components are smeared by the extraneous harmonics of simultaneous sounds.

	Goto’s solution to all these problems has been termed PreFEst or “Predominant-F0 Estimation Method” (Masataka 2000, 757).  PreFEst detects the melody and bass lines by evaluating the relative dominance of every possible fundamental frequency using an Expectation-Maximization (EM) algorithm.  It is an unusual algorithm since no estimation is given to the number of sound sources and works only in the following conditions: 

	The melody and bass sounds have the harmonic structure.
	
	The melody line has the most predominant harmonic structure in middle 	and high frequency regions and the bass line has the most predominant 	harmonic structure in a low frequency region.

	The melody and bass lines tend to have temporally continuous 	trajectories.(Masataka 2000, 757)

	Not surprisingly PreFEst involves two limiting band pass filters for bass and treble and prediction algorithms based on already famous scene analysis patterns and relative dominance of harmonic structure (Masataka 2000, 759).  What is surprising, however, is the preliminary results of PreFEst tracking applied to real CD audio tracks.  Of the audio sampled many of the pop tunes returned 90% successful transcriptions (Masataka 2000, 760).

	The results of Goto’s experiments prove that a well-defined system can extract pitch information for some western tonal music, but they do not finish the problem of polyphonic transcription.  The PreFEst method demonstrates what can be done with a series of well-defined rules.  Future combinations of genre analysis and similar rules to PreFEst for other kinds of music may be the most sound technique for polyphonic transcription.

Works Cited

Goto, Masataka, 2001. A Predominant-F0 Estimation Method for Real-World 	Musical Audio Signals: MAP Estimation for Incorporating Prior Knowledge 	about F0s and Tone 	Models. Proceedings of CRAC-2001 	(Workshop on Consistent & Reliable Acoustic Cues for Sound Analysis).

Goto, Masataka, 2001. A Predominant-F0 Estimation Method for CD 	Recordings: MAP Estimation using EM Algorithm for Adaptive Tone 	Models. Proceedings of the 2001 	IEEE International Conference on 	Acoustics, Speech, and Signal Processing
	V: 3365-3368.

Goto, Masataka, 2000: A Robust Predominant-F0 Estimation Method for Real-	time Detection of Melody and Bass Lines in CD Recordings, Proceedings 	of the 2000 IEEE International Conference on Acoustics, Speech, and 	Signal Processing
	II: 757-	760.