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6.5.2 Realtime Chord Recognition of Musical Sound: a System Using Common Lisp
Music
Takuya Fujishima
I designed an algorithm to recognize musical chords from the input signal of musical sounds. The keys
of the algorithm are:
1. use of "pitch class profile (PCPf. or an intensity map of twelve semitone pitch classes
2. numerical pattern matching between the PCP and built-in 'chord-type templates'" to determine
the most likely root and chord type.
I introduced two major heuristics and some other improvements to Marc Leman's "Simple Auditory
Model" so as to make it a practical one.
I implemented the algorithm using Common Lisp Music. The system worked continuously in realtime
on an Silicon Graphics 02 workstation and on Intel PC platforms running Linux. It could take the input
sound from the audio input, or from a sound file, and could display the recognition results on the fly.
In the experiments. I first used the pure tone and three other timbres from electronic musical instruments
to estimate the potential capability of the system. The system could distinguish all of 27 built-in chord
types for chord tones played in the above mentioned timbres. Then I input to the system a 50 second
audio excerpt from the opening theme of Smetanas Moldau. Without the two heuristics, the accuracy
remained around 80 percent level. When they were applied, the accuracy rose to 94 percent ... 196 out
of 208 guesses that the system made were musically correct. These experiments showed that the system
could recognize triadic harmonic events, and to some extent more complex chords such as sevenths and
ninths, at the signal level.
References
• Leman. Marc. Music and Schema Theory. Springer-V'erlag.
• Schottstaedt. William. Machine Tongues XVII. CLM: Music \ Meets Common Lisp. Computer
Music Journal. Vol.18. N'o.2. pp.30-38. 1994.
• Fujishima. Takuya. Realtime Chord Recognition of Musical Sound: a System Using Common Lisp
Music. Proceedings of the 1999 International Computer Music Conference. Beijing. China, pp.
464-467.
6.5.3 Speaker Normalization for Speech Recognition Based On Maximum-Likelihood Linear
Transformation
Yoon Kim
In speaker-independent speech recognition, where a pre-trained model is used to recognize speech uttered
by an arbitrary speaker, minimizing the effects of speaker-dependent acoustics is crucial. Acoustic
mismatches between the test speakers and the statistical model result in considerable degradation of
recognition performance. In this work, we apply linear transformation to the cepstral space, which
can be viewed as the Fourier dual of the log spectral space. Gaussian mixture is the most popular
distribution used for modeling speech segments. If we restrict the feature transformation to be that
of convolution, which is equivalent to filtering in the log spectrum domain, the resulting normalization
matrix exhibits a Toeplitz structure, simplifying the parameter estimation. The problem of finding the
optimal matrix coefficients that maximize the likelihood of the utterance with respect to the existing
Gaussian-based model then becomes nothing but a constrained least-squares problem, which is convex in
nature, yielding a unique optimum. Applying the optimal linear transformation to the test feature space
vielded in considerable improvements over the baseline system in frame-based vowel recognition using
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