Computer recognition of musical instruments : an examination of within class classification

This dissertation records the development of a process that enables within class classification of musical instruments. That is, a process that identifies a particular instrument of a given type - in this study four guitars and five violins. In recent years there have been numerous studies where between class classification has been attempted, but there have been no attempts at within class classification. Since timbre is the quality/quantity that enables one musical sound to be differentiated from another, before any classification can take place, a means to measure and describe it in physical terms needs to be devised. Towards this end, a review of musical timbre is presented which includes research into musical timbre from the work of Helmholtz through to the present. It also includes related work in speech recognition and musical instrument synthesis. The representation of timbre used in this study is influenced by the work of Hourdin and Charbonneau who used an adaption of multi-dimensional scaling, based on frequency analysis over time, to represent the evolution of each musical tone. A trajectory path, a plot of frequencies over time for each tone, was used to represent the evolution of each tone. This is achieved by taking a sequence of samples from the initial waveform and applying the discrete Fourier transform (DFT) or the constant Q transform (CQT) to achieve a frequency analysis of each data window. The classification technique used, is based on statistical distance methods. Two sets of data were recorded for each of the guitars and violins in the study across the pitch range of each instrument type. In the classi¯cation trials, one set of data was used as reference tones, and the other set, as test tones. To measure the similarity of timbre for a pair of tones, the closeness of the two trajectory paths was measured. This was achieved by summing the squared distances between corresponding points along the trajectory paths. With four guitars, a 97% correct classification rate was achieved for tones of the same pitch (fundamental frequency), and for five violins, a 94% correct classification rate was achieved for tones of the same pitch. The robustness of the classification system was tested by comparing a smaller portion of the whole tone, by comparing tones of differing pitch, and a number of other variations. It was found that classification of both guitars and violins was highly sensitive to pitch. The classification rate fell away markedly when tones of different pitch were compared. Further investigation was done to examine the timbre of each instrument across the range of the instrument. This conformed that the timbres of the guitar and violin are highly frequency dependent and suggested the presence of formants that is, certain fixed frequencies that are boosted when the tone contains harmonics at or near those frequencies.