Experiment 1b : Incomplete Tones, Same Pitch

In a natural situation where musical tones are often incomplete or overlapping, it would be desirable to be able to classify incomplete tones. To test this possibility, we attempted classification using only part of the tone to determine how this loss of information would affect classification performance. It was also hoped that this would shed some light on the salient features enabling classification.

Given that, in this experiment with FFT, a complete guitar tone is represented by a sequence of windows at 50 points in time, the first 10 points of the tone were pruned to exclude all information associated with the attack. The correct classification rate dropped to 89.3% indicating that valuable information for classification is contained in the attack. To further explore the importance of information contained in the attack, we attempted to classify with incomplete tones containing only the attack and a small portion of the decay. Initially, we attempted classification with the first 10 data points and achieved a 96.8% correct classification rate. This result was somewhat higher than expected, indicating that there is enough information in the attack alone to produce good classification results. The attack was then cut to five data points and achieved 97.6% correct classification. Overall, this indicated a classification rate with a short attack nearly as high as with the complete tone. In the next chapter, we will investigate the attack in more detail in an attempt to discover the key features of the attack which allow discrimination between tones.

A number of other subsets of the data set were tried as a basis for classification, namely: progressively smaller subsets from the attack and subsets of 20 data points taken at a progressively later stage of the decay. The results are summarised below in table 4.9. The table 4.9 shows that, given the data is synchronised with respect to the start of the tone, good classification results can be achieved with almost any portion of the tone. The best results, however, were obtained with segments from the attack. Even when the size of the subset was reduced to two data points, the classification rate exceeded that of the complete decay. We conclude that, for the guitar, the most valuable information for classification is contained in the attack but there is enough information in any portion of the tone to enable good classification. To further explore the robustness of classification with the decay, subsets of twenty data points were taken at various stages of the decay. From our review of timbre research in chapter 2, we expected that the power of the higher

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Portion of Tone % Class. Rate whole tone 97.5 attack (10pts) t=1:10 96.5 attack (5pts) 97.6 attack (3pts) 94.3 attack (2pts) 93.7 decay (40pts,t=11:50) 86.9 decay (20pts,t=11:30) 83.8 decay (20pts,t=21:40) 87.4 decay (20pts,t=31:50) 85.6

Table 4.9: Classification rates with reduced information using a portion of the complete tone.

harmonics might diminish at a faster rate than the fundamental in guitar tones. This would result in a reduced amount of information being available for classification for subsets taken from later in the decay. A surprising result was obtained in that the classification rates did not decline for subsets taken from the later portion of the tone. In other words, similar classification rates were obtained for subsets at any portion of the decay. This suggested that we should examine the relationship of spectral centroid with time over the duration of the tone to determine empirically if there is any change in the amount of spectral data available as the tone decays. The plot is shown in figure 4.9 below.

0 10 20 30 40 50 Time 26 27 28 29 30 Spec Cent

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We can see that, overall, the spectral centroid decreases with time but not by a large amount. This confirms earlier findings that higher harmonics attenuate at a faster rate than the fundamental and lower harmonics. We conclude that the timbre of each guitar tone is slowly changing with time but that there is still ample spectral information available to enable classification at the same rate. The finding that the timbre of a guitar tone varies with time suggests that comparing two tones that are not synchronised with respect to the attack may present difficulties.

Since very good classification results were obtained with just the first two data points of the tone, further classification was attempted with just one data point at various points in the tone. This is essentially a single snapshot of the frequency spectrum of the tone at a particular time. The results are set out in table 4.10 below.

Tone Sample(1pt) % Class. Rate attack (t=1) 85.0 attack (t=2) 91.8 attack (t=5) 87.5 attack (t=10) 86.9 decay (t=20) 81.9 decay (t=30) 81.9 decay (t=40) 76.2 decay (t=50) 80.6 mean spec (20pts,t=10:30) 81.3

Table 4.10: Classification rates with data from just one window taken at different points in time across the complete tone.

We observe that relatively good classification results are obtained with just one data point. In the decay section the correct classification rate was roughly in accordance with that for the mean value (81.3%) taken over a period of 20 points. Note again that the correct classification rate does not degrade as the power of the harmonics attenuate with time (except at t = 40). It is interesting to note that there is a rough correlation between the classification rates in table 4.10 and spectral centroid in figure 4.9. As with the larger subsets of data points, the best classification results are obtained with points within the attack - the peak being 91.8% at t = 2.

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