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Audio Spectrum of Musical Instruments

Lynch, 2

Results and Discussion

Plotting the graph of amplitude versus time produced little useable data. As can be seen in Figure 2, the result is essentially a large blob of indistinguishable data points. A few interesting effects can be noted, however. The plot increases and decreases in average height to follow the changes in volume of the artist. In this particular plot, taken from the violin sound sample, a sharp decline in amplitude is clear when the musician changed the direction of his bow. The plot becomes slightly more interesting when viewed over a very short time period which allows the sinusoidal waveform to become visible. This is shown in Figure 3.

Figure 2: Amplitude vs. Time

Figure 3: Amplitude vs. Time (zoomed)

More useful data was taken from observations of the power spectrum density plot. From this, it was possible to observe the actual frequency of the amplitude peaks and their period of repetition. These were used to find the note associated with the peaks by using the table in Appendix B. The results showing the first five peaks are given in Table 1, and the power spectrum density plots for each instrument are included in Appendix A, due to their size.

Table 1 - First Five Spectral Peaks (fundemental frequency in bold)

Musician	Instrument	Peak 1 Note	Peak 2 Note	Peak 3 Note	Peak 4 Note	Peak 5 Note
Scott	Violin	135 Hz C#3	523 Hz C5	1043 Hz C6	1565 Hz G6	2088 Hz C7
Mike	Saxophone	268 Hz C4	530 Hz C5	798 Hz G5	1065 Hz C6	1330 Hz E6
Dan	Trumpet	265 Hz C4	530 Hz C5	793 Hz G5	1060 Hz C6	1323 Hz E6

A few observations can be made easily from these graphs. First, the period of the peaks for the violin is twice that of the period for the saxophone or the trumpet. This indicates that the violin is actually playing an octave higher than the other two. Also, the saxophone appears to have a much lower intensity of peaks between 3400 and 4300 Hz. The same effect appears for the trumpet between 10000 and 11000 Hz. All of the signals fall off significantly at approximately 16000 Hz, which was the rated frequency response of the microphone. One final interesting observation is peaks 3, 4, and 5 for the saxophone and trumpet are the notes G, C, and E respectively. These make up the notes of the C major chord, which is often used in symphonies due to its pleasant sound.

A significant amount of noise appeared present in the data, and it is possible that some of the noise may have been improperly interpreted as peaks. This noise probably results from ambient sounds picked up by the microphone, such as computer cooling fans and conversation. There did not appear to be any appreciable 60 Hz interference. Deviation of the peaks from the actual values corresponding to the notes being played and the observed values is due to difficulty accurately reading the frequency of the peaks and improper tuning of the instruments.

Conclusion

This experiment showed the ease with which frequency content of an audio wave can be determined and it's practicality in the study of musical instruments. It appeared that there were several easily distinguishable characteristics between the different instruments, although the observations were only made for one note and on one instrument of each type. It is possible that the characteristics may not exist for different notes, for different instruments of the same type, or even different musicians playing on the same instrument. A statistical analysis should be conducted when time permits to determine if the differences can be used to identify the instruments.

Confirmation of the results of this experiment could allow for many practical applications. Knowing what frequencies are produced by an instrument and their relative intensities can allow the sound of a particular instrument to be synthesized electronically. Alternately, the appropriate patterns can be observed in order to attempt to determine with the aid of software which instruments are being played in a musical recording. It may even be possible to improve the design of an instrument by fine-tuning it so that the harmonics are actually evenly spaced intervals, as they should be.