#59 Measurement option of frequency spread

[JuleeHong]

Nevertheless, spectrographic analysis provides less effective definition on the frequency axis. Frequency spread, however, can be measured accurately using a spectrum. It is two-dimensional, the time-element being ignored (or technically, assumed to be a unity). The spectrum accordingly analyses all events during the frame-size and measures the accumulated energy in each frequency band. By setting the frame-size relatively large, we obtain values of k sufficiently small to allow very accurate readings of frequency. The frame-size was set at 131072, which with a sample-rate of 22,050Hz, gives a value of k of 0.1682.

k = 22050/131072 = 0.1682.

The advantage of this method is that we obtain a very accurate measurement of the frequency-spread.

The procedures involved in spectral analysis are as follows. The operator selects a particular ‘step-like’ event, of which he/she wishes to measure the frequency-spread in the spectrogram by clicking the mouse. The software logs the selected segments and plots a graph of the spectrum. The pitch name and frequency are provided automatically when mouse clicks prompt the definition of the nearest peak.

Actual frequencies can be determined by spectrum analysis, and the attached Figure shows spectra of the F#3 and G3 in bars 7-8. I have only shown the first three harmonics, but the software shows the entire frequency range, of which the usable maximum is half the sample-rate, (11kHz in my example). Although the upper frequency limit of electric shellac recordings of the pre-war era was about 5 kHz, the frequency-range of this analysis is up to 11 kHz.

The y-axis of spectral analysis shows relative decibel levels for each peak frequency. The strongest signal is taken as 0dB. In spectra, frequency widths usually indicate vibrato, but we need to select one frequency reading from the spectrum. Usually, a reliable solution is to take the strongest peak of frequency reading from the spectrum. The interval between the two notes is the ratio of their frequencies, which in Figure between the fundamentals is 190.7/182.8, or 73.25 cents.

[JuleeHong]