Hearing scientists have worked ever so hard in search of physical correlate of pitch in the mechanics or acoustics of sound sources. However, a pitch meter does it so effortlessly. Consider the odds.
Figure 1 presents two waveforms that generate the same musical pitch A3. The two signals were produced by different configurations of a string. The FFT analysis of the two signals are presented in figure 2. The two signals have the same prime component (166 and 165 Hz). The signal (top) has no fundamental but only odd partials, the resonant component is the first in the spectrum. The signal (bottom) is harmonic, but the fundamental (55 Hz) is not present in the signal, and the prime component (165 Hz) is the third partial. Despite these acoustic discrepancies, the ear perceives the same A3 and the pitch meter agrees with it. What does the pitch meter measure to arrive at the pitch A3?
If we could know, the data could offer insights on the principle of the auditory mechanism, and help in preparing hearing aids for sufferers of hearing loss.
This is not from experience but a possible approach which might be used in such devices, somewhat related to cepstrum analysis.
We expect A3 to contain very specific frequencies, specifically all multiples of 220 Hz.
Thus, to an extent, the spectrum of such an audio signal should be periodic.
Using an algorithm based on accentuating the maxima of a spectrum (This can even be done intelligently, knowing the relative amplitudes present in an oscillating string) and then performing a second fourier transform, the "Spectrum of the spectrum" can reveal a 220Hz periodicity in the spectrum.
If, instead 440 Hz would have stronger spectral line, it is more likely that our fundamental is A4 etc.
Note that even if we artificially remove a fundamental, the same basic periodicity should still be present, allowing for detection.
Hello,
can you offer the two signals to download?
Many greetings,
Christoph
@Christoph
Many thanks for your request. Unfortunately, the project does not encourage interested persons to work on the data of others. Rather, the individuals are encouraged to produce the stimuli themselves, analyse them, and be convinced by their own experiments that the concept is right. The primary reason for this position is that the analysis produce several different results depending on the software in use and the configurations of the software. For example, I used four different software to analyse the same signal and obtained four completely different results, Besides, different configurations of the same software produced totally different results for the same signal. And there arose the question: How does the pitch meter do it?
This problem arose some 19 years ago in my PhD years. We came to the conclusion to set out the methodology and allow others to replicate the experiment and convince themselves by means of their own data.
Now, I presented a paper at the 22nd International Congress on Acoustics last year (Buenos Aires). I was rather surprised that major international publishers and journals on acoustics and music invited me to submit the paper to their journal for republication. I didn't bother. However, the pressure continued. Finally I agreed to give the full paper to a journal and it was accepted without a question. The journal offers me the privilege to set up a group of researchers on this matter. Therefore, the aim is to get participants to replicate the experiment using different musical pitches to test the mechanical model in order to arrive at a large pool of data on this subject. It is therefore not encouraged that one participant analyses the stimuli of another. Otherwise, rather than make scientific progress on the subject, it would turn into a forum for controversies considering the technological limitations mentioned above. At request I can send you the copy of the original paper and you can see the methodology and better appreciate the significance of the project. Basically, just for some insight on the matter, this is the methodology:
(1) Take a string (on a guitar, for example).
(2) Produce any given musical tone (Say C4)
(3) Reduce the string to the shortest sub length possible.
(4) Tune the string using the tension head to produce the same tone C4
(5) Analyse the two signals and observe their spectral structures.
(6) Ask yourself how the ear or the pitch meter arrives at the pitch using the acoustic data obtained.
A global pool of data on this experiment would help scientists provide help for sufferers of hearing loss
Akpan
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