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Re: Frequency to Mel Formula


Certainly the circular or helical aspect of pitch is crucial, in many aspects of pitch perception. But there's also this one-dimensional scale that can be valid in some contexts. I hadn't said or known anything about this "half-pitch" concept, which would certainly bring in the whole octave equivalence complication. But is that what was used for the mel-scale tests and such? I didn't think so. Rather, the idea was to subdivide intervals into perceptually equal intervals ("equisection"). Of course, if the intervals are like 2 octaves or such, or the subject is musically savvy, that's going to bias the judgements based on the pitch circularity. But if the signals are something like narrow noise bands, maybe it would be possible to do the task while avoiding those cues of "consonance" and such?

The "half pitch" idea presumes a well-defined, or well-perceived at least, zero point, as well as a nonlinear mapping to try to get at. Plus it puts the likely result right where the octave is, at least for low frequencies. Did anyone actually use that approach? Richard Warren and Snorre Farner say several studies did so; I'm surprised; it seems like a bad idea. Wouldn't you almost always get a result of half pitch equal to half frequency? Is that the explanation for why the linear-to-log breakpoint ended up so high? Or did they really do equisection of intervals defined by two nonzero tone frequencies?

Stevens says they did both, but the curve he plots show only the equisection results: