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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