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Re: Frequency to Mel Formula
Pitch is composed out of two dimensions: chroma and tone height.
The mel scale has a wrong name. It is not the scale for melodies as
these are constructed mainly on the chroma scale.
(not completely, as the contour is also relevant)
The mel scale should have been called tone height scale.
Even absolute pitch perceivers, who make many octave errors, can
discriminate on the tone height dimension.
On 30 Jul 2009, at 02:22, Richard F. Lyon wrote:
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