Re: Frequency to Mel Formula

["Richard F. Lyon" <DickLyon@xxxxxxx>]

Diana,

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:
http://books.google.com/books?id=r5JOHlXX8bgC&pg=PA166&dq=pitch+curve+equisection&lr=&as_brr=3&ei=VudwStWOPIrykATalqz4Dg

Dick