Subject: Re: Frequency to Mel Formula From: Leon van Noorden <leonvannoorden@xxxxxxxx> Date: Thu, 30 Jul 2009 09:20:51 +0200 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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. Leon On 30 Jul 2009, at 02:22, Richard F. Lyon wrote: > 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