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Pitching in

 Dear Ralf, Richard and other Pitchers

 The "tutorial on pitch" has some missing fundamentals:

> A little tutorial on pitch...

> "Frequency = pitch" is a convenient way of measuring or marking
> pitch: The pitch of a sound may be measured by the frequency of a
> pure tone whose pitch is judged to be the same as the pitch of that
> sound  (e.g., Fletcher, 1934; Plomp, 1967, 1976; Terhardt, 1972,
> 1974; Terhardt et al, 1982). But neither the frequency scale nor its
> logarithm is generally proportional to perceived pitch.
>  ........ etc.

Yes. And to further reiterate the distinction between physical and
psychological concepts:  Pitch is a percept that for pure tones
is closely related to physical frequency (but not 1:1).  Sounds
perceived to be of the same pitch may have different physical
frequencies.  'Tis the job of us psychoacousticians to go a hunting
for the physical correlates of auditory percepts and vice versa.

> ............Richard's tutorial continued .........
> The mel scale and its relatives listed above apply only to pure
> tones, and not (or at least not directly) to music or speech. For
> complex tones, it is generally safe to assume that pitch is
> proportional to the logarithm of frequency. This is true over a wider
> range of frequencies for complex tones than for pure tones.

    To use the most popular sentence in human (mis)communication
today:   Whatcha talkin' 'bout Richard ????

   Complex tones comprise many frequency components.  Depending on
the relationship between the components, a single unified pitch or
multiple candidate pitches may be evoked. For a harmonic complex, that
is composed of components that are all multiples of a common
fundamental frequency, that fundamental frequency would likely be
the strongest candidate for a pitch match (as achieved by the ASA 1960
criterion).  This may be achieved even when the fundamental is not
physically present in the spectrum (= Missing F0 or residue or
virtual pitch).
                   In any case, harmonics are not equally spaced on a
log-frequency scale so I'm not sure which logarithm of which frequency
is being referred to.in the "tutorial".
                     The famous Green "profile" stimuli that comprise
components that are equi-log spaced sound far from tonal and are more
likely to be perceived as a collection of multiple, fuzzy pitches
(like someone sitting on a piano keyboard) than a sound with a unified
pitch sensation.
        Pitch is probably the most studied auditory attribute (at least
with the longest history of research).  Given some identifiable,
straightforward physical and physiological substrates, it is relatively
easy to evoke changes in and to measure (via generally relativistic or
ordinal response criteria).  Despite this long history of
investigation, however, all the issues are not resolved (no pun
           Pitch judgments are highly context sensitive.  Depending
on low-level sensory factors such as the "place" on the basilar
membrane activated by a preceding or succeeding sound, the sound being
judged may evoke different pitch judgments.  E.g. residue sounds that
differ greatly in spectral locus, may evoke ordinal pitch judgments
despite equality of F0.
     "Higher level", cognitive factors may also affect pitch judgments.
Different degrees of physical "mistuning" may be acceptable for a
sound depending on musical constructs such as tonality and how well the
mistuned sound can still "fit" into the scalar framework.
       I certainly don't mean to dishearten or discourage Ralf or any
other potential pitchers out there from seeking the fundamentals
about pitch perception.  Just wanted to share my awe, enthusiasm and
some knowledge about a sensational, if complex perceptual feature
of sound.

Since ear-ly
              Punita Singh