pitch

[Richard M Warren <rmwarren@xxxxxxxxxxx>]

Dear List,

I can't help jumping in on the discussion of pitch that developed into
much broader issues.  Al Bregman (27 August) comments on the need to keep
in mind the distinction between the stimulus and its percept, since the
same term can be used to describe both.  He regretted the lack of
appropriate verbal distinctions to separate the physical "SOUND 1" from
the experience produced by SOUND 1 which he called "SOUND 2."  On August
28, Dan Mapes-Riordan suggested that SOUND 1 should be referred to as
"acoustic wave" and SOUND 2 referred to simply as "sound."  The
troublesome confusion of stimulus and percept is not restricted to physics
and hearing.  Newton, in describing his experiments with light, stated
that it is incorrect to use such terms as red light and green light
since "...the Rays to speak properly are not coloured."  However, bowing
to convenience and usage, he did go on to use color terms to describe the
rays, and so I guess that unfortunately this inappropriate usage is bound
to continue even though it can cause trouble in psychophysical judgments.

Chuck Watson (27 & 28 August) divided "sense-based behavior" into two
categories:  (1) "Sensory Capabilities" (sensitivity, resolving power, and
channel capacity); and (2) "Response Proclivities" (tendencies to assign
specific verbal labels or to respond in specific nonverbal ways to
specific stimuli).  I agree wholeheartedly, but would like to take this a
bit further, perhaps further than Chuck would want to go.  I believe that
sensory capabilities, or the limits of sensory detection and
discriminability, are related pretty closely to limits imposed by physics
and built-in physiological limits (I imagine there is no argument on
this).  However, once we cross this threshold and enter the domain of
supraliminal stimuli, we are dealing with responses that are interpreted
whenever possible in terms of corresponding events and conditions in the
environment.  Indeed, that is what our sensory systems are all about --
keeping us alive and interacting appropriately with our environment.
Hence, there is an obligatory evaluation of all sensory input from
exteroceptors in terms of external physical correlates (hence the
confusion of SOUND 1 with SOUND 2).

The topic of physical correlates as a basis for evaluating supraliminal
sensory input leads me to comments made by Bill Hartmann (27 August)
concerning quantitative judgments of sensation.  He stated that the
previous discussion concerning pitch had not distinguished between
prothetic and metathetic continua, stating "Prothetic is associated with
amount; metathetic is a point on a scale.  Loudness is prothetic, we say
'More loudness.'  Pitch is metathetic, we say 'Higher pitch.'  We don't
say, 'More pitch'."  However, Stevens, Volkmann, & Newman (JASA, 1937, 8,
185-190) based their MEL scale of pitch upon direct quantitative
judgments.  They had their subjects adjust an oscillator to produce a
pitch one-half that of the standard for frequencies ranging from 125 Hz to
12,000 Hz.  Wever in his book "Theory of Hearing" (1949) noted that for
frequencies below 5,000 Hz (that is, for pitches within the range of
orchestral instruments) half frequency was judged half pitch.  This
suggests that the basic unit of musical scales (the octave) was used as
the physical correlate for quantitative judgments of pitch.

The only other experiment dealing with the scaling of pitch that I am
aware of from another lab was that of Siegel, (Am J Psychol, 1965, 78,
615-620), who also found that frequencies one octave below the standards
were judged to be half pitch (average of 48.9% for frequencies within the
range of orchestral instruments).  Since equal stimulus ratios produce
equal subjective ratios (the hallmark of a "prothetic" continuum), a
psychophysical power function can be constructed for pitch with an
exponent of unity.

Stephen Barrass (31 August) wrote that "colour hue," in addition to pitch,
is a metathetic continuum.  However, when a variety of colors (red, green,
and blue) were each mixed with white (Warren, Perception & Psychophysics,
1967, 2, 448-452), I found that quantitative judgments of the respective
hues were each inversely proportional to the square root of the percentage
of white in the mixture, which corresponds to a "prothetic" power
function with an exponent of 0.5 for each hue.  [For a discussion of the
evidence linking a square root rule to other types of visual magnitude
judgments and to their physical correlate, see Warren, Psychol Rev, 1969,
70, 16-30.]

Finally, the issue of the physical correlate for the power functions
relating sound intensity to loudness is discussed at some length in my
target article, "Measurement of Sensory Intensity," Behav & Brain Sci,
1981, 4, 175-223, and in Chapter 4 of my book, Auditory Perception:  A New
Analysis and Synthesis (Cambridge University Press) due out next month.

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