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From: harnad@mind.UUCP (Stevan Harnad)
Newsgroups: sci.med
Subject: Re: tone deafness?
Message-ID: <212@mind.UUCP>
Date: Wed, 12-Nov-86 02:22:53 EST
Article-I.D.: mind.212
Posted: Wed Nov 12 02:22:53 1986
Date-Received: Wed, 12-Nov-86 04:54:59 EST
References: <2376@bu-cs.bu-cs.BU.EDU> <3808@columbia.UUCP> <210@mind.UUCP> <3817@columbia.UUCP>
Distribution: net
Organization: Cognitive Science, Princeton University
Lines: 201
Summary: 2nd attempt to define standard psychophysics of absolute judgment

In article <3817@columbia.UUCP>, zdenek@heathcliff.columbia.edu (Zdenek Radouch) writes:
> The only problem with your "definition" is that it is as little explicit
> as those I was complaining about. I'll try to describe the ambiguity.
> Human ear can detect frequencies approximately from 20Hz to 20kHz.
> There is INFINITE number of frequencies (or pitches) in this range.
> The resolution of the ear is not infinite but certainly about two orders
> of magnitude higher than resolution necessary to identify notes in any
> musical system. A person identifying the pitch is basically determining
> if an unknown frequency Fx is from interval <Fmin,Fmax>. It's perfectly
> clear that the ability to do that will depend on the size [o]f the interval
> i.e., on ratio Fmax/Fmin.

The trouble is that your considerations conflate (1) detection,
(2) discrimination ("resolution"?) and (3) identification. The psychophysics
of each of these is different. Detection (1) is the judgment whether any
stimulus at all is detectably present, not whether it is discriminably different
from any other stimulus (2), nor whether it is absolutely identifiable
(3). Detectability is usually determined using signal detection
theory, calculating a d' for the distance of a given signal from noise
for a given subject. Discriminability (resolution) is measured, as I
indicated, by pairwise same/different judgments. With this method, the
"just-noticeable-difference," (jnd) can be calculated. In an isotropic
continuum (one that obeys Weber's Law that the perceived relative
intensity of a pair of stimuli will be proportional to the ratio
of the logarithms of their physical intensities) this jnd can be
thought of as a constant minimal increment, the smallest interstimulus
difference that you can "resolve" (relatively) along the continuum. The
jnd is never (as you correctly anticipate) infinitely small. It is a
psychophysical quantum unit.

So much for relative discrimination (2). Absolute identification (3) is
another matter, and, as Miller (op. cit.) pointed out, it does not generally
covary with the sensory continuum in question, or its specific "resolution"
properties, but depends on how the stimuli are represented -- i.e., on
exposure, learning, memory, and/or possibly also on innately tuned
feature-detectors. All things being equal, for a given (Weberian,
isotropic) sensory continuum, 7 +/- 2 subintervals are the maximum
number into which it can be partitioned before the error rate in
absolutely identifying which interval a given stimulus belongs to
rises precipitously. The same is true (up to a limit, related to the
size of the jnd) for any subinterval of a continuum; in other words,
if the range of alternatives (the confusability matrix) is reduced,
the resolution "grain" of absolute judgment IN JND UNITS becomes
finer; however, it remains 7 +/- 2 "chunks" or subintervals of any
given interval.

The only exceptions to these general principles are NONISOTROPIC
continua -- continua that show discontinuities or local
compression/expansions in the Weber function. Another way of putting it
is that the jnd size grows and shrinks along the continuum instead of
remaining constant (for log ratios). For continua of this kind the
"resolving" capacity of absolute judgment may exceed Miller's limit,
i.e., we may be able to identify more than 7 +/- 2 subintervals
reliably. This phenomenon is known as Categorical Perception. It is
exhibited (innately) by the chromatic frequency continuum (the visible
spectrum) as reflected in our color identification capacity, by
several acoustic continua (e.g., the "2nd formant transtition" along
the ba-da-ga continuum -- a one-dimensional variable in the
spectrogram) as reflected in our phoneme discrimination capacity, and
in the auditory frequency continuum, as reflected in the pitch
identification capacity of those with "perfect pitch" (including, as I
said last time, those with short-term perfect pitch -- "relative
pitch" -- while they retain a reference note in immediate memory).

Typically, in categorical perception, the boundaries of the absolutely
identifiable subintervals correspond to the compression maxima in the
Weber function: the regions where the jnds are the smallest. Here a
small physical difference (between categories) is perceived as being larger
than a large difference elsewhere (within categories). The book I
mentioned is concerned with the underlying mechanisms of this
phenomenon, including whether it is innate or derived form exposure or
learning.

> 1. Human ear can identify the ratio 1.0006. This is my estimate, comments
>    welcome.
> 2. The distance between two closest tones in western musical system
>    (12 notes per octave) is 1.06.
> 3. The octave has ratio of 2.
> If we divide the audio range into two halves (low and high), anybody with
> normal hearing can tell whether the pitch is high or low. That corresponds
> to range of abo[u]t 30.

For the correct psychoacoustic parameters of pitch discrimination I
must refer you to a textbook of psychophysics or audiology. However, I
again have to point out that "identify" is being misused, because
identification is an absolute judgment and is not, in general,
predictable merely from a knowledge of discriminability and sensory
ratios (apart from the 7 +/- 2 rule for any given interval). [I should
also add that, because of physics (the "overtone" series, or upper
harmonics of any raw fundamental pitch) as well as physiology (of the
cochlea and the auditory representation), the octave has a privileged
status in perception, so we should probably only be considering
sub-octave subintervals in calculating our resolving capacity, relative
or absolute.] And again, high/low identifiability is predictable from
Millerian considerations alone (so is hi, 2, 3, 4, 5, 6 lo), but no
more than that can be said a priori, especially if it is not known
whether or not the continuum in question is isotropic.

> As a result of my experience in music and acoustics I can tell you the
> frequency of a tone with approximately octave error i.e., factor of 2.
> This is a result of an exposure to music, not result of any training. Note
> that I don't satisfy your definition of having absolute pitch.
> 
> An individual with absolute pitch can identify interval of 1.06.
> Since there is nothing absolute or natural in the concept of measuring time
> and thus frequencies, this individual MUST HAVE GONE through some training,
> or at least he must have been exposed to the same thing I was.

I can't follow you here. What is "octave error" if I present you with
440 hz? What error range will you have? Semitone? Tone? Fifth? Octave?
Also, what is the difference between exposure to music and training?
Do you mean listening only? Have you never hummed a tune? And which of
my definitions of AP do you fail to satisfy? What most people call
"relative pitch" (i.e., temporary absolute pitch while remembering a
reference tone) is a kind of (temporary) "absolute pitch" too. Do you
have that? Finally, I can't follow at all the part about the
unnaturalness of frequencies. Would you say the same of colors (i.e.,
that they must have been trained)? It seems to me it's an empirical
question which instances of categorical perception arise from
training, which from exposure, which innately, and which not at all.

> You said "it must be given its correct (arbitrary, learned) "label" or name.".
> That's crude simplification. The person under test is performing quantization.
> i.e., labeling the unknown as "nth member of N" (even the person with absolute
> pitch is going to label all frequencies from <438Hz,442Hz> as "a1").
> N=10 (my case) doesn't imply absolute pitch; N=100 does! How about N=73?
> What's the definition?

A person has (long-term) AP if he can identify (or produce) -- in
isolation, and without a reference note -- any audible pitch to within,
say, the nearest eighth-tone. There may be an additional phenomenon
of the individual who can remember (hence identify or produce in
isolation), say, an A-440 to within a jnd, and using that, can
generate all the notes in the well-tempered A-440-based system to
within a jnd using that as a reference note (consciously or
unconsciously). This potential reference-based RECODING of the entire
continuum, however, seems to me to remove part of this problem from
the arena of sensory psychophysics and into that of cognitive
representation. [Note that such a person would not have the same
resolving capacity for stimuli in an A-445-based system, i.e., all the
jnd's in-between.] Miller gave a similar example of recoding when he
showed that, in general, we can only remember a string of 7 +/- 2
digits, e.g., strings of 0's and 1's. If, however, we overlearn the
decimal names for binary strings of, say, 1 - 20, then, using those
larger, recoded "chunks," we become capable of remembering a
correspondinly longer string of binary bits. [Note that all you need
is an absolute memory for one pitch, e.g., A-440, plus relative pitch
for the well-tempered scale, plus octave invariance, to accomplish all
the rest of "perfect pitch" by recoding.]

According to the theory of categorical perception, by the way,
"quantization" consists of the "bounding" of subregions of a continuum
by compression and/or expansion of the Weber function.

> Anyway, back to my original question. We have three people here.
> 1. "musical ignorant" that clearly identifies ratio of 30.
> 2. Me, identifying ratio of 2 after some training.
> 3. Person with absolute pitch identifying ratio of 1.06 after some training.
> It's clear that (3) remembered or learned more than (2) and somebody said
> that there is an evidence that the skills of (3) are inherited.
> I'd like to know what's that evidence.

The empirical question is not settled. J & W Siegel (in several articles
in the Journal of the Acoustical Society, reviewed in the
forthcoming categorical perception book I mentioned) found that
categorical perception for pitch could be trained, but it is not clear
that what they demonstrated was the long-term version or the familiar
short-term ("relative pitch") version, or whether or not there are
individual differences in how readily or to what degree people can be
trained in this.
 
> >				....As long as someone is not entirely
> >deaf, some frequency discrimination must be present.
> 
> Why? Seems to me that it'll depend on the actual hearing mechanism. Also,
> considering that most of the theories prefer acquisition in frequency
> domain, I would tend to disagree with your statement.

I can't follow this either. Hearing may vary in acuity for frequency
discrimination, amplitude discrimination, temporal resolution, and
verious aspects of timbre and acoustic pattern. I am just suggesting
that most people who call themselves (or are called) "tone deaf"
probably retain considerable frequency discriminative ability, and
have probably been called tone deaf either because they cannot carry or
or identify or recognize a tune, or perhaps they have demonstrated
diminished frequency discrimination. Production is clearly a different
problem from discrimination. So is tune identification and
recognition. I doubt that there is a condition (short of total
deafness) in which amplitude discrimination, etc., are relatively
spared and frequency discrimination is flat. Finally, what do you mean
"acquisition"? There are acquisition theories for identification and
categorical perception, but none that I know of for relative
discrimination, which most psychoacousticians and audiologists
consider innate, requiring, at most, some auditory exposure (i.e.,
something short of total sensory deprivation) in order to become fully
functional.
-- 

Stevan Harnad                                  (609) - 921 7771
{allegra, bellcore, seismo, rutgers, packard}  !princeton!mind!harnad
harnad%mind@princeton.csnet