From: mclaren
Subject: a blizzard of misinformation
--
Paul Erlich is a very smart fellow who has done
commendable work in looking up valuable references.
Alas, Paul often has a tendency to shoot from
the hip, based on incomplete or out-of-date info.
Such an example occurred when Paul Erlich
wrote that "the preference for stretched
intervals only occurs in melodic, not harmonic,
intervals" (or words to that effect).
This is a common enough canard, and it turns
out to be untrue. In actual fact unbiased listeners
uniformly tend to hear *both* melodic *and*
vertical intervals which are stretched as
"pure" and "just," while they tend to hear
unstretched small-integer ratio harmonic
*and* melodic intervals as "too narrow" and
"impure."
(I mention "unbiased" because it is always
possible to train yourself to recognize any
kind of interval from its beat structure if
you confine yourself to a narrow range
of very restricted integer-harmonic timbres.
This is why A-B-X tests using a wide variety
of different timbres in an objective psychoacoustic
experiment are so important. Simply setting
up a synthesizer and playing such-and-such
and interval and saying, "Oh, I can hear that
the interval is [fill in the blank]" is useless
in probing the human auditory system, since
you know what to listen for and thus have
unwittingly biased yourself.)
The evidence that listeners hear *both*
stretched harmonic *and* melodic intervals as
"pure" is cumulative, the data have been confirmed
by hundreds of experiments, and the evidence goes
back more than 160 years. C.J. Delezenne
in "Memoires sur les valeurs numeriques des
notes de la gamme," in Recueil des travaux
de la Societe des Sciences de Lille, 1826-1827,
was the first researcher to identify *both*
melodic *and* harmonic preference for
stretched intervals. Delezenne used an
adjustable monochord and meticulously
recorded the values his test subjects
heard as "pure" intervals in terms of
fractions of a Pythagorean comma (cents
were not yet a measurement in use).
The next researchers who duplicated these
results were Cornu and Mercadier, who used
a phonautograph (as scholars, you know what
this instrument is and require no explanation)
and by examination of the tracings on the
lampblack-coated camphorated cellulose
strips Mssrs. C & M were able to calculate
with precision the frequency of sounds impinging
on the phonautograph. Cornu & Mercadier
found that the mean intonation for a vertical
dyad heard as a "pure" major third was
1.251, close to but sharper than the just
5/4; a consecutive-tone series of tests on
musical subjects yielded the much sharper
value of 1.2666 for melodic "just" thirds.
See Cornu & Mercadier, "Sur les intervalles
musicaux," Comptes Rendus de l'Academie
Royale des Sciences, 1869a, pp. 301-308
for proof.
In 1876 Preyer found that vertical intervals
as large as 397 cents were still identified
by some subjects as "pure major thirds."
Preyer's results are suggestive, but not
conclusive, since he gave his data in terms
of an "index of sensitivity" to intervals
rather than in terms of analysis of variance,
as would be done today. Preyer's value
for the "pure" major third represents a
weighted average of the minimum and maximum
values cited by test subjects. For details, see
Preyer, W. T., Ueber die Grezen der Tonwahremung,
Jena, 1876.
In 1897-8 the extremely underrated acoustician
and music theorist Carl Stumpf studied perception
of the minor third by test subject under 3
conditions: melodic ascending, melodic descending,
and simultaneous dyad. His results show a marked
asymmetry in the spread of sharp vs. flat intervals
judged "pure." For the minor third, this means that
the test subjects were more inclined to accept
considerable flatting that slight sharping. Stumpf
concluded that the "point of subjective purity"
shifted toward flat minor thirds.
He conducted the same series of tests with major
thirds and found exactly the opposite tendency.
For major thirds, the point of subjective purity shifted
toward sharp thirds. Melodic intervals had to be tuned
significantly sharper to be perceived as "pure"
than simultaneous dyad major thirds, but *both*
had to be sharper than just to be perceived as
"pure." See Stumpf, C., and H. F. Meyer,
"Massbestimmungen ueber die Rienheit
consonanter Intergvals," in Beitraege zur
Akustik und Musikwissenschaft, Vol. 2, 1898,
for full details.
Moran and Pratt tested melodic and vertical
intervals but didn't give detailed breakdowns:
they state merely that there is an average error
of 18 cents for the intervals of the 12-TET scale.
They did, however, find that subjects were more
likely to hear intervals chosen from equal
temperament as "pure" and "just" than intervals
chosen because they exhibited small integer
ratios. It's unclear whether this was due to
the effect of familiarity with 12-tet, however.
See Moran , H. and C. C. Pratt, "Variability of
Judgments On Musical Intervals," J. Exp. Psych.,
Vol. 9, 1926, for more info--but not much more.
The article is very short on details, alas.
P.C. Greene cites exhaustive stats shows a
marker preference for melodic Pythaogrean
thirds: see Greene, P.C., "Violin Performance
with Reference to Tempered, natural and
Pythaogrean Intonation," Iowa Studies in
Music, Vol. 4, pp. 232-251, 1937, also
see Greene's JASA study published in the
same year.
Incidentally the entire University of Iowa
Studies series supervised by Seashore remain
Incidentally the entire University of Iowa
Studies series supervised by Seashore remain
a remarkable resource. I heartily recommend
these to *every* microtonalist as a compendium
of what performers actually *do*, as opposed
to the intervals they *claim* they play.
The second world war pretty much shut down
psychoacoustic research, so the next
significant papers on the subject are from
the late 1940s and the 1950s.
J. F. Nickerson, in "A Comparison of Performance
of the Same Melody in Solo and in Ensemble with
Reference to Equi-Tempered, Just and,
Pythagorean Intonation," PhD thesis, University
of Minnesota, 1948, found the same perception of
stretched melodic *and* harmonic intervals as
"pure" (although as usual melodic intervals had
to be stretched more widely than vertical
dyads before they were heard as "pure" or "just"
or "in tune.").
There are so many studies from the 1950s
and 1960s and 1970s that I will cite only
3 more: Ward, W. D., "Music Perception" in
Foundations of Modern Auditory Theory, Ed.
J. V. Tobias, 1970--more support for my
statement and more contradiction of Paul
Erlich's claim that listeners do not perceive
stretched vertical dyads as "just" and just
vertical dyads as "too narrow" and "impure."
In 1975 Terhardt and Zick published an
extremely interesting paper which links
of accompaniment required intervals
be stretched to be heard as "pure," while
other types of accompiment required that
be stretched to be heard as "pure," while
other types of accompiment required that
all intervals be contracted to be heard
as "pure." This applies to the vertical
intervals of the accompaniment as well
as to the consecutive intervals of the melody.
See Tehardt, E., & Zick, M., "Evaluation of
the Tempered Tone Scale in Normal,
Stretched and Contracted Intonation,"
Acustica, Vol. 32, 1975, pp. 268-274.
The most recent reference which refutes
Paul Erlich's claims and proves my
statement of fact is Sundberg, Johan,
"The Science of Musical Sounds,"
The Academic Press: New York, 1991,
page104: "In the case of the octave,
the craving for stretching has been
noticed for both dyads and melodic
intervals." Table 4.12 on Sundberg's page
102 gives "Average sizes and standard
deviations for dyads between vibrato
tones adjusted by musically experienced
listeners." Average for M2nd is 199 cents,
for Major third was 402 cents, for perfect
fifth 704 cents, for octave 1204 cents.
Notice that these are in fact dyads.
As mentioned, Paul Erlich is a smart
fellow with good intentions but occasionally
he does miss the mark by making a claim
which isn't based on fact. His posts contain
more errors than other people's posts merely
because Erlich posts more useful information
than most other subscribers. The total amount
of incorrect information in Erlich's posts as
a percentage is actually quite low.
--mclaren
