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Brain potentials during sleep: An investigation of electroencephalographic individual differences and their constancy

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ATTRIBUTES OF COMPLEX TOMES
by
William H* Diehte
A dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy,
in the Department of Psychology, in the Graduate
College of the State University of Iowa
August, 1940
ProQuest Number: 10592862
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ii
AC3D!OWLEDOMEHTS
The writer is very greatly indebted to Pro­
fessor Don Dewis Dor the many important suggestions and
criticisms given during the course of this investigation*
Thanks are due to Professor Arnold Small, Professor
^ilton Cowan, Professor Carl K* Seashore, Professor Grant
Fairbanks, and Professor Kenneth Spence for helpfulness
in^pVoviding subjects for this experiment*
Hi
TABLE OF CONTENTS
Part
Part
Part
Part
Part
Part
I* Introduction • • • • • • • • • » * « » *
II • Apparatus. * * * • . «
Page
1
• • • * * * * * *
7
III. Procedure and Results* * • * * • • • • *
10
IV* Control Experiments* * * * * ............. 34
V* Discussion
VI*
..........
57
Conclusions* . * .......... * * * * * * *
77
Bibliography* * • • • « « • * * • * * • • • * • * •
81
1
I*
INTRODUCTION
The characteristics of complex tones which are
commonly denoted by the term timbre have never been rigid­
ly determined or defined.
Musicians use a loose and
variable terminology in describing their tonal experiences,
and psychologists have done little more than to describe
the general and superficial aspects of a few simple types
of complex tones.
Because adequate information on timbre
was lacking, the present investigation was undertaken.
Its specific purpose was to discover whether or not com­
plex tones have identifiable attributes other than pitch
and loudness.
It Is generally admitted that all tones, both
complex and pure, have the attributes of pitch and loud­
ness.
There have been differences of opinion, however, as
to whether complex tones possess an attribute of timbre
or any attributes other than those of pure tones.
One
group of investigators has held that a complex tone Is
nothing more than a combination or blend of pure tones.
On the other hand, current writers In general psychology
and In acoustics often list timbre as one of the three basic
characteristics of tone.
of Ohm *s law of acoustics.
The first view is an outgrowth
This law combines a knowledge
of the physical nature of complex tones with certain facts
of auditory analysis, and states, in effect, that each
2
simple vibration in the stimulus gives rise to a simple
ton© which may be heard Individually.
The knowledge that
a complex ton© consists of numerous simple vibrations and
that trained observers can hear some of these as simple
tones seems to underlie the belief that all complex tones
can be accounted for psychologically as combinations of
simple tones#
Whether or not the data concerning auditory
analysis warrant this conclusion la open to question.
It is true that competent observers can "hear
out,” in turn, the partials of some complex tones.
As
many as the first ten can sometimes be distinguished.
Helmholtz (6) reports the hearing out of partials up to
the sixteenth.
In order to accomplish this, it was neces­
sary to us© a thin string having loud upper partials and
to strike the particular point calculated to give the
greatest loudness of the particular partial under obser­
vation.
Helmholtz points out the "considerable difficulty”
experienced by one who first attempts to hear the In­
dividual partials.
That the process is difficult and
slow is also Indicated by TItehener*
periment on clang analysis he ©ayes
In reporting an ex­
”SIx observers,
chosen without reference to musical training, heard the
third partial within twenty minutes from the beginning of
the experiment, and thereafter heard all the partials up
to and including the seventh” (16, p. 76).
k monochord
3
was used as the source of sound#
To obtain these results,
it was necessary to direct attention to the partial it
was desired to hear#
A brush was held to the string in
such a manner that, when it was struck lightly, only the
desired partial sounded#
When the subject had heard this
for a short time, the string was deadened and qiickly
struck again in a way which produced its normal tone of
many partials#
The observer tried to continue hearing the
partial when the complete ton© was sounded#
With all this
help, it still took up to 20 minutes to hear the third
partial, which, according to Helmholtz, is the one most
easily distinguished#
Certain results from the Iowa laboratory also
emphasize the difficulty of hearing out partials.
Lewis
and LIchte (9) asked subjects to Identify the particular
partial which was prominent In each of five complex tones#
In each tone, a partial was of greater intensity than
those adjacent to it in the partial series#
The tones were
of about two seconds duration and were presented in ran­
dom order#
The subjects, with one exception, were unable
to designate th© correct partials#
The tones were then
presented in pairs, and the subjects were asked to state
whether the two members of th© pair differed in timbre.
The subjects were able to differentiate the tones on
this basis#
4
Egan (5) studied the masked, absolute threshold
of* the fifth partial in a complex tone, under two con­
ditions#
In one condition, the partial was present during
the first half of the stimulus period; in the other
condition, during th© second half of th© stimulus period*
In other words, th© threshold was measured in one instance
when the partial was subtracted from the ton© while the
tone was sounding, and In th© other, when the partial was
added to the tone*
Hie threshold was several db lower
when the partial was added to th© ton©.
Th© point is
that a partial is apparently more difficult to detect in
the presence of other partials when attention is not
drawn to it by Its addition to an existing stimulus tone*
The difficulty of hearing Individual partials as
such may be contrasted with th© ease and Immediacy with
which differences among complex tones of the same pitch
and loudness can be noted*
It will be shown, for example,
that the complex tones used in this study were discrimi­
nated on the basis of timbre when th© duration of the
tones was only two seconds*
Furthermore, common experi­
ence show® that speech sounds are easily discriminated,
although th© durations of these sounds may be measured In
fractions of a second*
Many persons are incapable of
hearing out partials in all but the simpler tones, and
there are many tones the x>&rtials of which cannot be
5
detected by th© most competent listeners*
In such cases,
however* discriminations on the basis of timbre alone
can be made*
TItchaner recognised the fundamental prob­
lem when he wrote?
"Most of us, however, lack the training, and
some of us lack the ability, to resolve a compound
tone Into its simple components* TJnder these
circumstances, the ton© is Itself heard as simple,
but has upon It a certain colouring or timbre,
which varies with the various instruments11 (17,
P* 101}*
The conditions under which speech sounds and musical tones
are usually discriminated, and the conditions under which
the tones used in th© present experiment were scaled,
suggest that such tones are differentiated more or less
Immediately without analysis into constituent elements*
Th© investigation proceeded on the assumption
that complex tones are usually heard as single and that
they have fundamental characteristics denoted by the
term timbre*
The tones scaled in this experiment were
equated in loudness? and measurement© showed that, for
the observers used, the tones did not differ signifleantly
in pitch*
They must have differed, therefore, in som©
attribute or attribute© other than pitch and loudness*
It was the purpose of this study to determine those
attributes*
Boring (2) has suggested two criteria by which
an attribute may be established.
The first of these is
6
independent variability*
This requires that the proposed
attribute be a different function of stimulus variables
than is any other attribute*
The second criterion re­
quires that the attributes be sufficiently different so
that discrimination between them does not become diffi­
cult*
Subsequent discussion will attempt to show the
complex tones have attributes, aside from pitch and loud­
ness, which probably satisfy these criteria*
7
XX*
APPARATUS
The complex tones used in the investigation were
produced with a multiharmonic generator of electrostatic
typ©, the basic features of which have been described by
Eurtz and Larsen (7) and by Lewis and Larsen (8)*
This
instrument generates electrical currents which, after
amplification, are capable of producing in loudspeaker
or phones complex tones containing as many a© 18 consecu­
tive partial©.
All the partials are harmonic, that is,
their frequencies are integral multiples of the frequen­
cy of the fundamental component*
In th© tones studied,
the fundamental frequency was set at either 150 or 180
cycles*
The Intensity level and phase angle of each
partial were subject to control*
Th© output of the generator, after passing
through the amplifier and attenuation pad, could be led
Into a Western Electric 555 receiver in an acoustically
treated "dead” room (nonreverb©rant) for listening by a
single subject, or It could b© led to the phonograph re­
cording studio*
A vacuum tube voltmeter In the output
circuit of the generator made possible the measurement
of the intensity of the various harmonics*
the generator could be calibrated*
each time It was used*
In this way,
It was calibrated
The Western Electric receiver had
a
previously been calibrated by the Bell Telephone Labora­
tories*
The over-all response of* the recording equipment
was calibrated several times during th© course of the
study*
This was done by recording each of the 16 partials
at equal input intensity and then measuring the ampli­
tude of response
method*
on the record by means of the light-band
This method has been described by Buehm&nn and
Meyer (5)*
Each setting for any given ton© spectrum
took into account th© output characteristics of th© gener­
ator as well as the response characteristics of th©
particular system being used*
Many of th© complex tones were presented to th©
observers from phonograph records*
In the preparation
of the records, the generator was successively set to
produce th© various tones and these tones were recorded
separately on acetate disks*
Th© records were played on
a Magnovox Concerto phonograph, and the tones thus pro­
duced were the ones judged by the subjects*
The response
of this phonograph was known to b© approximately equal
for all frequencies used*
The response curve for this
phonograph is given by Saetveit (11).
Each series of
tones used was recorded four separate times.
In the
course of the experiment, no record was played often enough to cause any marked change In the nature of the tones
reproduced*
9
Practical considerations dictated the use of
the phonographic technique.
A more accurate set of stim­
uli would have been obtained if the generator output had
been connected to th© phon© in th© ^dead” room and the
subjects had listened there*
This would have necessi­
tated apparatus to make possible a rapid switching of the
generator from one tone to another*
While such equipment
is possible, its extreme elaborateness precluded its us©
in the present experiment*
Th© use of th© recording and
phonographic technique undoubtedly introduced some amount
of error*
It is felt, however, that with th© precautions
taken, this error was not large enough to affect the re­
sults.
Th© stimuli used probably did not differ greatly
from those intended.
Other equipment was used in certain control
experiments.
are discussed.
It will b© described when those experiments
10
III*
PROCEDURE AHD RESULTS
The first problem was to find different series
of tones each of which seemed to demonstrate a basic type
of change In quality or timbre, to obtain a psychological
seal© for the various series, and to state th© relations
between th© stimuli and th© responses*
Preliminary ob­
servations indicated that a seemingly important type of
qualitative change, tentatively labelled dulIness-bri &h tness, could be obtained by means of a series of tones In
which the midpoint of the energy distribution was gradual­
ly shifted upward along the frequency continuum*
A
particular method of changing the location of the mid­
point of the energy was then adopted and a series of tones,
the spectra of which are shown in Figure 1, was chosen to
be scaled*
In this figure, the relative intensities of the
V
partials in each tone are shown*
Each contour-line
represents the spectrum of one tone In the series*
The
points at which a given contour Intersects the 'vertical
lines for th© various partials Indicate th© relative In­
tensities of those partials in that tone*
Th© figure does
not indicate the intensity of one tone as compared with
another, nor does it Indicate th© absolute intensity of
a partial in one tone as compared with Its absolute in-
•
■
i
RELATIVE INTENSITY IN DB
11
5
6
7
8
9 10 11 12 13 14 15 16
PARTIAL
FIgurc 1
The Relative Intensities of tea Partials
In tach Tone of the D-b Series
The points at which, a contour-line Intersects trie vertical
lines Indicate the relative Intensities of the partials
In that tone.
The designation of the tone
is given at one end of the contour.
12
tensity in another*
The contour for the tone labelled
B-Q indicates that all the partials were of equal Inten­
sity*
The contour for tone D-15 Indicates that the 16th
partial was 15 db less Intense than the fundamental, the
15th partial 14 db less Intense than the fundamental, the
14th partial 15 db less Intense, etc*
In tone B-15, the
1st partial {fundamental} was 15 dfe less than the 16th
partial, the 2nd partial 14 db less intense than the 16th,
the 3rd 13 db less intense, etc*
In designating these
tones, the letter Indicates the direction of the slope and
the numeral indicates the difference in db between the
most Intense and least intense partials*
Th© series will
be referred to as the D-B series*
In the recording of this series, it was neces­
sary to adjust th© intensity level of each tone so that
lall tones would sound equally loud when played from th®
record*
Th© proper intensity levels for th© various
tones were determined in the following manner*
was recorded at a standard reference intensity*
Tone B-G
Tones
B-15 and D-15 were each recorded at several different in­
tensities in the region assumed to give equal loudness
with the B-G tone*
Three observers then compared th©
loudness of th© B-G ton© with the loudness of B-15 at each
of th© recorded intensities and selected th© Intensity of
B—15 which sounded most nearly equal in loudness to th©
13
B-0 tone*
When th© Intensity of the B-15 tone had thus
been determined, th© Intensities for the other tones In
the series between B-0 and B-15 were found by linear
interpolation between the values for the intensities of
B-15 and B-0*
In similar fashion, one of the D-15 tones
was selected as being of equal loudness to B-G, and the
values of Intensity for the tones in between the two were
secured, by linear interpolation#
Each tone in the series
was then recorded for a duration of about two seconds#
Th© onset and cessation of th© tones were mad© gradual ©nough to prevent transient effects#
The fundamental fre­
quency was 180 cycles#
The tones of this series were scaled by the
method of paired comparisons, first with a preliminary
group of 25 observers, then with a final group of 255*
The subjects were students, most of them undergraduate,
in music, speech, and psychology*
For the preliminary
group, th.© experimental procedure was such that each tone
in the series was paired with every other tone.
For th©
final group, each ton© was paired with not more than
four other ton©®, these being the two neighboring tones on
each side In th© series#
Tones at th© extremes of the
series were paired with only two or three tones*
Thus,
B—6 was paired with B-5, B-G, B-9, and B-12, while D-12
was paired only with D-15, D-9, and D-6, and D-15 only
14
with D-12 and 0-9*
Th© number of inter comparisons in
tine final sealing was restricted because the preliminary
work had shown that the pairs eliminated were discrimi­
nated so easily that the results were useless in the com­
putation of the scale*
For both groups of observers, each
of th© pairs was presented twice, the order of members
being reversed the second time*
Th© subjects who were used for the final scal­
ing were handled In groups ranging in size from 7 to 40*
Each group made at one sitting all the judgments re­
quired
in connection with thescaling of th© D-B series
and of
two other series,which will
be mentioned later*
Th© total time required was about 45 minutes*
All
possible orders for the three groups of judgments {relat­
ing to
th© three series) were
used, each about the same
number
of times*
group of judgments, three
Within each
orders of pairs were used, about an equal number of sub­
jects being given each order*
The same tone never
appeared in two consecutive pairs*
The procedure in obtaining judgments was as
follows:
A representative sample of tones from the
series was played to give th© subjects a general survey
of It*
Tones B-15 and B-12 were then played several
times, and the subjects were instructed that these tones
should be taken as arbitrarily defining the term "bright.**
15
Tone© B-15 and B-12 were then played, several times, and
the subjects were Instructed that these tones should be
taken as arbitrarily defining th© term “dull*”
D-15 were then played alternately several times*
B-15 and
The
subject® were told that they would hear pairs of tones
and that they were to indicate after each pair whether
the second member was brighter or duller than th© first*
They were told to guess, if necessary, and to make a
response for each pair*
In the course of th© judgments,
th© criterion was not given again except In a few instanc­
es when th© subjects felt uncertain about it*
From th© data obtained, th© scale values were
computed according to th© method of Thurston© (15), Case
V*
The values for th© preliminary and final scales are
shown in Table 1*
The first column designates the tones
of th© series, the second and fourth columns give the
values for the two scale® when B-15 Is the sero point,
th© third and fifth colxunn® give the differences between
adjacent tones In the scale®, and the last column give®
the final scale value® from an arbitrary zero point.
In
Figure 2, the scale values are plotted against stimulus
values*
It will be noticed that the value for the B-0
ton© In the final scale Is given In parentheses in Table
1*
It has been mentioned that each D-B series was re-
16
Table 1
Scale Values for th© D - B Series of Tones, for th©
Preliminary and Final Groups of Observers
Tone
B-15
Preliminary
Biff. Final
t m a x Grouj
uroup Biff. Final Group
Group
(B-033.000)
(B-15*.b00T
*000
D-12
473
288
709
389
1.859
1.936
.736
B- 0
- .793
793
(.000)
(2.652)
2.672
.540
B- 3
-1.182
1.470
1.387
.549
D- 3
-1.891
.761
.725
•662
D- 6
-2.179
.473
•130
.595
D- 9
-2.652
.000
.130
3*212
793
.793
3.445
.798
B- 6
4.091
4.010
B- 9
1. 439
559
.789
4.650
4.799
1.998
.527
B-12
5.326
5.119
.227
B-15
5.553
2.467
493
5.612
2.960
17
LU
ZD
_I
>
CD
CO
D-3
B-3
B-9
B-15
TONE
Figure 2
Scale Values for the Tones of the B-B Series
The dotted line connects the values obtainted when the
aeries was scaled with the preliminary group; the
solid line connects the values obtained when
the series was scaled with the final group*
ID
corded four times®
In two of the four recordings, th©
B-0 tone was later discovered to be defective*
This
made it necessary to omit from th© computations the re­
sults on all pairs in which the B-0 tone occurred*
a result there is no scale value for this tone.
As
It has
arbitrarily been given a value halfway between those of
tones D-3 and B-3.
This value, 2*562, corresponds very
closely to the value of B-0 In the preliminary scale,
which was 2*672*
(This arbitrary location of B-0 has
been taken as the aero point for th© scale as given In
th© right-hand column of Table 1.)
Since the two scales
show a elos© agreement, it seems reasonable to accept this
value for B-0 as a good estimate*
The agreement shown
by the two scales throughout suggests that th© necessary
omission of data on pairs containing th© B-0 tone did not
result In a serious defect in the final scale.
Th© re­
liability of the scale will be discussed later.
Th© physical nature of another series of tones
which was scaled Is Indicated in Figure 3.
Again the
figure shows only the relative Intensities of the par­
tial s of individual tones.
Each contour represents the
spectrum of a single tone*
In the designation of the
tones, the letter indicates the type of spectrum (P for
peaked and V for V-shaped), and the numeral indicates the
number of db by which the intensity of the two middle
RELATIVE
INTENSITY IN DB
I
\
\
\y-i2/
\v-m/
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
PARTI AL
Figure 5
The Relative Intensities of the Partials
in Each Tone of the V-P Series
The points at which a contour Intersects the vertical
lines indicate the relative intensities of th©
partials In that tone. The designation of
the tone is given with each contour#
partials differs from that of th© first and sixteenth
partial©*
series*
This series will be referred to as the V-P
A series of this general type was scaled with
the preliminary group of 25 subjects*
On the basis of
these results* the particular stimulus values shown in
Figure 3 were selected for use
in the final scaling*
The change in this series sounded quite similar
to that in the D-B series*
Consequently, the same terms
were used when th© judgments were mad©.
Th© same subjects
were used as for th© D-B series and th© general proced­
ure was similar*
Each ton© was paired with every other
tone in th© series, and each pair was used twice to allow
for a reversal of members in th© second presentation*
Tone P-18 was used as an arbitrary definition of the
term '’bright,*1 and ton© ¥-18 was used as an arbitrary
definitlon of th© term ''dull.”
Computations from th© data (Thurston©1s Method,
Case V) yielded the seal© values given in Table 2.
The
first column designates the tones, the second gives the
scale values when V-1S is the zero point, the third
gives the values when B-0 Is th© zero point, and the
fourth column gives the scale distances between adjacent
tones In th© series*
In figure 4, scale values are plot­
ted against stimulus values*
The curve Is very slightly
sigmoid, and it will be noted that the scale Is of small
21
Table 2
Scale Values for the V - F Series of Tones
Tone
V-18
Scale
(V-I6N.OOO)
*000
Scale
{B-0».000)
Diff*
-**513
.121
V-12
*121
-.392
.204
V- 6
.325
-.188
.188
B- 0
.513
.000
•310
P- 6
.823
.310
.584
F-12
1.407
.894
.262
F—18
1.669
1.156
TONE
' 11 1 «'urn***,r
—
■- ■ — ■ ----------------------- -
•
■
--------
"
*
Figure 4
Scale Value® for the Tones of the V-:
Series
The scaling was done with the final group.
magnitude*
Thai*© are seven tones in the V-P aeries as
compared with 11 in the D-B series, and the amount of
stimulus change is about the same in both, yet the magni­
tude of the scale for the V-P series is only about onefourtii as great as that for the B-B series*
One other series was scaled with the large
group of subjects*
The series consisted of five tones,
labelled 0-18, 0-9, B-Q, K-9, and E-18*
these tones was as follows*
each ton© of the series*
The nature of
There were 16 partial® in
In tone 0-18, the odd-numbered
partial® were at one level of intensity, and the ©vennumbered partlals were all at another level, the former
being 18 db more intense than the latter*
In tone 0-9,
the odd-numbered partlals were 9 db more intense than
the even-numbered partlals*
In £-18, the even-numbered
partlals and the fundamental were at one level of in­
tensity, and the odd-numbered partlals (other than the
fundamental) ware at another level, with the even par­
tial© being 18 db more intense than the odds*
In £-9,
the evan-numberad partlals and the fundamental war© 9
db more intense than the other partlals*
There was an
Important reason for keeping the Intensity of the funda­
mental at a high level*
The frequencies of the even-
numbered partial® were integral multiples of the frequency
of the second partial; thus they formed a harmonic series
to which partial 2 was the fundamental.
For this reason
the primary pitch of the E tones tended to be that of the
second partial*
It was to avoid this effect that the in­
tensity of the fundamental component was mad.© equal to
that of the ©ven-numbered partial®.
Th© B-G ton© In this
series was the same as the B-Q tones In the other two
series.
These tones will be referred to as the 0-E series.
The intensity at which each tone was recorded to get equal
loudness was determined in a manner similar to that
used for the tones of the D-B series.
The method of paired comparisons was again used.
Bach ton© was paired with every other one, and each pair
was presented twice.
The subjects were asked to judge
whether the second member of a pair sounded wfuller” or
”thinner” than the first member*
Ton© E-18 was used as
an arbitrary definition of the term ”thin,” and 0-18 as
an arbitrary definition of the term "full.”
yielded the scale values shown In Table 3.
Computations
Scale values
are given with both 0-18 and B-0 as ssero points.
scale is plotted in Figure 5.
The
It will be noted that the
magnitude of the scale is larger than that for the V-P
series and smaller than that for th© D-B series.
The
figure also shows that there is a reversal, 0-18 having a
greater scale value than 0-9.
0-18
0-9
B-0
TONE
E-9
E -18
Figure 8
Seal© Values for th® fonee of the 6«*B Series
fhe sealing was done with, the final group#
Table 3
Scale Valuea Tor the 0-E Series of Tones
■Tone
Scale
(£-0**000)
Beale
(O-ife»*000)
0-18
*000
- .759
0- 9
— •104
- *863
B- 0
*759
*000
£- 9
1*991
1.252
£-18
2*615
1.854
Biff.
— *104
.863
1.232
*822
The reliabilities of these three scales may
now be discussed*
manners
These were determined in the following
Starting from the scale values, the theoretical
proportions which they demand were computed*
(In this
experiment, a proportion is the per cent of times that
one ton© of a pair was Judged brighter (or thinner) than
the other member*)
The theoretical proportions were com­
pared with the proportions experimentally obtained and
the discrepancies noted#
For example, the D-B seal© de­
mands that 0-9 should be judged brighter than D-12 in
*800 of the cases*
The experimental proportion was
•821$ the discrepancy is *021*
If a discrepancy is more
than four times the probable error of the observed pro­
portion, the difference is too large to be due to samp­
ling error, and the scale value Is unreliable*
Under such
circumstances, the hypothesis that the theoretical pro-
27
portion Is the true proportion would b© untenable because,
if It were true, the observed proportions could not have
occurred by chance*
A criterion for reliability can be
established by selecting a representative proportion and
determining Its probable error for the number of cases
Involved*
Any discrepancy greater than four times this
probable error Indicates an unreliable scale value.
For
the present scales, four times the probable error, as­
suming *75 to be a representative proportion, Is .072
(N » 255}•
The mean discrepancy between the theoretical
and observed proportions for the scale derived for the
D-B series was *032*
There were two differences which were
near the criterion value of .072*
One was .070, the
other was *069, and the next largest was *057*
In view
of the low value of the mean discrepancy and the small
number of extreme differences, the scale on the whole
would seem to b© quite reliable.
The poorest correspondence between theoretical
and observed proportions was found in the scale derived
for the V-P series*
The mean difference was .054, which
is less than the criterion value of .072.
There were,
however, seven Individual discrepancies larger than
this, ranging In size from *078 to .089.
The value of
the mean difference may be taken to indicate that the
28
scale as & whole approximates that which would have been
found if a more reliable method had been used, but the
seven large differences show that specific scale distances
ar© unreliable*
The mean difference between the theoretical and
observed proportions for the scale based on the 0-B series
was *027*
ly s
There was only one extreme difference, name­
*096*
This discrepancy was for the pair 0-9 and
0-18, which had reversed scale values as compared with
their positions in the physical series.
Mot only was
the difference large, but the scale values demanded that
0-18 be judged thinner than 0-9 a slight majority of the
times, whereas the reverse occurred.
The reversed posi­
tions of these two tones is therefor© not reliable*
The
smallness of the mean discrepancy suggests that the relia­
bility of the rest of the scale is fairly good.
The reliability of the three scales, particu­
larly the scale for the V-P series, could probably have
been increased through the use of Thurston©1© Gas© III
or Case IV*
It was felt, however, that for the purpose
of this study the additional refinement was not necessary.
The scales are considered to be sufficiently accurate to
serve as a basis for the conclusions to be drawn from
them*
These conclusions are based on the general nature
of the scales rather than on scale distances between
specific tones.
The general form of the second scale is
probably essentially correct*
The reliability of the
third scale Is fairly good except for the reversal*
The
reliability of the first seal© is cplte acceptable, and
Its general nature is confirmed by the close similarity
to the scale derived when the D-B series was used with
the preliminary group.
It may be noted that the mean dis­
crepancies for the first and third scales are of about
the same magnitude as the mean discrepancy reported by
Tnurstone (15} *
After these scale© had been derived, certain
procedures were undertaken in an attempt to evaluate the
second and third series In terms of the criterion by which
the D-B series had been Judged*
Specifically, th© prob­
lem was to determine the degree of brightness (as de­
fined by the D-B series) possessed by tones V-18, P-18,
E-IB, and 0-9, these being the extremes of the other two
series of tones*
In order to do this, each of these tones
was paired with tones of the D-B series, and observers
were asked to judge whether the second member of the pair
was brighter or duller than the first*
For each tone,
the point (In the D-B series) of subjective ©quality in
brightness waa found*
Tones In the D-B series which were
on one side of this point were judged brighter than the
tone whose brightness was being determined; on the other
30
sidle, they were judged duller,
The scale value of the
point of subjective equality was found by linear inter­
polation,
For example,V-18 was judged brighter than
0-3 43 per cent of the times, and brighter than 0-6 62
per cent of the times,
The scale values of these two
tones are 1*956 and 1*387#
The point of subjective e-
quality {50 per cent point) for ¥-18 is found by linear
interpolation between these two values to be 1*716#
Preliminary judgment® made by a small group of
subjects gave some indication of the points of subjective
equality In brightness (in the D-B series) for each of
these four tones*
On this basis, certain tones were se­
lected to be paired with V-18, others to be paired with
P-18, 0-9, and E-18 for judgments by a larger group*
The
tones making up the various pairs can be inferred from
Table 4*
Ton© V-18, for example, was paired with B-12,
B-9, B-8, and B—5*
Bach pair referred to by the figures
in the upper four row© of the table was judged six times
by each of 89 subjects#
The figures indicate the per
cent of time© that the tone designated at the left was
judged brighter than the tone designated at the top#
The most difficult pairs to judge were those
containing ton© E-18*
This was probably due to the fact
that E-18 seemed to sound as though It consisted of two
somewhat separate tones, th© fundamental ton© and another
Table 4
Percentage of Timea Ton© in Left-Hand Column Was
Judged Brighter Than Tone In Top How
Tone
E-IS
¥-18
F-18
0— 0
E-18
E-18
B-12
19
23
B-9
B-6
B-5
D-5
D-6
62
39
17
47
43
26
61
39
23
69
51
41
72
29
D-9
D-12
12nd)
ton© an octave higher*
This effect of a separate tone an
octave above the fundamental was due to a fact previously
mentioned, namely*
that the even-numbered partlals
formed a harmonic series to which th© second partial was
a fundamental.
This partial series was therefor© heard
more or less as an entity which stood out from the funda­
mental*
The difficulty of judgment is reflected in the
figures for E-18 in the row next to the bottom in Table 4#
The per cents are not greatly different for the differ­
ent pairs*
Such a result Indicates a certain amount of
ambiguity In the brightness of ton© E-18#
Evidently this
tone did not have a definite degree of brightness which
could w&slly be compared with that of the other tone of
the pair#
It can also be seen that the proportions do
not approach th© 50 per cent mark*
It was thus necessary
to make another attempt to find the point of the D-B
series to which ton© E-18 was equal in brightness*
Because
of the apparent difficulty of judging pairs containing
this tone an attempt was made to Improve the conditions
under which the judgments were given.
Th© subjects were
again Instructed to judge whether th© second member of
the pair was brighter or duller than the first member.
The pairs of tones were presented in groups of nine.
Each
odd-numbered pair In the group consisted of tone B-18 and
one of the selected tones from the D-B series, while each
even-numbered pair consisted of two tones from the D-B
series which differed enough in brightness so that the
judgment called for by th© instructions was moderately
difficult or easy*
This method had several advantages.
Tone E-18 was not presented In every pair, th© confidence
of the subjects was maintained by the intersperslon of
pairs easily Judged, and the criterion of Judgment was
re-established by ©a<ih pair consisting of two tones from
the D-B series.
For these reasons, the results given in
Table 4 for E-18 (2nd) are considered more reliable than
those which were first obtained for this tone*
The
differences In the results again suggest a possible am­
biguity In the brightness of tone E-18.
sults were obtained from 35 subjects.
The later re­
Each subject mad©
12 judgments per pair.
The point of subjective ©quality (50 per cent
point) In the D-B scale was determined for each of these
33
tones from th© results given In Table 4#
The method of
computation has been Indicated, except for the fact that
the value for P-18 was obtained by extrapolation.
The
brightness of these tones in terms of th© D-B seal© Is
given In
Table 5*
Th© first column gives th© values when
tone B~0 is taken as the zero point of th© D-B scale;
the second, th© values when D-15 is the zero point of
the scale.
Table 5
Points of Subjective Equality in Brightness for ¥-18,
P-18, 0-9 and E-18, Given in Terms of
Scale Values of the D-B Series
Ton©
Scale Values
(B-6=.000)
V-18
j?-18
0- 9
E-18
- .956
.551
-1.820
- ,661
Scale Values
<D-15=.000)
1.716
3.205
.832
1.991
34
tf%
A•
OOHTROL EXPERIMENTS
Pitch Matching
The results of two control experiments remain
to he reported*-
It ha® been stated that the pitch of a
complex ton© may change with changes in it® structure*
Bannister says:
wTh© more pronounced the overtones, es­
pecially th© higher ones, the higher the pitch appear©
to bett (1, p* 894}*
If this were true, it might be main­
tained that the judgments on which these scales were based
were actually judgments of pitch differences between the
tones*
The purpose of the first of these controls was
to see if the pitch of the complex tones in these series
varied with the change In structure*
The general pro­
cedure was to measure the pitch of the complex tones by
matching them in pitch with a pure tone.
When the com­
plex tone and th© pure ton© sounded equal In pitch, th©
frequency of th© pur© tone was taken as a measure of the
pitch of the complex tone*
Th© apparatus was arranged so that th© output of
th© tone generator and that of a beat frequency oscilla­
tor were both led to th© receiver (phon© at which the
subject listened) through a single-pole double-throw foot
switch*
?dien th© switch made contact in one position,
th© output of the generator was connected with the re-
35
celver*
Contact with, the switch in the other position
connected the output of th© beat frequency oscillator with
the receiver*
(A GH type S13-B oscillator was used a**
long with a OR type 546-A mlcrovolter and a OR type 539-S
variable (increments! frequency) air condenser*)
The out­
puts of th© two sources were also led directly to the
horizontal and vertical plates, respectively, of a
cathode-r&y oscilloscope*
By means of Lissajou figures
on the oscilloscope, the frequency of the oscillator
could be equated to the fundamental frequency of the com­
plex tone*
The frequency of the oscillator could be
manipulated either by means of the main dial or the incre­
mental frequency condenser*
The loudness level of the
oscillator ton© was 40 db at 180 cycles.
The intensity
level of the mfst Intense partial in th© complex ton©
was 60 db, th© intensities of th© other partlals being
determined by the structure of the tone*
Subject and ex­
perimenter were in an acoustically treated nonreverberant
room*
The judgments were obtained as followss
subject was seated in a chair and blindfolded.
The
The re­
ceiver was suspended from the celling, and the subject
placed a hand behind it to hold it against his left ear.
Hi® foot was placed on the switch, and his right hand was
placed on a string running iioriaontally at the front edge
36
of the arm or the chair*
By pulling this string, the
subject could manipulate the incremental frequency con­
denser and so control the frequency of the pure tone.
After th© subject was in position, the experimenter set
the incremental condenser at aero and manipulated the
frequency of the oscillator tone by means of the main dial
until it equalled the fundamental frequency of the com­
plex tone, as evidenced by the fact that the appropriate
Lissajou figure
on th© oscilloscope became motionless.
The condenser dial was then set at a point far removed
from aero, a master switch was thrown to put the receiver
in the circuit, and the subject was given the signal to
go ahead*
The subject, by moving the foot-swlteh,
listened to the two tone® alternately in whatever order
he desired, meanwhile matching pitches by adjusting the
frequency of the pure tone*
When the match had been
made, the experimenter recorded the setting of the incre­
mental condenser, which was calibrated In cycles per
second above and below aero.
If th© oscillator and gener­
ator had not drifted In frequency, a zero setting meant
that the frequency of the pur© tone was equal to the
fundamental frequency of th© complex tone.
A setting of
plus two meant that th© frequency of the pure ton© was
two cycles higher than the fundamental of th© complex
ton©.
A setting of minus on© meant that the frequency
57
of th© pur® tone was one cycle lower than the fundamental
of the complex tone#
After th© reading had been taken,
the condenser dial was again set at some point far re­
moved from zero, and another match was mad©#
After each
10 trials, the degree to which the generator and oscilla­
tor had drifted apart in frequency was checked*
This
was done by changing the arm of the variable condenser
until the Lissajou figure of the oscilloscope was again
motionless, indicating that th© (fundamental) frequencies
of the two sources were the same.
vari&bl© condenser was then taken*
Th© reading of the
It was assumed that
a condenser value halfway between the readings at the
beginning and end of th© 10 trials was the same as that
which would have been obtained If, during the period of
the 10 trials, th© condenser had continuously been kept
at the position necessary for equal frequencies, and then
its average position for th© period had been computed.
For example, If the oscillator had been set at equal
frequency with the variable condenser dial at zero and if
at th© end of 10 trials the dial had to be set at plus
two for equality of frequency, it would have been assumed
that th© average point of equality (average zero point)
was plus one*
Later, each judgment would have been cor­
rected accordingly*
Thus, a reading of plus three would
have been changed to plus two, and a reading of minus one
38
would have been changed to minus two*
After this correc­
tion reading had been taken, the oscillator was again
set so that the frequencies of the two tones were equal
when the variable condenser was set at ssero, and the next
10 trials were run*
The discrepancy between th© two fre­
quencies at th© end of the 10 trial® was typically about
on© or two cycles*
This arbitrary correction method
introduced errors into the individual readings, but it
was assumed that th© averages for each subject were
little affected because the errors were probably distribut­
ed in chance fashion*
Th© subjects were graduate students in psycholo­
gy* Each
subject made lOO judgments
on each of two tones*
On the first day, 80 judgments were mad© on tone A and
50 on tone B, in that order*
On the second day, there
were first 50 on ton© B and then 50 on tone A*
Th© two
complex tones matched by any on© subject were either
B—15 and 0*15, F-14 and V-14, or E-3G and 0-30.
These
tones were the extreme ones of th© three scaled series, or
tones similar to them*
Th© last four tones listed differ -
ed somewhat from th© extreme tones of the V-P and 0-E
series because the matching was done before the final
forms of these series had been determined*
Table 6 presents the results for the eight sub­
jects
who matched th© pitch of tones
B—15 and D—15*
The
39
results are given in terms of cycle® per second*
Each
value indicates th© mean frequency, in cycles above or
below th© fundamental frequency of the complex tone, of
the pure ton© which was equal in pitch to the complex
tone*
Thus, when subject J© had adjusted the frequency
of the pure tone until its pitch seemed equal to the
pitch of th© complex tone, the frequency of the pure tone
was, on the average, 1.93 cycle® higher than the funda­
mental frequency of the complex tone.
This value may be
taken as a measure of the pitch of tone B-15, as heard
by tTe*
It may be compared with the value *64 cycle
representing the pitch of the other tone for the same sub­
ject*
For this subject, the two complex tones differed
in pitch by 1*29 cycles.
E©suits for the group are given in the bottom
row of figure© in the table.
Th© reliability of th© dif­
ference was computed with the formula for the Fisher t
test.
(Th© standard error is equal to the standard
deviation divided by N - 1.)
The difference, .57 cycle,
is not as large as its standard errorj therefor© the
two tones did not differ significantly in pitch for the
group.
For subjects F'e and Me, tone B-15 was signifi­
cantly higher in pitch than B-15.
For subject Bi, there
was a significant difference in the opposite direction.
It should b© noted that the means of these three subjects
have rather large standard errors.
40
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41
In Table 7, the result© are shown Tor the
seven subjects who matched tones P-14 and V-14.
These
two tones did not differ significantly in pitch for the
group, as Indicated by th© fact that the standard error
of the difference is larger than the difference*
For six
of the ©even subjects, th© tones differed signiflcantly
in pitch*
For subjects Ho, LI, and Pa, tone P-14 was
significantly higher In pitch than Y-14$ for Ir, SI, and
Ta, the reverse was true*
The standard errors of sub­
jects Ho and LI are rather high*
Results for the third pair of tones, B-30 and
0-30, are given In Table 8*
Again the two tones did not
differ significantly In pitch for th© group, the standard
error of the difference being larger than the difference*
Four of th© Individuals show significant differences*
For subject Ha, tone 0-30 was signif lcantly higher than
B-30, while for Or, Ri, and Wl, ton© E-30 was higher*
For two of these three groups, th© difference
between the means for the two tones was less than one
cycle*
For all three groups, the difference was not as
large a© Its standard error*
In non© of the groups were
the significant individual differences consistently in
on© direction.
Many of the Individuals having signifi­
cant differences also show high standard err os.
These
results therefor© seem to indicate that the changes In
Results
P-14
for
and
Individuals and Group When a Pure Tone Was Matched
inPitch
to Tones
¥-14*
Means Represent the Average Frequency of the Pure Tone in
Cycles per Second Above or Below the Fundamental
Frequency of the Complex Tone*
42
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Means Represent the Average Frequency of the Pure
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44
harmonic structure In the three series had no consistent
and significant effect on th© pitches of the tones*
This conclusion holds only for these tones at
the frequency of ISO cycles*
Any broad generalisation
that harmonic structure does not affect pitch is made im­
possible by results obtained with similar tones at dif­
ferent fundamental frequencies, namely t
at frequencies of 560 and 540 cycles*
D-15 and B-15
The two tones at
the frequency of 560 cycles contained only eight partlals,
and the two at 540 cycles contained only five partlals*
At each frequency, each of three observers mad© 100 judg­
ments on ton© D-15 and 100 on B-15*
It can be seen that
in every case, ton© D-15 was higher In pitch than B-15.
(Th© difference for these two tones at th© frequency of
180 cycles was In the same direction. )
Four of the
differences are statistically significant, on© Is very
nearly so, and one is low*
Why th© ton© with the greatest
emphasis on the high partlals should be the lower of the
two In pitch is difficult to explain.
These results are
contrary to what might be expected on the basis of
Bannister*s statement, previously quoted.
At any rate,
the results show that only limited conclusions can be
drawn from the data obtained for the frequency of 180
cycles*
(See Table 9 for results mentioned above.)
Two interesting facts may be noted in passing*
45
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45
The first is that a given complex tone may differ signi­
ficantly in pitch for two individuals judging it.
In
Table 8, it may be seen, for example, that tone B-15
differed in pitch by 6,85 cycles for subjects Sa and Mi.
The standard error of the difference is only .55 cycle.
Table 7 shows that for subjects Pa and SI, tone V-14
differed In pitch by 4*31 cycles with a standard error of
.52 cycle.
Table 8 shows that for subjects Di and Ha, tone
E—50 differed in pitch by 3.75 cycles while the standard
error is only .17 cycle.
All these differences are
statistically significant by a wide margin.
Many other
such differences can be found.
The other fact, which Is related to the first,
is that for many Individuals the mean frequency of the
pure tone differed significantly from the fundamental fre­
quency of th® complex ton© of equal pitch.
The usual
assumption was mad© that an obtained mean will not differ
from the true mean by more than three times Its standard
error*
Therefore, if the difference between the fre­
quency of the obtained mean and the fundamental frequency
of the complex tone was more than three times the stan­
dard error of th© obtained mean, it follows that the true
mean differed by some amount from the fundamental fre­
quency of the complex tone.
On this basis, there are 35
instances (In Tables 6, 7, and 8) In which th© mean
frequency of the pur© ton© differs significantly from
the fundamental frequency of the complex tone.
The dif­
ference© are from 3 to 30 times as great as the standard
error of the mean*
These differences may have been due
to a loudness difference between the pure and complex
tones*
Snow (12) has shown that the pitch of pure tones
in this region is lowered when their loudness is increased.
However, the fact that not all these differences are in
the same direction does not support this interpretation*
These two kinds of differences lend interest to
th© result® plotted in Figure 6*
This graph show® the
distribution of all individual means for all the tones*
Th© total number of means is 46*
For certain pairs of
individuals, th© differences in the pitch of these complex
tones were shown to be reliable*
Thirty-five of these
means differ reliably from zero*
This evidence suggests
that this curve is based on factors other than errors of
observation*
If It should prove to be true that there are
reliable individual differences In the pitch of a given
complex ton©, the fact would be of great theoretical
importance to those Interested in audition.
The implica­
tions of these results seem worthy of further study*
It may also b© of Importance to note that, for
the individuals who matched the complex tones with a fre­
quency of 180 cycles, the effect of practice seemed to be
48
Hi
NUMBER OF CASES
10
DEVIATIONS
IN CYCLES
Plrmrc 6
The T>.is trVrp11ion of the Individual hoans of
Frequencies of Pure Tones Which Were
hatched in Pitch 771th Complex Tones
■ne
The abscissa scale represents frequency in cycles above
and below tee fundamental frequency of the complex tone.
49
to lower the frequency at which th© pure tone was set*
Individual means for the first and last 50 judgments on
each tone were computed*
10*
Group means are shown in Table
For four of the tones, the mean of the last 50 judg­
ments was lower than that of the first 50*
The mean of
Table 10
Means of First 50 Judgments and Means of Last 50 Judgments
When a Pure Tone Sas Matched in Pitch to a Complex
Tone* J&ach Mean Is th© Average for All
Individuals Matching th© Given Tone.
Tone
B-15
B-as
F-14
V-14
E-3G
0-30
-1-50
-50-100
1.68
1*69
2.33
*25
*36
-1.19
-1.85
- *62
2*53
-1.00
- *62
- *90
.85
— *41
All Tones
th© last SO judgments for all groups was 1*26 cycles lower
than the mean of the first 50 judgment s•
Th© mean of
the last 20 judgments for all groups was 2.23 cycles low­
er than that of the first 20*
This evidence indicates
that the pitch of complex tones may be higher for an un­
practiced or naive listener than it Is for a practiced
or sophisticated listener*
Such facts might give rise to
th© type of statement made by Bannister concerning th©
effect of complexity on pitch*
It should b© mentioned
that In each group half of the subjects judged th© tones
in A B B A order and half in B A A B order, taking A and
B to represent the two tones of any pair*
Practice ef­
fects were therefore counterbalanced for the two tones.
B.
Quality Matching
The matching technique was also used to investi­
gate the possibility of another type of relation between
pitch and brightness.
An attempt was made to see whether
the brightness of a complex ton© could b© expressed or
matched by the pitch, of a pure tone or, in other words,
whether a pure tone could, by being manipulated in fre­
quency, be equated to the quality of a complex tone.
The subjects listened alternately to a complex tone and a
pure tone*
Their task was to set the pure tone at the
frequency at which it best matched the timbre or quality
of the complex tone*
Two complex tone© differing considerably in
brightness were matched.
cated in Table 11.
Th© structure of each is indi­
Th© numbers Indicate the intensity
Table 11
Relative Intensities of Partial© in Complex Tones Used
in the ”Qxiality Matching” series. The Intensity
of Bach Partial Is Given In db Below
the Bevel of the Most Intense Partial.
Partial 1
2
3
4
5
6
7
8
9
10
Ton© A 10*4 13.2 0.0 13.6 19.9 23,4 25.4 26.9 28.4 30.4
Ton© B 12.0 21.0 26.5 30.0 29.0 24.5 17.0 0.0 14.5 19.5
51
of each partial In &b below the level of the most intense
partial*
The Intensity level of the most intense partial
in each, tone was 70 db*
The pure tone was set at a level
of Intensity which made it sound, for the subject, equal
In loudness to the complex tone.
The fundamental fre­
quency of the complex tones was 135.5 cycles*
The
apparatus was similar to that used for the pitch matching
except that a different frequency-measuring system, known
to be accurate, was used*
Th© subject manipulated the
main dial of th© oscillator*
Th© tone with the region of energy peaking
sharply at the third partial was somewhat smooth and dull.
The tone with the region of energy peaking sharply at the
eighth partial was bright and somewhat "nasal*”
The
subject was Instructed in th© nature of the task and told
that two tones, differing markedly in quality, were to
be matched by a pure tone*
The fact that it was th©
quality of the ton© which was to be matched, was emphasised.
For the first few trials, each subject matched the funda­
mental pitch of the complex tone.
The experimenter point­
ed this out to the subject, who was told that the pitch
of the tone© was irrelevant and that the task was to
match th© two in quality*
If the subject persisted in
matching the fundamental pitch of the complex tone, he
was asked to try for some other setting which better ex­
pressed the quality of hie complex tone.
The seven subjects used can b© divided into two
groups*
One group consisted of three graduate students in
psychology who had had several years of advanced musical
training.
Each of these subjects persisted In matching
the fundamental pitch of th© complex tone.
Their reaction
was that the quality match was almost equally good over
a wide rang© of settings, and that pitch similarity then
became th© deciding factor in making the qualities most
nearly equal*
The other four subjects had had little or no
musical training.
Three were graduate students in
psychology; on© was an undergraduate student in psychology.
Each of these subjects mad© 50 judgments on each complex
tone.
The distribution of the judgments is given In
Table 12.
The table shows, for each subject and for the
group, the per cent of settings falling in each class
Interval.
The sisse of the class interval Is 66.65 cycles,
and th© midpoints of alternate Intervals are at the fre­
quencies of partial® In the complex tone.
The frequen­
cies of the midpoints of the Intervals are given in th©
first column of th© table.
The indented numerals indicate
Interval midpoints halfway between the frequencies of
two consecutive p&rtisls.
Th© frequencies of tn© third
and eighth partial© are underlined.
The table shows that for each subject, the dis-
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tribution of settings for tone A was different from the
distribution for tone B*
For subject Eg, the majority
of tli© settings for ton© A were in th© frequency region
of th© second partial (266*8 cycles); for ton© B th©
majority were in the frequency region of th© fourth par­
tial (633,2 cycles)*
For subject Lo, the change from
ton© A to tone B was marked by a decrease in the number
of settings in the region of th© second and fourth partials, and an increase in the number near the eighth
partial*
For Mi, the change caused a decrease in the num­
ber of settings at th© frequency of the second partial
and an increase in th© number at the frequency of th®
fourth partial*
For subject Gr, the wide distribution of
settings was shifted upward and the scatter was increased.
Results for th© group show that, for ton© B as compared
with tone A, there was an upward shift and an increased
scatter in the distribution of judgments.
Th© number of
settings at th© frequency of th© second partial decreased,
and there was an increase in the number in the region
of the fourth and eighth partials*
There seemed to be a tendency to set the pure
tone at frequencies on©, two, or three octaves above the
fundamental frequency of the complex tone.
This is in­
dicated by th© number of settings close to th© frequen­
cies of th© second, fourth, and eighth partials*
For
example, subject bo had 40 per cent of th© settings for
tone A in th© region of the eighth partial (three octaves
above the fundamental) even though there was very little
©n©rgy in the complex ton© at that frequency.
There may
also have been a tendency to strike a compromise between
the fundamental frequency and th© frequency of the
prominent partial*
For subject Eg, the settings at the
second partial for tone A and at the fourth partial for
tone B may have been a compromise between th© first and
third partial© in the first case and between th© first and
eighth partial© in the second case.
There is little consistency in the results from
subject to subject except for th© general fact that there
were more high settings for tone B.
If the brightness of
complex tones were an attribute very similar to th©
brightness of pure tones (supposedly parallel to that of
pitch), ther© should have been a greater similarity of
results among th© subjects, and the scatter shown In the
judgments of each sub ject except Eg should not have oc­
curred.
It seems, therefore, that the brightness of
complex tones Is distinct from the pitch-brightness of
pure tones*
The subjects themselves were not sure that they
were making their judgments In accordance with the In­
structions given*
One subject suggested that h© may
actually have been finding a pitch of the pure tone which
was the beat representation of the mas© of pitches in the
complex tone*
If this was true, the procedure in judging
was similar to that used by the subjects of Ekdahl and
Boring (5).
Other subjects expressed doubts as to whether
they were actually matching the qualities of th© two
tones*
It should also be noted that the subjects typi­
cally took about an hour to make 25 judgments, of which
perhaps half the time was given to measuring th© fre­
quency of the settings*
It is apparent that the judgments
were not immediately given*
These facts of variability,
doubtfulness, and slowness in performance tend to ©tipport
the conclusion that the brightness of complex tones is
not similar to the pitch-brightness of pure tones*
57
V.
DISCUSSION
In considering tines© results, the first question
which arises concerns the meaning and importance of th©
dimension of brightness as derived from, and defined by,
the D-B series*
Several factors suggest that this is a
rather important dimension of ton© quality*
During the
experiment it was evident that the judgments of bright­
ness could be made without great difficulty on the part of
the subjects*
It seemed to b© a relatively simple matter
for them to attach, the terms bright and dull to th© ex­
tremes of the series and then to make judgments on th©
basis of the given criterion*
It will be recalled that
th© duration of the tones was only two seconds*
The ease
of judgment appears more important when It is noted that
th© stimulus difference between successive tones in the
series was not large and that in the final scaling no tone
was paired with any other more than two steps removed
from it in the series*
The magnitude of the D-B scale, as
compared with the magnitudes of the other scales, shows
that the extremes were markedly different.
This has some
meaning In Itself, for strongly characteristic extremes
might be expected if the type of change were basic*
This
evidence tends to support the subjective impression that
there was a fundamental type of change In this series*
The existence of the change and tne nature of the cnange
58
are very easily grasped and seem to Tit in readily with
normal experience in hearing ton© qualities.
The close
correspondence of the preliminary and final scales also
suggests that the type of change is clear-cut and easily
grasped.
The possible generality of the brightness dimen­
sion is indicated by the fact that series based on other
types of stimulus change showed systematic differences in
brightness* according to the meaning given to that term
by th© D-B series.
One series was constructed in which
a group of five partial® of greater intensity than the
other® was moved* in successive tones* to higher and high­
er frequencies.
In another series a peaked region of
energy was moved higher and higher.
Both series showed*
according to introspective report* an increasing bright­
ness.
It is possible that brightness may also be re­
lated to vocality in an important way*
A series was
recorded which changed gradually from a ton© with the
physical characteristics of a sustained vowel "oh" to one
with th© physical characteristics of a sustained "ah* 11
a® these were determined by Lewis and Tuthlll (10).
To
most listeners* the series seemed to change gradually
from an "aw" to an "ah."
At the same time, it showed
a change in brightness as defined by the scale.
lh©s©
59
Introspective report© serve to Indicate tne possibility
that the attribute of brightness, if established, may be
found to be an Important factor in many types of quali­
tative change*
The D-B series and those mentioned In the pre­
ceding paragraphs as showing a similar change in bright­
ness had one thing In common*
Their spectra show that In
successive tones, th© central point of the energy dis­
tribution was shifted along the frequency continuum*
This suggests that brightness la a function of the loca­
tion on th© frequency continuum of the midpoint of the
energy distribution*
If this were the entire cause of
brightness changes, th© wa;y in which th© energy was
distributed around the midpoint would have no effect on
brightness#
Th© V-F series was originally devised In an
effort to determine whether changes in the concentration
of energy would cause brightness differences*
A study of
the spectra of th© tones in the V-F series will show
that the midpoint of the energy in the tone was th© same
throughout the series and that th© change was in th©
manner of distribution of this energy around the midpoint
(see Figure 3)#
The type of qualitative change In the
V-P series seemed much like that in the D-B series*
However, the two series were easily distinguished*
heard separately, each could be identified*
When
The like—
60
ness of the two series Is suggested by the fact that the
use of the same two terms In judging the P-B and V-P
series never caused any confusion during the experiment.
Furthermore, the task of comparing tones V-18 and P-18
with tones from the D-B series and making judgments in
terms of brightness did not seem to be difficult.
Th©
resulting functions (see Table 4) imply that there was
little ambiguity in th© judgments.
One method of showing the relations between the
D-B and V-P aeries has been used in Figure 7.
Th© ab­
scissa represents brightness scale values as determined
for th© D-B series*
The ordinate represents scale
values for either the V-P or o-E series.
Tone B-G is
the zero point of the scales on th© ordinate and on th©
abscissa*
Th© horizontal line in the figure represents
a portion of the D-B scale.
Bach point on this line
stands for a tone in the D-B series and shows, by reference
to the abscissa, th® seal© value of that ton© in the
series*
Bach point on the other curves indicates two
values for th© ton© it represents.
Reference to the or­
dinate gives th© scale value of that ton© in its own
series.
Reference to the abscissa shows the brightness
value of that tone, as brightness was defined by the DB series.
Th© method by which this was determined has
been described*
To take an example, th© point for V-18
61
E-18
-18
D-9
B-9
x
V-18
0-9
D-B SCALE VALUE
Figure 7
Showing Certain Relations of the V-P
and O-E Series to the D-B Series
Tii© horizontal line represents part of the D-B scale*
The scale values of the tones on this line are given
by reference to the abscissa# Each point on the oth­
er curves indicates two facts about the ton© it rep­
resents* Reference to th© ordinate gives the scale
value of that ton© in its own series*
Reference to
the abscissa gives its brightness value in terms of
the D-B scale# Tone B-0, represented by the point
at which the curves intersect, is taken as the zero
point for each scale*
62
Indicates that its seal© value in the V-P series was
-*SX3 and that it has a brightness scale value of* -#936*
If an X series wore Independent or the bright­
ness seal© in the sense that th© X quality could vary
while brightness was held invarlab 1 ®, th© curve for that
series would be a vertical line*
If each tone in the X
series had equal seal© values for both brightness and the
X quality, th© point for any tone would b© equally dis­
tant from the central zero point in both horizontal and
vertical directions*
A series of auoh points would make
a line with a slop© of 45°*
This curve might possibly
mean that th© X quality and brightness were entirely
separate attributes, and that the tones In the series just
happened to possess the two attributes in ©qaaL amounts.
It would be much more likely to mean that th© X quality
and brightness were the same attribute.
If an X series
were represented by a line with a slope of less than 46°,
this would mean that the X series varied less In terms
of th© X quality than in terms of brightness.
If the
slope of th© lln© were greater than 45°, this would
mean that the X series varied more In terms of the X
quality than in brightness*
The curves for the V-P and O-E series pass
through th© B-Q point of th© D-B scale because all th©
series contained that ton©, which Is taken as a reference
65
point* Tli® V-P curv© approximates, very roughly, a slop©
o
or 45 , although the upper half deviates towards til©
vertical and the lower half deviates In the direction of
th© horizontal*
Th© error of the location of these points
on the scale la probably great enough so that the exact
slop© of the line is not meaningful*
accepted as being approximately
45
If the slope Is
°, th© phenomenological
similarity of the scales is not proved*
It Is still
possible that the V-F seal© might have been judged on
the basis of some entirely separate attribute which
happened to give nearly the same scale values as the
brightness attribute*
This is rather improbable, and some
relation between the two scales seems to be indicated*
In so far as it Is safe to draw Inferences from these re­
lations, it may be said that they support the conclusions
reached on an introspective basis.
It would seem that
brightness, as defined by the B-B series, was probably
an Important factor In th© scaling of the V-F series*
From the relative magnitudes of th© two scales, it is
apparent that th© V-F type of stimulus variation Is less
effective In producing brightness changes than Is th©
D-B type of stimulus variation*
It Is also possible that each series had two
(or more) attributes and that there was an attribute com­
mon to both which caused the relations shown In Figure
This possibility will b© considered later*
7
.
64
It should be noted that the nature or th©
stimulus change In the V-P series from V-X3 to B-G Is
somewhat hard to classify*
It conforms to the original
Intention that the midpoint of the energy remain at the
same point on the frequency continuum, yet It is actually
a change from concentration of energy at two separated
points to an even spread of energy#
The effect of tones
having two or more regions of energy concentration needs
further study#
The meaning of the O-E series may now he dis­
cussed#
Ever since th© time of lielmholfcg, psychologist©
have been pointing out th© fact that a tone consisting of
only odd-numbered partial© has a peculiarly individual
quality, resembling that of th© low notes of th© clari­
net#
The extreme 0 ton© of th© series had this indi­
vidual quality#
The quality of the extreme E tone has
been mentioned#
E-18 seemed to sound like two tones,
one an octave above the other#
Th© relations of this
*
series to the D-B series are also shown in Figure 7, and
the meaning of th© locations of the individual points has
been indicated#
Th© two halves of th© curve almost form a right
angle#
This might be Interpreted as meaning that the two
halves of th© series were characterised by two different
attributes#
It might also b© interpreted as moaning that
65
th© series was judged on th© basis of an attribute en­
tirely independent of brightness, but that a brightness
factor, increasing from both ends towards the middle, was
also present#
In Figure 7, a line drawn directly from
th© point for V-18 to that for P-18 would be almost
vertical.
A vertical line, it lias been stated, would in­
dicate an attribute independent of brightness.
It is
probable that the brightness factor was not of primary
importance in the scaling of this series.
The O-E seal©
shows no characteristics which are explained by the
brightness changes in the series.
A theory as to the
cause of the brightness increase from th© ends of this
series towards the middle will be given later.
er brightness of the
6
tone over the
0
The great­
ton© was probably
due to the previously mentioned ”split” Into two tones.
On© effect of the prominence of this octave ton© was
evidently to add brightness or something confused with
brightness#
If these two qualifications are accepted, the
probability is that th© series was judged primarily In
terms of an attribute independent of brightness.
Certain logical considerations will show by
analogy what the basis may have been for th© judgment© of
the tones In this series.
A study of the Interval re­
lation© (in terms of the musical scale) between th©
partial© In each type of tone will show some interesting
66
differences*
In a ton© consisting only or th© fundamental
and th© even-numbered partials, up to and including the
sixteenth, these Intervals between partial© are primarily
octaves, fifths, fourths, major thirds, and minor thirds.
Such musical interval© are all very smooth or consonant,
and some of them are very thin or empty-sounding*
In a
tone consisting only of the odd-numbered partials, up
to and including th© fifteenth, th© Intervals between the
partials are a major sixth, diminished and augmented
fifths, major and minor thirds, major seconds, and minor
sevenths*
These intervals are either the fuller-sounding
consonances (th© ones last to be accepted as consonances
In th© development of music) or the dissonances*
The
same type of differences for the two tones can be shown
for th© Intervals between th© fundamental and the higher
partials*
On© type of ton© contains many Intervals com­
monly considered to sound thin and smooth; the other con­
tains many intervals usually considered to be full or
dissonant*
3 uch
an analysis suggests a possible basis for
th© original selection of the terms wfulltt and "thin” to
describe these tones*
Since musical intervals have
usually been thought of as forming a continuous series
from rough to smooth or from dissonant to consonant, it
might be argued by analogy that th© change from full to
thin might be a single dimension in complex tones*
67
Ife is possible that a more representative and
clear-cut full-thin series might be obtained with a slight­
ly different method#
The first tone of the series might
be one consisting only of odd-numbered partials*
In
successive tones, the taking away of the high partials
might bring about a change toward thinness#
After a
certain number of partials had been taken out, th© tone
would hav© the same fullness-thinneas as on© consisting
of the fundamental and tue even-numbered partials.
latter tone would be the next in the series.
The
Th© sub­
traction of partials from It would then continue th©
change in the direction of thinness*
Such a series would
probably not hav© the complicating brightness factor which
entebed into the
0-1
series (as will be explained later).
The full-thin dimension would then be entirely a func­
tion of th© Interval relations between the partials.
Th© analogy with musical Intervals can b© carried
over to a consideration of a possible new factor or
attribute in complex tones, that of roughness or harsh­
ness.
Helmholtjs (6 ) noted that when strong partials
above the seventh were present In a ton© its quality was
likely to be cutting or rough, and he ascribed this
quality to dissonances between partials*
It should be
noted that any two consecutive partials above the sixth
(seventh and eighth or above) form a dissonant Interval of
68
a second,
Th© seventh and eighth partials make an In­
terval of a major second.
For consecutive partials higher
and higher In th® series th© interval gradually becomes
smaller; for partials 15 and 16 the Interval Is a minor
second*
Because major and. minor seconds are among th©
most dissonant of the musical Intervals, It is conceiv­
able that any two consecutive partials above th© sixth
might add an element of roughness or harshness to th© tone*
On this assumption, and on the basis of preliminary
work, a series was constructed to demonstrate roughness*
Each tone in the series contained the first six partials
and two partials above the sixth*
partials 2, 3, 4, 5, and
6
The intensities of
were, respectively, 4,
16, and 20 db below that of the fundamental*
8
, 12,
The Inten­
sity of each of th© two partials above th© sixth was
always 10 db below that of the fundamental*
In th© first
ton© of th© series, the two high partials were the 7th
and
8
th, in th© second they were th®
8
th and 9th, in
th© third they were the 9th and 10th, and so onf those
In the last ton© of the series being the 15th and 16th*
Twenty-five graduate students in music and
psychology served as observers in a study of th© roughness
series*
These observers gave Introspective reports on
to© series before th© possible nature of the tones was
discussed, and also after th© experimenter had defined
69
brightness and roughness#
In th© reports given before
the definition of attributes, there were (1 ) three state­
ments to th© effect that there was an element of harsh­
ness In the tones which increased throughout the series,
(2 ) three statements that th© tones changed from mellow
and round to pointed, (5) two that the series changed
from darls to nasal quality, (4) two that th© tones be­
came less pleasing, and (5 ) a scattering of other state­
ments, each made by only on© person*
After obtaining these statements, th© experi­
menter explained the concepts of brightness and roughness,
and used certain tones to define th© terms*
IXillness
and brightness were defined with two tones, each of which
contained all of th© first
10
partial© except th® seventh
and ninth*
Applying previous terminology, one of these
tones had a
0-10
spectrum; the other had a B- 1 0 spectrum*
In other words, in on© tone the tenth partial was 10 db
less intense than the fundamental; in the other, th©
fundamental was
10
db l©s® intense than th© tenth partial.
Tones containing these particular partials were used in
order to avoid any Important element of roughness and
to define brightness entirely In relation to th© fre­
quency of the median of th© energy distribution.
D-1Q ton© was used to define smoothness.
Th®
The same tone
with an Inharmonic partial inserted was used to define
roughness*
70
When th© subject® had heard, the defining tones,
introspective reports were again obtained*
Nineteen sub­
jects said that roughness was present and that It increased
continuously throughout the series*
that th© roughness was
Two subjects said
greatest in th© middle of the
series*
On© said that roughness was not present In th©
series*
Reports were also obtained concerning brightness
and concerning the dissimilarity of brightness and rough­
ness*
Nineteen observers said that brightness Increased
in th© series} on© said that no brightness change was
present*
Fourteen observers said that th© two charac­
teristics were distinguishable as separate attributes;
seven said that the change should be called dullnessbrightness or that the two characteristics were the same*
It seems reasonable to assume, on the basis of
this evidence, that roughness is probably a basic at­
tribute of complex tones*
Th© majority opinion that th©
series contained a roughness element which increased
from the beginning to th© end supports this assumption*
The opinion that brightness Increased throughout the
series is to b© expected when th© definition of brightness
and the nature of th© series (energy shifted upward in
frequency) are considered*
The fact that the majority
of observers heard the two attributes as separate Is In
further support of this assumption*
Those who reported
71
them to be separate attributes probably heard, them as
such*
Those who reported them as one attribute might,
with further observation, rind them to be distinguish­
able*
The great majority of* the reports indicated that
roughness increased throughout th© series*
Roughness
may therefor© be said to be a function of the presence
of consecutive high partials In th© ton© and of th@ir
position In th© sequence of partials*
(The higher th©
partial nmnbers of the two consecutive partials were,
the greater was the roughness of the tone*)
If it Is assumed that roughness Is a basic
attribute of complex: tones and is a function of the stim­
ulus conditions stated above, the interrelations of th©
three series can be explained#
It must first be recog­
nised that the X>-B series changed in brightness and In
roughness*
Th© latter change was due to the fact that
consecutive high partials became Increasingly prominent
from th© B to th© B end of the series*
In the following
discussion, It must b© kept clearly In mind that "bright­
ness as defined by th© D-B series" means a combination of
brightness and roughness*
Brightness In th© new sense
refers only to that quality which is a function of the
frequency of the midpoint of th© energy, when not compli­
cated by any roughness element*
Brightness in this sense
72
is best defined toy th© D— 1 0 and B— XO tones containing
only partial® 1, 2, 3, 4, 5,
6
,
8
, and 10*
The probable explanation for the form of the
0-E curve In Figure 7 and for the relation between the D-B
and G—B series can now toe given*
The relation between the
two aerie® seem® to have been affected toy the presence of
an element of roughness in tooth series*
sumed that the extreme
0
It may toe as­
tone and the extreme B tone had
little roughness (because the effects of consecutive high
partlals were minimised as a result of the low intensity
of alternate partial®} and that th© B-G ton© had con­
siderable roughness (due to the presence of consecutive
high partial®}*
Because th© D-B series contained a
roughness element which increased toward the B end, the
brightness, a© defined toy the D-B series, of the B-G
tone would toe greater than that of th©
0
and E tones*
Thia would give rise to the relation shown In Figure 7.
If further speculation is permitted, it may toe
assumed that all tones In the G-E series had approxi­
mately the same brightness, in th® new restricted sense
of th© term, because th© midpoint of th© energy had th©
same frequency location in all tones*
On th© basis of
this assumption, it might to© said that the fulinessthinness dimension Is independent of brightness*
Th©
series previously suggested for establishing an inde­
75
pendent Tull-thin dimension contained no consecutive high
partial® and might therefor© show fullness—thinness to
be independent of roughness*
Theoretically, that series
and the 0-E series taken together might therefore estab­
lish the existence of a separate attribute*
Th® element of roughness was probably the fac­
tor relating the D-B and V-F series*
A study of the V-P
series shows that the strength of consecutive high partials, in relation to the level of the fundamental, in­
creased throughout the series*
It is probable, then,
that the V-P series, like the D-B series, Increased in
roughness*
Th© result was that the tones of the V-P series
showed a similarity to those of the D-B series in terms
of th© characteristics of the latter*
the relations shown in Figure 7*
This gave rise to
It is possible that the
phenomenological similarities between the two series were
caused by th© similar roughness changes and that th©
differences were caused by the fact that brightness, In
the restricted sense, increased In the D-B series ahd
remained constant throughout th© V—P series*
Xt is also
possible that the roughness contributed by the consecutive
partials became greater as their intensity increased in
relation to the intensity of the fundamental#
This
would explain th© fact that the extent of th© P half of
the V-P scale is greater than that of the V half (1*156
to *513)*
74
The possibility of a relationship between th©
attributes of smoothness-roughness and fullness-thlnness
needs to be considered#
On logical grounds, It Is possible
to conceive of th© two as forming a single dimension
changing from thin through full (both being relatively
smooth) to rough*
This dimension would be considered a
function of the decreasing simplicity of th© frequency
ratios (musical Intervals) between the partial©*
Accord­
ing to this view, there could be a continuous and gradual
change in this one large dimension from the extreme 2£
tone to th© extreme tone of the roughness series*
On
the other hand, It might be argued that th© two attri­
butes are not related and that to consider them as a
single dimension is to commit a stimulus error*
Further,
study of th© nature of these attributes Is necessary be­
fore this point can be decided, but careful introspective
analysis seems to indicate that the two attributes are
entirely different*
The difference between th© two views can be
shown by reverting to th© analogy with musical Intervals*
The first view would b@ Illustrated if the intervals
were to b© arranged in a single series from the thinnest,
smoothest, and most consonant to the roughest and most
dissonant and if the series were considered to be a single
psychological continuum*
Such a series would have th©
75
Interval of th© octave at one end and the major seventh
and minor second at th© other*
The second view
would
he illustrated If musical intervals were considered as
belonging to two separate classes* consonant and dis­
sonant*
A thin-full seal© of consonant intervals {from
the octave to the minor third or minor sixth) could he
made* and also a smooth-rough seal© of dissonant inter­
vals (from the diminished fifth to the minor second}*
The two classes would he considered qualitatively dis­
tinct#
Whether or not the past practices of psycholo­
gists in classifying musical intervals have any
pertinence to the point at issue is open to question*
As
previously stated* th© tentative conclusion at present is
that the two attributes are psychologically distinct and
cannot be combined into a single dimension.
It should be pointed out that the qualitative
change In the D-B series might be Interpreted as being a
change in volume or In density*
Superficially at least*
the series seemed to Increase In density and decrease in
volume from the B to th© B end#
Since high-frequency
partial® became increasingly prominent in the series and
because raising th© frequency of pure tones Increases
their density and decreases their volume {15, 14), a
comparable change in the D-B series may have occurred#
Whether volume and density will in the future be shown
76
to to© basic attributes of complex tones is problematical*
Th© terms brightness and brilliance are rather
commonly used by musicians*
The term brilliance is often
applied to style of composition or performance, tout it is
also used to refer to th© qualitative aspects of sounds*
It may toe used In speaking of general pitch level ; thus,
when a piano Is tuned to a higher frequency standard, the
brilliancy is said to toe increased*
Brilliance or bright­
ness are also used to refer to timbre*
The tones of a
trumpet may be spoken of as toeing more brilliant than
those of th© same pitch from a cornet*
Brilliance in
this sens© probably refers to a combination of bright­
ness and roughness, such as that heard In the B-B series*
The musician may us© the term dull In an evaluative sense,
and h© would probably object to Its use In describing
one extreme of the brightness continuum*
In practice,
he perhaps uses the term mellow rather than th© term
dull#
It should be mentioned that the B-Q tone of th©
D-B series did not have a very pleasing quality*
Th©
tone® became progressively more pleasant and musically ac­
ceptable toward th© B ©nd of the series*
77
VI*
CONCLUSIONS
The data from the experiment on pitch match­
ing showed that the Judgments on which the scales were
based did not result from differences in pitch among the
complex tones*
The evidence seems to warrant the conclusion that
complex tones have, In addition to pitch and loudness, at
least three attributes*
These are brightness, roughness,
and one tentatively labelled thinness-fullness or full­
ness*
third.
Th© first two are probably more basic than th©
Brightness is a function of the location on the
frequency continuum of the midpoint of the energy dis­
tribution*
The results of the quality-matching experiment
suggest that the attribute of brightness in complex tones
is not similar to the attribute of pitch-brightneas in
pure tones*
Roughness has been shown to bo present In
tones containing consecutive high partial© above the sixth
and to be a function of the location of such consecutive
partials in the whole sequence of higher partials.
Full­
ness has been shown to be a function of the relative
presence of odd- and even-numbered partials.
If a certain amount of speculation and of extra­
polation of the data is permitted, It seems possible to
state In a more basic fashion the stimulus variables and
th© nature of the functions for the last two attributes.
78
It was shown that the existence of a certain frequency
ratio (musical Interval) between the partials of a com­
plex tone resulted in the presence of roughness.
As th©
complexity of this frequency ratio Increased (as the
interval changed from a major to a minor second), rough­
ness increased*
This principle may b© extended to apply
to ratios more and less complex*
It can hardly be as­
sumed that there Is no roughness In tones not containing
consecutive high partials above the sixth,
Zero rough­
ness I® probably present only In a pur© tone.
Intro­
spective observation suggests, however, that in such
tones the amount of roughness would be very small and
that these tones would differ very slightly In roughness*
On the basis of these assumptions. It can be said that
roughness is a function of the complexity of th© frequen­
cy ratios among the partials in the tone, and that rough­
ness doe© not grow rapidly until that complexity has
reached the point of Including a frequency ratio of seven
to eight (Introducing the Interval of a large major
second)•
Th® extreme tones of the series giving a full­
ness change have also been shown to differ In the degree
of complexity of the frequency ratios between the partials
(octaves, fifths, etc*, as against a diminished fifth,
minor thirds, etc,)*
Again, the principle may be applied
79
to the ratios in tones other than those or the 0—£ series*
Th© elimination of* high, partials from tone E-18 would,
in all probability, further decrease fullness*
Tones of
greater fullness than that of 0—18 could probably be
found*
If these assumptions are made, It may be said
that fullness is a function of the complexity of the
frequency ratios between the partials of the tone, and
that It grows rapidly to some point of complexity (perhaps
that at which the Interval of the major second enters)
and grows very slowly after that point*
The result of this speculation is, then, a
scheme, admittedly greatly oversimplified, in which
roughness and fullness are different functions of th©
same variable*
In a certain range of stimulus variation,
roughness Is conceived to grow at a slow rate and full­
ness at a rapid ratej in another rang© of variation,
fullness Is conceived to grow at a slow rate and rough­
ness at a rapid rate*
This formulation In no way contra­
dicts the view that roughness and fullness are unique
and distinguishable attributes*
Their existence could
b© established by means of Boring's criteria*
Th© question may be askeds
necessary to complex tones?
Are these attributes
According to the present
viewpoint, they are to be found in any complex ton®*
If a tone contains partials above the first, the midpoint
80
of* energy i® above the fundamental and some complexity
of frequency ratios is present.
Therefore, some amounts
of brightness, roughness, and fullness must be present*
If any one of these attributes Is reduced to zero, the
sound must be heard as a pur© tone*
Impressions gained
from introspective observations of these tones are not
contradicted by the statement that any complex tone
contain© some amount of each of these attributes*
It is not suggested that th© number of attri­
butes is limited to three*
There may be other attributes
as basic as brightness and roughness, as well as others
of a more restricted nature.
The three attributes put
forward her© may not be sufficient to characterize com­
pletely Important types of variation in timbre*
For
example, the series of tones Imitating the physical
characteristics of th© sustained vowels nohtt and ’’ah”
were described by introspective report as changing In
both brightness and roughness*
But to say that this
series could be adequately described in these terms would
be to go considerably beyond the evidence*
It is be­
lieved, however, that the three attributes will be found to
characterise th© main features of many types of quali­
tative variation in complex tones, and that further study
will refine their definitions and show more clearly
their importance to auditory theory*
81
BIBLIOGRAPHY
1*
Bannister, H* Auditory phenomena and their stimulus
correlations*
In Murchison, C*, (Ed*), Handbook of
General Experimental Psychology* Worcester, Mass* s
Clark Univ* Press, 1934. Chap. 16.
2*
Boring, E* G* The relation of the attributes of sen­
sation to the dimensions of the stimulus. Phil.
Sol*. 1935, 2, 236-245*
3.
Buchisann, G*, & Meyer, E. Eine neu© optisch© Messmethod© filr Graimnophon-platten. Elektr* ffachr. Tech*,
1930, 7, 147-152.
~
4*
Egan, J*
5.
Ekdahl, A. G., & Boring, E* G* The pitch of tonal
masses* Amer* J* Psychol*. 1934, 46, 452—455*
6.
Helmholtz, H* L. F* Sensations of tone*
(Trans,
by A. I. Ellis.) Hew Yorks Longmans, Green, 1895*
7.
Eurtz, £, B*, & Larsen, M. J* An electrostatic audio
generator* Electr. En&ng;. 1935 (September), 1-6.
8.
Lewis, D*, A Larsen, M* «T. Measurement of masked
auditory threshold*
J* exp. Psychol*, (accepted
for publication).
9*
Lewis, D*, & LIchte, W* H. Analysis of a percepti­
ble series of partials in a vocal sound*
J. exp*
Psychol.. 1939, 24, 254-267.
Work In progress*
10.
Lewis, D*, & Tuthill, C* Resonant frequencies and
damping constants of resonators involved In the pro­
duction of sustained vowels ”0” and ”Ah." J.
acoust. Soc. Amer*. 1940, 11, 451-456.
11*
Saetvelt, J* G* Revision of the Seashore Measures
of Musical Talent. Unpublished Doctoral Disserta­
tion, Univ. Iowa, 1939.
12.
Snow, W. B. Chang© of pitch with loudness at low
frequencies.
J* acoust. Soc. Amer*, 1936, 8, 14—
19.
82
13*
Stevens, 3* S* The volume and. intensity of tones*
Amer. J* Psychol*. 1934, 46, 397-408.
14*
Stevens, S* S* Tonal density.
1934, 17, 586-592*
15.
Thuratone, L* L* An experimental study of nation­
ality preferences.
J* Ren* Psychol*, 1928, 1,
405-424*
18*
Titehener, E* B. Experimental psychology* Hew
Yorks Macmillan, 1901. Vol* I, Fart XX*
17.
Xitehener, E. B* A textbook of psychology*
Yorks Macmillan, 1921*
J* exp* Psychol*,
Hew
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