The immediate problem was: What is the relation between the width of
interval used and the pleasure got by hearing the motive _a-b-a_ and
_b-a-b_, where _a_ is always the lower tone. The method of procedure
was to take a fixed tone (460 vibrations in the first case) and get
a series of observations on successive progressions _b-a-b_ where
_a_ differed from _b_ by 4, 8, 12 ... 56 vibrations. The greatest
difference thus is approximately a musical whole tone. Then a series of
observations was taken on _a-b-a_ where _a_ similarly differed from _b_
by 4, 8, 12 ... 52 vibrations. The progressions were given in irregular
order, that there might be no chance of the observer getting into a
fixed habit of replying. The intimate relation between the pleasure
in successive musical tones and the pleasure in musical harmonies
suggested naturally the question whether the feeling-value of these
unmusical progressions was not somehow dependent upon the affective
character of the simultaneous presentation of the same tones. Therefore
after a progression had been given once and judgment recorded, the
two tones used were given as a "harmony," that is simultaneously,
and a judgment taken as to its agreeableness. This was immediately
followed by the same progression, thus giving opportunity to observe
the relation between the feeling-tone of the interval as it appeared in
successive and in simultaneous presentation.
The results of this part of the investigation are graphically
represented in the following plates. Tables I and II indicate the
feeling-value of _a-b-a_ where _a_, the lower tone, is 460 vibrations,
and _b_ is from 4 to 56 vibrations in addition, and the feeling-value
of _b-a-b_ where _b_, the higher tone, is 460 vibrations and _a_ is
from 4 to 56 vibrations less.
[Illustration: PLATE VI.]
The base-lines from which the vertical lines to the curves are drawn
represent the feeling-tone 4, the indifference-point. Above comes 3,
2, 1 and below 5, 6, 7; each square represents a unit. The horizontal
abscissæ represent the width of the interval; the arrows indicate the
musical intervals. The observers are given by initials. The first
evident fact for both average curves of Plate V is that the maximum
pleasure does not coincide with a musical interval, but comes with an
interval four or eight vibrations less than either the half or the full
tone of the musical scale. While in both cases the first elevation
of the curve comes before the semi-tone, _b-a-b_ shows a decrease of
pleasure as the whole step is approached while _a-b-a_ rises again. The
order _a-b-a_ is liked better than _b-a-b_.
Public-domain text, read in full here on John Shaqi.
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