All of the sounds used in this study were recorded in our studio with
the virtuoso violist mentioned previously
playing a number of notes both with and without
vibrato on the viola. They were analyzed using the high resolution
fundamental frequency tracker of Brown and Puckette (1993). Sounds segments
were chosen which represented a range of frequencies and and which had
a standard deviation in frequency of 2 cents or less.
in column 3. The notes and
# were originally recorded
as
and
and resampled to give a more uniform
spacing of the 4 frequencies chosen for the experiment. Graphs of
frequency vs time for these sound segments are found in Figures 1 and 2.
Frequencies in these graphs are in cents with respect to A440.
Average spectral intensities in dB for the unmodulated sounds are reported in columns 6-16 of
Table 2,
where the number labeling the column is the harmonic number.
Intensities are given relative to that of the most intense component,
which is assigned the value 0 db. The values of components are given
up to a harmonic number beyond which all intensities are down by 20 dB or
more. The (maximum) amplitudes of the maximum component (16 bit sample values)
are 9000,
12000,
13000, and
9500.
The geometric means of the vibrato sounds were calculated from 172
values/s. These values were calculated from overlapping 50 ms
segments of sound. For the vibrato amplitudes of this study the geometric and
arithmetic means are equivalent (differences on the order of .1
cent) and will be referred to simply as the
mean. The vibrato was then labeled by this mean frequency
for purposes of identification. The unmodulated sound was resampled
to have the mean frequency and frequencies equal to the mean
3 cents,
6 cents,
9 cents,
15 cents, and + 21
cents. The positive assymetry was chosen as some string players claim
to hear the high side of the vibrato. With this system of
nomenclature then, a match of the vibrato pitch to the unmodulated
sound labeled +15 would mean that the pitch center of the vibrato is
15 cents above its mean for that subject.