Introduction to Acoustics

Mean spectrum level (dB)
–30
–40
–50
–60
–70
–80
–90
0 1000 2000 3000 4000 5000 6000
Frequency (Hz)
Fig. 16.17 Long-term-average spectra curves obtained from
an untrained male speaker reading the same text at 6
different degrees of vocal loudness. From top to bottom
the corresponding Leq values at 0.3 m were 93 dB, 88 dB,
85 dB, 84 dB, 80 dB, and 76 dB
Variation of vocal loudness affects the spectrum
slope as illustrated in Fig. 16.17, which shows longterm-average
spectra (LTAS) from a male untrained
voice. In the figure loudness is specified in terms of the
so-called equivalent sound level Leq. This is a commonly
used time average of sound level, defined as
Leq = 10 log 1
T
�T
0
p 2
p 2 0
dt ,
where t is time and T the size of the time window. p and
p0 are the sound pressure and the reference pressure,
respectively.
When vocal loudness is changed, the higher overtones
change much more in sound level than the lower
overtones. In the figure, a 14 dB change of the level
near 600 Hz is associated with a 22 dB change near
3000 Hz, i. e., about 1.5 times the level change near
600 Hz. Similar relationships have been observed for
professional singers [16.47]. In other words, the slope
of the voice source spectrum decreases with increasing
vocal loudness.
The physiological variable used for variation of vocal
loudness is Ps. This is illustrated in the upper graph
of Fig. 16.18, comparing averaged data observed in untrained
female and male subjects and data obtained from
professional operatic baritone singers [16.45, 46]. The
relationship between the Ps and MFDR is approximately
linear. It can be observed that the pressure range used
by the singer is considerably wider than that used by the
untrained voices. The MFDR produced with a given Ps
by the untrained female and male subjects is mostly
The Human Voice in Speech and Singing 16.2 The Glottal Sound Source 681
Mean MFDR (l/s 2 )
2000
1500
1000
500
0
0 5 10 15 20 25 30
SPL at 0.3m (dB)
Mean Ps (cm H2O)
95
90
85
80
75
70
65
60
Untrained females
Untrained men
Baritone means
196 Hz
139 Hz
278 Hz
300 500 1000
2000
MFDR (l/s 2 )
Fig. 16.18 The top graph shows the relationship between
the mean subglottal pressure and the mean MFDR for
the indicated subject groups. The bottom graph shows the
relationship between MFDR and the SPL at 0.3 m for a professional
baritone singing the vowels /a/ and /æ/ at different
F0s. (After [16.45] p. 183, [16.46] p. 184)
higher than that produced by the baritones with the
same pressure.This may depend on different mechanical
characteristics of the vocal folds.
As we will see later, SPL depends on the strength
of the excitation of the vocal tract, i. e. on MFDR. This
variable, in turn, depends on Ps and F0; the higher the
pressure, the greater the MFDR value and the higher the
F0, the greater the MFDR. The top graph of Fig. 16.18
Part E 16.2