(Fig. 4). In the kargyraa voice, the estimated laryngeal airflow curve has two peaks in each period.
From our physiological observation, the VFs vibrate
twice in each period of the FVF vibration, and the
estimated laryngeal airflow curve showed that in one
of the two vibrations of VFs, the closing of VFs were
not completed (Fig. 5).
Sound f
EGG
SPECTRUM [d
PECTRUM EdB]
lloH
Lygea l
Fig. 4: Inverse filtered laryngeal airflow of pressed
voices for two singers.
Sound
EGG
Airflow
airflow
Fig. 5: Inverse filtered laryngeal airflow of kargyraa
voices for two singers.
All the power spectra of the estimated glottal airflows showed an increase of power in the range from
1 to 3 kHz, which is where the second formant frequency which corresponds the whistle-like overtone
appears in throat singing (Fig. 6-8).
Fig. 8: Inverse filtered airflow spectrum of karygraa
voice for two singers.
A 2 x 2-mass model
For a physical simulation of the VF and FVF vibrations, we propose a 2 x 2-mass model as a selfoscillating model of VF and FVF vibrations (Fig. 9).
This model was devised by introducing a two-mass
model for the false VFs to the ordinary two-mass
model for the VFs. The mechanical transmission of
vibrations between the VFs and FVFs were not considered. The laryngeal ventricle is a cylinder whose
sectional area is uniformally 5 cm2 and height is 16 cm
and not deformed. In the simulation the 2 x 2-mass
model oscillated stably. The simulation of laryngeal
movements using the 2 x 2-mass model agreed with
the above assumptions for the two laryngeal movement patterns of throat singing for both the pressed
and kargyraa voices (Fig. 10). The 2 x 2-mass model
can simulate ordinary glottal source in the same way
as the two-mass model by setting suitable model parameters [3].
Trachea MFVocal tract
Ps Ug - Uf Pi
False
Vocal Fvocalse
foldsvocal
Laryngeal folds
Ventricle
Fig. 9: 2 x 2-mass model for the VFs and FVFs.
0 1 2 3 4 5kHz O
2 3 4 5kHz
Laryngeal airflow
1000 cc/s
Sound waveform
LJ "
Fig. 6: Inverse filtered airflow spectrum of normal voice
for two singers.
Fig. 10: Laryngeal airflow obtained by using 2 x 2-mass
model
(left: pressed voice, right: kargyraa voice).
Laryngeal voice model
From the physiological observations and estimated
laryngeal voices, we assume (1) in pressed-voice production, VFs and FVFs vibrate in almost opposite
phase; (2) in karygraa-voice production, two closed
Fig. 7: Inverse filtered airflow spectrum of pressed voice
for two singers.
