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  Figure 9. Articulatory area function parameters plotted as functions of FE. Curves show approximations derived from trend line equations.
denominator is the consistent identification of the double formant. We feel justified in concluding that our results confirm the double formant phenomenon as a prereq- uisite for the overtone selection and enhancement in
AMH’s overtone singing technique.
Central to the present account is the “double formant” hypothesis, which attributes the phenomenon of over- tone singing to VT filtering. However, the inverse filtering results also suggest that overtone singing involves a pho- nation type different from that in conversational voice, making the source spectrum slope less steep and thus boosting the amplitudes of the higher overtones. These findings replicate and extend previous investigations of overtone singing. Bloothooft et al. (1992) undertook an acoustic study of an experienced overtone singer and suggested formant clustering as an explanation and also noted an extended closed phase of the vocal fold vibrations. Using impedance measurements, Kob (2004) analyzed a form of overtone singing called sygyt and interpreted the overtone boosting as the result of formant clustering.
Parallel vibrations of the ventricular folds have been documented in throat singing (Lindestad et al., 2001). How about this possibility in AMH’s overtone singing? Our inverse filtering data clearly rule out the existence of a laryngeal mechanism that selectively amplifies and enhances individual partials.
Overtone singing clearly requires an extremely high degree of articulatory precision; for each FE, two cavities need to be shaped such that they produce resonance frequencies that match each other within a few tens of Hertz. How can the underlying motor control be organized? It is prob- ably relevant that some of the articulatory configurations shown in Figure 6 are used also in speech. The lateral pro- file for FE = 1,096 Hz resembles the articulation of retroflex consonants (Dixit 1990; Krull and Lindblom, 1996). A narrow pharyngeal constriction is typical of [a]-like vowels and pharyngealized consonants (Ladefoged and Maddie- son, 1996). The VT for FE = 3,202 Hz has a “palatalized’ tongue shape similar to that used for the vowel [i].
It would also be relevant that the articulatory param- eters varied systematically with FE. This is illustrated in Figure 9. It shows how AMH varied the lip open- ing area, length of palatal constriction, larynx height, front cavity volume, and pharynx area as a function of FE. It is evident that the values of each individual articulatory dimension are aligned along smooth con- tours running between its values in FE = 1,096 and 3,202 Hz. This lawful patterning suggests that it would be possible to derive VT shapes intermediate between those for FE = 1,096 and 3,202 Hz by interpolation. A rough description would be to say that the VT shapes are located along a trajectory in the articulatory space that runs between a retroflex and pharyngealized [a] and an [i]-like, palatalized tongue profile.
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