Chen-Gia Tsai
Pipe model of a Kargyraa singer's vocal tract
The melody pitch f1 (the center frequency of the first formant) in Kargyraa voices is determined by the mouth opening. A perturbation method predicts the resonance shift caused by a bore enlargement at a position x0 of a pipe with a irregular geometry (e.g., Fletcher & Rossing 1991). During a performance of Kargyraa, the bore diameter of the vocal tract changes at the lips, a pressure node for all modes. Hence, an enlargement of mouth opening leads to an increase in the center frequencies of the first and second formants (Tsai 2001).
Figure: (a) Spectrogram of a Kargyraa song "the far side of a dry riverbed" (Audio file). (b) and (c) are two snapshot spectra of (a). They show f2=2f1.
This pipe model does not predict (1) the small bandwidth of the first and second formants, and (2) "mode-locking" f2=2f1. I hypothesize that periodic vorticity bursts at the diffuser-like supraglottal structures are responsible for producing the strong components at f1 and 2f1.
Subharmonic generation
In Kargyraa, there is a nonlinear coupling between the two pairs of the vocal folds, which can lead to either entrainments or chaos. While 1:2 entrainment can produce beautiful voices of Kargyraa, pathological voices with the involvement of chaotic vibration of the ventricular folds have a hoarse quality (ventricular dysphonia).
Based on recordings of high-speed images of the laryngeal movement, Lindestad and collogues (2001) reported that during Kargyraa singing the ventricular folds vibrated with complete but short closures at half the frequency of the true vocal folds, thus contributing to subharmonic generation.
Autonomic functions
It seems that stiffness of the ventricular folds cannot be manipulated by will, because they contain very few muscle fibres. However, the constantly increased ventricular function and repetitive closure may lead to new functional and anatomical changes in the interior of the larynx (such as ventricular hypertrophy) and, possibly, to a new system of innervation.
On the other hand, evidence of psychoemotional, cerebellar or midbrain (e.g., parkinsonism) types of ventricular dysphonia suggests sub-cortical influences of the ventricular folds.
It is interesting to note that Tibetan monks do not practice their vocalization. They improve the control of the ventricular folds through meditation! Meditaion is a conscious mental process that induces a set of integrated physiologic changes termed the relaxation response. The elastic property of the ventricular folds may be affected by meditation through autonomic functions. They become so relaxed that they vibrate with complete closures at half the frequency of the true vocal folds. In contrast, emotional stress can lead to adduction and vibration of the stiff ventricular folds with incomplete closures. Because lower subharmonics are weak in such melancholic voices, they sound rough (see "Roughness induced by subharmonics").
Tibetan monks stated repeatedly that while singing overtones one should always make a special effort to attune heart and mind to the meaning of the holy moment (Smith and Stevens 1967).
An overtone singer and researcher related the psychological mechanism underlying overtone singing during meditation to "a higher sound awareness":
When we meditate by way of singing the need to make pleasant or even beautiful sounds moves to the background. It is not the singing that decides whether we enter a truly meditative state of mind. More important is that we listen to ourselves, that we search for the voice inside. We are not concerned with personal judgments about our voice, nor with the personality in our voice. Singing harmonics automatically focuses the mind more than most other types of singing, because we essentially sing just one tone and listen to its internal dynamics. Overtones demand from us a higher than normal sounds awareness. They fulfil a service in certain spiritual traditions and have a built-in symbolic association with 'thing high'. They have the exceptional ability to unite voices to the highest degree and a tendency to unify the body and the mind. (van Tongeren 2002:207)
It is my hypothesis that overtone singing focuses the mind automatically on the weak pitch of the prominent nth harmonic. This form of meditation is designed to lead one to a subjective experience of absorption with the object of focus. From a viewpoint of neuroscience it seems appropriate that a model for this kind of meditation begins with activation of the prefrontal cortex and the cingulate gyrus. Brain imaging studies have suggested that tasks requiring sustained attention are initiated via activity in the prefrontal cortex, particularly in the right hemisphere, and the cingulate gyrus appears to be involved in focusing attention. In an excellent review paper on the neural basis of meditation, Newberg and Iversen (2003) proposed a neurophysiological network possibly underlying meditative states. They discussed the prefrontal cortex effects on thalamic activation, posterior superior parietal lobule deafferentation, hippocampal and amygdalar activation, hypothalamic and autonomic nervous system changes, autonomic-cortical activity, and neurotransmitter activity. Although their model may provide a general framework for studying the neural basis of meditation, it should be noted that there are categories and subcategories of meditation that may be associated with different neural activity. For example, overtone singing by Tibetan monks belongs to the meditation category in which the subjects focus their attention on a particular object. When the object is the melody composed of overtones, the mental task and thus neural activity may differ from the meditation technique that focuses the mind on an image, phrase, or word, because of the involvement of supraglottal structures.
Nitric oxide mechanisms
Nonadrenergic, noncholinergic (NANC) nerves, which cause relaxation of airway smooth muscle, have been described in several species including man. Nitric oxide appears to account for all the NANC response in human central and peripheral airways in vitro. A recent review on meditation stressed the importance of the involvement of nitric oxide during meditation (Esch et al. 2004, see also Kim et al. 2005). Based on these findings I propose a model for Tibaten overtone chanting:
The loop underlying Tibaten overtone chanting can be described as: (1) a monk adducts and relexes the ventricular folds; (2) he sings overtones; (3) he focuses his mind on the weak pitch of reinforced overtones; (4) this concentration triggers autonomic functions and nitric oxide mechanisms that in turn lead to a relexation of the smooth muscles in the supraglottal structures.
References
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