The thickness of the vocal folds do not fit into two static categories such as thick or thin nor M1 and M2. The vocal folds change their length and their thickness in a continuous manner as the sung pitch is raised or lowered. In this they meet the myoelastic theory of vocal fold function as well as the aerodynamic theory that emphasis the Bernoulli Principal to assist with vocal fold closure.
A newer element was introduced by Ingo Titze that addresses the effect on the vocal folds of a standing wave in the vocal tract. When the tendency of the vocal tract to resonate desecrate frequencies (formants) is matched to phonated tone that contains some of these frequencies a standing wave is created within the vocal tract. This standing wave will, because it has inertia, resist both the opening and closing of the vocal folds and in this way greatly assists them in transferring their energy into the vocal stream (please see footnote). It is as if the standing wave is a pneumatic spring into which the vocal folds move and that spring works in both directions, open and close. The gives the vocal folds stability to function more freely in their shortening/thickening and lengthening/thinning actions.
But, the crucial element of this progression is the tuning of the vocal tract to match available harmonics in the phonated tone. Each pitch we sing will have a broad spectrum of harmonics if the tone is produced efficiently by the vocal folds. For example, a breathy tone has few harmonics because the vocal folds do not come together for a sufficient length of time. This is also true of falsetto; the anterior of the vocal folds are not completely closed.
Given a well produced tone from the phonation process (phonated tone) the singer must be trained to make adjustments in the vocal tract in order to match the vocal tract potential frequencies (formants) to the actual frequencies produced by the phonated tone. When this occurs the vocal tract will increase the loudness (amplitude) of those frequencies. In most cases only about two or three frequencies are so amplified. And, surprisingly it is seldom the fundamental that receives this boost in loudness.
The lowest two formants of the vocal tract determine the vowel that is being sung or said. And each vowel or modification of a vowel gives different formants. The two lowest formants are called the vowel formants for obvious reasons.
As the voice ascends in pitch an one vowel it will eventually reach a point where that vowel can no longer find a phonated tone harmonic to resonate. At that point the vocal tract no longer has a standing wave and there is no longer the benefit to the singer of the pneumatic cushion to stabilize the vocal folds. As a result, the vocal folds tend to become asynchronous and do not open and close as a unit. The result is a ‘break’ in the voice and we have now entered into the first sign of a passaggio.. This discomfort will usually continue for about a minor third interval as the pitch continues to rise and then, magically, we find ourselves in another register where the same vowel is once again able to resonate a harmonic of the sung pitch. Or we are not able to find a new register.
In short, passaggi and registers do exist but they exist more because of mis-tuning the vocal tract such that it does not match the harmonics of the phonated tone. If the sung vowel is changed or slightly modified when the ascending pitch enters that area where the vocal tract is unable to resonate the original vowel correctly, the problem of the passaggio will likely not appear.
Try this. Sing an ascending octave that goes over your passaggio on the vowel /a/. As you feel yourself approaching your passaggio, change the vowel to an /i/ or /e/ (or /u/ or /o/) and when above your passaggio go back to the /a/ vowel. Done correctly you will very likely not experience the clumsiness of your passaggio but instead be able to sing smoothly over it. The reason? By changing to the more closed vowel at the beginning of the passaggio you re-tuned the vocal tract to a vowel whose formants will match some of the frequencies of the sung pitch in that area.
Footnote from Reg on “The Vocalist”.
“I’d have said that it alternately –assists- and –resists- the operation of the previously un-stabilized folds. As I’ve mentioned before, the process of feedback not only greatly reduces the source impedance, it brings stability to that impedance as well”.