What was not expected was the relatively high correlation between vocal fold thickness and absolute fundamental frequency of phonation...As can be seen, the thickness of the folds appears to be reasonably similar at each fundamental frequency no matter if the subject was male or female or had a high-pitched or low-pitched voice. Thus, it appears that the per-unit mass of the folds relates to the frequency produced no matter how massive (or not) these structures are naturally. (Hollien p. 400)Hollien later explains the correlation between thickness of the folds, variations in length and overall mass. Although the bass folds must lengthen considerably to achieve C4, in the end, the vibrating mass is the same as with the coloratura who does not have to lengthen very much to sing the same pitch. This very complex experiment at least tells us there is an optimal fold depth and length index for a given pitch produced by a given voice. If that depth/length relationship (Stretch and Substance) is not achieved, there must be compensatory measures (usually pressing and raised breath pressure).
At this juncture, we can pedagogically conclude that during phonation of a given pitch, there must be a balance between fold thickness (depth) and lengthening that adheres to a gentle closure of the folds such that the fold cover is not trapped. The next area of concern is therefore how the muscles that govern fold closure (Lateral Crico-Arytenoids and Inter-arytenoids) respond to increased breath pressure.
Just to be thorough, I must mention the Posterior Crico-arytenoid (PCA). It is responsible for abducting (draw apart) the folds. Muscular activity has been observed in the PCA during phonation, which would be unexpected. I have a couple of theories on that. Since all muscles are paired, it is possible that when the adductors (Lateral CA) are dominant (as expected during phonation) that the abductors (Posterior CA) provide counterbalance. It is also possible by the vector of their contraction that PCA counters the vector of the Crico-thyroid, that stretch the folds for pitch.
Finally I must address the secondary adductive function of the Thyromuscularis (external TA). I mentioned above that this muscle contracts slightly inward and since its vector is more or less the same as the CT, when the folds are elongated, they tend to come together a little more. This secondary adduction must be taken into account. Sometimes inefficiency occurs not because the IAs or the LCAs are functioning inadequately but rather because the folds are not lengthened enough for the desired pitch. There can be many variations on how a given fundamental frequency is obtained. It is theoretically possible that the vibratory cycle occur without the top of the folds closing. This mode of vibration would be possible for folds that are too deep (TA-hyperfunction). This is the second sound I demonstrated on the first clip.
I will stop here for now. We will continue soon with breath, resonance, etc...