Fig 1.
Schematic representation of vocal fold tissues, indicating three main layers: epithelium, lamina propria, and muscle.
The lamina propria is further differentiated into a superficial, an intermediate and a deep layer. The intermediate and deep layers constitute the vocal ligament.
Fig 2.
Two contrasting cases for obtaining a similar fo range.
(a) A steep stress-strain curve with small elongation, and (b) a shallow stress-strain curve with large elongation.
Fig 3.
Relations between logarithmic fundamental frequency ratio (high/low) and the respective vocal fold length ratio (long/short) for vocal fold tissue characterized by different B-values (from Eq 3).
A value of L1 = 0.7L0 was assumed.
Table 1.
Raw data of body mass, vocal fold length (L0), stress-strain relationship for vocal fold tissue, and average fundamental frequency range.
Vocal fold lengths were measured in specimen available to us (unpublished data), except for the African elephant. The variable ε = (L-L0) / L0.
Fig 4.
Empirical data from Table 1, (a) cadaveric vocal fold length L0 versus body mass, (b) minimum and maximum fundamental frequency versus body mass, (c) derived minimum and maximum fundamental frequency versus cadaveric vocal fold length L0, (d) B-value versus cadaveric vocal fold length L0; the trend line was calculated without one outlier (rhesus monkey).
Fig 5.
Contour plot of predicted fundamental frequency range (high/low, fo2/fo1 ratio) for morphological variables B and L2/L1.
The range depends on two important factors: the rotational flexibility of the laryngeal framework, which facilitates L2/L1; and the B value that quantifies the tissue stress response to elongation. For a given B value, a larger fundamental frequency range can be achieved with greater rotational flexibility. For a given L2/L1 ratio, a larger frequency range can be achieved with a greater B value. Note that the changes in the B value are not large to achieve a larger frequency range for a given a given L2/L1 ratio.