We may use the same principles to derive the effects on formant frequencies of closure associated with various consonantal places of articulation. Labial closure, as noted above, amounts to a local constriction at the open end of the acoustic tube. Since all the resonances have a node at this point, constriction at the lips lowers all the resonance frequencies.
``Velar'' closure occurs over a range of places in the vocal tract, often classified into front and back velars. The front velars occur in my speech adjacent to front vowels; back ones next to back vowels. It is likely, though perhaps not proven, that this coarticulatory effect is a continuous one, not the result of a categorical division of velar consonants into front and back allophones. However, as a general rule, the front velars do have a particular acoustic structure which is shared by all of them, and not shared by back velars, namely the characteristic ``pinch'' of F2 and F3, where they move towards each other, finally almost merging just at the point of closure. Consider the effects of a constriction at or around node N3 and antinode A6, i.e., at the back of the palate or front of the velum. The locations of N3 and A6 are very close to one another, and a somewhat distributed closure such as may be made by the tongue dorsum will have a constricting effect on both. This would result in lowering the A6 resonance, namely F3, and raising the N3 resonance, F2. This is in fact the commonly observed acoustic effect of front-velar closure.
Back velars have a constriction away from this location, in which an F3 antinode and an F2 node occur quite close to each other. As one might expect, they do not show this pattern of F2-F3 approximation.
Alveolar closure occurs between the F2 antinode at the lips and the F2 node at the palate. It thus contributes to both sums in Relation 1, above. The effect is therefore a balancing one. Apical closure is partly like node constriction, and partly like antinode constriction. If there is already node constriction (i.e., high F2), apical closure adds to both node constriction and antinode constriction; the result, on balance, is greater relative antinode constriction, and according to Rayleigh's rule, a lowering in F2. If there is already antinode constriction, i.e., lowered F2, then apical closure will have the opposite balancing effect, resulting in greater relative node constriction, and a rise in F2. Note that the balancing effect must be partial rather than complete; a low F2 will be raised, and a high F2 will be lowered, but the raising and lowering will not reach the midpoint.
This pattern is precisely the observed pattern of F2 changes when apical closure occurs; the ``locus theory'' for coronal consonants describes this effect. If a vowel with high F2 is adjacent to an apical consonant, then the transition into the consonant lowers F2; conversely a low vocalic F2 will rise, in the transition into an apical consonant. Even the detail that the ``locus'' is virtual rather than fully realized is explained: the relative imbalance between the node and antinode sums in Relation 1, above, is evened out by adding constants to both, but it is not completely restored. Therefore the transition to an apical consonant will move in the direction of the balance point, but will only move a fraction of the distance toward it, according to the size of the node and antinode sums in Relation 1, relative to the contribution of the apical constriction to each one.
The coronal ``locus'' has often been claimed, without apparent understanding, to reflect some deeper articulatory reality, so that there is some underlying resonance at the never-attained locus frequency that is characteristic of an actual articulatory state. But we see that this effect is entirely an artifact of the node-antinode balancing due to a constriction between a node and an antinode. No cavity has been isolated which resonates at this hidden frequency. Here we see that this deeper articulatory reality does not exist. There is no locus.
Rayleigh's rule can thus be applied to explain the finest details of formant structure, not just for vowels, but for transitions to consonants also. Its explanation of the locus theory must be considered an important step for the science of acoustic phonetics.