Piecewise--planar representation of vowel formant frequencies

The first three formant frequencies for 778 steady-state tokens of 30 nonretroflex vowel types uttered by a female speaker are found to lie close to a piecewise-planar surface (expressed numerically as 0.634F1 +0.603F2 -- 0.485F3 -- 366 = 0, for F2 greater than 0.027F1 +1692 and 0.686F1 -- 0.528F2 -- 0.501F3 +1569 = 0, otherwise). The rms distance of the vowels from this surface is only 86 Hz. The intersection between the two planes is a line of nearly constant F2, corresponding closely to the F2 of a uniform vocal tract of the same length as our speaker's. The piecewise-planar representation also suggests a way to test the hypotheses of uniform and nonuniform formant-frequency scaling between speakers.