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≳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.