This commentary focuses on the nature of combinatorial properties for speech and the locus equation. The presence of some overlap in locus equation space suggests that this higher order property may not be strictly invariant and may require other cues or properties for the perception of place of articulation. Moreover, combinatorial analysis in two-dimensional space and the resultant linearity appear to have a “special” status in the development of this theoretical framework. However, place of articulation is only one of many phonetic dimensions in language. It is suggested that a multidimensional space including patterns derived in the frequency, amplitude, and time domains will be needed to characterize the phonetic categories of speech, and that although the derived properties ultimately may not meet the conditions of linearity, they will reflect a higher order acoustic invariance.
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