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.

This commentary focuses on the claim that perceptual demands have caused the linearity exhibited by locus equations. I discuss results of an experiment demonstrating that, contrary to Sussman et al.'s claims, locus equations do not have relevance for the perception of stop consonants. I therefore argue against the plausibility of the orderly output constraint.

The debate on the origin of the locus equation is circular. In this commentary the locus equation is obtained by way of a theoretical model based on acoustics without recourse to articulatory knowledge or perceptual constraints. The proposed model is driven by criteria of minimum energy and maximum simplicity.

Locus equations offer promise for an understanding of at least some aspects of perceptual invariance in speech, but they were discovered almost fortuitously. With the present availability of powerful machine learning algorithms, ignorance-based automatic discovery procedures are starting to supplant knowledge-based scientific inquiry. Principles of self-learning and self-organization are powerful tools for speech research but remain somewhat under-utilized.

In their important work on locus equations, Sussman and his colleagues have helped to simplify the theoretical problem of how human listeners identify place of articulation contrasts among consonants, but much work remains before this problem is solved.

Locus equations contain an economical set of hidden (i.e., not directly observable in the data) parameters of speech that provide an elegant way of characterizing the ubiquitous context-dependent behaviors exhibited in speech acoustics. These hidden parameters can be effectively exploited to constrain the huge set of context-dependent speech model parameters currently in use in modern, mainstream speech recognition technology.

Sussman and colleagues provide no evidence supporting their claim that the human vocal production system is specialized to produce locus equations with high correlations and linearity. We propose the alternative null hypothesis that these features result from physical and physiological factors common to all mammalian vocal tracts and we recommend caution in assuming that human speech production mechanisms are unique.

The orderly output constraint (OOC) is extraneous. Talkers “speak in lines” in its absence. Further, there is no perceptual motivation for an OOC; perceivers ignore the linearity between F2 at consonant-vowel onset and F2 in the vowel. In any case, the analogy with bat and barn owl localization systems underlying the theory is extreme, Sussman et al.'s comments to the contrary notwithstanding.

Although an individual speaker's productions obey locus equations, whether listeners' perceptions are based on them needs further exploration. Comparing the results from the perceptual experiments to predicted identifications, one sees qualitative similarities and some discrepancies. However, the variability of locus equations and individual consonant-vowel (CV) tokens across speakers seems problematic if listeners are using locus equations for perception.

Understanding spoken language involves far more than decoding a linear sequence of phonetic elements. In view of the inherent variability of the acoustic signal in spontaneous speech, it is not entirely clear that the sort of representation derived from locus equations is sufficient to account for the robustness of spoken language understanding under real-world conditions. An alternative representation, based on the low-frequency modulation spectrum, provides a more plausible neural foundation for spoken language processing.

An alternative account of the locus equation phenomenon based on recent theories of speech movement planning is provided. It is similar to Sussman et al.'s account in positing that our productions are tuned to satisfy auditory constraints. It differs by suggesting that the locus equation effect may be an epiphenomenon of a planning process that satisfies simpler auditory constraints.

Sussman et al. state that auditory systems exploit linear correlations in the sound signal in order to identify perceptual categories. Can the auditory system recognize linearity? In bats and owls, separability of emergent features is an additional constraint that goes beyond linearity and for which linearity is not a necessary prerequisite.

Locus equations fail to provide adequate abstraction to capture the English phoneme /g/. They also cannot characterize final consonants or their relation to pre-vocalic consonants. However, locus equations are approximately abstract enough to define the upper limit on phonological distinctions for place of articulation. Hence, locus equations seem to mediate phonetic and phonological perceptual abilities.

Two issues are addressed in this commentary: the universality and the “psychological reality” of locus equations as cues to place of articulation. Preliminary data collected in our laboratory suggest that locus equations do not reliably distinguish place of articulation for fricatives. Additionally, perception studies show that listeners can identify place of articulation based on much less temporal information than that required for deriving locus equations.

The effort to understand speech perception on the basis of relationships between acoustic parameters of speech sounds is to be recommended. Neural specializations (combination-sensitivity) for echolocation, communication, and sound localization probably constitute the common mechanisms of vertebrate auditory processing and may be essential for speech production as well as perception. There is, however, no need for meaningful maps.

Although neural encoding by bats and owls presents seductive analogies, the major contribution of locus equations and orderly output constraints discussed by Sussman et al. is the demonstration that important acoustic information for speech perception can be captured by elegant and neurally-plausible learning processes.

Sussman et al. describe an ecological property of the speech signal that is putatively functional in perception. An important issue, however, is whether their putative cue is an emerging feature or whether the second formant (F2) onset and the F2 vowel actually provide independent cues to perceptual categorization. Regardless of the outcome of this issue, an important goal of speech research is to understand how multiple cues are evaluated and integrated to achieve categorization.

Using an articulatory model we show that locus equations make special use of the phonetic space of possible locus patterns. There is nothing articulatorily inevitable about their linearity or slope- intercept characteristics. Nonetheless, articulatory factors do play an important role in the origin of simulated locus equations, but they cannot, by themselves, provide complete explanations for the observed facts. As in other domains, there is interaction between perceptual and motor factors.

The locus equation proposal ignores a fundamental difference between human speech perception and nonhuman echolocation and sound localization, offers a questionable account of the function of consonant-vowel coarticulation, and is further undermined if the effects of other forms of coarticulation are considered. The function of coarticulation is to convey phonetic information rapidly and reliably.

A systematic relationship between the acoustic structure and phonemic content of speech raises the possibility that processing strategies similar to those described in animals with highly specialized hearing may also operate in the human brain. This idea could be tested by analyzing animal communication calls into locus equations and using those as stimulus tools in neurophysiological studies of auditory neurons.