Grassmann's law

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For Grassmann's law in color theory, see CIE 1931 color space.

Grassmann's law, named after its discoverer Hermann Grassmann, is a rule of phonology in Ancient Greek and Sanskrit which states that if an aspirated consonant is followed by another aspirated consonant in the next syllable, the first one loses the aspiration. The descriptive (synchronic) version was described for Sanskrit by Panini.

Here are some examples in Greek of the effects of Grassmann's Law:

[tʰu-oː] θύω 'I kill an animal'
[e-tu-tʰeː] ἔτυθη 'it was killed'

[tʰrik-s] θρίξ 'hair'
[trikʰ-es] τριχές 'hairs'

[tʰap-sai] θάψαι 'to bury (aorist)'
[tapʰ-ein] τάφειν 'to bury (present)'

In the reduplication which forms the perfect tense in both Greek and Sanskrit, if the initial consonant is aspirated, the prepended consonant is unaspirated by Grassmann's Law. For instance [pʰu-oː] φύω 'I grow' : [pe-pʰuː-ka] πεφυκα 'I have grown'.

The fact that deaspiration in Greek took place after the change of Proto-Indo-European *bʰ, dʰ, gʰ to /pʰ, tʰ, kʰ/, and the fact that no other Indo-European languages have Grassmann's law, show that Grassmann's law developed independently in Greek and Sanskrit; it was not inherited from PIE.

Grassmann's Law is also known to occur in Ofo an extinct and underdocumented Siouan language.

Diaspirate roots

Cases like [tʰrik-s] ~ [trikʰ-es] and [tʰap-sai] ~ [tapʰ-ein] illustrate the phenomenon of diaspirate roots, for which two different analyses have been given.

In one account, the "underlying diaspirate" theory, the underlying roots are taken to be /tʰrikʰ/ and /tʰapʰ/. When an /s/ (or word edge, or various other sounds) immediately follows, then the second aspiration is lost, and the first aspirate therefore survives ([tʰrik-s], [tʰap-sai]). If a vowel follows the second aspirate, it survives unaltered, and therefore the first aspiration is lost by Grassmann's Law ([trikʰ-es], [tapʰ-ein]).

A different analytical approach was taken by the ancient Indian grammarians. In their view, the roots are taken to be underlying /trikʰ/ and /tapʰ/. These roots persist unaltered in [trikʰ-es] and [tapʰ-ein]. But if an /s/ follows, it triggers an "aspiration throwback", in which the aspiration migrates leftward, docking onto the initial consonant ([tʰrik-s], [tʰap-sai]).

Contemporary scholars are divided on which of these approaches is correct. The linguist Ivan Sag has pointed out an advantage of the ancient Indian theory, namely that it explains why there are no patterns like hypothetical "[trik-s] ~ [trikʰ-es]". The underlying-diaspirate theory incorrectly predicts that these should occur.

References

de Reuse, Willem J. (1981). Grassmann's law in Ofo. International Journal of American Linguistics, 47 (3), 243-244.
Sag, Ivan. A. (1974) "The Grassmann's Law Ordering Pseudoparadox," Linguistic Inquiry 5, 591-607.

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