Grassmann's law, named after its discoverer Hermann Grassmann, is a dissimilatory phonological process 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 version was described for Sanskrit by Pāṇini.
Here are some examples in Greek of the effects of Grassmann's Law:
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-ɔː] φύω 'I grow' : [pe-pʰuː-ka] πέφυκα '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 show Grassmann's law, has been argued to show that Grassmann's law developed independently in Greek and Sanskrit, i.e. that it was not inherited from PIE.[1] The evidence from other languages is not strictly negative: many IE branches, including Sanskrit's closest relative Iranian merge the PIE voiced aspirated and unaspirated stops, and thus it is not possible to tell if Grassmann's Law ever operated in them.
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In Koine Greek, outside of the context of reduplicating syllables, the alternations involving labials and velars have been completely levelled, and thus Grassmann's law only remains in effect for the alternation between /t/ and /tʰ/, as in the latter two examples above. It makes no difference whether the /tʰ/ in question continues PIE *dʰ or *ɡʷʰ-.
Thus alongside the pair [takʰús] 'fast' : [tʰássɔːn] 'faster' displaying Grassmann's law, Greek has the pair [pakʰús] 'thick' : [pássɔːn] 'thicker' from the PIE etymon *bʰn̩ɡʰ- (established by cognate forms like Sanskrit bahú- 'abundant' since *bʰ is the only point of intersection between Greek p and Sanskrit b), in which the /p/ in the comparative is a result of levelling. Similarly, [peútʰomai] ~ [puntʰánomai] 'come to know' from PIE *bʰewdʰ- has the future [peúsomai]. Contrariwise, only /tʰ/ dissimilates before aspirated affixes like the aorist passive in /-tʰɛː/ and the imperative in /-tʰi/; /pʰ/ and /kʰ/ do not, as in [ˈpʰatʰi] 'speak!'.
Cases like [tʰrík-s] ~ [tríkʰ-es] and [tʰáp-sai] ~ [tapʰ-eîn] 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 ([tʰrík-s], [tʰáp-sai]). If a vowel follows the second aspirate, it survives unaltered, and therefore the first aspiration is lost by Grassmann's Law ([tríkʰ-es], [tápʰ-os]).
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 [tríkʰ-es] and [tapʰ-eîn]. But if an /s/ follows, it triggers an "aspiration throwback" (ATB), in which the aspiration migrates leftward, docking onto the initial consonant ([tʰrík-s], [tʰáp-sai]).
In his initial formulation of the law, Grassmann briefly referred to ATB to explain these seemingly aberrant forms. However, the consensus among contemporary historical linguists is that the former explanation (underlying representation) is the correct one.
In the later course of Sanskrit, (and under the influence of the grammarians) ATB was applied to original monoaspirates through an analogical process. Thus, from the verb root /ɡah/ ('to plunge'), the desiderative stem /jiɡʱakʰa-/ is formed. This is by analogy with the forms /bubʱutsati/ (a desiderative form) and /bʱut/ (a nominal form, both from the root /budʱ/ 'to be awake'), originally PIE *bʰudʰ-).
The linguist Ivan Sag has pointed out an advantage of the ancient Indian theory, namely that it explains the fact that there are no patterns like hypothetical "[trík-s] ~ [tríkʰ-es]", which are not ruled out by the underlying-diaspirate theory. From a diachronic standpoint, the absence of these patterns in Greek is explained by the Proto-Indo-European constraint against roots of the form *T...Dʰ-.
Grassmann's Law is also known to occur in Ofo, an extinct and underdocumented Siouan language. The law is found in compounds such as the following:
A similar phenomenon occurs in Meitei (a Tibeto-Burman language) in which an aspirated consonant is deaspirated if preceded by an aspirated consonant (including /h/) in the previous syllable. The deaspirated consonants are then voiced intervocalically.