Grassmann's law

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For Grassmann's law in color theory, see Grassmann's law (optics).

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:

  • /ú-ɔː/ θύω 'I sacrifice (an animal)'
  • /e-tú-ɛː/ ἐτύθη 'it was sacrificed'
  • /rík-s/ θρίξ 'hair'
  • /t-es/ τρίχες 'hairs'
  • /ápt-ein/ θάπτειν 'to bury (present)'
  • /tá-os/ τάφος 'a grave'

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 /u-ɔː/ φύω 'I grow' : /pe-uː-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, suggests that Grassmann's law developed separately in Greek and Sanskrit (although quite possibly due to areal influence from one language to the other), i.e. that it was not inherited from PIE.[1] Another reason is that Grassmann's law in Greek also affects the aspirate h < s developed specifically in Greek but not in Sanskrit or most other PIE branches. (For example, *segʰō > *hekʰō > ekhō, ἔχω "I have" with dissimilation of h ... kh, but the future tense *segʰ-sō > heksō, ἕξω "I will have" was unaffected as aspiration was lost before s.) 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.

In Greek[edit]

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 ταχύς /takʰús/ 'fast' : θάσσων /tʰássɔːn/ 'faster' displaying Grassmann's law, Greek has the pair παχύς /pakʰús/ 'thick' : πάσσων /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, πεύθομαι /peútʰomai/ ~ πυνθάνομαι /puntʰánomai/ 'come to know' from PIE *bʰewdʰ- has the future πεύσομαι /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 φάθι /pʰátʰi/ 'speak!'.

Diaspirate roots[edit]

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[clarification needed] 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 that an assumption of ATB would require multiple root shapes for the same basic root in different IE languages whenever an aspirate follows in the next syllable — e.g. d for Sanskrit, t for Greek, dh for Proto-Germanic and Proto-Italic (which have no dissimilation) — whereas the theory with an underlying aspirate allows for a single root shape with dh for all languages.

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 /dʑiɡʱakʰa-/ 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. However, ATB fails to account for reduplication patterns seen in roots with initial aspirates, such as Greek /títʰeːmi/ 'I put' with an unaspirated reduplicated consonant, and so ATB needs to be enhanced with a stipulation that aspirates reduplicate as their unaspirated counterparts. 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-.

Other languages[edit]

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:

  • óskha ('the crane') + afháⁿ ('white') → oskạfha ('the white egret')

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/, /s/) in the previous syllable. The deaspirated consonants are then voiced between sonorants.

  • /tʰin-/ ('pierce') + /-khət/ ('upward') → /tʰinɡət/ ('pierce upwards')
  • /səŋ/ ('cow') + /kʰom/ ('udder') → /səŋɡom/ ('milk')
  • /hi-/ ('trim') + /-tʰok/ ('outward') → /hidok/ ('trim outwards')

Hadza, spoken in Northern Tanzania, exhibits Grassmann's law in its lexicon, but most obviously in reduplication:

/tʃe~tʃʰeʔe-mae/ 'look at each other', from /tʃʰeʔe/ 'look'

In Hadza, /h/ has no effect on aspiration.

A similar effect takes place in Koti and other Makhuwa languages, where it was dubbed Katupha's law in Schadeberg (1999). If two aspirated consonants are brought together in one stem, the first loses its aspiration. The effect is particularly clear in reduplicated words: kopikophi 'eyelash'; piriphiri 'pepper' (cf. Swahili 'piripiri'); okukuttha 'to wipe'. This is slightly different than in Greek and Sanskrit, in that the two syllables need not be adjacent.

See also[edit]


  1. ^ See discussion in Collinge (1985:47–61)