¹ English /ŋ/ and /h/ are examples of phonemes which have mutually exclusive environments but whose phonetic dissimilarity has (supposedly) prevented their being considered allophones of the same phoneme. The fact that there are phonetically dissimilar phonemes with mutually exclusive distributions did not escape the notice of the pioneers of phonemic theory (see, for example, Daniel Jones, On Phonemes, TCLP 4.77–8). They also realized that such phonemes constitute an exception to the general rule that the relation between any two phonemes is one of contrast. Thus Trubetzkoy wrote: ‘Les sons impermutables ne peuvent en principe former aucune opposition phonologique distinctive’ (Principes de phonologie 34), but had to admit also that ‘des sons impermutables qu'aucune particularité phonique commune ne rapproche en les distinguant du reste des sons du système considéré peuvent néanmoins former des oppositions secondairement distinctives’ (ibid. 35). He then called the relation between such phonemes one of indirect contrast, demonstrating for example that German /ŋ/ and /h/ are indirectly contrastive by means of the words hacken ∼ packen ∼ Ringe ∼ Rippe, i.e. both phonemes directly contrast with /p/. But a similar relation of indirect contrast obtains between allophones of the same phoneme. Thus English [k_i] and [k_u] are indirectly contrastive in this sense, as in the words keep ∼ reap ∼ cool ∼ rule, i.e. both allophones contrast directly with /r/.

² The material used in the examples is partly my own and partly taken from P. W. J. Nababan, A phonemic analysis of Batak (unpublished M.A. thesis, University of Texas, 1958). My own knowledge of the language is the result of informant work with Miss Minar Tobing and Mr. Apul Tobing, both of Silindung. There are eight vowel phonemes in the language: /i e ε a ɔ o u ә/. Note that /e/ and /ε/ are distributed in a very similar fashion to the two phonemes about to be described. I have confined my remarks to one pair of phonemes so as not to complicate the exposition unduly.

³ Lg. 17.348 (1941). This approach is, of course, by no means confined to Harris. The earliest definition of this type is that given by L. V. Scherba in his Russkije glasnyje v kačestvennom i količestvennom otnošenii 14 (Petersburg, 1912): ‘[the phoneme is] the shortest general acoustic representation of a given language, capable of being associated in this language with semantic representations.‘

⁴ I have purposely avoided the familiar term ‘complementation’. Two classes complement one another when all particulars in question are either members of one class, or members of the other class. When a linguist says that two allophones are in complementary distribution, however, what he means is that their ranges do not overlap, which is quite a different thing. When A and B are complementary subclasses within a larger class, it is possible to specify B uniquely as soon as A has been stated, since it is equivalent to non-A. When, however, A and B are mutually exclusive, all that one may assert is that the range of B is either equivalent to the range of non-A or contained within the range of non-A, but there are clearly many ways in which the latter circumstance may work out. Moreover, in cases of true complementation the total range of the two complementary classes is given in advance, and need not be obtained by adding together the ranges of the two member classes. Thus in geometry the sum of two complementary (acute) angles is by definition 90°. In phonology, however, the total range of a pair of so-called complementary segments can be established only by adding the ranges of the two individual segments. Matters are made more complicated by the fact that the phonologist often (perhaps most of the time) is dealing with more than two potential complementary ranges. I see no way of defining complementation for more than two member classes.

⁵ This second solution is in effect the one which linguists have adopted, though there has been no explicit discussion of the matter. As far as I know, Harris is the only linguist who has even mentioned it: ‘We continue the search [for segments which are complementary to each other] until we can no longer find a segment which is complementary to all the previous segments’ (Methods in structural linguistics 61).

⁶ That it is possible to group mutually exclusive allophones in more than one way was pointed out by Harris (Methods 72). Other linguists had already pointed out the general possibility of competing phonemic solutions, e.g. Yuen Ren Chao in his famous article on non-uniqueness (now reprinted in Readings in linguistics 38–54) and André Martinet in his review of Trubetzkoy's Grundzüge der Phonologie in BSL 42:2.23 (1942–5).

⁷ The only kind of economy which has received attention in the literature on phonemic theory is economy in the number of phonemes set up. Trager and Bloch wrote in 1941, for instance: ‘We must bear in mind also the principle of economy: the analysis to be preferred is one which accounts adequately and accurately for all the facts with the smallest number of separate phonemic entities’ (Lg. 17.235). Most linguists have, however, agreed that this type of economy is not an important criterion in phonemic analysis. Thus Hockett sets up four principles to act as guides in phonemic analysis: the principle of contrast and complementation, the principle of phonetic similarity, the principle of neatness of pattern, and lastly the principle of economy. He remarks finally: ‘Instances where the principle of economy unambiguously points to one interpretation rather than another usually turn out to be cases in which the other three principles would eventually lead to the same choice, without the addition of the fourth’ (A course in modern linguistics 110). One wonders why the principle is worthy of the name at all, if its usefulness is merely to corroborate the operation of the other three. In a sense Hockett is quite right in placing no great reliance on his principle of economy, since the number of phonemes set up for a language is the result of applying a different principle, namely choosing the phonemic solution which entails the smallest number of allophonic statements. In the Toba-Batak example the more economical solution of the two proposed is not the one which sets up fewer phonemes.

⁸ I do not wish to examine the validity of the term ‘free variation’. Some linguists may perhaps prefer to regard all allophones which contrast at all as belonging to different phonemes. In that case my statement can be emended to read: though allophones which do contrast belong to different phonemes, allophones which do not contrast do not necessarily belong to the same phoneme. In such a system contrast would constitute a sufficient but not a necessary proof that allophones belong to different phonemes.