OF NOMINATIVES AND DATIVES^469Thus, in a language with only two "true vowel" phonemes, i.e.,
phonemes that can always serve as the peaks of syllables, one must specifi
cally (and to the exclusion of the other vowel) include the phonetic value
[a], or a [+cpt] (or [—hgh]) point in phonetic space, while the other must
include the phonetic value [ә], or a [—cpt] (or [+hgh]) point in phonetic
space. In a language with only three "true vowel" phonemes, one must
specifically include a [+cpt] (or [—hgh]) point in phonetic space, one must
specifically include a [—cpt, +grv] (or [+hgh, + bck]) point, and one must
specifically include a [—cpt, + grv] (or [+hgh, —bck]) point, giving an
isomorphism to [a], [u], [i]. Of course, as we try to deal with the dependen
cies of the internal organization of any full phonological system, there will
be functional alternatives that seem to exist, there will be very complex
relationships among various categories of sounds, and so forth. But the
essential principle remains the same.
In fact, if we consider together the various generalizations such as
those just illustrated, we can see that we can derive generalizations of the
following form: if a language L has N "true vowel" phonemes — recall the
functional definition underlying this notion in syllable structure — they will
be defined by the differentiation of the following feature-specifications of
phonetic space as realizations of the N different phonemes. In other words,
we have said nothing about the entire range of phonetic realization of the N
vowels of a system, we have only said that certain values must be kept dis
tinct, values that can be specified independent of any specific language, and
with which all languages' vowel systems are compatible. We have specified
what we would call the "foci" of the phonemic categories, rather than the
entire range of them. And then the so-called phonetic universe can be
known only to the extent that we can constrain phonological systems in
terms of its potential foci for the purpose of such linguistic universals about
phonological systems. Further, for any set of phonological systems, we can
relate one to another by specifying that a particular phoneme category in
one system is defined by a focus that is included in specified way in the
range defined by some other focus in another system. (Thus, in the example
above, the range defined by the focal schwa (or [-cpt] - [+hgh] - point) in
the two-element "true vowel" system is, as it were, formally split into two
distinct functional units, with the two foci [i], [u] in the three-element sys
tem within the phonetic range of the two-element [ә].)