Grammatical representations are in turn represented in linguistic expressions — prototypically, in sounding. Here the relationship is more complex than it is between semantics and grammar, in that it is both natural and conventional.
In the interpersonal and textual domains of content, it is often natural: thus interpersonal content tends to be represented prosodically by movements or variant levels in pitch, and textual content tends to be represented by prominence achieved phonologically (e.g. by the major pitch movement in an intonation contour) or sequentially (e.g. by using distance from initial position in the clause as a scale of prominence).
In the ideational domain, the representation is usually conventional; but, even here there is a relationship of analogy, where we find in the sounding modes of organisation similar to those of wording (and therefore of meaning).
Systemically, we find that the system construes a phonetic space — notably the vowel space; and that this provides a model for semantic space.
Structurally, we find that sound is structured both as chains of segments (e.g. rhythmic units interpreted as syllable complexes) and as configurations of segmental constituents (e.g. syllables interpreted as configurations of phonemes).
Blogger Comments:
This is clearly Matthiessen, rather than Halliday. For Halliday, the natural relation between semantics and grammar is between meaning (e.g. participant) and grammatical form (e.g. nominal group). To be consistent with Halliday's formulation, the relation between grammar and phonology is the conventional relation between grammatical form (clause, group, etc.) and phonology (tone group, foot, etc.), where relations can not be said to be natural. (If the relations were natural, the phonological expressions of all languages would considerably more similar than they are.)
However, Matthiessen switches track in this exposition from the relation between the grammatical stratum and the phonological stratum to the relation between the content plane and the expression plane, where relations between interpersonal and textual meanings and prosodic phonology can be said to be natural.