Martin (1992: 433):
The limitations of this procedure should perhaps be stressed again at this point. First, cohesive harmony is a measure of texture, which is just one aspect of textual unity; it does not account for unity deriving from register and genre. Second, cohesive harmony is a measure of experiential texture; it has not been developed to the point where it takes into account the interaction of strings and chains with interpersonal, textual and logical structure. Third, cohesive harmony focusses on componential cohesion; it does not treat organic relations realising CONJUNCTION and NEGOTIATION.
 Cohesive harmony is not a measure of texture. According to Halliday (1994: 334), the resources that give texture to a piece of discourse are those of the textual metafunction — both structural (thematic and information) and cohesive (reference, ellipsis-&-substitution, conjunction and lexical cohesion).
Hasan's (1985: 94) cohesive harmony, on the other hand, as developed at that time, is concerned with the harmony between the 'outputs' of two metafunctions: the textual and the experiential:
The output of the textual function are the chains and the interactions; the outputs of the experiential function at the rank of clause and group is what the interaction is built upon. Thus cohesive harmony is an account of how the two functions find their expression in one significant whole.
 According to Hasan (1985: 52):
The unity in any text … is of two major types:
- unity of structure
- unity of texture.
Her chapter on unity of text structure (1985: 52-69) discusses this in relation to context — which Martin misconstrues as register — on pages 54-9, in relation to genre on pages 59-68, and in relation to both on pages 68-9. On Hasan's model, genre (= register) is concerned with textual identity (Hasan 1985: 97, 110).
 Cohesive harmony is not a measure of "experiential" texture. See the clarification in  above.
 More accurately, as Hasan (1985: 94) put it:
No doubt the concept of cohesive harmony can be further refined by bringing the logical and interpersonal functions into the picture.Textual structures are already included in the model; see  below.
 Cohesive harmony does include the organic relations of non-structural cohesion — Hasan's conjunctives, adjacency pairs and continuatives — but as Hasan makes clear (Hasan 1985: 85), she doesn't discuss these, or textual structures, for reasons of time and space:
I shall ignore instantial lexical cohesion, all organic relations, and all forms of structural cohesion. This is not because they are less important, but because time and space are limited.
This extract from Martin (1992) is intended as the first part of a critique of Hasan's cohesive harmony, as a prelude to introducing his own version. As can be seen from the clarifications above, it is merely a misunderstanding and misrepresentation of Hasan (1985).