Martin & Rose (2007: 296-7):
Alongside genre, the main construct used by functional linguists to model context is known as register. In SFL, register analysis is organised by metafunction into field, tenor and mode. The dimension concerned with relationships between interactants is known as tenor; that concerned with their social activity is known as field; and that concerned with the role of language is known as mode. Halliday has characterised these three dimensions of a situation as follows:
Field refers to what is happening, to the nature of the social action that is taking place: what it is that the participants are engaged in, in which language figures as some essential component.
Tenor refers to who is taking part, to the nature of the participants, their statuses and roles: what kinds of role relationship obtain, including permanent and temporary relationships of one kind or another, both the types of speech roles they are taking on in the dialogue and the whole duster of socially significant relationships in which they are involved.
Mode refers to what part language is playing, what it is that the participants are expecting language to do for them in the situation: the symbolic organisation of the text, the status that it has, and its function in the context. (Halliday and Hasan 1985: 12)
As language realises its social contexts, so each dimension of a social context is realised by a particular metafunction of language, as follows:
Taken together the tenor, field and mode of a situation constitute the register of a text. As its register varies, so too do the kinds of meanings we find in a text. Because they vary systematically, we will refer to tenor, field and mode as register variables. This model of language in social context is illustrated in Figure 9.1.
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[1] This is very misleading indeed. In SFL Theory, register is not a means of modelling context. Register is a functional variety of language, modelled as a point of sub-potential variation on the cline of instantiation from language system to language instance.
Context, on the other hand, is the culture modelled as a semiotic system that is realised in language. Field, tenor and mode are the metafunctional dimensions of context, but not of register. Different configurations of field, tenor and mode features (Hasan) are realised by different registers of language.
This misunderstanding occurs in Martin (1992), and proliferates through the subsequent publications of Martin, his one-time students, and the less theoretically competent members of the SFL community.
[2] This is misleading, because, in the case of mode, Martin & Rose have selectively omitted the section of the quote that contradicts their model. Cf Halliday & Hasan (1985: 12):
The MODE of discourse refers to what part language is playing, what it is that the participants are expecting language to do for them in the situation: the symbolic organisation of the text, the status that it has, and its function in the context, including the channel (is it spoken or written or some combination of the two?) and also the rhetorical mode, what is being achieved by the text in terms of such categories as persuasive, expository, didactic, and the like.
That is, in SFL Theory, what Martin & Rose model as the purpose of a genre is modelled as a system of mode, the textual dimension of the culture as semiotic system.
[3] This is misleading, because it is not true. What is true is that SFL Theory maps the metafunctional dimensions of language — ideational, interpersonal and textual — onto the stratum of context as field, tenor and mode, respectively. What is not true is that each metafunctional dimension of context is simply realised by its metafunctional counterpart in language. For example, the cultural field of science is realised by interpersonal propositions as much as it is realised by ideational sequences of figures, and their structural elements are given various textual statuses in terms of theme and information.
[4] This is misleading, because it is not true. Moreover, it is a misunderstanding of Halliday & Hasan (1976: 22):
The linguistic features which are typically associated with a configuration of situational features — field, mode and tenor — constitute a REGISTER.
That is, it is not the contextual features of field, tenor and mode that constitute a register, but the features of language that are typically associated with a configuration of them.
In SFL Theory, the field, tenor and mode (features) of a situation characterise the instance of context (situation) that is realised by an instance of language: (text). Here again, Martin & Rose confuse different planes: context vs language, and different points on the cline of instantiation, in this case: register vs text.
To be clear, in SFL Theory, field, tenor and mode are not register variables; they are the dimensions of the culture, whereas registers are functional sub-potentials of language.