What would music look like if instead of looking ‘notionally’ for kinds of meaning we looked for types of structure (particulate, prosodic and periodic) and worked out the systems behind each type of structure and then asked what their complementary functions were and only then compared music to language or image?
Giving priority to the view ‘from above’ means that the organising principle adopted is that of system: the grammar is seen as a network of interrelated meaningful choices. In other words, the dominant axis is the paradigmatic one: the fundamental components of the grammar are sets of mutually defining contrastive features (for an early statement, see Halliday, 1966a). Explaining something consists not in stating how it is structured but in showing how it is related to other things: its pattern of systemic relationships, or agnateness (agnation, a term introduced into linguistics by Gleason (1965: 199)…
More specific to the methodology itself, Halliday (1985: xiv) outlines the SFL approach, as part of his explanation that SFL does not take a syntactic approach to modelling language:
However, not even the SFL approach will succeed in modelling music as a semiotic system because music is not a semiotic system: the sounds of music do not realise meanings. Of course, music theory and notation are semiotic systems, as are the lyrics that accompany music, but the sounds themselves are not expressions of content. Instead, music activates what the neuroscientist Edelman calls 'value' systems in the brain, which, in turn, with other systems, underlie feelings and emotions. In terms of Halliday's (2002: 388) evolutionary typology of systems, music can be seen as social (value, but not symbolic value), like the pheromonal systems of eusocial insects. Halliday & Matthiessen (1999: 509):
A biological system is a physical system with the added component of "life"; it is a living physical system. In comparable terms, a social system is a biological system with the added component of "value" …. A semiotic system, then, is a social system with the added component of "meaning". Meaning can be thought of (and was thought of by Saussure) as just a kind of social value; but it is value in a significantly different sense — value that is construed symbolically. … Semiotic systems are social systems where value has been further transformed into meaning.