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I open this new section because the discussion opened by Just plain Bill is somewhat different from the preceeding one. The question is particularly interesting.
I don't think that the mnemonic syllables of percussion traditions would be amenable to a true linguistic analysis. They do not involve a linguistic syntax, they merely stand for the music - but not for its sounds. More specifically, they do not "mean" the sound music for which they stand, they are not merely metalinguistic; their meaning (and their syntax) is largely the same as that of the music.
I must confess that the only such tradition that I really know is the dum-tak of Arabic music: it certainly does not represent the sounds of the music for which it stands. A percussionist singing these syllables may form an idea of the music represented, but no listener would recognize them as the sounds of the music to be played.
This situation is to some extent comparable to that of music notation: written music does not represent sound music. Busoni writes that the notation and the performances of a piece of music are all transcriptions of the work. The same could be said, I think, of the mnemonic syllables - all the more so that the music for which they stand probably is of oral tradition - that is, it is not fixed as a Western musical work is.
One main difference of course is that mnemonic syllables usually have the same temporality as the music itself, while notation switches off the flow of time. Another aspect, however, is that the syllables are more easily notated than the music for which they stand, using the standard writing of the language to which they correspond.
As to the general comparison between musical and linguistic rules, I do think with kosboot that GTTM is not a good example, because what it emulates is the cognitive turn taken by Chomsky in his later writings, not the linguistic one of, say, Syntactic Structures. Better examples of the comparison include works by Powers ("Language Models and Musical Analysis", 1980), Monelle (Linguistics and Semiotics in Nusic, 1992), Agawu (Music as Discourse, 2009), Molino (in Musique en jeu, 1975, etc.), Nattiez, and others.
See http://www.popflock.com/learn?s=Music_theory#Basics_of_common-practice_part_writing - what do these phrases mean? -- naught101 (talk) 02:52, 9 August 2018 (UTC)
Browsing through this article, I discover a section that I had not noticed before, Music_theory#1750-1900.
One first reads that although Western theory became a world standard, other theoretical traditions survive, among others "the long and rich musical traditions unique to ancient and current cultures of Africa" - the paragraph does not say which traditions, where in Africa. Whether these really "describe specific forms, genres, performance practices, tunings, and other aspects of music theory" remains to be demonstrated. Some African traditions certainly evidence forms, genres, performance practices and tunings, but it is not obvious to me that their theoretical description is not mainly Western.
The section then has a paragraph about Sacred harp music which, it says, "uses a different kind of scale and theory in practice". The description that follows of "Secret harp theory" merely indicates that it practices solmisation on three notes (fa sol la), with a staff notation using three different note shapes for these three syllables. A quick look through the Sacred_Harp article evidences that it actually makes use of four syllables (including mi) and four note shapes.
Is this really all what has to be said of modern theory of music, 1750-1900? Do the musical tradition of "ancient and current" cultures of Africa belong to the period 1750-1900; do they really include a theory? And is "Sacred harp theory" the important point of Western theory in the same period, while four-note solmisation practice probably is documented from the Renaissance onwards, and four note-shapes notation certainly existed decades before Sacred harp music? (See Shape-note hymnody in the New Grove Online).