Notes? Who? Me? Nah - just your imagination. Never touch the things…
I should borrow Arbo’s moniker and claim “I’m Not Irish”!
You have to be able to hear them or they wouldn’t be there!
Haven’t seen Larsen’s book so can’t comment properly informed, but maybe I’d phrase a similar intent in a different way to that you report, Diane. Cuts and taps are not, for the most part, notes in the melody as such. They are not pitch-specific other than that they are respectively above or below the note they articulate. The point is the break in the main note. The sounds produced by correctly executed cuts and taps are, of course, “notes” in the general musical sense that they have pitch and duration, but they are not usually required to be at any particular in-tune pitch in the scale or key you are playing in. When you cut, say, an E by lifting L3, you are not playing an A, although that is what grace-note you would write in in classical notation. Pitch-wise that cut will produce a very short, flat A, but that fact is not significant in terms of the function of the ornament. Cutting with R1 will serve just as well, producing a flat G note if anyone cares. By definiton because of the physics/mechanics involved, taps are very nearly always the neighbouring note below the one being ornamented, and will sound at nominal pitch for that fingering, but again, that is not terribly relevant to their function.
I think something like that is what Grey Larsen must have been trying to express.
That’s the theory. In practice, it can sometimes matter what pitch you cut to, I think. For example, you can produce subtle variation by cutting the same note with different fingers in a sequence of cuts. A cran is a sequence of cuts to different higher-but-not-accurately-pitched “notes” - the cuts chosen and the sequence of them will affect the “flavour” of the cran - there was a thread about this a while back… Also, in tunes in some tonalities/modes, certain cuts will sound odd: - in The Contradiction Reel, to pick on a recently discussed tune, in the 4th section there is a figure cef#e where one would naturally cut the f# - if you do so with R1 it works OK, but do it with L3 and you get a cut which is between A and G# in pitch, which sits more comfortably in the tonality of the piece than the flat Gnat you get with a R1 cut. The difference is noticeable, though you wouldn’t actually object to either, theoretically, aesthetically or functionally - especially if like Arbo you were going for using some G naturals anyway despite the key-signature.
FWIW, I also think that the distinction between ITM “ornamentation as articulation” and “classical ornamentation” is not quite so clear-cut as some would like to make out - there certainly are differences, but equally there are overlaps.
You might also like to consider the probability that none of us here are any damn good - we aren’t up to doing it “properly”! Probably wouldn’t be here if we were… 