I'll take it step by step. Don't take it personally...
Frank wrote:But look Carlos, I am of the opinion that fingers must travel and all fingerings during the study phase must be addressed.
First thing: it's not true. Second thing: if they all must be addressed, what are we going to do? A nice D trill D-C-D-C 1 5 1 5??? Come on, please...
PS "it's not true" because it's like telling a dancer that "during the study phase" they must learn to walk with the left foot along with the right hand... because one must try everything.
Frank wrote:Honestly, I have found the problem of thumb articulation to be more widespread than that of the fourth finger, which is why 2-4 remains a comfortable fingering even when spanning two white keys ... clearly if there were a black key involved things would change and certain choices would be more "obligatory".
The 1-3 trill is executed with a mixed articulatory/rotary movement. The comfort lies precisely in that: the rotary movement also guarantees a certain power, which is why it is preferable to 2-3 and 1-2. The 2-4 trill on two consecutive white keys is pianistically total bullsh*t, with all due respect to you. In my opinion, you have never tried it, and if you have, you probably did it wrong. You don't learn how to do trills from books.
Frank wrote:There are those who believe that for every x notes of the trill, the fingering should change due to fatigue issues, and one of the paths can be 1-3, 2-4, 3-5, and anagrams of combinations... polyphony permitting, perhaps performed by other fingers.
"There are those who believe", "I have found"... Frank: I know how to play the piano, okay? So if I take the liberty of writing that your fingerings don't work, most likely, I am right...
PS a finger change generally requires one of the two fingers to remain unchanged; otherwise, it is impossible at speed. Therefore, the changes you suggest do not work for two reasons: what I just said and, second, that 2-4 and 3-5 are not valid fingerings on two consecutive white keys, as I have already said..
Frank wrote:Tout to say that my example was a basis to exemplify the concept of variants (the crux of the matter) and anyway I do not disdain 2-4, also because one has to deal with the pianist's fingers, and the thumb and pinky are typically the most problematic fingers. Not that problems shouldn't be solved, but if someone doesn't find 2-4 comfortable, it is an opportunity to practice.
2-4 does not work on two consecutive white keys (repetita iuvant!), if you want to waste time practicing it, go ahead, but don't suggest it to someone asking for suggestions to solve technical problems that you yourself cannot solve. There is no reason to practice with that fingering. One can use the others I indicated, and having played quite a bit of piano repertoire, I think I can give my opinion without needing Uncle Frank who always pulls out some "variant" or some ad hoc treatise. With this, I am done.