I agree with much of what you have said actually. I too had my scales organized to practice based upon physical shapes and fingerings. However in the first sentence of my post I specified "learned/taught." To learn/teach D major, then Ab major, then B major, e.g. makes no sense to me.
Ah, fair enough. I wouldn't personally go right up to 7 sharps before introducing flat scales, but I'd certainly work on similar system of adding one at a time. Actually, I should also stress that my own lists were by no means meant to reflect any specific order. It's just to identify which of the two basic thumb principles each individual key follows.
The issue of the tetrachords is theoretical, but demonstrates the nature of related keys; in fact one might say that related-keys are those that share a tetrachord. (I've never heard of applying tetrachords to minor scales.) The fact that a new sharp or flat is being added is precisely because of the structure of the tetrachords of the major scale (each WS, WS, HS, connected to eachother by a WS) must be maintained as we advance by 5ths. E.g., when we use the 2nd tetrachord of C major (G,A,B,C) as the first of a new scale, it is obviously now the start of G major. When we attempt to complete the scale with (D,E,F,G) we are confronted with the wrong sequence of intervals (WS,HS,WS).
I can see that this does work- but it really isn't "because" of the tetrachord. Otherwise, why would natural minors not abide by the same progressive system? The fact that natural minors operate the same way (regarding key signature) without involvement of tetrachords strikes me as a pretty conclusive proof that tetrachords are a mere consequence
of the real cause of scales. The reason scales work as they do, with regard to black notes, is basically mathematics. Because of a symmetry issue, major scales work with tetrachords. However, natural minor scales work the same without them. The tetrachords are an incidental effect, not a cause- which is why natural minors (without the same symmetry) do not require such things, in order to include the very same order of accidentals. The tetrachord is just one part of the fact that every time you add/subtract a sharp or flat, only one single note is changed compared to the previous key. Why only focus on merely 4 similar notes when 7 out of 8 pitches are actually the same? I think it's actually rather simpler to notice that one note is changed each time, than to worry about a specific tetrachord. Personally, I judge all minors from the key signature and then think of any raised notes as adjustments. This way, you focus on the unity and further reinforce the principles from majors- rather than on the erratic way that minor scales might appear when viewed in an isolated context. It's far less confusing when your point of departure is the same basic key signature progression as for majors.
With a moment's thought, we can see that the proper intervalic sequence is fixed by raising the penultimate note by a half step: (D,E,F#,G) = WS,WS,HS. This is precisely why F# is the first sharp in the key signature. I think this is very important musically, as it is sequentially and systematically extended.
Absolutely agreed. I just don't understand why this necessarily requires analysis of tetrachords. I think a change of one accidental makes it easier. Not that I'm disgusted by the concept of tetrachords or anything, but I don't think they are the foundation block so much an interesting pattern that can optionally be focussed upon. Personally, I'm more interested in the single note that is different
to an adjacent key- not four specific notes of the 7 that are common to each. I don't see why these four notes are any more or less significant than the other three shared notes.
As far as the thumbs issue, I again recognize this very important feature that you are discussing, so much so that I believe there is extreme value in practicing scales simply alternating the thumb and the other fingers. This is especially helpful for training the thumb to immediately pass under the hand to its next assignment as soon as it releases the note it played. (This can and should be done with arpeggios too.)
Absolutely- certainly a useful one.