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By reading your and others answers, I'm realizing that both Solfege and the numbers each have their place. If I'm practicing a diatonic pattern in different keys using the numbers helps me re-enforce the note I'm supposed to play. Perhaps with enough practice my mind would instantly translate "sol" to 5 and "fa" to 4. If I'm sight singing perhaps solfege is more appropriate.
For me, the hardest part to grasp/accept has been the odd number of notes in a beat. Ten (10) notes in a beat would mean 5-tuples every half beat (not impossible, I've played music with odd time signatures 5/4, etc) and similarly for 14 notes (so 7-tuples every half beat). When practicing I'm trying to keep each note the same length which is difficult if I can't count it more slowly and work my way up. At these speeds, however, it's really play it as fast as your fingers can move, so maybe I'm over thinking it.
My music instructor is a professional musician and he has encouraged me to transpose my written music up a whole step (and other transpositions). In a Gig, a singer started singing 1/2 step down from his rehearsal pitch and the entire band of professionals all transposed down 1/2 step from the written music to remain in-sync with the singer. It nearly blew my mind when I heard he's also transposed a minor or major 3rd and really can do any transposition. Over time I've learned that transposing on the fly is possible. You just have to practice and practice it!
Hearing the root note can be difficult if you haven't learned how. I liked what Tim said: listen for bass guitar; or I say the lowest note you can hear. That's likely the root! I'm a trumpet player and I'm learning that sometimes the root note is not played by piano because it's being played by base. So in some cases, the guitar might not play the root note either which might make things confusing to you until you "hear" it that way.
So the tone row G,Ab,B,C (intervals are half-step, minor 3rd, half-step) are last 4 notes of C harmonic minor scale match this pattern. See diagram at en.wikipedia.org/wiki/Minor_scale. I don't consider this a tetrachord even though Wikipedia's definition allows it.
