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comment Can one measure the “distance” between chords? If so, how?
What exactly do you want to measure by your distance? For example two C maj chords in two registers far apart would be close or not? What about two chords like C 5+ 7 and Db min 6?
comment Games for the young piano student?
I don't know about young kids, but in my experience a lot of piano beginners enjoy playing 4 hands, esp. when the accompaniament I play is jazzy or in some way contains a strong rythmic element.
comment Is it normal for frequent guitar playing to be accompanied by wrist pain?
Whether it's better to consult a doctor or fellow guitarist depends on the doctor and the guitarist. I agree with you on average, but a knowledgeable player might give a way better advice than an inexperienced (with regard to music-related cases) medical professional. In fact, I had an accident when young and I would not be able to play today if not for my parents who made sure I had been treated by the right doctor (instead of leaving me in the care of the first one we got to).
comment How important is warming up before playing an instrument?
@Édouard I've once heard a concert where the main performer was using, among others, a special bass guitar with metal neck. However, as it was cold outside, but warm inside, the instrument would go totally out of key even after a short period of time.
comment How to determine the name of a chord from knowing the notes I am playing?
Note that for more complex chords it's impossible to know its name from just the notes. The context is essential (and even then it might be ambiguous). For example 343343 (i.e. G C♯/D♭ F Bb D♯/E♭ G) could be both G7♭5♯5♭10 if followed by some C minor, or A7♭5♭913 (no root) if followed by version of D minor (esp. if the bass guitar plays A as a base).
comment Chord analysis: b13 or #5
I think that you should add to your post that the context is jazz (right now it's a bit misleading). For example, in jazz there would be a bass note somewhere down that would justify the G natural being b13 instead of just b6.