Should a pupil hear a piece played before studying it?
If the pupil's imagination needs stimulation he should hear the piece well played before studying it. If, however, he is merely too lazy to find out the rhythm, melody, and so forth, and rather relies upon his purely imitative faculty, he should not hear it, but be compelled to do his own reading and thinking.
[THEORY]
Why the Pianist Should Study Harmony
Do you recommend the study of harmony and counterpoint to the piano student?
By all means! To gain a musical insight into the pieces you play you must be able to follow the course of their harmonies and understand the contrapuntal treatment of their themes. Without the knowledge gained through a serious study of harmony and counter-point your conceptions will be pure guesswork and will lack in outline and definiteness.
Why so Many Different Keys?
Why is it supposed to be necessary to have fifteen keys to complete the circle of fifths? Why would not twelve suffice, and thus avoid duplicate keys?
Not fifteen, but twenty-five tonalities complete the circle of fifths, theoretically, and they are all necessary because of the many harmonic turns that occur in modern music and which could not be intelligently demonstrated unless we use the tonalities with seven, eight, nine or more sharps and flats. For otherwise we might have to change the signature so frequently as to become utterly confusing to even the most musicianly reader. C-sharp minor has but four sharps, yet the scale of its dominant (its next relative) has eight sharps.
The Relation of Harmony to Piano-Playing