2 and 4 are mentally the most taxing and fatiguing ways, no doubt; but they also serve best to develop the memory and what we mean by "scope," which is a faculty of great importance.
The Conditions Which Dictate Speed in Playing
How fast or slow should Schubert-Liszt's "Auf dem Wasser zu singen" be played? What modern parlour pieces would you recommend after Bendel's "Zephyr"?
Even if I did believe in metronomes, as I do not, I could not indicate speed for you or for anybody, because it will always depend upon the state of your technique and the quality of your tone. For modern parlour pieces I suggest the two volumes of Russian piano music published by G. Schirmer, New York. You will find pieces of various degrees of difficulty there from which you may select what suits you best.
To Work Up a Fast Tempo
Which is the best way to work up a fast tempo?
The best help is to hear the piece or part which you have in mind played quickly by another person, for this aids you in forming the mental concept of it, which is the principal condition to which all ability is subject. There are, however, other ways which each one of us must find for himself: either by a gradual increase of speed until you reach your individual maximum or by starting at once at full tilt, even though some notes should drop under the piano and then be picked up in subsequent repetitions. Which of these two or any other ways is best for you no one can tell; your musical instinct will guide you if you follow it cautiously.
The Best Way to Work Up a Quick Tempo
Is it ever a waste of time to practise a piece over and over again for months as slowly as a beginner and with utmost concentration? After having done so and gradually working up a tempo, I then find I cannot play so fast as I want to. Is it not wise to begin all over again as slowly as possible? I prefer to work this way, but have been told that one gets "stale," studying the same music for a long time.
Do you advise practising with or without the pedal?