How are syncopated notes to be played?
Notes occurring an entire beat of the prescribed time are, when syncopated, to be played between the beats. If the syncopated notes occupy only a fraction of the beats they are played between the fractional beats.
A Trill Begins on the Melodic Note
In modern compositions should all trills begin upon the note which is written, presuming there is no appoggiatura before the note? Is the alternation of the thumb and the second finger desirable in the playing of a trill?
Where not expressly otherwise stated (by appoggiatura) trills usually begin upon the melodic tone (the note which is written). Change fingers when those employed get tired. For extended trills the use of three fingers is advantageous, while in shorter trills two fingers will preserve more clarity.
Position of Auxiliary Note in a Trill
In the accompanying example of the trill should the auxiliary note be a tone or a half-tone above the principal note? If the half-tone, what would be the name of the auxiliary note?
The episode you quote moves evidently in the tonality of G minor. The trill stands on B-flat. As the auxiliary note of a trill is ever the diatonic sequel of a stated note it must, in this case, be a whole tone above B-flat, namely C. Since the piece is written in D major there should have been a "natural" marked under the sign of the trill.