I came across the above quotation recently in a 100-odd-year-old Crescendo magazine. It illustrates a way of thinking about tremolo: that it may be played at different speeds, but it is not a subdivision of the underlying pulse. I don't think of it that way; I would have said tremolo can be metered or unmetered, but this quotation might account for some comments I have occasionally heard from veteran mandolin orchestra members, saying that playing fast repeated notes as a subdivision of the beat is not an example of tremolo at all -- and those videos promising to help you play fast, clean tremolos (by playing ever smaller subdivisions of the beat) are not talking about tremolo, at least not in the more traditional sense. Most people won't care what was said in a 100-year old quotation, but since that was an era of great achievement (as well as popularity), I think it's helpful to reexamine.
Part of the interpretation of the classical mandolin repertoire is figuring out how to use tremolo to create the illusion, as much as possible, of a sustained note. That may involve pushing ahead of the beat, or slowing down behind it. Or it might involve speeding up and slowing down, without relation to the underlying pulse.
Here is an example of a classical tremolo using all these ideas, creating a lovely sense of phrasing that adds much to the dramatic tension of the music. Thanks to Shu-Mi Huang.
In my view, those divide-the-beat-ever-smaller approaches can be great technical exercises in preparation for metered tremolo, or right hand technical development in general. But perhaps a more direct route to tremolo playing is to focus on the physical sensation of the hand playing repeated notes, as they change from slow to fast and back. Tremolo doesn't have to be fast, after all; sometimes it's even more effective, played slowly.
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