My music teacher recently pointed out to me that, when performing a trill (alternating between two notes very quickly) the finger for the higher note should be placed slightly lower on the string than it would be when played individually. In other words, when performing a trill the frequency corresponding to the usual position of that note is ever so slightly higher than it should be. I know that stringed instruments like the Violin, Viola and Cello are not "well-tempered", which leads to many such subtle changes in frequency when it comes to double-stops, trills etc. But is there a clear, physical explanation for this phenomena? Or is it an auditory illusion?
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$\begingroup$ This might be more appropriate for music.stackexchange.com. In particular, as a physicist who doesn't play string instruments, I don't really know if trilling alters the pitch/timbre of the note (it generally will if and only if the period of the trill is shorter than about the duration of the attack, when the vibrations are reaching steady state). It's also a pure question of music, not physics, as to what trills should sound like. $\endgroup$– user10851Commented Mar 3, 2015 at 1:23
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$\begingroup$ @ChrisWhite I don't think it's appropriate for music.stackexchange.com because my question does not pertain to how I should perform a trill, but rather to why the string produces a different frequency than it should when playing the same note (position) but in a regular passage (not a trill). The remark you put between parentheses is quite useful by the way. Could you elaborate please? $\endgroup$– entrelacCommented Mar 3, 2015 at 14:58
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2 Answers
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If you are playing in just intonation (where, when you play two notes, they are in the same harmonic series), then it would depend on which notes in particular you are playing and which key you are in, because the frequency of each note would be related to the tonic (by ratios) and independently of each other. Some intervals are thus wider or narrower than the equal temperament which is common nowadays in tuned instruments. (Equal temperament effectively 'averages out' all the intervals by taking the 12 tones in an octave and dividing them equally; one semitone is measured as 100 cents.)
I would propose that your teacher just wanted a brighter upper note (by tuning it slightly sharper) to give your trills more definition.
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Normally fretting a string requires pulling the string down, which adds tension to the string. If a string is already fretted then the greater tension must be offset by using a lower position for the upper fret.