As a pet project of mine, taking advantage of my background in Artificial Intelligence, I decided to devise a computer program to calculate violin fingerings. By doing this, I have gained some insights which I thought I would share.
A computer program to calculate fingerings based on musical context (ex. timbre) was out of question, so I focused on a criterion that would be easier for the computer to evaluate: fingering efficiency. Namely, I developed an algorithm were fingerings that required the less amount of shifting, changing strings, etc. were considered better, as they are easier to execute.
Computer programming, because you have to translate everyday concepts into what is basically a mathematical model, has a way of revealing hidden corners of a problem, such as, for example, hidden assumptions or inconsistencies. For the purpose of the algorithm, I considered three standard hand postures as a basis - first finger adjacent to second, second adjacent to third and third adjacent to fourth. These correspond to the fundamental half-whole-whole tone, whole-half-whole tone, and whole-whole-half tone hand postures. I did not consider finger extensions (ex. the whole-whole-whole tone hand posture which can be uncomfortable for some hands in first position). This is actually a simplified version of what I ended up coding, but enough for the purpose of this blog entry!
Upon modeling what we consider first, second, third, etc. position, I quickly found out that we are actually simplifying the amount of positions that are really possible on the violin. In fact, for example, the position starting on F on the D string is not really the same position as the one starting on F#, although we usually call both second position. We can see that applying a standard hand posture on the first puts the 4th finger on B-flat, whereas on the second it goes up to B-natural. For all my years of playing I never considered these different positions, but alas, when I needed to formalize the concept of positions for a computer algorithm, I understood how they are actually different. In fact, for the algorithm to work well, it works not with first, second, etc. position, but rather with E-position, F-position, F#-position (all of these on the D string), etc.
Since developing the program, I have been using it to finger orchestral passages automatically (which I use as a basis for my fingerings, correcting for musical reasons when necessary). It's a nice to have (a standard 10 note passage can result in literally billions of different possible fingerings that the algorithm sorts out in a few seconds). However, developing the program has fundamentally changed how I think about positions, and I have started to think more and more about positions in terms of what note the first finger is anchored to, like in the program. Ex. now I need to shift from E-position to G#-position, not first to third. What at first was a surprising approach actually feels very logical now and I am more aware of where exactly I am in the fingerboard now. All because "G#-position" is more exact than "third position", which could also refer to "G-position" (considering the D-string here).
Other interesting insight is how often the program outputs fingerings in what we usually call half-position. Turns out violists got this right; violinists tend to underuse it because it's easy to just extend the fingers. However, a lot of passages really are easier fingered directly in half position, with much less tension in the hand. The fingerings suggested by the program have, if nothing else, at least motivated me to do a thorough study of half position!
For added historical context: Our system of positions is actually, in part, derived from the musical notation system. At first (we can confirm this in the treatise of Leopold Mozart) only two positions were considered - whole (which we would now call first, third, fifth, etc.) and half (which we would now call second, fourth, sixth, etc.) The whole position basically had notes on lines in the G-clef fingered with the 1st and 3rd finger, and notes on spaces fingered with the 2nd and 4th. In half position, this was reversed. This meant that choosing the position was basically a matter of matching the hand to two different notation patterns. These two positions then diversified into the ones we know today, which also take into account the position on the fingerboard. However, they still reflect the underlying logic of the whole and half position. They are not entirely derived from actual physical positioning, but rather the "musical" positioning as dictated by the way music is notated. This is why first, second, third, etc. positions assume different physical positions depending on what scale the music is in.Tweet
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