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Finger Patterns II

June 22, 2007 at 12:49 AM

If we looked at the violin mathematically, we would quickly come to the conclusion that the instrument is impossible.

Last week I posted on finger patterns. If we limit ourselves to finger patterns that contain no interval (between adjacent fingers) greater than a major third we can come up with 54 finger patterns. If we cut it down to no interval greater than a minor third it becomes 27 patterns which cover probably 98% of anything we’ll ever see.. This excludes what I would call twisted patterns the most likely of which has one covering a fifth with adjacent fingers.

If you calculate the number of ways you can put four fingers down on four strings (regardless of interval) without twisting the fingers (e.g. no 1st finger on C on the G string with the second finger on F on the D string etc.) then there are 4*4*4*4 or 256 different patterns. A large number of these have some plausibility.

That makes 27 X 256 or 6912 finger patterns in any given position. If we then say that moving up the fingerboard in half step increments there are 16 usable positions (with 1st finger as the starting point) then that makes 110592 more or less possible finger patterns over the entire fingerboard. I have excluded some finger patterns from this and probably not excluded some unusual combinations but the mathematics of the possibilities are daunting.

These numbers are a bit of a red herring but, bear with me as I make a point.

Remembering the dictum that “all technique is local”, it isn’t totally ridiculous to consider all these possibilities of individual patterns as independent events. Playing a pattern in a high position introduces new issues. The shape of the hand is entirely different, the intervals vertically on the string and across strings are very different. There is something legitimately unique and special about every possibility.

In spite of all this it is impossible to approach this problem one pattern (grain of sand) at a time. If you strictly practiced 10 patterns a day it would take 302 years to get through them. What would it be like if we practiced all the possible sequences of patterns?. The combination of 110592 things taken 2 at a time [usually notated C(110592,2)] is 6,115.239,936 -- over 6 billion!! Then add bowing patterns, rhythm patterns, articulations etc. and you can see the silliness of such a “monkey at a keyboard” reductionist approach.

Thankfully almost no one approaches the violin this way. Even Sevcik, in spite of his tendencies, didn’t go to the tiniest fraction of such lengths. Like any reasonable discipline, violin playing demands a more analytical approach. No one intending to take a journey plots all the possible routes to the final destination. We have criteria like distance, time, road quality, traffic and congestion etc. that we take into account. While on the trip we make adjustments based on available information.

We solve violin problems just like we solve trip planning problems, analytically. It seems to me that the following principles are appropriate.

1. The 80/20 rule applies. Most of the repertory is played with just a few patterns. The patterns, wwh, whw, hww, and www are ubiquitous. (h = half step, w = whole step, m = minor third)Because of this we probably quit thinking in terms of finger patterns even for these simple patterns. This comes back to bite us when we start to learn thirds. Even simple patterns should be approached consciously until we can identify them rapidly. Remember that the pattern wwh can be played in 256 different string combinations in just first position alone.
2. We need to develop pattern matching skills. This takes practice. There is no point in practicing passage work of any sort without explicitly identifying the finger patterns used. The more willfully this is done early on, the more automatic it will become later. The placement of fingers on the fingerboard is more important than the notation of finger patterns on the score; however, placing fingers without consciously thinking of the physical relationship of the fingers is the road to a dead end.
3. The study of changes in finger pattern is as important as the understanding of finger patterns themselves. This includes understanding the timing and priority of changes.
4. The rhythm of changes in finger pattern is not strictly correlated with changes in the melody or harmony of the piece. There is almost always a technical rhythm that is different from the musical rhythm. The technical rhythm is subordinate to the musical (harmonic and melodic) rhythm. One should always look for the earliest possible opportunity to establish a finger pattern and the pattern should be based on the next notes to be played not necessarily the current harmony.

I suspect that there are many more issues that I haven’t yet thought of or learned. I do appreciate comments and critiques. What methods do you use to study finger patterns?

From Martin Butler
Posted on June 23, 2007 at 4:58 AM

The Tibor Varga system uses some very basic left hand exercises for learning finger patterns. Ask any Varga student about the hours they have spent on F3 or F4! F1 is a simple system of alternating semitones and tones or each pair of consecutive fingers in one position spanning the interval of an augmented 4th. F3 is an exercise (which sounds like Bartok) where every pattern of 1234 is played within the confines of a tone. That is, no interval is wider than a tone. The first pattern is all semitones. The next is 123-4. Then 12-34. And so on. The maximum stretch pattern is 1-2-3-4 or again an augmented 4th. Then the 1st moves up a semitone. Every variant is played. At the end 1234 is one semitone higher so that the student can continue up the string. Again all the fingers have to stay down and the hand position should not change.
1234
123-4
12-34
1-234
1-23-4
1-2-34
1-2-3-4
-12-3-4
-12-34
-123-4
-1234

F4 is a variant of this - it uses the same patterns but not with consecutive fingers.

1323
1-323 etc.

It heats up the muscles in the palm of the hand and is the best thing I know for warming up before a rehearsal or concert. In fact I can hear my wife practising it now!

Martin

PS There are other Varga exercises but these are the most common. It beats working on Sevcik or Schradiek and having to buy all those book!

From Corwin Slack
Posted on June 24, 2007 at 11:19 PM

Thanks for sharing this. Did Varga have a notational system for finger patterns in etudes and pieces?

In my last two blogs I have outlined a couple of options and I am trying them. I am currently in favor of notating patterns them with letters (h = half step, w = whole step, m = minor third, and M = major third but arranged vertically on the page at the place where the finger pattern changes.

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