June 2007

Finger Patterns II

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 64 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?

2 replies

Finger Patterns

I recently started to learn Dont Opus 35 No. 2. At slow tempos it is hardly any more difficult than Kreutzer No. 2 but as the tempo moves up it is enormously difficult. This is an excellent etude for mastering finger patterns. But there are many patterns and it is hard to remember all of them. I am in my mid-fifties and the upstairs isn’t working any faster. I found myself looking for a way to master this etude faster.

Robert Gerle wrote a great book on practicing. In it he advocates analyzing and practicing finger patterns. He lists 21 finger patterns and numbers them from 1 to 21. My teacher encourages using finger patterns. His nomenclature for the patterns is a bit more logical than Gerle’s but it is still a catalog and we have only named 8 patterns so far.

Unfortunately there are a lot more than 8 or 21 finger patterns. In fact in a short afternoon of looking I found at least 9 patterns in etudes from Dont, Paganini and Wieniawski that are not included in Gerle’s catalog. I even found one pattern in the Dont No. 2 that Gerle didn’t catalog. Two of my teacher's eight patterns are not included in Gerle’s list and they each have a total span of 4 half steps (and I have examples in the etude literature of their use.)

In the span of a major 6th on one string (a major 10th over two strings) there are 54 possible 4 note patterns if we exclude any intervals (between adjacent fingers) greater than a major third. (The interval of a fourth between two fingers is like playing octaves across two strings between adjacent fingers. It is possible but rare.)

Then add the possibility that adjacent fingers could cover a fifth (e.g. first finger on A on the G string, second finger on E on the D string) and that is quite a few more patterns to name and remember.

It is just too many.

I have discovered (re-discovered?) another possible nomenclature for finger patterns that I think may have more value. Instead of a catalog of finger patterns that could never be retrieved from memory in any useful way I propose a descriptive nomenclature that includes useful information in the name itself.

My nomenclature would include three underlined digits. Each digit would represent the number of half steps between adjacent fingers. So the standard pattern of half-whole-whole (e, f, g and a) that Gerle calls pattern three I would name 122. Whole-half-whole would be 212, whole-whole-half would be 221 and whole-whole-whole would be 222.

Fingered octaves (whole step ) would be 232 and chromatic fingered octaves would be 141.

Covering a fifth with adjacent fingers would be notated as 0 (e.g. Paganini Op 1 No 4 measure 16 which would probably be notated 012 even though only two fingers are sounded). Of course if one were playing very virtuosic literature they might conceivably use intervals larger than 4 half steps (a major third) so they are free to notate using larger numbers. The famous Paganini pattern of 4 A's would be notated 555.

There are a lot of numbers on a typical page of edited music so my notational proposal is that interval patterns should be underlined. They shouldn’t be circled or boxed because that typically indicates a section number.

The disadvantage of this system is that it takes three numbers to write a finger pattern. Here are some advantages:

1. It is fully descriptive
2. Although the description is physical it does help a student discover the harmony.
3. In time the student will quickly start to grasp the number of half steps between adjacent fingers. The need for the notation will diminish.
4. Changes in finger patterns will be quicker to grasp. Szigeti said that in any shift focus on the finger that moves the whole step in a change of finger patterns. (I am paraphrasing and extending the notion. So forgive me.)
5. The system is complete and totally extensible for any situation. While many of the possible finger patterns are rare or impractical they can all be described in a completely logical way.

There are some possible extensions of the idea:

1. It may be advisable to notate shifts as a number of half steps. This could improve the accuracy of shifting.
2. In some passages notating a pattern of four fingers is not terribly helpful. In these cases a patterns of two and three fingers could be notated by describing the number of half steps between pairs or troikas of fingers.

I am putting this to work. I would appreciate thoughts or comments on this. If anyone has seen this before please provide a reference.

Update:

See my comment below.

I also think that you can notate patterns using letters to avoid confusion with fingerings.

h = 1 = half step
w = 2 = whole step
m = 3 = minor third
M = 4 = major third

so the standard pattern of two whole steps and a half step could be notated wwh etc.

2 replies

My shoulder rest...

Tough subject for the day -- My shoulder rest. I don’t have one and have not since the early spring of 1998.

While I was a teenager I read one of the Applebaum interviews with Nathan Milstein. I recalled very clearly that Milstein said that the function of the left hand was to hold up the violin. I intuitively said yes but I had neither the will nor the means to drop my shoulder rest. I had been steered into a dead end.

I can look around me and see many players who are much better than I am who use a shoulder rest. Perhaps it is right for them. I have some deep reservations but lacking their physical and mental make-ups, I’ll never know.

I do know that dropping the shoulder rest was like breaking a dam that was impeding my progress. I could not have done it without a very insightful teacher who himself had dropped the shoulder rest and who had gone through relearning process.

There were several fundamental understandings I had to gain to make this transition to no shoulder rest.

1. Lifting the shoulder was not a correct solution
2. There was no need to hold the violin up with my chin and shoulder. (There are plenty of pictures of great violinists tuning their instruments who clearly cannot turn just the peg but have to hold the scroll in their hand)
3. The adaptation of the left hand, if done properly, would improve my technique not limit it.

Several events started me forward:

1. I bought an early 20th century violin by a famous maker in the summer of 1997.
2. That fall I was asked to sit concertmaster (a rotating position) in a town-gown orchestra I was a member of.
3. The student conductor gave me bowed and fingered parts that had some errors in them. I asked him who did it and hired his mentor, the man who fingered and bowed the parts, to explain them to me. He became my teacher. (And he corrected the transcription errors made by the student conductor).
4. Teacher didn’t insist that I immediately drop the shoulder rest but he made life quite painful for me. It became clear I was going to have to change.
5. I showed my newly purchased violin to a prominent violinist who owned several by the same maker. He doesn’t play with a shoulder rest and he didn’t offer to let me use one when I played his instruments. I was humiliated.
6. After my turn as concertmaster I dropped my shoulder rest and never picked it up again.

How has it gone?

It was quite difficult at first. Changes and improvements happened in quanta not gradually or continuously. Vibrato never was a problem. Shifting upward on the first three positions was relatively easily mastered. Down shifting, especially on the G and D strings in the lower positions took a while. Learning to cross the bout efficiently and smoothly was a very long process. It took lots of adjustments.

It would be delusional to say that I have perfected the transition but I am clearly a better player today than I was before the switch. I would encourage others to make the jump but I offer several cautions.

1. Don’t lift your shoulder. Don’t lift it permanently, don’t lift it momentarily, don’t lift it to shift. Just don’t lift it. (The picture on my profile is my standard playing posture.)
2. Get someone to show you how to do it. Best choices
a. Someone who has made the change
b. Someone who never used a shoulder rest
c. Someone who doesn’t lift his/her shoulder.
3. Don’t linger between using it and not using it. Take the plunge.

There are several other things to consider.
1. Don’t drop your thumb under the neck (pointed back to the scroll) when you shift. The thumb will gradually drop as you shift upward.
2. Work early on to get rid of first finger dominance. The hand needs to be rotated to the neck and the balance of the hand should be between the second and third fingers. The violin should rest on the little shelf at the base of the first finger when you form it into a hook and push the base knuckle forward. This is easy to say but it takes a lot of concentration to make this work.
3. Don’t curve your palm too much. When you reach the bout the base of the palm should be under the violin, not hitting the bout.
4. Keep your elbow under the violin.
5. Practice Yost!
6. Practice legato as frequently as possible (including the Yost scales). You can hide all sorts of technical defects in between up bow and down bow. You have to hear your technique to improve it.

Don’t set unrealistic expectations. Don’t compare yourself to others. You will improve but this isn’t the hidden secret to greatness. It is a wonderful route to betterness.

37 replies

School Music II

Well Texas does it again. The all state audition etudes for violins for 2007 are Kreutzer #32 and deBeriot Op 123 No 20. I posted previously on Texas's choices for All-State etudes

How many of you can reach into your library for the deBeriot? When they announced the etude choice Schirmer had exactly 7 copies in print. After an executive decision Schirmer decided to send it back to the printer.

The Schirmer edition was edited by Harold Berkley who noted in an introduction that they come after Dont Opus 35. Based on my eyeballing it I would say that some of the etudes are definitely post-Dont but many are similar or easier.

I think that Dont (or higher) level etudes for all state auditions are a conceit. But this is an improvement on last year where Paganini Op 1 No 16 was one of the selected studies.

Perhaps all-state level players can do this well enough but the same etude are used for region orchestra auditions and many high school teachers require them for chair auditions for all of their first violins.

4 replies

Chromatic vs. Diatonic Half Steps

There seems to be some confusion on the difference between a chromatic vs. a diatonic half step. In her blog entry Starling-DeLay Day Five: Kurt Sassmannshaus' violin master class Laurie quotes Professor S. who quotes Dorothy Delay "All 1/2 steps are not created equal," Prof. S said. Dorothy DeLay simplified it somewhat, she said that "if the notes have the same name, the half step is wide."

The first part is true but the second is not. A chromatic half step (e.g. g to g# or aflat to a etc.) is smaller than a diatonic half step. (e.g. G to A flat or G# to A etc.).

I haven't the skill or background to demonstrate this myself so I will appeal to authority. Earlier I reviewed How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin in a blog entry.

One of the major points of this book is that a chromatic semitone is smaller than a diatonic semitone. Chapter 3 of the book deals directly with this.

Duffin adds some interesting quotes.

From Leopold Mozart ...according to their proper ratios, notes with flat signs are a comma higher than those in the same position with a sharp sign. For example D flat is higher than C#, A flat higher than G#, G flat than F# and so on.

From Johann Joachim Quantz The large semitone has five commas, the small one only four. Therefor E flat must be a comma higher than D#....

I would be interested to know if anyone can cite other authorities that would support the Delay-Sassmanshaus assertion of the opposite.

6 replies