A - FOREWORD
If anyone tells you: treat the thicker string heavier, the thinner string lighter, everyone with common sense will agree. Or: If you push too hard, you can crush the vibration; that makes sense too.
But it seems in cello lessons, common sense often has ceased.
A miracle is expected by holding the stick with one of the fingers slightly different - and of course the result is an illusion.
Well, the secret lies in common sense, thinking through and experiencing, experimenting with the obvious movements.
But it is difficult to swim against the stream of old traditions, as odd and obviously silly these traditions might be.
This article may contradict our traditional way of thinking about bow technique.
It is a systematic analysis into the elements contributing to our quality of sound.
It is independent of individual hands and instruments.
It will create insight into the process of sound production and sensitivity with exercises to realise improvement.
When it comes to bow technique we seem to be confronted with a multitude of opinions, little questionable secrets and virtually nothing sure. Most talks are about how to hold the bow. Of course there are many opinions, because we not only have different instruments, bows and strings, but we also have even more different fingers, hands and arms.
Unfortunately the kind of advice about the bow hold is mainly about the teacher's hope that the feelings in their own hand and their sense of comfort and control might be transferable to the student's body. This hope is unquestioned and replaces real insight and dialog. Virtually every soloist and teacher holds the bow different, and swears it is the only and correct way.
This article heads into a completely different direction:
focussing on the relationship between the bow hair and the vibrating string, the very place all our sound is created. It makes us rethink, feel and listen.
To get a glimpse into the direction we take, I suggest an introductory exercise (test):
INTRODUCTORY TEST EXERCISE:
a) We take the bow and hold it with our best bow hold.
We play a 2 beat note on the A string (any finger) very light with a quite fast bow just ate the start of the fingerboard (we might try this also on the different strings).
b) Now we play the same note with a very slow bow and very heavy (pushing hard) at the same point of the string, start of the fingerboard. The string will be dragged to the side and give a not nice sound at all .--
c) We repeat the exercises a) & b) with a bad bow hold.
We may experience that the way we do things on the string is more important than how we hold the bow.
As it is in this extreme case, it is even more in detail.
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B - INTRODUCTION
About 15 years ago a student of mine, a teacher of physics, asked me: "If you hold the bow like me, it still sounds like you; if I hold the bow exactly like you, it still sounds like me.
I went into so much trouble to hold the bow like you, but it basically didn't change a thing. You must do other things different than me, things you haven't told me."
About 20 years before I read about the great cellist Gregory Piatigorsky's accident: he had broken his thumb and had to play the Dvorak cello concerto on the same night; he had no time to go to hospital. He played with the bow in his fist and - nobody noticed! He was praised for his sound.
If the bow hold would be the most essential element of a good sound, how could this have happened, especially since he had never practised with this barbarian "fist" technique?
The answer is, he did everything important right, just with a clumsy bow hold.
In this article we will go through the essential elements of a good bow technique - trusting that all of you have a better bow hold than the fist.
Often string players are focussing on the varieties of holding the bow, probably because it is an essential element of the first lessons. We have to teach it, have to decide how we do it; we can't skip thisstep of explanation to a beginner. All string players have their own thoughts about it - and every single professional player seems to have a different bow hold and swears it is the only one.
But are there enough objective facts about bow technique, which are beyond personal opinion and personal hand and arms, which can make a difference?
Yes, there are!
Good players follow these objective elements of technique often intuitively, and sadly enough they are usually neither taught nor even known.
If we compare professional performers, we can find they do many things in common - not how they hold the bow - but what they do with the bow on the string. These common "things" are the essential elements, which make our sound full, round and alive - or if neglected harsh and inflexible. In this analysis I will focus on the five elements, which are contributing to our sound production and explain their positive and negative effects. Knowing the essential elements create an understanding of the process of sound production. Once this process is understood, the reader will be able to produce the quality of sound by will and knowledge, improve sound quality, clarity, volume, softness or strength according to taste.
The effects of these five elements interact with each other; they are also dependent on which string we play and how high we play with our left hand in the positions.
I separate the five essential elements into two classes, the invariable and the variable elements.
The two invariable elements are:
1. The bow tilt
2. The direction of the bow
The three variable elements are:
3. The weight / pressure on the string
4. The contact point of bow and string
5. The bow speed
Each element contributes to the quality and character of sound.
The variable elements are interdependent. That means, when I change e.g. the bow speed, it might require changes of the other elements, weight/pressure and contact point.
Above all there is one fundamental process, based on the the nature of our string, which when fully understood, is able to make us understand and feel the process of sound production altogether. I will start with this normal to us, but in some sense weird way of producing a sound.
C - THE PROCESS OF SOUND PRODUCTION
The bowed string instruments are different to all other instruments with strings: Once the sound is there, we can sustain it. We execute it by doing something appearing normal to us, but which is weird in some sense (This process as described here is as compact and essential like the "Einstein Formula" about energy. The first sentence contains the complete question and answer about bow technique).
We move the bow in one direction to sustain a vibration in two directions.
Some common sense should tell us that pulling the string continuously with sticky glue in one direction would be the worst of all things when we wish it to vibrate in two directions.
But nature supplies us string players luckily with a curious behaviour of the string: the string does the best it can to maintain the same vibration, the same as if we would pluck it. In fact the string of a particular tension and length has its one pitch, a fixed vibration. Every sound or noise we create on this string relates to this pitch, even the screechiest and scratchiest sound. All scratchy noises are harmonics of the basic pitch. We can't break out of being confined to it.
The bow hair has tiny grooves, which are made sticky with rosin. These sticky hooks pull every single vibration of the string to a position of a certain tension - dependent on pressure and speed. When the tension gets too high, the string rushes back and is pulled again. Within this process of pulling the string does its best to vibrate continuously. The continuous pull plus the stubborn vibration ensure that the amplitude and the pitch of the string can remain the same. This means we can play a sound on the string instrument, which does not diminish and dies down. By pulling a little bit more or less we can manipulate the amplitude and change to exactly the strength of sound we desire.
This looks very promising - and it is - but we need to keep in mind that the process of dragging the string in one direction and expect it to vibrate into two direction is indeed an unusual thing, a vulnerable process, and certain conditions need to be fulfilled to produce a good result. It is in fact a conflict, which we need to resolve by means of special techniques.
This is different to plucking a string and can give us an insight into the reasons why to do what and where with the bow - if understood in all its consequences. In difference to a harp or guitar it limits the choice of locations where we can produce successfully a good sound. It can easily happen that the string refuses to move back and does not vibrate properly, which sounds as if the sound gets crushed. And it can happen as well that the full vibration does not fully develop; instead the string can split into divisions, harmonics, and the intended pitch might not appear clearly or not at all.
We come to the essence of bow technique:
The constant awareness of the effect of the bow on the string and its ability to vibrate freely in two directions underneath the bow. Therefore we need to keep in mind:
We need to activate the string by dragging the bow.
We can stop the vibration of the string by dragging the bow.
We need to be aware, that we make the string vibrating. Simultaneously we must allow the string to vibrate freely.
A good bow technique is a successful constant balance between making the string vibrate and not doing anything more than creating the optimal vibration.
Therefore the tilt needs to be right.
Therefore the angle needs to be perpendicular.
Therefore we need always to listen for the sound,
how light or strong we play,
how slow or fast we move the bow,
where we play with the bow on the string.
With an open ear and a compassion for our poor string's ability to vibrate freely we intuitively react to the sufferings of the string, which may produce a forced, harsh or squashed sound; or we react on the strings failed attempt to vibrate fully and add a bit to reach full vibration.
Every little bit too much or in a wrong spot or wrong direction reduces the vibration again. On the other hand to produce the fullest sound, we need to go to the limit of speed and pressure imposed on the string, just to the borderline before the vibration would start to diminish again (too heavy) or on the other hand start to fall apart into harmonics (too light). This limit is surprisingly light.
The typical violin student's sound is a forced sound, from forte to mezzo forte and piano, everything sounds forced. Already the beginning of a note is harsh, starts with a scratch.
The typical sound of all good violinists is light, the beginning of every note is pure, created by a light bow, allowing the freeness of vibration.
On the cello we need to give a bit more due to the heavier strings, although we can play the A string nearly as light as a violin string.
I will discuss here the five elements separately and at the end of this article I will dedicate a chapter to the nature of our string, which relates in a surprisingly grand way to our every day surrounding.
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THE TWO INVARIABLE ELEMENTS
1 - THE BOW TILT
On the violin we tilt the bow away from us, on the cello we tilt the bow towards us. Why? Because we hold the instruments the other way around, the violin with the tail piece towards us, the cello with the neck towards us. On both instruments we do actually the same with the bow: We tilt the bow away from the bridge. And why? We want the sharp edge of the bow hair with the weight towards the fingerboard, the looser hair with less pressure towards the bridge.
The reason for playing on this particular tilt is: towards the bridge the string has a very small and dwindling amplitude. The swishing bow hair with hardly any weight does not create an audible noise there. Would we reverse the tilt, the bow hair swishing on the larger vibrations towards the fingerboard would cause an audible sandy noise. If we try, we can hear it.
Why don't we play always with all hair on the string? We need to keep always in mind, that the vibration of the string goes two ways - whereas the bow drags one way and not only creates the vibration of the string, but can also stop or inhibit the vibration. The flat surface of all hair is so large, it would inflict with the free vibration of the string; this may result in an unclear sound, a distortion of the intonation or even a cease of the vibration. Naturally the violin with thinner strings is more effected by too much hair on the string.
The requirement for the tilt of the bow is a constant requirement, not variable (see below the exception).
EXERCISE (1a): - Learning the correct arm / wrist / hand movement
We play a very slow slur from the lowest to the highest open string - very gradually, allowing double stops in the transition. We watch carefully, that the relation between hair and stick remains the same - we watch the space between stick and hair. We try in both bow directions, starting with both, up or down bow (violin: GDAE-EADG, cello: CGDA-ADGC)
WATCH THE BOW - NOT THE HAND
We should watch the bow (not the hand) and let the arm and hand do what it does naturally to ensure the correct tilt. In a good technique the demand is not put on the hand but the (audible) result on the string.
More on the cello than on the violin students are often taught to move from one string to the other with an active wrist movement. This is a wrong thing to do. The active wrist movement gives the bow instantly a different tilt and through this a lack of control in sound and reaction. In spiccato passages it can stop the bow from jumping after string crossings. A typical indication for this mistake is, that the bow hair gets caught on the corner of the side.
EXERCISE (1b): - Noticing wrong wrist movements
This is rather a demonstration of a wrong technique than an exercise. It is very useful to do in order to eliminate wrong movements (Especially cellist should do this exercise).
a) We put the bow with the tip on the string.
b) We watch the tilt of the bow at the contact point.
c) We move our wrist up (and down) to reach the next string.
Probably with horror we will notice the failure of reaching the next string, the impression to have done a useless activity, which distorts the bow tilt instead of letting us reach the next string.
We might realise, that our sound problems on the A and C strings has to do with this (useless) activity. We need to watch, that the bow tilt on all strings remain the same, otherwise we lose sound quality and control.
An exception to the tilt is for "spiccato". We might play in spiccato with the bow flat on the string, with all hair. The unified friction of all hair produces a better jump. We neglect the roughness of the sound because we want it.
In so called "flautato" passages, which are passages with a very soft sound including possibly an somehow "airy" sound with some slight husky noise, we may play very lightly with a high speed stroke above the fingerboard (nearly carrying the bow) and use the bow flat on the string. We do it this way in order to have more contact with the string making up for the loss of contact through over lightness.
2 - THE DIRECTION OF THE BOW
Since the string vibrates naturally sideward, in a 90 degree angle to the string, the bow should move in the same direction as the string vibrates, which means exactly perpendicular to the string and parallel to the bridge. With any other angle the bow hair will cover an uneven or additional area, which would cause a swishing movement under the hair, adding a "ffff" noise to the clear sound of the string. When the bow is too slanting, the bow hair can inhibit the string from vibrating altogether or at least from sounding well. This happens easiest on the thinnest string, on the cello the A string or the e string of the violin, since the inherent force of the string to vibrate back is quite weak; the thinner the string the weaker is its power to vibrate as a whole.
Violinists and viola players can see their bow when they play and keeping the bow parallel to the bridge is not too difficult. This looks different for the cellists. From the viewpoint of the player it is nearly impossible to see if the angle is correct. Most students play naturally unfortunately parallel to the floor. This causes a slant in the bow direction, as the cello is not held straight (We sit straight - or better: should sit straight - and the cello has to give way to the left, crossing over at the centre to the right).
EXERCISE (2a): - Realising when the bow is straight
I recommend getting a stiff carton, cut out the space for the bridge and let someone (teacher) hold this carton like an enlargement of the bridge, exactly level with the bridge. Now we put the bow still on the string, parallel to the carton on 3 spots: nut, middle and tip. We watch that the distance from the bow to the carton is absolutely the same all along the carton. Then we remove the carton and try to memorise, that this angle is straight. We repeat this reality check for each string.
If we notice, that our contact point moves up and down on the string during bowing, it indicates that the bow direction is incorrect. When the bow direction is correct, the bow will remain exactly on the same spot of the string. It causes an effort to move the contact point up or down. This effort is involuntary done by having a wrong bow direction.
There is no exception for playing the bow at a right angle.
I have frequently heard the advice for cellists to play the C string steeper into the room than a right angle. This advice is actually useful, but inaccurate. When we play a correct right angle on the C string it 'looks as if' the bow points steeper into the room than a right angle, but it is not (So we might as well go for the optical illusion to produce the correct angle).
From the shoulder as the centre, all our natural arm movements are circular. We want our bow direction to be straight. This is of course a conflict.
If we follow somehow our natural tendency slightly and play a bit of a curve, the bow will move towards the fingerboard, when we come close to the nut. If our choice of bow speed and weight was a good one for the middle of the bow, it looks very different, when we apply at the nut 5 times as much natural weight (see next chapter) together with also changing the contact point to double the distance from the bridge. It can't sound well, but happens often.
I suggest two exercises to get aware of the movement and to create a new feeling for the straight line we need to achieve.
EXERCISE (2b): - Getting a feeling for our arm movements
We do this exercise in 3 steps; each exercise is played with a full up bow from the very tip to the nut:
1) First we do excessively the wrong thing: We play with our bow arm an obvious circle. We observe what happens.
2) Now to counteract this arm circle we play an "anti circle", a circle the other way round (eg. around the music stand), starting at the tip far away, coming close in the middle and moving away again towards the nut.
3) Now we find the middle way, the straight line. We observe now the contact point of bow and string, not our arm. The bow needs to stay exactly at the same contact point; towards the nut we need to feel that the bow asks our arm to move out again and not to follow our natural inward circle.
EXERCISE (2c): - Getting a feeling for our hand pulling and pushing
(Many of you might know this exercise)
1) We grab the bow with our left hand, holding it at the tip and putting the bow with the tip on the 2nd string (violinists may lean the scroll against the wall for the stability of the violin). The bow should point now away from the instrument without being hold at the nut (During a lesson the teacher may hold the bow).
2) Now we place our right hand on the nut as if we would do when we start playing. We watch exactly where our index finger and little finger are placed. We release our thumb and glide now with our fingers along the stick. The contact point of our fingers should not move.
Probably we will feel, that the hand wants to move away at the middle of the bow and pressure increases when we approach the strings.
If we have gained the perfect feeling for a straight line, we will feel always the same pressure on the inside of our fingers, and our contact points wouldn't move.
To get the feeling for the perfect straight line, we should repeat this exercise regularly until we feel always the same pressure and until our fingers don't move up when we approach the strings.
The same movement, which moves our fingers up when we approach the strings moves in real playing the bow towards the fingerboard and makes the sound heavy and scratchy.
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THE THREE VARIABLE ELEMENTS
3 - THE WEIGHT / PRESSURE ON THE STRING
(To the distinction of weight and pressure: If we believe it or not, the string does not care, if it receives pressure or weight, it just reacts on the grams imposed on it.)
I will start the chapter with two measurements, which will highlight the complexity and nature of the problem. The first measurement (A) shows the limit we can exert with the bow on the string on the different parts of the bow from nut to tip, the second measurements (B) shows how much and how different pressure we need to apply on the stick to receive even pressure on the string.
Where would you think we can we apply more pressure on the string, play stronger, at the nut or on the tip? Or is this individually different? - I asked several professional players receiving opposite answers: some said, you can apply more pressure on the nut, some said on the tip.
The truth is absolutely clear; we can apply the following top possible pressure at the different parts of the bow:
(A) TOP POSSIBLE PRESSURE on the string:
nut 1/4 middle* 3/4 tip
violin: 2.5kg 800g 300g* 350g 450g
cello: 8 kg 1.5kg 700g* 800g 850g
* the pressure is limited in the middle of the bow by the stick touching the string/hair. This limit is dependent on how much the bow has been tightened and how strong the stick is. I used a normal play tension.
With surprising ease we can put our bow at the nut comfortably down and by just resting on it, not even heavy, exceed by far the top possible pressure of the middle and the tip of the bow.
At the tip I measured a painful 7kg pressure (on cello) on my index finger to achieve a mere 850g on the string (the bow seemed nearly to break at the stage; the bow hair touched the stick in the middle).
(B) THE EFFECTIVENESS OF PRESSURE EXERTED ON THE BOW STICK.
This is one of the most important measurements. If we press constantly with the same pressure on the stick, we DO NOT receive even pressure on the string. The pressure we exert on the stick with our fingers creates a very differnt pressure on the string dependent with which part of the bow we play. The efficiency is different because of the pivot effect due to playing the bow on one end. If we push very hard playing at the tip, it creates hardly any pressure on the string whereas at the nut our full arm weight crushes down with full efficiency.
For this measurement I take here the example of 300g as used to play a good forte on the cello. To achieve this constant pressure on the string we need to apply the following varied pressure on the stick (hand weight at the nut / * pressure on the index finger at the tip):
( ------- constant pressure on string: 300g------------ )
nut 1/4 middle 3/4 tip
negligible (lift slightly) 500g* 850g* 1.4kg* 2.5kg*
This table shows the effectiveness and ineffectiveness of weight and pivot (between index finger and thumb).
I can't emphasize enough how important this measurement is. The structure of the bow, being held at the very end, creates a pivot. The effect of our arm weight vanishes already at 1/4 length of the bow. From there on we need to increase the pressure on our index finger to maintain the pressure. When we play two long notes on the C string on the cello (as in a scale), often the bow starting at the tip starts with an unclear sound: we need to start this bow slowly and with added pressure.
Or more important even the other way around: If we are able to make a good sound at the tip with just the bow eight, we need to DECREASE the pressure of our index finger continuously towards the nut and let our arm weight NOT effect the pressure on the string, but lift it off, or we will play an unintended crescendo towards the nut! Or we will hear crunch noises coming close to the nut. Every note at the nut will start with a scratch.
SHORT TEST FOR PRESSURE EFFICIENCY
a) We put our bow down at the tip and push very hard. With our left hand we lift the tip off the string, continuing to push hard to test how light or heavy the bow rests on the string. We will feel, it is easy to lift the bow off.
b) We put the bow down at the nut and push very hard. With our left hand we try to lift the bow off the string, continuing to push hard. This will be a hard task, we can't lift the bow.
Now it makes sense, that in all orchestra parts the first (heavy) beat of the bar is traditionally played with a down bow. Accents are played with a down bow, pianissimo is played at the tip. This is following the natural weighting of the bow.
Diminuendo is easy to play in a down bow with the pressure naturally diminishing; therefore the last note of a piece is usually a down bow, declining occurs naturally. Therefore a diminuendo in up bow close to the nut is very difficult - we have to observe the sudden increase of weight.
I was taught in a master class (with janos Starker) the special secret, that with a good bow technique we can play with the same strength at the tip as at the nut. This is of course physically impossible. The master lived in illusions.
There are some surprises: Don't we imagine that we can play the best forte sound in the middle of the bow? No, the middle of the bow is the place where we can apply the least pressure. The structure of the bow, the concave curvature of the stick let stick and hair meet there earliest.
Most musicians I showed this tables were surprised about the results.It means that professional players are able to play all their life a perfectly even forte or piano without even knowing how they do it!
We might ask ourselves, how is this possible, that professional musicians do exactly the right thing and don't know what they are doing, or are even convinced they are doing the opposite? The question is answered surprisingly easily.
Musicians became musicians because they are interested in the aural result; they listen what they are doing, they don't primarily watch and analyse. Their drive to become a musician is the fascination of sound and some inner knowledge, that they are able to manipulate sound, that they will be successful in all their efforts to produce the desired image of sound quality.
A good musician reacts on the aural information of a bad sound instantly: We do it by trial, error and intuition, and we do it often right despite wrong teaching. I might be the only musician who measured the bow pressure. And - I would not have done it, would I have not have been taught so much nonsense presented with a ridiculous security and authority. I wanted to know the true facts.
I asked some beginner students of mine to keep exactly "this" strength of sound, from the very nut to the very tip; I asked them to listen very carefully and most of them manipulated skillfully the bow with all its complex changes in hand and finger pressure & weight, without actually knowing what they were doing! Just by ear.
THE BORDERLINES: TOO MUCH AND TOO LITTLE PRESSURE
The most fundamental rule is that the string needs to be able to vibrate freely underneath the bow in two directions. We can probably imagine rightly that when the string is too much pushed down this will inhibit the string to do so. We can actually visually observe that it can happen that the string gets dragged to one side by over pressure. For example when we play above the fingerboard with high pressure and low speed. A somewhat donkey like sound appears. Already slightly too high pressure can distort the intonation, flatten the pitch.
On the other hand we need a minimum pressure to make the string vibrating. Especially on the C string (cello) it happens frequently that the string doesn't react instantly to the bow movement. This string is quite thick and lazy and needs quite a lot of pressure/weight (and slower speed) to oblige.
Something similar we experience with any bow stroke too close to the bridge. If the bow is too light, harmonics will occur; higher pressure (or lower bow speed) is needed to make the string vibrating in its whole length. We need however not to forget that the speed of the bow and the weight operate together.
THE DIFFERENT STRINGS
The different diameters of the strings ask for a different weight / pressure. The top strings (E on violin / A on cello) need to be played very lightly, whereas the bottom strings ask for a bit heavier treatment.
So many players are afraid of the open E string (violin) - A string (cello), crossing over to them, because they sound "sharp", harsh. The sharp sound is just the result of playing the highest string with the same weight as the lower ones. They need to be played remarkably lighter.
On the violin the posture of the instruments supports the demands of the pressure. By lifting the arm high to reach the G we rest a bit heavier on the string, just right.
On the cello it is the opposite. Players reach over to the A and play it often too heavy, especially at the nut, whereas they could often add a bit for the C string.
THE DIFFERENT PARTS OF THE BOW
As we can see in the table of measurements, we play naturally heavy at the nut. We have not to apply any pressure at the nut, or we will over push, we will crush the string. Except on the C string on cello to reduce our arm plus hand weight even when we play forte.
We might avoid altogether the first few cm of the bow at the nut. The bow is there unresponsive, the weight too heavy. I was told by my first teacher to start every note at the very nut and did so, although it always produced a crunching noise (see: D - THE TAUGHT STANDARD). I had already studied 1 year tertiary until in a master class the great cellist Enrico Mainardi - to which I had received a scholarship - told me: "You don't need to start there, the bow doesn't respond. Just start always a couple of cm off the nut; sounds better." That was the first time, anyone in my learning history argued from the reason of sound, after 12 years of playing!
The opposite is at the tip. We might be able to create a clear sound on the highest string starting from the very tip; but even there we might need to help a bit with pressure from the index finger. On the lower string we need certainly to push on the index finger to get a good start; how much we push is dependent on the string we play on and the dynamic we want to achieve.
Because we have to execute at the tip a multiple of pressure as the result, it is an ideal area for subtle dynamics. I like to use the upper bow for forte passages in Vivaldi to Mozart. We can push hard without the bow getting too heavy on the string, and we can happily go for a range of dynamics without unpleasant sudden reactions from the string. Every action is scaled down like with a system of sprockets and gears.
There is a very simple demonstartion of the difference in weight we can apply at different points of the bow.
Nut) We push the bow down at the nut and attempt to lift it with the left hand: it is impossible!
Tip) We attempt to push the bow down at the tip as hard as we can.: We try to lift it at the tip with the left hand: despite all the force we apply with the right hand, the bow lifts easy as a light weight stick!
We can test the effectiveness of pressure at all different points of the bow.
As mentioned one of the most common mistakes is to apply the same pressure on the stick for all strings and for all parts of the bow. We need to be aware of the two systems from lighter to heavier. The strings demand from the bow the following treatment:
* Top string needs light weight; develops to bottom string heavier.
* The nut is naturally heavy, the tip light. We need to counteract with taking off weight towards the nut, adding pressure via the pivot between thumb and pointer finger towards the tip for an even sound. Otherwise unintended crescendos towards the nut appear and a thinning of sound towards the tip.
We also should only rarely use the lowest part at the nut, because our arm rests there too heavy. This part should only be used for heavy passages like portato and accents.
I had students who habitually developed a crescendo towards the nut, when they returned for a (full) down bow. They rushed to the very nut and 'whoom' appeared this growth of sound. Being made aware that their arm weight increased rapidly at the lower part of the bow, their ear opened up for this unintended increase of volume.
Often - or better usually - going back to the very nut is not necessary, it causes problems; we can change bows 5 or 10 or even 20cm away from the nut; why go all the way back?
Many beginners release weight / pressure at the change of direction of the bow and also when they cross strings. It is beneficial to watch the distance between hair and stick and make sure that we don't lift the weight off at the change of bow direction.
EXERCISE (3a): - For the change in bow direction (see also Exercise 5b)
We play a scale counting 2 beats per note, then 2 beats rest. During the rest we do nothing! We don't lift the bow weight. We watch that bow hair and stick remain exactly the same. (We also watch that we don't change the contact point when we start playing). We listen carefully, that the beginning of the note is clear.
Hint: When we feel the activity as coming from the elbow (instead from our fingers or hand), the beginning of the note will start more naturally; the bow will pull the string in a more organic way, less noises will occur.
As we will learn in chapter 5 (bow speed), we start the movement not in full speed, but let the string develop its full vibration.
EXERCISE (3b): - Learning to play lighter
1) We hold the bow above the E string (A string for cello), the tip hovering 2cm above the string.
2) We relax the hand and rest the bow on the string. We stop actively holding the bow, loosen our grip to a mere touch. If the bow slides away - instead of holding it with the hand - we lean just that much on our index finger that the bow does not slide away.
3) Without any additional effort or extra movement we move slowly this light bow. We might be surprised, that this light bow is enough for a sound.
4) We do the same again, this time with a finger on the string and vibrato.
5v) for violin - We play a whole piece that lightly.
5c) for cello - We play a long note on the D string and the next note lighter on the A string. The A string will not sound louder and harsher if done correctly (watch the bow tilt).
EXERCISE (3c): - The different treatment of the strings
Weight / pressure work hand in hand with bow speed and contact point. It is difficult to isolate them. More exercises regarding the pressure / weight can therefore be found at the bow speed section. We can already try:
1) We play a scale with even dynamic (violin: G major / cello: C major)
We play the scale in separated 1/4 notes.
We play the lowest string heavier and lighten the bow when we go up string by string - and opposite on the way down.
At the same time we play with less bow on the lowest string and increase the bow speed slightly string by string on the way up (and decrease on the way down).
With some practice we will achieve a scale with an absolutely even dynamic ( f , mf or p )
2) We now play with the same weight and the same bow speed the whole scale.
We will notice, that on the bottom string the sound will not be clear enough (too much bow speed) and that on the top string the bow is too heavy, needs to be lighter and faster.
Even weight (even if done correctly regarding the appropriate pressure) and bow speed does not give an even sound for all strings. Each string requires a different treatment.
An excellent demonstration of the aspect of pressure / weight is gives by the great violinist Jascha Heifetz. In consideration of the weight/pressure on different parts of the bow Heifetz chooses very carefully in which part of the bow he plays a passage. (click here to watch)
We will notice the passage of double stops in the lower quarter. He uses reduced hand weight to ensure not to produce over pressure (therefore not at the very nut), but reliable natural weight as application. We can also notice, that virtually all notes except staccato and spiccato are played in the upper half, very light. The high bow speed for shorter notes gives evidence for the lightness of the bow. We never hear a forced note.
4 - THE CONTACT POINT OF BOW AND STRING
Suggestions from the build of the instrument
The string of a harp we can play (contact) anywhere, it will always respond. Therefore the harp is built in a way that we can easily access the strings at any point. The string of the harp vibrates freely after it is plucked, whereas on the string instrument the string has to vibrate under the constant pressure of the bow. Naturally this peculiar case limits the area where we are able to play the string and can produce a satisfying sound.
Already the build of a string instrument limits the area where we are at all able to access the strings with the bow. String instruments have a special cut out at the ribs to make space for the bow movement. This 'cut out' frames the area where the strings are accessible, from the bridge to the start of the fingerboard. On the violin this area is about 5.5cm out of 32.5cm of the whole sounding part of the string, on the cello 10.5cm out of 69cm; lets say it covers about the 6th part of the overall length of the string.
Furthermore the cut out suggests that the maker of the instrument planned to leave enough space for all different kinds of expressions and situations, because the build is a factor we can't alter. The sixth of the string must cover the possibility to express all ranges from fortissimo to pianissimo, from high to low pressure, quick to slow bow movement and for open strings to high positions.
This seems commonsense but it means on the other hand that playing a particular expression like: fortissimo at a range of two octaves above the open E string on a violin might only be possible within a very small area. This particular area is from 0.5cm to 1.5cm distance from the bridge with an average bow speed, with a high bow speed slightly more to the fingerboard, with a slow bow speed slightly more to the bridge (out of this tiny range), an area as small as a 30th of the overall length of the string! This suggests that we need to know more about the areas to choose from.
The question to ask is, why is the reaction of the string so different when we change the contact point?
EXERCISE (4a) - Tests at different contact points
The contact point is the point where the bow touches the string. The bow pulls the string through friction making the string vibrate but if chosen incorrectly can also stop it from vibrating.
To feel what is happening, we try out the extreme possibilities:
a) different bow speed and pressures very close to the bridge
b) different bow speed and pressures above the fingerboard
c) different bow speed and pressures in the middle between bridge and fingerboard.
By trying out we instantly understand the pattern of behaviour of the string:
a) Close to the bridge we can apply a high pressure, but need to play with a slow bow speed. The sound is sharp.
b) Close to the fingerboard we need to play light and need to keep up a minimum bow speed, not too slow. The sound is softer.
c) In the middle it seems we can use quite a range of bow speed and pressure, but can't go to any extremes.
We will also find that every contact point allows a range of bow speeds and pressures. For example when we play the same bow speed at the same contact point, we can allow quite a range of different pressures. Or when we play with the same pressure we have quite a range of speed changes available before the sound starts to suffer.
Nevertheless we can easily experience the limits of bow speed and pressure at one contact point. We need to keep up an awareness of where we are on the string or an unwanted sound or noise might occur unexpectedly.
To test and experiment all these options is extremely important. Only, when we have experienced an option, we will use it. What we haven't done, we will never choose by purpose! There is nothing wrong with experimenting with too harsh, too soft noises. If we haven't experienced the limit, we might think we know and miss out a vast range of sound, just because we didn't dare to try.
REASONS FOR THE DIFFERENT CHARACTERS OF SOUND
Now that we have experienced the character of sound and reaction in different contact points, we need to ask, why is the character so different? An understanding will help us to choose more in detail.
To a) Close to the bridge the sound is sharp, because high harmonics are sounding.
What happens is, we put stress on the string on a point close to the end. The string is now forced by the bow to have at this point a larger amplitude. The enlarged amplitude at this point is too close to the end to be able to produce a (huge) amplitude of the whole string. Rather it encourages the string to divide in partitions (which the string easily does). These partitions are harmonics. If we play too close to the bridge we will hear only harmonics, we will not hear the root note at all. A fast bow speed will also encourage harmonics, as the vibrations of the harmonics are also are faster.
We need to move at least so far away from the bridge, that the string manages to vibrate as a whole. A slower bow speed encourages the whole string to follow. Moving away from the bridge we come to the point where the whole string starts to vibrate. But still the sound is quite sharp, because it allows harmonics to occur.
The sharp sound close to the bridge, which includes harmonics, carries quite well, even in piano. It seems louder than the amplitude would suggest. The fact that the sound carries well and we can apply a higher pressure makes it a good area to play forte and fortissimo.
To b) The sound above the start of the fingerboard is softer. The more we move away from the bridge the more we cut out high harmonics.
Why does the string react so easily in this area compared to closer to the bridge?
The answer is that the vibration of the string is like a lever of the string. We pull the string with the bow on the outer border of the amplitude; the larger the amplitude of the vibration, the longer is the lever. Above the fingerboard we have a long lever and pull with the bow on this lever. The string as a whole responds quickly - but can be pushed down easily as well.
We might try out the absolute extreme and play with the bow exactly at the middle of the string, at the location of the harmonic of the octave. The bow will just drag the string to one side, even when we apply hardly any pressure. The bow will not allow the string to vibrate underneath it. It is as if we don't let go of the lever and hold it in our hand: it doesn't go back, doesn't allow the string to vibrate freely.
We need to be cautious. When we apply too much pressure at this contact point the bow can drag the string to one side and we can hear only a noise with no clear pitch. If we watch the string we can observe how the string tries desperately to vibrate in vain. As soon as we can hear the intonation going down it means the vibration starts to collapse. We need to keep the bow here light and can't play too slow.
Also, when we watch the amplitude of the string (easier to see on the lowest string) we can see that the largest amplitude occurs quite early. When we add more pressure, the amplitude gets smaller, NOT larger! That means, if we push harder, the sound gets softer! It is very educational to watch this process and realise, that often we might over push and play with too much pressure achieving a smaller sound!
To c) The middle range seems to be the everyday range. It gives us enough scope to play with average speed and pressure from forte to piano. But it is good that we know the other areas and their borders. A drop in intonation, a squashed sound, the collapsing of the string means we need to move the bow quicker or play lighter. Too many harmonics announce that the root note is on the way of disappearing. Positively, when we want to play fortissimo, we know that closer to the bridge the string can take more pressure.
Trying out the different ranges of the contact points has opened us up to play with more knowledge.
THE CONTACT POINT ON DIFFERENT STRINGS
The responsiveness of a string is related to its diameter: A thin string reacts faster and its vibrations have a smaller amplitude; it is easier crushed by weight/pressure.
This means the thinner the string is, the closer to the bridge the contact point should be. The fatter the string, the more we need to move the contact point away from the bridge.
This means forte on the E string (violin) or the A string (cello) needs to be played closer to the bridge than a forte on the G string (violin), C string (cello). The lowest strings are in fact unresponsive close to the bridge; on the other hand they can bear to be played above the start of the fingerboard.
THE CONTACT POINT IN HIGHER POSITIONS
The amplitude is dependent on the length of the sounding string. The only part of the string, which is important is the part, which sounds: from our left hand finger, which determines the note - apart from the open string - to the bridge. For example the sounding length of an open string is exactly double to that of an octave higher. The sounding length of two octaves above the open string is only a quarter of the open string. The frequency of the vibration is also 4x as fast as the open string. It is as if we don't use now the whole instrument, but only a shrunk version: we use only a quarter of the string.
Would the instrument be smaller, we would naturally choose a different contact point, related to the small size of the instrument.
Concerning the contact point, we need to change the contact point according to the sounding length of the string.
As an example, when we play an open string and play at the start of the fingerboard, we touch the string at c. an 8th of its vibrating length.
When we play one octave higher (at the point of the harmonic, but not using it and pressing the finger down) the sounding length is exactly half of the open string. That means, when we play on the same contact point as before, we touch the string at a quarter of its length! We will crush the string easily; we need to half the distance to the bridge to get the comparable contact point.
When we play two octaves above the open string, our original contact point will touch the string at the middle of the sounding string. This compares to the middle of the open string, when we play the open string. This would be so out of the way, it is inaccessible because of the build of the instrument, and if we try, it doesn't work.
We found out before that the three different contact points a), b) and c) have a certain effect on the sound. The contact point can only account accurately for one length of the string. In this case this is the open string and the first position since there is quite a tolerance within each range.
For a full understanding of the contact point though we need to describe it according to the sounding length of the string. That means that all characteristics for eg. the medium range, the most frequent area of playing, is not always in the middle between bridge and fingerboard. This location is the middle value for first the position only. When we go up into the positions, keeping the same contact point and pressure can sound awful. All relationships concerning the contact point will shift dependant on where we put the finger.
One detail needs to be considered independently of the sounding length: As mentioned before the string is not flexible extremely close to the bridge; we need a minimum distance of at least 4-5 times the diameter of the string in order to expect the whole string to react and not the harmonics to dominate. This minimum distance relates to the diameter of the string (and not the absolute length) and seems to appear as a constant; it interferes with a perfect calculation according to the sounding length only.
Many players experience that the sound gets squeaky in the high positions eg. when they play a scale over 3 or 4 octaves. The reason is simply the lack of consideration for the change of the length of the sounding string and accordingly the need to shift the contact point to the bridge.
Especially on cello many players play the A string more towards the fingerboard than to the bridge. The reason is a lack of control in bow direction and bow tilt (see Exercise 1b / 2b)
EXERCISE (4a) - Finding the best contact point
The easiest way to find our best contact point for a passage is like this: we play a passage with our normal bow speed and pressure, starting at the very bridge (This will sound scratchy) During the passage and repeating several times we move gradually away from the bridge until the sound is clear and stable throughout the whole passage. This point of contact is the very best for this passage.
Other passages, with different dynamics, character, bow length and height of left hand position will demand a different point of contact. We have to test again.
This sounds like a lot of work. But then, the test takes only a few minutes, and once we have done it ten or twenty times (less than an hour of our life) we acquire already quite a solid knowledge.
In (natural) harmonics the string sounds always as a whole. But it divides itself into (even) parts, and each part vibrates like a complete string with still points, beginning of the vibration to the large amplitude and declining again to the still point from where it moves to the next identical section of the harmonic. As we learned before, playing close to the bridge encourages the string to produce a large amplitude not in the middle of the string, but in a segment of the upper part of the string close to the bridge. Because of the nature of harmonics, this section becomes multiplied into even segments throughout the length of the string.
The closer to the bridge we play, the more divisions - higher harmonics - we are able to produce. This means too, if we want to play just the first harmonic - the octave of the open string - we should not go too close to the bridge or the tolerance of this harmonic dwindles.
When we play very close to the bridge the tolerance - the area, where we can play the harmonic - of the first harmonic is very small; when we play at the beginning of the fingerboard, the area where we can play this harmonic is large, in fact, we can hardly play any other harmonic.
The string is capable of sounding as a whole and producing a harmonic at the same time. It is also capable of producing several harmonics at once. The character of our sound is in fact to a large part determined by the root note plus a selection of joining harmonics. This selection depends on our contact point, pressure/weight and bow speed. A scratchy sound has an over balance of high harmonics, a pure scratch is missing the root note and produces only harmonics, sometimes such a high cluster that we can't hear a clear pitch.
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5 - THE BOW SPEED
Bow speed is in my opinion the most neglected aspect in string instrument teaching. In my tertiary studies time was spent on controlling the contact point, bow direction and weight, but bow speed was hardly mentioned. Nevertheless I find today that a conscious use of a variety of bow speeds is what makes our sound alive and interesting. It is the most flexible element. When we change quickly the contact point, it makes a noise. If we play around with weight/pressure, we easily push too hard. But with bow speed we can react very fast. We can bring out a single note within a slur; we can create all kinds of atmospheres, of subtle crescendos with changes of bow speed. It is the most wonderful tool of expression.
Bow speed is inseparable of the theme of 'the amount of bow' to take, these two are virtually one and the same problem.
I divide this chapter into two parts, each representing one part of the process of playing.
a) The issue of the first one is to get the string started, to make it vibrate as a whole, the acceleration of the bow.
b) The issue of the second one is the sustaining sound, aspects in constant speed.
a) GETTING STARTED, THE ACCELERATION PERIOD
The process of getting started needs to happen more often than we think. In fact, every single bow needs the initial impulse of making the string vibrate; there is no change of bow without coming to a standstill before we go the other way even if the time span of the standstill is only very little.
To start a new note takes time. The initial movement with the bow will pull the string in the same direction as the bow moves. The weight applied to the bow combined with the stickiness of the rosin pull the string in one direction. Once the tension grows too high for the string moving to the side with the bow, the string rushes back under the bow, and so the first vibration will occur. This first vibration is in its essence not different than one from a plucked string; it is pulling the string from a standstill.
Now we need to accelerate the bow to the desired speed. That means that if we think about how much bow we use for different notes to achieve an even sound with an even bow speed we need to account for the time it takes to stop, start again, accelerate and finally reach the desired speed. Eg. when we play a 1/1 note (semibreve), the starting and stopping will take about a 16th of the length of the bow. If we play a 1/8 (quaver), starting and stopping will take half of the bow length used! Out of this follows that the shorter a note is, the relatively less bow we need to take to achieve the continuity of sound character.
When we see great performers, it is striking how much bow they use for 1/4 notes or 1/8 (dependent on the tempo) and how little bow they use for fast, detached passages. Most students use too much bow for fast, detached notes and could use more bow for all notes, which allow time for indulgence in a sustained sound.
It is interesting to see how the great violinist Yehudi Menuhin uses an extreme range of bow speeds supplying him with a large range of sounds. (click below to watch)
(this recording runs in over speed; the movements are too fast, the pitch too high; it doesn't make a difference for our observation.
EXERCISE 5a) - Uneven bow length / even sound
I recommend playing a study with 8/8 per bar and a bow division of 6/8 slurred and two separate. If we use the same amount of bow for each quaver without consideration if they belong to the slur or are separate, the separate notes will stand out as louder and rougher. We need to take for every note, especially shorter notes, the time for acceleration and slowing down into account. If we use considerably less bow for the sparate notes, about 1/10 of the bow, the figure will sound even.
COMMON MISTAKES - Attempts to skip the acceleration period
There are different ways players try to tackle the problem of over and over again starting to make the string vibrate. One of the options often exercised is that players start every single bow with a jerk assuring the string will vibrate instantly once the direction is changed. The jerk creates an accent, which is characteristic for many players. As successful as this technique is getting the full sound started, it develops a habit, which once acquired will automatically inject these accents even when a smooth start of the note is required. I have seen especially viola and violin players who inject this little throw of the bow with each change of bow. Naturally their variety of expression is very limited.
Another similar option is to inject a pressure accent each time we change the bow. I was taught by my first teacher that every single note needs to start with articulation. These kind of trained habits have the disadvantage that they happen automatically and don't connect to a musical expression, although they are actually a musical expression and eliminate other expressions.
Another disadvantage of this option is that this habit of applying extra pressure replaces the awareness of how the string reacts at the different parts of the bow or at different contact points. It happens therefore that the extra pressure is applied at wrong locations; for example when the bow has moved towards the fingerboard, the accent creates a crunch, makes a good response impossible instead of creating a better response.
EXERCISE 5b) - Creating sensitivity for the start of a note (see Exercise 3a)
The following Exercise is one of the most helpful for bow technique in general. I recommend, doing it regularly starting with it as a warm up. This exercise can change the sound of a player in days and will over years create a deep knowledge of conscious sound production.
I developed this specifically to control the beginning and end of a note:
1) We play a simple scale counting between 1 or 4 beats per note (each length has its own benefits)
2) After each note we take two beats rest. During this rest we do nothing; we don't lift our weight / pressure. We don't move our (bow) fingers.
The rest gives us a chance to focus on the beginning of the sound production of the note, which is the most critical point - and usually the most neglected one. If we look at the essential technique of playing, we need to change the direction of the bow every few notes or every note. The point of change is our every second experience of playing. During the very first move of the bow into the new direction we either initiate a good sound or a bad sound. The beginning decides if the sound during a whole bow will sound scratchy or clear. If the string does not react fully, often it will not respond and improve to the end of the bow. The very start of the note is the essence of our good or bad sound. I can't overemphasize this moment. Nevertheless it is usually neglected from the first lesson to the tertiary diploma.
3) We rest during the two beat rest on the string with the same weight as we start playing.
(Why? - In most pieces we don't have a rest before the next note. This exercise is a slow motion version of our everyday bow change. We learn in this slow speed NOT to lift our bow at the end of our stroke, eliminate unwanted noises and lack of control; we learn to control this very moment of change).
At the nut, our natural hand weight might already be too heavy, especially on the high strings.
At the tip we will notice, we need to add pressure for a clear start, especially on the low strings.
4) With the same weight as we are resting on the string we start moving the bow in a manner comparable to driving a car:
We start moving from nothing, gain our intended final speed and slow down again to the end of the stroke. The end of the stroke does not need to be the end of the bow.
If we control both, starting weight, plus keep the weight down at the end - and gradually develop a controlled speed finishing in a controlled slow down, we will be amazed, what beautiful sounds we can make: how intentionally strong we can play, how light we can play; how refined the beginning and end of the note sounds.
It also makes us notice if we rush to the end of the note in order to come to the end of the bow, which is unfortunately common but creates an unwanted crescendo. To avoid this habit, we just don’t play to the very end of the bow but only as far as the bow carries us in an even speed and sound.
To give a hint: we best feel the start of every new bow from our elbow, not our fingers or hand. Bow movements are large arm movements and should be perceived and felt as such. We will notice, that our thinking from the elbow eliminates unintended starting noises.
As we will see here below in b) of this chapter, we need to consider also on which string we are playing.
If we are not happy with a note, we might repeat it instead of going to the next note.
b) ASPECTS IN EVEN BOW SPEED: THE DIFFERENT STRINGS
The difference in material and diameter of the strings requires different bow speeds (and weight). The thinner the string, the faster we can play it and the less it can cope with a slow bow. The fatter the string, the slower we need to play it and the less it can cope with a fast bow speed (comparable to the different weight/pressure on the four strings).
In comparison it would be like this (on cello the difference is far more pronounced): playing the A string (E string on violin) is like kicking a light plastic ball, which flies off into the air. The high strings are like plastic balls. Whereas the C string (and to some degree the G string on violin) is like a canon ball of iron; we would just hurt our foot by trying to kick it. The A string we start lightly. We can't play the thin string too slow. The heavy weight "C" needs to be started slowly and with some weight, and once it is going we can speed up - the iron ball and the bow on the C string. Starting the C string in full speed results often in a harmonic instead the root note.
The key ingredient to a good sound is a high sensitivity for what the string is doing underneath the bow and the capability of reacting quickly to the messages given from the string as they are responded in sound and how the string feels.
For me, the prototype of the correct bow speed, a positive example is the technique of the great cellist Rostropovich. I never heard any harsh, pressed note of him; nevertheless he has one of the biggest sounds a cellist ever produced. As a student I thought, he would push the bow very hard, but has a cello to get away with it. The more I got to know about bow technique, the more I realised: his big sound is often played with a light bow. He has the perfect feeling for the combination of the highest possible bow speed related to the contact point and the pressure he applies. Both, pressure and contact point are less flexible; the element to work with, to go to the limit is the bow speed. We need to develop a feeling of how far we can go until the string splits into harmonics, the sound "breaks". Rostropovich is the master of the feeling where this limit is. - On the violin, Jascha Heifetz, David Oistrakh and Augustin Dumay belong for me into the same category; they never produce a scratchy note, the realise the limit before it happens, although I don't connect hem with the hugeness of sound of Rostropovich.
D - THE BIG COMMON MISTAKE: THE (DISTRUCTIVE) TAUGHT STANDARD
Example: Strips / stickers used as bow division marks
We should imagine that a musical instrument is taught with a focus on sound. But often it is not so. Unfortunately a large majority of students start to play an instrument with a kind of chart on what to do, a kind of good behaviour kit for string instruments.
To this chart or kit belong technical instructions, which don't consider the kind of instrument, of string or bow, not even kind of age and hand, and not even sound!
The kit includes instructions on how to hold the bow and how much bow to use, independent of dynamic and string.
One of these instructions in training students is to divide the bow into even quarters. This is recommended by the Suzuki method.
Every quarter is treated the same, on the nut or at the tip. The quarters are used for a large variety of tempos (!) and for all dynamics (which virtually disappear) and for all strings.
Most students trained like this suffer from an inflexible, unmusical sound with no phrasing.
I had several students coming to me complaining: my sound is wooden (rough); it's just not nice. Do I need another cello or do I do something wrong? They were often musical students. They felt guilty or wrong to start a bow slowly, not heading straight for the division mark or to the very ends of the bow.
The habits created by quarter divisions are disastrous.
musical students are made tp play unmusical.
The division does not leave space fopr dynamics, does not leave space for the difference of strings; it kills aural perception and replaces it with an unmusical attitude of things to do and not to do.
The taught standard (and wrong belief) is:
1) Never experiment and try out anything.
2) Follow only instructions.
3) All parts of the bow need to be treated the same.
4) We neglect the different treatment of strings.
5) We play all dynamics with the same speed of bow.
6) When dynamics could upset bow divisions, we better leave them out. If everything sounds the same it does not matter.
7) This strict technical instruction is better than letting the students find their own division and amount of bow by intuition and is better than flexible instruction.
8) Neglect the quality of sound. Don't ask questions. We don't instruct musically, but technically. This is just the way an instrument is played. Don't search for a certain sound, just go on.
9) To kill our intuition to react on the sound the bow produces is a good way to become a fine musician.
Does this sound absurd?
How many of us were fed with all kinds of instructions without the teacher being able to explain any reason! And why? There was no reason except the teacher was taught in the same way, not asking questions.
The experience of being able to improve sound with knowledge is unknown. Most teachers believe, when we correct and again and again the bow hold and our finger movements and play with "feeling", the good sound will come.
Often it doesn't. Many students are dissatisfied with their sound. They feel limited by what they are allowed to do. They have no knowledge on how to improve simple problems like a sharp, scratchy, weak or forced sound.
I repeat here, that I asked some beginner students of mine to keep exactly "this" strength of sound, mf or f from the very nut to the very tip; encouraged to listen very carefully most of them manipulated skillfully the bow with all its complex changes in pressure & weight, without actually knowing what they were doing!
Even a beginner student naturally searches for a good sound, will choose a suitable part of the bow, and gives in to a certain degree to the demands of the different strings.
How beneficial would it be to preserve this intuition and just enrich it with some guidance and knowledge!
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E - THE THREE VARIABLE ELEMENTS WORKING TOGETHER
The effort in producing a sound with the bow has boundaries from two sides:
1) We need to make the string vibrate as a whole, get it going as soon as possible and maintain the vibration; we need a certain minimum pressure, minimum bow speed and enough distance from the bridge to get the vibration of the whole string started.
2) At the other end we must not exceed a maximum pressure, a maximum bow speed and not too much distance from the bridge (above the fingerboard); otherwise we will drag the string to the side to which the bow is moving, the string suffers under too much pressure and can't vibrate back and forth. It feels as if the sound breaks; with enough pressure a donkey like noise might appear.
It is artificial to treat the three variable elements separately. They work together and against each other. I use here as an example the extremes, playing very loud and very soft.
PLAYING THE LOUDEST FORTE:
The loudest forte we can play - according to above:
a) heavy weight / much pressure
b) contact point close to the bridge
c)) fast bow speed.
If we try all variables together we will realise the pressure needs to be immense to make the string respond in a fast speed and close to the bridge; in fact we experience a limit. The breaking of the sound into sharp harmonics demands we give up one of the extremes or two or a bit of all.
When we give up the fast speed, it will work; when we give up close to the bridge it will work until the pressure is too high for the contact point; when we give up the high pressure we need also to reduce our bow speed dramatically. We will be surprised how strong the sound can be with less pressure. Pressure is needed; more pressure causes a larger amplitude up to a limit; this limit is also determined by the bow speed; beyond the limit of the largest possible amplitude higher pressure will reduce amplitude and volume in the same way as a slower speed would cause it.
PLAYING THE SOFTEST PIANO:
The softest we can play:
a) very light
b) above the fingerboard
c) as slow as possible for a continuous sound.
If we try all variables together, the sound will be so soft that we need to call for silence and switch off all noises in the room in order to be heard. This extreme can exist in a concert hall at the disappearance of a very soft note - when the audience is silent and we can hear a pin dropping. This kind of pianissimo is useless in any passage.
We can play a good piano sound by giving away one of the variables or a bit of all.
We should keep in mind that the instruction "piano " covers two kinds of expressions. The first has the meaning of "soft", the other the meaning of "quiet".
We can play a very soft piano light above the start of the fingerboard with quite a high speed. We receive a soft, but quite voluminous sound Good examples are the Brahms Sonatas in G major, d minor (violin) and the Sonata e minor (cello). This kind of piano is often indicated with dolce. If played extremely light with a fast bow speed in pianissimo, we call it flautato.
The other character of piano - quiet - we play with little bow, small amplitude, in the middle between bridge and start of the fingerboard; it is used when we play unimportant figures, not belonging to the theme, as it occurs often in chamber music accompaniment figures; we give another instrument the chance to stand out.
I have heard often the statement, that we should play piano closer to the fingerboard and forte close to the bridge. I hope that this simple theory has by now been modified:
In high positions we need to move closer to the bridge.
In slow bow movements we need to play closer to the bridge.
On the highest string we need to play closer to the bridge.
I mention here some typical examples, where we need to play close to the bridge in piano: For violin: the beginning of the Bach d minor double concerto. For cello the beginnings of 'The Swan', Rachmaninov's 'Vocalise' and the slow movement of Haydn's cello concerto in C major. We should play so slow and so close to the bridge that the sound is clear - if we come too close to the bridge, the sound can break; if we are not close enough to the bridge, the sound can tremble and feel squeezed. We should also have the feeling of having always a bit of bow left over, to play a tiny bit closer to the bridge than necessary; this gives us more freedom of interpreting and not being limited by the length of the bow.
Here an interesting question to one of our great violinists in history, Antonio Vivaldi:
Why did Vivaldi chose to instruct players to play as close as possible to the bridge (ponti) in pianissimo when he knew that you need a quite high pressure to get a clear pitched sound? The answer is simple. He didn't want a clear sound. He wanted by purpose the icy sound of the high harmonics, the sound we usually avoid.
When we know the reasons why a note is clear and not clear, of course we can choose by purpose an unusual character of sound. The same understanding which makes us master the good and clear sound, makes us master the purposefully bad, harsh, icy, dark and donkey sounds.
THE DIFFERENT STRINGS
The E string (A string on cello):
As the thinnest string the top string needs to be played as relative to the others
a) lighter, especially at the nut
b) closer to the bridge
c) with more speed, especially at the start
The G string (C string on cello)
As the fattest string it needs to be played as relative to the others
a) heavier, especially at the tip
b) more to the fingerboard
c) with a slower speed, especially at the start
The E string (A string on cello) has a certain sharpness. For soft passages we might choose to play instead in a higher position on the A string (D string on cello).
On most cellos the D string is the string with the least volume, a volume weak string, ideal for piano. In forte passages from low to high we might choose to skip the D string and go straight from a higher position G string to the A string.
Close to the bridge we need:
a) to play heavier
c) to reduce bow speed
Above the fingerboard we need:
a) to play lighter
c) with a faster bow speed
E1 - DOUBLE STOPS
Usually after a while of playing an instrument we have developed quite a good feeling of how much pressure a string can take, and consequently we don't push too hard. This feeling seems suddenly to vanish when we play double stops. We don't think we push that hard, but we can hear we do so. It seems our natural reaction to play lighter on a harsh sound, stops to function. In order to reach the second string, we push instead of reaching and of course the sound is harsh, pushed. We should instead kind of juggle between the strings (play from one to the other) until we find exactly the middle, where we can touch them lightly.
The other mistake is that many players move the bow in double stops too slowly, as if they are waiting to set the balance right, and drag the bow half playing, half searching. Double stops need a higher minimum speed and a light bow.
Another problem is the grinding noise at the nut when we play chords (as in Bach Sarabandes). The reason for this grinding noise is our heavy arm weight at the nut. Chords are usually started at the nut. We might look at the weight table to check the pressure. We easily achieve 10x the necessary amount for a forte! If we start chords at the nut with just our hand weight, adding nothing, suddenly the beginning of the note will be full and round without a scratchy start.
I watched quite a number of cellists to play double stops with a flatter hand than usual and dragging the bow leaning outwards.
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E2 - THE STACCATO BOW
A) In the definition for string players
For string players the name staccato does not refer primarily to notes with a short character as it does with piano but rather to the way the notes are technically produced. The staccato bow refers to notes played successively in one bow direction. In this chapter I refer to the latter use of the name only.
In this chapter I will start with the Exercise and then turn to the description.
1) We hold the bow with the tip hovering c.2cm above the string (see EXERCISE 3b).
2) Now we let the bow down onto the string and let the string carry the bow; the bow might slip;
3) We lean firmly on the index finger;
4) We take all other fingers off the bow (except the thumb of course). Now the bow rests on the string, pushed on the string and not slipping anymore by leaning on the index finger.
5) Without changing this disposition we play a very short bow and stop again(as if we started to play by mistake)
6) We play another and another short note, with just using 2cm of bow while not letting go of the pressure on our index finger.
7) We try the same in a rhythmical pattern of 4 (+4).
This technique works from the tip to the balance point.
From this point on the tip of the bow would not keep balance if we don't put our other fingers down again. Our technique of staccato changes here. We play several accentuated up bows in a row and allow the bow to jump (The dots marking the staccato don't mean that the bow needs to jump).
If we run out of bow we might add a little circular movement at the nut and thus we will be able to continue the jump in up bow virtually continuously on the spot.
By taking the other fingers off the bow except the index finger we are forced to use the pivotal technique. If we are not used to it, we might be surprised how little pressure on the index finger is sufficient to keep the bow on the string. If we are surprised, it indicates that we were still clinging to the habit of holding the bow too tight in order to prevent it from falling.
The staccato bow works only when the beginning of each note comes clear. For this clarity we need a good contact of the bow on the string; we have not to let go of our leaning on the bow. This good contact can also initiate the bow to jump off the string when we come closer to the nut.
Many beginners attempt a staccato
bow by lifting the bow off the string. The staccato
doesn't develop. The lifting of the bow creates a very soft beginning of each note and we will just hear a bit wobbly note instead of a staccato. For staccato every note needs full weight, or we will not be able to hear the rhythmical pattern of the staccato
figure. The bow needs to jump off the string, bounce off as we would jump off in oder to jump high up.
B) - Notes with staccato dots
The characteristic element of the spiccato bow is that it jumps off the string. This technique is often mixed up with a staccato dot on top of the note, indicating a short character of the note. Composers indicate (usually) a musical expression and not the technical execution. That means a succession of short notes has primarily to sound short, independent of whether the bow jumps or not.
If the example above would be taken from a Baroque or Mozart Sonata, we might not try to make the bow jump, but play swift strokes (with gaps to the next note) with much bow in the upper third of the bow, creating short notes without the strongly marked noise of the bounce. This character of short strokes suites melody notes without percussive effect.
If these dots would be written in accompanying parts during the early Classic period, we would emphasize the rhythmical support instead of the melodic flow. As a general rule, the more important the melody is, the more bow we use and move away from the bow jumping; if the note is repeated (as in Mozart and Haydn sometimes 64 times and more) we let the bow jump, providing a rhythmical cushion for the other instrument(s) playing the melody.
For later compositions, from the Romantic period onwards, a dot on a note in a part for a string instrument includes usually the idea of a percussive noise at the beginning of the note. This shift in style has to do with the change of the construction of the bow by Tourte (see chapter F3) and the consequent change of the bow hold and new possible sound effects.
E3 - THE SPICCATO BOW
When we play notes with an accent at the beginning of each note in a quick succession, the bow starts to jump; it does it by itself if we don't counteract. This shows us that notes with accents and the spiccato bow have technically a very close relationship.
I might explain the process of the bow jumping with two common analogies:
1) - When we want to jump, what do we do first? We go into our knees; we go down so that we can jump higher. If we are standing fully straight, don't go down, we can't jump.
2) - If we want a ball to bounce up, we have firstly to bounce it down. Every ball jumps differently and if we want it to bounce to a specific height we have to test this ball. We try how much we need to push so that it bounce exactly to the height we wish. The ball tells us by its reaction what we have to do. We can't make the ball bounce quicker or higher as it naturally does, we have to go with it. In order to be the master of the ball we have to cooperate and oblige.
The same is with the bow. The spiccato bow has two elements: firstly the up and down movement, the bounce, and secondly the right left movement making the sound. First we will attend to the up and down movement, the bounce.
In the same way as we have to test the ball in order to know how we have to bounce it, we have to test the bow. We have to find out how strong we have to bounce the bow on the string to make it jump up to a certain height - which is correlated to a certain amount of time. The higher we bounce, the longer it takes. The more bow we take, the longer it takes. The fastest spiccato we achieve with very small strokes (a few mm) and a tiny jump. We need always to maintain a good contact with the string, so that the bow can bounce off.
Once we know how the bow reacts we can apply that much bounce that we know exactly when the bow comes back on the string. This ensures that we can play a regular rhythmical pattern without the bow getting out of control.
Since the bounce is based on the natural properties of the bow, the best place for the spiccato is where we as a player can manipulate the bow with the least added impact. This point is the balance point of the bow. At this point the full weight of the bow rests on the string, right and left divided into even parts. We find this place out by holding the bow between two fingers and watch that neither of the sides go up or down.
The spiccato bow relies on the bounce, relying on friction with the string. As an exception this technique works best when we play with a bow tilt where all hair touches the string; we give up our normal tilt.
To get to know the bounce quality of our bow we find the balance point and bounce the bow firstly without right and left movement, silently. We take three different speeds for the bounce:
a) slow 1/4, moderato speed, the bounce is quite high
b) 1/8, based on the same crotchet speed; the bounce is lower;
c) 1/16, based on the same crotchet speed
d) We try the same sequence a),b),c) in a quicker speed
e) Once we have gained a good feeling for the natural bounce at different locations - a hand width more to the nut as well as to the tip. We also attempt different speeds.
f) Now we add the second element of the spiccato bow, the right and left movement. The bounce is only effective when we don't use too much bow. So we add a tiny bit of right and left movement, half a cm to 1cm, not more. We can observe the amount of bow used by watching the end of the silver wire. When we play the 1/8 or 1/16, we should - to start with - play every beginning of the beat with a down bow and accentuate every note coming on the beat.
E2) Another method to approach the spiccato bow is starting from the bow resting on the string. The spiccato bow has a strong accent at the start and then bounces off. This is similar to any note with an accent with the difference that usually the accent fades into a softer dynamic with sound instead of a break. When we play short notes with an accent in quick succession, the bow starts to jump and the movement turns naturally into a spiccato bow. We need to keep in mind to arrive for the next note with enough pressure on the string to play the next accent. The bow needs to land down on the string at every end of a note (which is the beginning of the next note) and use the pushed down string as the trampoline to jump up again.
Many beginners starting to try out the spiccato bow, use too much bow. The bigger the movement, the slower and clumsier is. Usually between 1/2cm to 2cm is plenty.
The second mistake is often that the spiccato is played to close to the nut. Beginners feel they have more control there. However it doesn't bounce there by itself; it is heavy and clumsy. We need to go at least to the balance point and just trust that the bow can bounce. The more we shift the play area towards the tip, the easier we can apply regular pressure. As we know the pressure gets less effective towards the tip. we can use this fact to push the bow quite strong and with high regularity, but with little effect of pressure. tis ensures an equality of pressure and a higher control. We can watch here the spiccato areas of Jacqueline Dupre and Yoyo Ma in Elgar's 2nd movement of the cello concerto. the amount of bow with both is not more than 2cm per stroke.
HINT FOR PRACTISING SPICCATO PASSAGES
Often spiccato passages demand fast left hand fingerings, which can be technically hard and can lead also to coordination problems between right and left. The best method to tackle the problem is like that:
We slow the speed right down and keep all techical details the same including the amount of bow. The pressure on the string is as normal, the same as in speed; the contact point on the string as well as the part of the bow need to be the same; also we use as little bow as in speed - usually c 1- 2cm. Between all notes will now occur a rest; the notes will sound jerky, it feels like stuttering on the string. During the rests we prepare our left hand. We play the whole passage about three times in this jerky slow miniature movement mode. Then we play it at the required speed. The run will flow with a much higher precision than before.
The sautille bow
The sautille bow is a very quick spiccato bow, in speed of a tremolo. Its effectiveness depends on the right place of the bow. The best place is on most instruments are just beyond the middle towards the tip. By changing strings we need to observe that the tilt of the bow doesn't alter.
Famous sautille passages with string crossings are the arpeggios in the Dvorak Concerto for cello, or in the Mendelssohn Concerto for violin. In both cases the success of the sautille depends on finding the right place on the bow and the right contact point. The shortness of the stroke needs to be maintained as well as the control of the bow tilt. As soon as the player uses too much bow or changes the tilt of the bow, the sautille bow will turn into a legato arpeggio. We need to apply as much pressure as for a spiccato on one string at this contact point and place of the bow.
Students try often to carry the bow, holding it instead of bouncing it down and trusting that the string will bounce it back. When the bow lands on the string with not enough weight the bow will stop jumping.
The spiccato bow often also stops jumping with the change of strings. There are two reasons, one, that the weight application changes with the string change by not letting the arm follow the bow movement (when a player uses wrist and movement only), and secondly often combined with this, that the bow tilt changes. The bounce ability changes dramatically when we change playing with all hair to playing with an edge only.
I advice playing the critical passages slowly through and watch the bow tilt, feel for the change of weight between the last note on the old string and the first note on the new string and try to have the same weight application. In speed it can help to give an extra little bounce on the last note of the old string.
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F - THE BOW HOLD
The great cellist Gregory Piatigorski taught that the fingers on the bow hand have to touch each other; the great violinist Wolfgand Schneiderhahn taught that the fingers need to be held separate to cover a larger area. Nicolo Paganini held the wrist very low; Fritz Kreisler held the wrist very high. Pablo Casals held two fingers on the stick, two on the nut; Cassado/Totellier taught that the 2nd finger is the centre and is placed on the ring; Andre Navarra taught that for many strokes the bow can be held with only index and little finger and let fingers 2 and 3 loose.
I learned with Marcal Cervera (Cassado/Tortellier school) to play with very active finger and wrist movements including studies played with a still lower arm.
I learned with Christof Henkel (Starker school) to avoid active finger and wrist movement; I learned to lean my arm always inwards; I observed the great cellists Rostropovich and YoYo Ma doing the opposite as well.
Virtually every soloist holds the bow differently. There are certain schools, but in the end, every one finds their own variation. It is disturbing that nevertheless the bow hold is taught excessively dogmatic. Why would that be?
I felt the secret lies in the teacher's own feeling of control and security in his hand. The teacher does its best to convey his/her feeling of comfort and control. To put it clearer, the teachers voice and desire is: "If you would only hold the bow not only close but exactly like me, you could play with the same control as me and manipulate the sound like me; you would understand my persistence." This hope is unfortunately in vain because other fingers with different proportions and nerves feel differently, settle in a different position of security and comfort. I found even a slight difference in posture dependent on which bow I play and on what kind of strings and cello I play.
Nevertheless our position of the hand and fingers is important. I suggest going to Youtube, study covers of CD's and old records, look at photos of soloists in magazines and newspapers, read about options and try them all out. Not every idea works for every hand, but some ideas will be new and open up new feelings and experiences.
The posture of our fingers has NOT much to do with bow technique, but just with comfort and security - which is important. As a student I was intrigued to observe at summer classes how student A (studying with teacher 1) improved by holding the bow how teacher 2 suggests. At the same class student B changed from teacher 2 to teacher 1 and improved also! Today I understand why: By doing something new, different, the students started listening again and improved their sound by reacting intuitively instead of habitually and unresponsive. It had nothing to do with their fingers. Their conscious knowledge of technique had not improved. I observed many cases, where the improvement vanished again after a few weeks and either the old habit or a new habit evolved, neither with improvement of sound.
If any one happens to go to a master class and is told to improve sound and technique by holding a finger different than before, it might be wise not to listen to the words of the master. So many fantastic players teach a standard, often rules they don't follow themselves. They play intuitively well but teach some technically unimportant details. I found it is worth to listen to and watch these masters, but its not worthwhile to listen to their beliefs.
Above all, good players do things in common, as in bow technique so also in bow hold; some of these "things" are visible, others are not. Here are some common aspects of all good bow holds.
Most importantly we hold the bow as light as possible. Once we manage that, we hold it even lighter. Indicator for lightness is a loose thumb. The thumb - opposite to the fingers - has to counter the pressure of all fingers. A light thumb guarantees light fingers; as light as possible.
In my teaching experience every beginner holds the bow too tight, and I virtually expect that the student's thumb might hurt for half a year. The thumb has to counter the pressure of all other fingers and the student is not ready to trust the bow resting on the string and hold the bow lightly.
The posture of the thumb should be: we shake our hand and look how our loose thumb looks like; this is the correct posture of our thumb on the bow. No pushing in or out. Everyone has their own posture. In general I found a higher position of the thumb usually relaxes the thumb more.
EXERCISE 6a) - Elimination of the fear of dropping the bow
Especially with beginners the one reason that the bow is held to tight is the fear of dropping it. The attempt of playing light does not even risk holding the bow really light. In order to experience real lightness, we eliminate the fear of dropping the bow:
We leave our instrument in our practice room and take our bow to the bedroom. We hold the bow above the bed. In case it drops, it will fall soft. We rest the tip on the pillow. Now we loosen our grip very gradually. Instead of holding the bow up, we lean a tiny bit on the index finger, just enough to stop the bow from slipping down the pillow. We completely relax the whole hand, the whole grip.
For a few times we also might gradually allow the bow to drop on the bed; that gives us the knowledge of how little is necessary just before the bow would drop.
We go back to our instrument and hold the bow as light as possible. We might repeat this exercise on another day until we are sure that the lightness of our bow hold on the instrument is the same as above the bed.
Tight fingers don't allow the bow to vibrate and don't allow the hand to be flexible enough. The bow needs to be allowed to give in to the vibrations of the string. As a safeguard against losing the bow we have a natural reaction to tighten the bow when we play stronger or faster. We can trust that playing very light is secure.
F1 - THE DIFFERENCE OF CELLO AND VIOLIN BOW HOLD
Some violin teachers teach cello, some cello teachers teach violin. They should be aware of the following: Considering the different positions of the instruments, we hold for both instruments - violin and cello - the bow very similar. Because the violin is up high, the fingers lie on top of the bow, including the little finger on top. Coming down to the cello, this posture would be uncomfortable for the wrist, so we give in and let the fingers slip over the stick until the fingertips reach over the ring, including the little finger.
F2 - ADJUSTMENT FOR BAROQUE MUSIC
Our present construction of the bow was invented by Tourte during the early Beethoven times. The sound we can produce with his construction formed the sound for strings since his time - although Tourte did not play an instrument! This single master developed first the movable nut to tighten the hair, then later the concave shape, the kind of curve, constructed the tip, he determined the angle of wood cut, the heating method and the kind of most suitable timber! No one has improved on his ideas since.
The more we shift the fingers towards the nut end, the harder, stronger and accentuated the sound becomes. This is suitable for Beethoven, Brahms to 20th century music. For early classical to Baroque music we might choose to shift our hand on a normal bow slightly towards the middle of the bow. At this place we can't use the strong pivot between thumb and index finger any more and the beginnings of the stroke turn softer, accents are less pronounced, the whole sound softens; we can't produce a Dvorak ff anymore.
I find experiments with Baroque bow hold highly interesting: We tell more or less a student to give up all beliefs in bow hold and just hold the bow different. We tell them: it's Baroque, and suddenly its ok., even for the most stubborn fanatic in bow hold! Although this new bow hold has certain characteristics, it will sound like us, we will play as well and as bad as with our usual bow hold. I compare it to the "Piatigorski" experience (see INTRODUCTION). Although the player has never played with this bow hold, he/she can manage after one minute to play with the Baroque bow hold as well as with the usual bow hold! Our technique is unaffected.
I found though that one technical mistake seems to creep in with the change: In our usual bow hold we use the index finger as a lever and put pressure on it. In the Baroque bow hold this habit in the index finger tends to pull the bow into a slanting direction - we lose playing parallel to the bridge. It seems essential to watch our bow direction more than usual, be aware and even practice playing in a straight line - even if we do it correctly in our common bow hold.
F3 - STEADY HOLD
In general we attempt to find a position for all our fingers to be able to play at the nut and at the tip with exactly the same touching points of the fingers at the bow - nothing should change; this constancy gives us security in every playing situation.
Some players play especially double stops with an altogether flatter hand as they play usually.
Some player's hands are too dry or too sweaty for a constant grip. We shouldn't be worried about that. These players should practice smooth repositioning. The tip is the best spot for that.
I observed fantastic players who reposition their little finger virtually every time they come to the tip - and it doesn't affect the flow of their play.
A LAST WORD TO THE BOW HOLD
Some of my student friends went to study with a famous teacher at the time, who let them play for a full year open strings. They were not even allowed to use their left hand at home! In my first year in Australia, this teacher gave a concert in Melbourne. His sound was terrible. He must have been c 65 years of age, and every single note was pushed, unpleasant.
It went through my mind, that this man, whose edition of the Beethoven Sonatas I admired - his fingerings and bowings were impeccable - just had problems with the bow.
Might it be, that every student had to go through the painful process trying to master the production of sound by focussing on hand posture and movement.
The process of sound production must have remained obscure to him to his old age.
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G - THE BOW ARM
Our bow arm is for our technique more important than our hand. Compared to our left hand, where the millimeter position of a finger determines our intonation, the movements with the bow are big, larger than our fingers can stretch and faster than our wrist can move. In a piece of music we often alter our left hand by 2mm and move at the same time our bow twice half a meter. Bow movements are large and are executed with our arm, not our fingers, and not our wrist.
Still some teachers believe that we play a tremolo with our wrist. The wrist is one of our slowest moving joints. Often we might think, we move the wrist, but really, we shake our hand from the elbow. Our elbow can move as fast as a rabbit scratches and makes our hand shake. Even our small bow movements are best initiated from the elbow, as if the brain of our bow movements sits in our elbow joint and organises the bow, asks the upper arm for some help and orders the hand to shake.
To support this activity from the elbow we hold the elbow in an active position - not too low. We also roll the whole arm a tiny twist towards the instrument: the hand turns slightly to lean on the pointer finger and the elbow moves slightly out and up. With this slight twist we economise our body to use weight and pressure more efficiently (the shoulder needs always to be relaxed and down).
I found the focus on the energy coming from the elbow and the slight twist in the arm one of the few single technical elements of posture, which contributes to a good sound. Focusing on this way of thinking, within 5 minutes the sound can change. We can view the bow plus the hand as a unit, which starts its movements form the elbow. Fingers give in like the hair of the bow.
The slight twist or roll supports the gradual change from weight to pressure. Going to the tip, with the elbow moving a bit up, a natural pivot acts between thumb and index finger; it seems that we do nothing additional to exert pressure, it occurs naturally.
H - THE EFFECT OF ROSIN
Rosin is this fantastic stuff that makes the bow hair work. Without rosin the bow just glides smoothly over the string, just as a turned upside down bow would do it, just gliding along on the stick.
Rosin is in fact a natural glue. Our bow hair has layers of microscopic scales, which make the rosin get trapped along the edges when we rub it on (artificial fibres are too smooth and rosin doesn't adhere).
Bow horsehair under the microscope. Note the edges.
The rosin- glue pulls the string at every vibration to a position of a certain tension, which ensures that the amplitude of the string can remain the same, if our pull is the same. It has also the property that the amount of rosin doesn't alter the situation too much - it does it a bit. With most glues we could expect that a bit too much or too little could change the reaction dramatically, like bow and string sticking together and after half an hour stopping to have no effect. It is not too sticky as to drag the string too far. Rosin somehow produces the same result for hours, even days of play. Rosin has the admirable quality that it sticks just the right amount and lasts exposed on the bow for weeks.
Nevertheless more or less rosin has an effect on this. More rosin makes the bow more sticky and increases the friction. Therefore when we freshly rosin the bow, the sound is suddenly rougher, as if we would play harder. Usually we push the bow down more to increase friction; rosin does the same, it increases friction. With more rosin we play as we would with more weight without being aware of it and without being habitually used to it. We can make up for this uncontrolled effect by tilting the bow with fresh rosin a bit more than usually.
TOO MUCH ROSIN
Many players use too much rosin. The purpose of the rosin is that the hair sticks to the string, but too much rosin has the effect that the hair does not touch the string itself but instead the rosin on the string. Rosin are tiny sandy particles like glue granulates and when too much fresh rosin is on the string we hear rosin on rosin like sand on sand; granulates rubbing aginst each other. The sound is rough and actually inhibits the string from reacting fully.
After putting rosin on the bow we should clean the string a few minutes afterwards so that the rosin of the bow will pull the string again and not rasp along the rosin on the string. It is surprising how much clearer the string will sound.
I recommend strongly not to rosin the bow every time we practice, but about every third practice and not freshly just before a performance but ten minutes before the end of the last practice before the performance. Fresh rosin increases the friction and can make the bow react unexpectedly strong, the bow can jump away in spiccato as if we push too hard.
Nevertheless we need enough rosin. We should not need to push for the start of the sound, but the grip with the string should occur quite naturally.
I - THE BAROQUE BOW / playing Baroque music with our bow today in Baroque style
The bow during the Baroque perio was held more to the middle of the bow.
The bow bend concave instead of the convex bend of our bow today.
the nut/frog could not be shifted.
Some bows were held more like our bow, otheres like the viola da gamba, where the middle finger has to tighten the string.
Altogether the tension was much lower.
The bow was not played at the very nut at all.
Because of the lower tension the weight we can apply was totally different.
After the reconstruction by Tourte around 1800, the bridge was recunstructed, then the neck and later also the strings.
Since the reconstruction of the bow by Tourte c 1800 we can apply on the nut/frog a weight of 5-10kg, whereas in the middle and upper third the limit is c 700g .
The weight of 700g is slightly above the limit we can apply with a Baroque bow in all parts, due to the low tension of hair.
Harsh accents, instant accents like we know it fro Beethoven or Brahms were impossible.
Therefore Baroque music should be playedwith our bow today in the middle to upper third of the bow.
There the accents are softer.
Also stronger dynamics are achieved rather with using more bow instead of pushing down.
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- THE NATURE OF OUR STRING
When we hear a siren we can estimate from the pitch of the noise how much energy is used to propel the siren. The higher the pitch, the more energy is used; the lower the pitch the less energy is used.
With a string it is a totally different matter. The pitch of a string is independent of energy. It is a potential, which can be transformed into sound when we apply energy. The more energy we apply the louder the sound will be, the larger the amplitude of the string; but as for its pitch, it remains the same, from the softest to the loudest sound. The string seems to have an inherent persistence to keep its pitch against all odds, it doesn't matter if we pluck it, blow against it or even play it with the bow.
I will compare this behaviour to another related vibration we are familiar with:
In 1596 Galileo was sitting in a church and - obviously a bit bored - turned his mind to different matters. He made a strange discovery: the lamps swung in an absolute regular rhythm, independent from the amplitude of the swing. The same we can observe with a swing in a playground: if fast or slow, high or low, it will pass the pole in a regular rhythm. The impression of getting quicker stems from the gain in hight and therefore speed: to make it in time for the pole, the swing needs to go quicker the higher it is.
This behaviour is called the pendulum principle and it is so precise and reliable that it became the principle we rely on to tell us the right time. The pendulum of the clock goes one beat per second. Even if we push the pendulum, it will just wobble a bit but then continue with its regular beat with a stubborn persistence. The pendulum is pulled every single beat by a tiny hook, which brings it back to its starting position, so that the amplitude of the pendulum doesn't die down and stops.
Exactly this stubborn persistence we find in the string. It seems natural to us that the string does not go up in pitch when we play stronger (although this can happen with a bad quality string; instead of only the amplitude getting larger the low quality material stretches). All instruments are based on the total reliability of pitch. After the piano has been tuned, the "A" is an "A" even when we don't play it, when it is silent. On some instruments the name is written on the silent key. The potential counts and is predictable.
But there is one major difference between bowed instruments and other instruments with strings. With a piano, a guitar or a harp we initiate the sound, and once vibrating, the string is left to itself until it dies down - as the pendulum would die down without being pulled by the hook. But the bow pulls the string back to its original position with its tiny hooks, sticky with glue, in the same way as the pendulum in the grandfather clock.
The pitch of our "A" tuning fork is 440 Hertz (vibrations per second). The pitch of the grandfather clock is a 1 Hertz tick (if it is set up properly!). Although we can't perceive the tick of the clock as a pitch, it has the same characteristics, and leads us to assume, that for nature in general - though not for human ears - it is a sound: a sound too low to be heard with our ear.
We have probably all observed, that when we play a note, an instrument close by will pick up this note and start resonating, like a willingness to join in. In fact the other string will even join in, if the pitch is very similar, not exactly the same. And not only the one string will join in, but all strings, which are in the row of natural harmonics (see next chapter). E.g. if I play a low D on the cello, the open D string and the A string will join in. When I suddenly stop the bow, these open strings continue to ring. All instruments in the same room will join in, just a bit softer.
This correlates to an interesting parallel behaviour of the grandfather clock: when one clock ticks in one room, the other clock in the room will join in. If they are a bit out of time, they will assimilate and tick together; if one is set a fraction faster, they will assimilate. They show the same tolerance as the strings. This means, that the second tick is not a series of one time off events. The clock perceives it as a pitch, which can be distinctively picked up. The stubbornness of our string and the reliable constancy of the second tick is exactly the same thing. Geometrically the speed pattern of both is a sinus curve. Only forceful intervention can interfere with this physical behaviour - like stopping the pendulum with the hand or pushing the bow too hard on the string.
Any physical body able to vibrate has its specific vibration, its specific pitch; some resonate better, some not so well, dependent on the consistency of shape and material and of course the ability to vibrate at the location they are: a tuning fork does it by pointing up freely, the same as a high rise, a lantern or Centrepoint Tower in Sydney. They spread around them their vibration, their sound initiated by the wind, too low as we can hear it, and all bodies able to join in vibrate in their pitch or row of harmonics. We often see trees in the wind swaying together, similar in size and material, joining in harmony.Perhaps we are surrounded by much more sound and harmony as we imagine or as we are able to hear (even if our perception is not killed by earphones blocking our ears).
We can hear the vibrations of the audible harmonics (see next chapter about the nature of harmonics); we can't hear vibrations beyond the range of our ears. But vibrations can go as low or lower than 1 Hertz and much faster than our range of hearing, c 20 000 Hertz.
Is there is a connection to much higher harmonics? During history, musicians, painters, scientists drew parallels from musical vibrations to further dimensions. Many believe that the range of colours is an extension of musical notes and keys, in the mathematical ratio of harmonics.
I am interested in the general perception: we have a vibration / wavelength and if we add energy to it, it becomes effective. E.g. if a light beam enters from outer space, may it be white or coloured by a red shift, it has firstly a potentiality, which is its colour, secondly it has an energy level, which makes it more or less visible.
Scientists like Albert Einstein, Stephen Hawkins were hoping to find the formula for everything. They based it on energy. But what was first, the energy or the wavelength energy is driving on? The wavelength / vibration is defined without energy, before it, like a string in silence - not vibrating, but confined to its pitch - or colour. There is no energy without vibration, without a wave length. Perhaps if we look for the first origine, waves / vibrations give us more of an indication than energy.
- THE NATURE AND HISTORY OF HARMONICS
A vibration does not only trigger off its own pitch on another instrument but also other notes. These are the natural harmonics of this note. It also triggers off lower notes, which include this note in their row of harmonics. As mentioned, when I play a low D on the cello, the open D and A string will resonate, which are the second and third harmonic.
But also, when I play the open D string and hold the first finger down on the C string to play the note D, this D will start resonating. It will resonate with the octave above, which is the note played with bow, and not the note hold down.
Harmonics are straightforward, even divisions of the string by 2,3,4,5 etc.; the string divides itself into even parts. Each partition vibrates with still points in between, or knots. We might know this behaviour also from a skipping rope: We give it a twist and the rope splits into a double swing with a still point in the middle. Each of the partition has exactly the same size, e.g. the partition into 5 splits the string into exactly 5 even parts with 4 still points in between.
The speed of the vibration relates exactly to the division in space: If I split the whole length into 2 equal parts, the frequency of the vibration doubles. If I split the whole length into 5 parts, the frequency will be 5x of the whole length vibration.
The first harmonic (split into 2) is the octave of the root note,
the separation into 3 parts is the fifth (plus one octave),
the separation into 4 is two octaves above the root note (2 x 2),
the separation into 5 is the third (plus two octaves)
the separation into 6 is the fifth (3 x 2 - plus two octaves)
the separation into 7 is the seventh (plus two octaves) - actually a bit lower than our 7th,
the separation into 8 is three octaves above the root note (2 x 2 x 2)
the separation into 9 is the ninth (three octaves plus 1), which is also 3 x 3, the dominant of the dominant.
Often we can't hear all divisions, because harmonics follow the mathematical principle of canceling each other out:
e.g. 1/6 is audible;
2/6 equals 1/3 - we hear 1/3;
3/6 equals 1/2 - we hear 1/2
4/6 equals 2/3 - we hear 2/3 = 1/3 harmonic
5/6 is audible (equals 1/6).
In terms of vibration, the calculation is easy: A division by 2 gives double the speed; a division by 6 gives 6x the speed. One octave above the A of 440 Hertz is the A of 880 Hertz.
The ratios of the harmonics when discovered caused a revolution. In Western culture the discovery goes back to the Greek mathematician and philosopher Pythagoras (c 600 BC). At this time, their measuring sticks were crude as anything, guesswork. Now, with the absolutely accurate division of harmonics, the musical string was the ideal device for measurement. But not only that.
Up to this time mathematics including geometry were seen as a human invention, very practical though for the purpose of land division, but nevertheless imposed. Nothing in nature showed that perfect triangles, squares or division and multiplication were a given thing by "the Gods"; it was low and practical. The musical string became the birth of physics, the practical implication of mathematics on nature, the proof that mathematics and geometry was a "given by the Gods"! Pythagoras got so exited he exclaimed: "God is number!" and as he found the newly confirmed principles of music in the spheres, he called the movement of the stars: "The music of the spheres!"
Looking at the typical stubbornness of the string - he could see the same stubbornness in the orbit of stars and planets. What surprises me with the orbit of planets, is that when they are hit by a meteor, they just wobble and continue their orbit. It seems too stable than just the balance of gravitation and escape velocity. It seems not impossible, that the vibration of our earth with a "Hertz" of one year is similar to a sound wave, elliptic, a double sinus shape, as stubborn, of the same nature as the string and not impossibly sending waves in some form related to its "pitch", might it be a field of gravity or light / energy we can't perceive. Was there more in Pythagoras' feeling for what is connected to his discovery as we think today?
Pythagoras did not know that our micro cosmos is a mirror image of our cosmos. As mentioned before, our Western culture is focused on energy. But don't we get the stability of our world from the stability of vibrations? Energy is flighty. We need to check a cable if there is energy flowing in it at all. The cable with or without energy has the same colour, has the same mass based on the stable orbit of electrons. Like the pitch of the string, the orbit is stable; not up and down like energy.
When a heater heats up, colour and shape do not change. In our everyday life we rely on the fact that the clothes we put on in the morning are the same as in the evening before, that the steps in the dark are the same as during the day: No up and down in size and shape dependent on energy. We rely on the total persistence of orbits / wavelength / vibrations. Like the name on the key of the piano, we rely on the persistence and stability of materials around us. Can gravity, the compatibility of chemical elements be explained with harmonics? I talked to several physicists: but no one could answer me, no one researched this direction.
A Roman average student knew more about harmonics than our high school students or even a recipient of a diploma in music and musicology. Our time bypasses to a high degree knowledge and recognition of music, vibrations, noise. Einstein invented a silent fridge and for a decade he could not find anyone interested in the project. His model is lost. I would love one.
Typical for Western culture, shortly after his discovery Pythagoras observed the awkward truth about harmonics: If you add up 8 octaves from the root note or add up the 12 fifths of the circle of the fifths, you don't arrive at the same note, but (80 to 81) apart. So Pythagoras decided - certainly not according to his happy exclamation "God is number": Lets change God a bit, and he reduced the natural fifth to our fifth of the Western culture today (including Arabia, which adopted Pythagoras teaching as well) in order to keep the octave perfect.
Later our Western culture introduced also the "well tempered tuning", proposed first by Rumi in 1482, later successfully by Werckmeister in 1691 and heavily supported by J.S.Bach enabling him to play in more than a few keys on the organ, which you can't retune quickly. This change in tuning is the reason that our culturally trained ear feels that natural scales of other cultures like of Japan, and American Indians are for our ears out of tune. If we listen carefully to natural harmonics (details see below), they will seem for our ears to be out of tune, although we started determining what is in tune by natural harmonics!
Interestingly enough the idea to introduce "well tempered tuning" was in China proposed as early as Ho Tscheng-Tien (370-447), but was rejected because of "doing violence to the figures" - Pythagoras too would have been rejected in China! We must mention here that actually Pythagoras was well travelled and well studied. Among the countries he went to learn were Egypt and Persia. Persia was connected via the silk route with China, and China had its knowledge established as early as 2596 BC, two thousand years before Pythagoras. In Chinese philosophy the incongruence between 12 fifths and 8 octaves is seen symbolically as the way of eternal change according to the wisdom of the "I Ching".
The perception of harmonics, although probably subconscious, goes even further back, and as I believe to the very beginning of our language.
In all Western languages (Indo-European) our word for singing or song is identical to the word: swan (Sanskrit: svan). If you have ever heard a swan sing, it is a surprise and an ear opener: This bird has voice chords, which can produce only harmonics! The more exited it gets, the higher the harmonics.
When our ancestors created their first words, they shaped a word for singing: We do now the swan, we sing according to harmonics like the swan!
The natural harmonics are the basis of our major scale as here demonstrated in the key of C:
C (root note/2nd/4th/8th /16th harmonic);
D (9th harmonic);
E (5th /10th harmonic);
F (11th harmonic);
G (3rd / 6th /12th harmonic);
A (13th harmonic);
Bb (7th / 14th harmonic);
B (15th harmonic)
All notes of the major scale are included up to the 16th harmonic!
All other semitones are based on later harmonics, which already lead as well to quartertones. (1)
The next new note in the natural row is the 19th harmonic (18th being 2x9, octave of 9), the Eb, the single most important note in our minor scale, and second note of the triad determining the minor mode determining. The medieval Christian law disallowed to finish a piece in a minor chord, as it was "not wanted by God" - establishing, that God somehow favoured the harmonics 2 - 16, and created harmonics from 17 to 64 by mistake! This law was not broken during the rough and lawless medieval times through to the whole Renaissance.
The 21st harmonic is the first quartertone occurring, absent in all Western scales (it occurs in folk music from Sweden to the Mediterranean; there was and is no notation for it).
The 23 harmonic, the Tritone (the interval from C to F#) was regarded as the devils interval (Diabolus in musica).
If we go to Arabia, although they followed the Pythagorean correction, they indulged into minor scales and quartertones and used them in sacred songs.
When we go as far as India - beyond the area of the Pythagorean correction - using the 27th, 29th and 31st (and even 54th to 63rd) harmonics is used to increase the built up of tension towards the climax in their Ragas for more than a thousand years.
This might give us a different picture of our early ancestors: they didn't sing only on one note, a drone - of course they probably did that too - as we all learnt in an extremely narrow Western perception of the history of music: Our early ancestors sang using our major scale at the time language started to shape itself!
The teachings of traditional Western history of music are: Humans used first one note, like a drone, then 5 notes (the pentatonic scale) then 7 notes and now 12 notes (twelve tone music). The view of this music history has been consistent from the earliest writers like Pachelbel to today's TV shows: Today we are much better and much more intelligent and advanced than our ancestors (not to forget "primitive" cultures using quarter tones, double as advanced as 12 tone music). It seems an overdue task to rewrite the history of music completely.
As humans started to speak, they sang already in a major scale, like the swan does!
As they started to shape their early root words, they were already skilled singers. This might also give us a hint, that the same fine ear allowing our ancestors to imitate birds and critically distinguished how they sing was very likely a precondition for the spoken language.
(1) Our medieval Western culture developed a distaste for the harmonics beyond the 16th, which I still fail to understand.
The 17th harmonic is Db, very important in the Phrygian mode where it is the second note of the scale, important in Spanish and especially flamenco music; the philosopher Aristotle warned not to use this scale, because our emotions might get out of control!
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AUTOBIOGRAPHICAL NOTES / HISTORY OF MY TEACHERS AND TECHNIQUES
I have been a cello teacher for 35 years, during the last 20 years in the Blue Mountains in Australia. Like many musicians I have gone through many schools. My first teacher, Herr Steinhauer, was an old man, who had still studied under Hugo Becker. I learnt playing the cello like codes of good behaviour: That's how you do it, no question asked; the great Hugo Becker told so! To this belonged, that where ever I could manage it, I had to form right angles: the fingers at the bow had to touch at right angles; the fingers of the left hand had to form right angles to the fingerboard, standing upright on the tip forming right angles with the string; the right wrist was kept propped up. The upper arm had to stay at the body except when playing in the upper half of the bow. Right and left thumb had to be forced to be bent at all times, as close as possible to right angles - a duty I escaped at all times except during the lesson (When later thinking about all these right angles, I couldn't escape the association with a swastika - possible curves had all turned into right angles).
I was unable to produce a big sound. When nevertheless carried away with passion it started to hurt in my upper arm and inside the right shoulder blade (if you experience this pain, give your whole right arm a slight anti clockwise turn and let the elbow come up - it will probably disappear).
Piatigorski described Hugo Becker's sound as terrible, the air full of dust (rosin). Unfortunately the quite beautiful collections of Sebastian Lee's studies are still today printed in the Hugo Becker edition. Guidelines include e.g. playing a whole study in crotchets (1/4notes) with the whole bow, independent if A or C string. I remember I felt nearly physically sick from the ugliness of sound when I had to play in the desired "technique".
My first tertiary teacher, Marcal Cervera, had been assistant of Caspar Cassado and worked closely together with Paul Tortellier. He tried to activate my bow hand with all kinds of exercises, including playing Duport No 7 without a mm of arm movement, just fingers and wrist. Bow technique was observed as a set of rules again; this time the goal seemed to be an aesthetic perfection for the eye, for both right and left hand. I can't remember the quality of sound ever entering a discussion. As students we all watched our hands.
During these studies I received a scholarship to a master class with Enrico Mainardi. He was the first great cellist I met and he focussed totally on sound. When I played the first time for him, he told: you don't need to start every down bow at the nut (to show myself as a good student I had started specifically just at the nut); the first few cm's don't sound, it's too scratchy, just start here. He started every section somewhere else. He didn't have much explanation except: that's where this passage sounds best. He had the most beautiful sound. When asked technical questions he answered with the set of rules he had learned. But he didn't stick to them - we all could see it (I found that many excellent musicians had their beliefs in what they do, but they didn't do it. Their intuition was so powerful, it overpowered any rules; in contrast to me they had a sunny and happy lack of noticing this incongruence, which freed them up to put music first).
My next master class was with Janos Starker. In many aspects he was the opposite of Mainardi. Although I found he also judged himself from listening, he didn't teach so. He taught like most traditional teachers to observe visually what you do with your body. In difference to my former teachers he focussed on relaxation and efficiency and he observed the whole body from head to toe. He had a down putting language and warned if a student wouldn't oblige his techniques they would end up as a cripple. He told me my left hand was excellent and my bow hopeless, too many wrist movements: Please redo everything what you have just learnt!
I changed teacher and became student of Christof Henkel, former assistant of Janos Starker. Like many students of great cellists and "schools", he followed Starker literally. I had to copy fingerings and bowings from his music, which had Starker's bowings and fingerings marked. Still today I don't listen to students of Starker, even when they play very nice, because I can predict where the slide is and even the speed of shift. Technically I learned about bow direction and contact point, but seen from today I observe a strange absence of mentioning bow speed and amounts of bow to consider. I remember us students trying to get the spiccato right in Dvorak, all trying with lots of bow and pressure, hoping for the miracle to happen. For me, Starker and his students lack the grandness of expression, which comes by indulging in the flexibility of bow speeds as we know it from cellists like Rostropovich, Maisky and DuPre.
After my diploma in 1976 I studied Classical guitar and gave during the following years c a hundred concerts for solo guitar. My comeback on cello started with giving away my editions of Bach and Beethoven, buying new copies and writing in my own bowings and fingerings. I searched for music I never played before and recorded in 1993 the 2nd Suite of Benjamin Britten as well as the 6 Suites for cello solo by J.S.Bach, Brahms Sonata e minor and Schubert's Sonata for Arpeggione.
In 1987 I was asked to teach violin at the Coffs Harbour Music Education Centre, because the violin teacher had left unexpectedly mid term. After first refusing I took it as a chance to get more to know about violin playing. I had played before every now and then and could play anyting I know by ear. I took now a few lessons, learnt to read and we discussed the difference in techniques due to the different posture and size of the instrument. I practised regularly and made it during half a year to grade 6! All my students had learned the Suzuki method, which gave me an insight into the original method, of which the cello Suzuki method is a poor imitation. I sent a correction of the cello method to the Suzuki foundation, which was refused on the grounds, that I hadn't taught the (uncorrected) method for a sufficient number of years (sic). This was the end of my involvement with this organisation (I also took all the division marks off the student bows).
During the last two years I had thanks to my regular local concerts the possibility to reduce my teaching load and have the privillege to be able to practice every day for a good amount of time - the first time since my study years (I changed to teaching only hourly sessions - no 30min lessons - and instead a lesson every fortnight; I can only recommend this arrangement).
I need to mention my surprise that during the last one and a half years I learned in my mid fiftieth more than during my whole tertiary training! I encourage anyone to believe in progress at any stage of their life. As long as our mind, ears and hands are still good, we usually have a more practical approach, our mind is more critical and we have a better attitude to discipline - not fanatic, but strict at the right time - as a result we learn faster.
TO THE HISTORY OF THIS ARTICLE
Already during my studies I got very annoyed by the lack of certainty about elements of bow technique. Every new teacher threw me into a different corner; what used to be right was wrong now. I was taught some consistent facts like the straight bow direction, but no one ever would explain why. In my teaching experience I gradually found out that in order to demonstrate the bad effects of an incorrect bow hold, I needed to exaggerate or even create by purpose a bad sound, whereas I needed to put an effort different than the bow hold into showing my best sound. I became aware that I cheated. I remember going home after one lesson and trying to do the opposite: I played my best sound with a bad bow hold and a terrible sound with my best bow hold. To my horror it worked. On this day I started my systematic research.
I wanted to publish my research in 1997, but realised it would be very difficult to publicise and looked into an academic avenue. In 1998 I was offered in one Australian University a Masters degree, at another a PhD. However one supervisors showed little understanding of the matter and wanted to redirect the project into a thesis about the difference of the traditional bow hold and the Baroque bow hold - as it seemed to me an aspect, which will anyway be understood, if the thesis would not be narrowed down. The other supervisor suggested to leave all material like it is, but embellish it into three times as many words, to meet the standard of a PhD (don't you like articles, which don't come to the point?). I didn't end up going ahead with any of the academic offers.
Now, 10 years later and having reviewed the text many times I am hoping that by putting this article simply on my website I will be able to reach the readers interested, searching like me once for definite answers in bow technique. Any comments are welcome.
Georg Mertens, Katoomba 2008
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