Dancing the Helmholtz on a String (2,104 Hours)

Every cellists desires a sweet and resonant tone, but what is the secret that differentiates a rough scraping bow from a beautiful and pure buzz?   In an effort to answer this question, a curious German physicists named Hermann von Helmholtz, peered into a “vibration microscope” in 1863 and saw something that changed our understanding of sound. They didn’t have slow motion video technology and wouldn’t for another 70 years, but what Helmholtz discovered was as clear to him as the video below…

You may have already heard of the “stick-slip” action of the string and the bow hair, but the way the string slips and returns to the hair is fundamental to a pure tone quality.   In the first fraction of a second, all is chaos, but the pattern that emerges within the dancing string is a magical side effect of the nature of bowed instruments, like pistons on a train wheel transforming that straight line motion of the bow into a rolling rotation on the string itself.  This circular wave of a cello string is called Helmholtz Motion after our intrepid German physicist mentioned above.

When viewed from above the wave appears to be tracing out a familiar elliptical “eye” shape (shown in blue below) and this standing wave pattern is what our eye actually sees when we bow the string.   This very unique vibratory pattern is specific to bowed instruments such as the violin or cello, and is what gives these marvelous instruments their characteristic rich bumblebee sound.

Figure 1

Well this is all very cool display of physics, but I imagine at this point you are wondering “how does this impact my cello playing”?   Well for starters, the motion described above is the idealized version and is only the result of very good bowing technique.  When we use improper technique, the pattern gets distorted which results in poor tone and unwanted noises.  For example, using too much or too little bow speed, or letting contact point drift up and down the string can cause the hair to stick to the string too long or in wrong part of the wave which results in a diminished irregular wave, a more gritty tone, and plenty of unnecessary string noise…

Basic Elements of Good Bow Technique:

There are TWO basic ingredients to maintaining a pure Helmholtz wave:

  1. Steady contact point:   This means no sudden changes of the distance from the bow hair to the bridge.  This is easier if your bow is parallel to the bridge.  Changing the contact point changes where the wave re-sticks to the bowhair, and should only be done with great intention during longer notes.  For shorter notes, alter the contact point by lifting and resetting the bow entirely at opportune points between notes.
  2. Matching your bow speed with your bow pressure:  the more weight you apply to the bow, the faster the bow speed must be.   However, to keep things interesting, when you are closer to the bridge, you need more pressure but less speed!  Confused?  Welcome to the cello.

The Schelling Diagram (below) clears things up a little bit by showing the range of viable pressures at various contact distances from the bridge.  The range of clean sounding Helmholtz motion is shown in yellow.   By wandering into the areas outside of the yellow region you will discover the source of sound effects for horror movies.   The term β simply describes the contact point as a fraction of the total string length, so smaller values of  β are closer to the bridge, and larger values are closer to the finger board.  Notice how the range narrows  as you get closer to the bridge, requiring more force and greater precision, and widens as you get closer to the finger board, requiring less force and less precision.

Schelleng Diagram

The range of viable forces near the bridge vary by around 30%, but near the fingerboard they can vary by more than 5000%.   Since the different strings require such different forces to activate them, this makes string crossings and chords quite a bit more challenging when playing near the bridge because the pressures required are far more precise and differentiated.  Whereas playing nearer to the fingerboard, the required forces are much more similar for adjacent strings and can even overlap.


The Importance of Equipment, Strings, Intonation, and Bowing Tricks:

There are many other variables that impact Helmholtz motion, such as the diameter and elasticity of the string, the stickiness of rosin, resonance and responsiveness of the cello itself, the difference in mass and tension of strings during string crossings, etc.   All of these elements must be taken into account, and adjusted each time you change rosin or try out a new brand of strings.  Playing in tune will also make Helmholtz motion a bit easier to begin or maintain because the cello won’t resist new vibrations that match the overtones of an open string or those of a note that is already resonating in the wood.   Granted this resonance doesn’t work as well for dissonant intervals (ie major and minor 2nds), but it does still work if your strings are particularly resonant (Evah Pirazzi Golds are excellent at this).

As you saw in the first video above, Helmholtz  Motion is not necessarily instantaneous.  This is because the force required to start the string moving is greater than that required to simply maintain that motion.  Any delay in responsiveness no matter how short can dramatically impact sound quality. As a general rule a faster responding setup usually means a brighter sound.   Brighter is not always better, and many cellists who can’t afford cellos that have both speed and depth will sacrifice depth of sound for speed by fitting their cello with brighter and more responsive strings because a higher pitched sounds can still be fairly sweet if you can achieve more pure Helmholtz motion.   Hence the popularity of tungsten wound C and G strings…  extremely responsive compared to their chromium wound counterparts, but also quite bright sounding.  There has also been a move towards altering the mass, tension, and elasticity of strings so that adjacent strings aren’t quite so different.  This can be seen in the evolution from standard Jargar strings to the more modern Larsens, EPs, and Thomastiks.

Some cellists will compensate for a reluctant C string by plucking it right before bowing it.  This  little trick gives the string an initial momentum and reduces the force required to start Helmholtz motion.  This is also why starting an accented bow stroke is relatively easy: the initial force is always sufficient.  To compensate for the initial resistance when playing an unaccented note, you can start off with low pressure, and gradually sink more weight into the string in the middle of the bow stroke to get a fuller sound, then ease off the pressure at the end of the stroke.  This is like the gentle sinking motion a boat makes when lolling in and out of the water.


Consequences for Continuous Bowing

One important consequence of the stick-slip wave motion is that the direction the wave travels (clockwise vs counter clockwise) depends on the direction of the bow.  If the bow is going in the opposite direction, then the string would release in a clockwise direction (instead of counter-clockwise).   This has significant implications for bow direction changes.  Some controversy has arisen over whether or not it is possible to create an inaudible bow change by continuing the momentum of the original string vibration: the so-called “endless bow”.  However a Helmholtz wave moves very much like a train wheels, propelled in a circular motion by straight line cranks and pistons (ie the bowing itself).    Much like a rolling iron train wheel, the circular energy of the wave has it own momentum once pushed into motion.  Changing bow directions reverses the rotational momentum of the wave and inverts the wave pattern, which requires both time and energy.   It is impossible to invert the wave without cancelling or at least disrupting the original wave.  This means that there will always be a small disruption in the generation of sound from the strings no matter how good your technique is.  All you can do is minimize the pause by making it as short as possible and maximizing residual resonance of the sound via room acoustics and if you are very lucky: an extremely resonant cello.




Interdependence (1315 Hours)


Sifting through the detritus of 2013 and the wisdom imparted by successes and failures of the prior year, the month of January is usually one of reflection and sober optimism for growth, advancement, and in some cases healing.   In my case, this reflection took nearly the entire month of January, and finally resulted in a list of “cello resolutions” for 2014.  What took so long?  Well, my initial lists were bogged down with details and nuances that would have resulted in unfocused and unproductive practice sessions.  So in an effort to refine the focus of my studies, I narrowed it down to a scant 10 technical skills and 6 musicianship skills.   I tried to make it shorter, but alas, my ambition has once again outstripped common sense wisdom.  To simplify the situation, I decided to write out a short definition for each of these skills so they could be organized by shared characteristics for more efficient practice.   Perhaps not surprisingly, the definitions revealed how interdependent these skills are, so that a deficiency in one would lead to a limitation in another.   Likewise, improving in one area should create new possibilities in mastering other skill sets!   The skills are listed below along with the set of related technical & musicianship skills listed by number/letter in parentheses (). 

I have printed this list and put in the cover of my cello workbook, so I can review it before each practice session in order to plan my goals for that day.

Technical Skills:

1) Double Stops & Chords – Playing two notes simultaneously with good tone quality,intonation, and relaxation (2, 3, 4, 6, 7, 9)
2) String Crossing – Switching between two strings while maintaining the contact point, tone quality, left hand position, and rhythm (4, 7, 9)
3) Finger Spacing – The ability of the left hand to feel the position of the notes before they are played (4, 6, 8)
4) Intonation/Relative Pitch  – The ability of the ear to anticipate the pitch of the notes before they are played (A, F)
5) Playing Faster – Increasing the tempo without sacrificing rhythm, tone quality, or musicality (2, 3, 6, 7, 8, F)
6) Relaxation – The ability to recognize sources of tension and then release it quickly, fully, and dynamically (A)
7) Rhythm, Counting & Timing – Giving notes their proper length according to the tempo and pulse (2, 6, 8, F)
8) Shifting – the ability of the entire body (mostly left arm) to feel the position of the notes and the distance between them along the string  (4, 6, A)
9) Tonalization – Manipulating the friction of the bow on the string via speed, pressure, and contact point to produce a sound as distinct as a human voice (4, 6, 7, A)
10) Vibrato – wavering the pitch of the note by relaxing the left hand as much as possible (3, 4, 6, 7, 8)

Musicianship Skills:

A) Confidence/Game Face – Believing in the ability to rise to a challenge, releasing mistakes quickly, focusing on the task at hand.  Keeping a poker face in the instance of performance mishaps.
B) Ensembles – Playing with other musicians while maintaining proper timing, intonation, tonalization, and dynamics (4, 7, 9)
C) Performance – Sharing current progress with an audience either live or via YouTube, once per month (A)
D) Analyze Music Theory of Bach’s Suites – Using knowledge of music theory & “musical geometry” to gain a deeper understanding of Bach’s genius and insight into how to play the Suites
E) Perform two movements of Suite no 1 – Learn the Minuets I&II and the Prelude from the first Suite with enough proficiency for competent performance (A)
F) Sight Reading – Being able to accurately render notes, in proper time, pitch, articulation, etc by reading faster than a given tempo. (4, 7)

I’ll be starting in a quartet in mid April, I’m currently working on the Bach Minuets I & II from suite no.1, and I will be posting a video in the next week or so from the end of Suzuki Book 4 (most likely Tchaikovsky’s Chanson Triste).  So I am well on my way to achieving my musicianship goals for 2014!  The technique goals are ongoing, and I’m sure I’ll be refining that list continually as the year goes on and my understanding of the fundamentals deepens.  

To all of my fellow musicians (and anyone who is trying to learn something new!) I wish you great success in the coming year!!


A Quantum of Harvey (1027 Hours)

Human Cochlea (Auditory Inner Ear)

A while ago I purchased some workbooks from Cassia Harvey on amazon in order to beef up my library of left hand finger exercises. The books were originally recommended to me by an academic source concerning the topic of adult cello students, and I read of several teachers who had found that the series made up for many of the deficits in the Suzuki and associated Method books and had led to breakthroughs and more rapid advances in struggling students. Never one to turn down a glowing book recommendation, I made a few forays into the beginner and intermediate books and saw that they had some very nice utility, but eventually the demands of my practice schedule compelled me to put this extra-curricular activity aside for the moment and focus on the material from in my weekly lessons. That is until recently, when I read a new and somewhat controversial blog post at the Bulletproof Musician about shaking up your repetitive practice routine with a random interval technique, and I was prompted to reexamine several cherished beliefs.  I had serious doubts about the benefit of this technique, especially in the case of beginners like myself because repetition seems like a necessary way of ingraining the muscle memory required to play this mercurial & nuanced instrument.

I still think there is certainly merit to the repetition technique and its ability to wear a grove in the mind’s ear, but after looking at the neuroscience on the topic and being somewhat convinced that my previous comfortable assumptions were in error, I decided to give randomness a try. I didn’t use any distinct methodology because the training effect on one person is a one-way non repeatable experiment with no control group. I just selected random measures from pieces and never repeated any one more than a few times before moving on.  After several days of this, I can report that it seems to be fairly effective, and at least as effective as doing many linear repetitions. In fact, while I feel less comfortable with my pieces, I can tell that shifting during sight reading already feels easier and more accurate (verified by tuner). And even though my Suzuki pieces “feel” less familiar, I can tell I am playing each note with greater ease and technical proficiency than I might have with straight repetition in the same time period.

Initially, I was worried that doing less than 5-10 repetions would cause my inner ear’s tuning to fail to latch on to the tone, but there seems to be some cumulative effect of hearing a bunch of relative intervals that warms up the ear at least as effectively as repetition. I think it has to do with the harmonic resonance of overtones reinforcing each other the same way they do in a chord or to a lesser degree in a scale. This is amazing because it points to growth in working memory for hearing relative (and even short term absolute) pitch. Anyone familiar with the double slit experiment in quantum mechanics may realize there is a similarity here between single electrons causing interference patterns and notes causing you to essentially remember “harmonies” even though the notes are seperated by minutes and even hours… Its kind of mind blowing.

Anyway, getting back to my original point, I discovered something similar to this kind of randomization in the books by Cassia Harvey, but its methodically intentional. She sets up her scales in a rhythmically, melodically, and harmonically “randomized” pattern that is both intuitive enough to sight read and yet nearly impossible to memorize or get comfortable with. I am very good at memorizing pages of music just by ear and by feel, but this material is some how randomized rythmically and melodically so that you can anticipate the next the note, but it still defies any attempts at comfort or zoning out in mindless repetitions. Her fingerings on these scales combine ear training, with shifting, and scale/fingerboard geography. The rhythmical variations are also designed to help you break past mental speed barriers in shifting, of which I have many! Her material is an exceedingly rich vein that makes spending 90 minutes on scales seem to fly by and yet be far more profitable than doing simple scales or arpeggios.

I realize this post probably reads like a Cassia Harvey ad, so for clarity, I am not affliated with Cassia Harvey in any way. I just read an unrelated masters thesis on adult cello education in the digital age earlier this year and her name came up in the sited sources. Btw, the book I am getting the most out right now is her two octave book.