Resonance, Tuning, Tone, and Intonation (Quick Update)

I recently “misplaced” my cell phone for a few days and was forced to realize how much I depend on this little device to play the cello.  This is because my favorite tuner is an app on my cell phone called PitchLab, which I use tune the instrument to a very high degree of accuracy.  Although when I lost my cell phone, I wasn’t too worried because I usually just use it tune the cello, and not during actual practice.  Besides, I do have other tuners and an old phone with ClearTune on it.  However, the extra degree of accuracy on PitchLab was far more important than I realized.  It can tune my cello to such a high degree of accuracy that string resonances are easily apparent when I play in tune which allows me to actually practice without a need for a tuner.   Yes  …my tuner makes my tuner unnecessary.  By contrast, when I used my old ClearTune app, I was able to get the strings to within 2 cents of the actual note, but this wasn’t good enough for the sympathetic string resonances to really kick in, so my pitch accuracy during practice was only in the 10 cent range.  2 cents off in tuning leading to 10cents off in the ear?   That is what is referred in math as a multiplier effect, and this is caused by missing an audible and tactile cues of string resonance that is in my case apparently more accurate than pitch hearing itself.  To be able to benefit from string resonance, at least on my student cello, I need an accuracy tighter than 0.1hz or about 0.5 cents on the A string.

So what causes string resonances?  Well they are related to overtones.  When you play a note, it vibrates at multiple frequencies other than the strongest one (ie the one that shows up on your tuner).  These other frequencies (called overtones) will align with the main frequencies and overtones of the open strings causing them to vibrate in sympathy.  This causes the whole cello to resonate in subtle yet quite lovely and complex ways which makes the tone much more enjoyable.

String resonance is a gentle feedback mechanism that cello players use to tell when they are in tune.  The other side of string resonance coin is that when you play slightly out of tune, the overtones won’t quite line up, and the resonances can even work against you causing the cello to vibrate in ways that make the note unstable in pitch or somewhat muffled, particularly when you play the notes in quick succession.  This can even happen on a cello that is in tune but being played with bad intonation.   On a cello where all the strings are a little bit off pitch, it is impossible not to have negative or misaligned resonances with at least two strings, and if you are resonating with one of them, then you are still playing out of tune and likely messing up your ear!  In terms of tone production, misaligned resonances are essentially what creates a wolf note, and a cello that is out of tune is basically playing lots of little wolf notes, but instead of being loud and obnoxious sounding, they will instead be dull, muted, or less stable in pitch or volume.

Playing out of tune can make legato notes sound choppy, double stops feel like one string just won’t activate quickly enough, produce dull muted tone, and alter the general response of your cello.  Needless to say, playing on a cello that is even slightly out of tune can result in a wasted or at least frustrating practice session, because the response of the cello is so radically different that you might as well be playing with a rubber mute.

You could also make a case that playing on a cello that is tuned to equal temperament will cause these kinds of bad resonances on the lower two strings when compared with Pythagorean or Just intonation.  This is because, unlike the latter two tuning methods, many notes on an Equal Tempered cello won’t have overtones that are pure frequency multiples of the lower strings, unless you’re playing a basic key like C or D or G where the 5ths will at least be somewhat accurate.  I haven’t tested Pythagorean tuning thoroughly enough on my cello to make any solid claims about this, and will have to do a little more experimentation and research.  It should be noted that string resonance matters mostly for playing solo music.  If you are playing with a piano or with an ensemble, then Equal Temperament is pretty much required, and the resonances will be mostly harmonic ones between instruments and this is happening directly in the wood, the air, and the room itself, and not just between the strings of a single instrument.

…After rereading this post, I realize that if my teacher reads it, she will most certainly redouble her efforts to get me to use my tuning fork more often, and I am sure she would be right!

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.



Targeting Tone (1713 Hours)

This last weekend, I performed The Swan at a recital.   Despite the difficulty of the piece and the surprise presence of a microphone a couple feet from my endpin, the 1700 hours of preparation worked, and I managed to not fall flat on my face.  Yo Yo Ma, I was not, but honestly, I cannot imagine how I could have played it any better at this point in my cello career, and in many ways I felt like I played it much better than I have any right to at my age and experience level.   Yet it was not a fluke either, and I know that my ability to expressively control my tone has improved rather dramatically since my recording of the Minuets.  In the weeks leading up to the performance, I was beginning to feel increasingly confident that I finally stumbled upon a recipe to consciously improve the sweetness and sensitivity of my tone rather rapidly – or at the very least, decrease the raspy clumsiness.   During this time of preparation, I have been writing and adding details to this post, but I wanted to wait until I tested these practice techniques in a public performance before I posted them here.

Now, with the help of my teacher, I have a set of focus points and exercises that have allowed me to rapidly improve tonal and expressive control.  This is truly amazing because for the longest time, the path towards attaining a smoother and sweeter tone seemed so incremental that the totality of it  was very abstract and shrouded in mystery.   It feels like a fog has lifted and I am seeing the cello again for the first time, and I am excited to share with you what I have gleaned so far…


Smoother Bow Starts:

The sweetest notes enter the scene like a whispering wind or a prowling cat.  I have often wondered: how the heck do cellists do this?   It is such a cool trick, yet it turns out that the basic principle of this technique is fairly simple.  It rests on the fact that the pressure required to get the string to begin oscillating is a great deal less than the weight used in the middle of a stroke.   Through a very instructive bow exercise learned in my lessons I found that for each location on the cello, there is a precise minimal pressure to activate the string and that there is a rather easy way to learn this pressure:

Begin by lifting the bow off of the string and then lowering it slowly until it makes contact again.  Now wiggle the bow back and forth across the string in tiny movements, less than a millimeter.  If the bow pressure is too light, the hair will slide over the string making a small raspy hissing thin sounding tone.  However if you use too much pressure, the hair will latch onto the string and you will hear an audible accented “chirp” or “crunch” sound if you continue the motion into a full bow stroke.  In between these two extremes of force is a “Goldilocks Zone”, where the hair just barely latches onto the string during a micro-wiggle.  At this precise minimal pressure, if you continue the motion into a full bow stroke, the string will activate smoothly and cleanly without hiss or scratch or chirp.  Voila!   You have found the pressure needed to make a string sing without making it cough first.

It’s important to note, that the amount of force required varies greatly depending on the stroke you use, the position of the note, the part of the bow used, the bowing direction, speed, acceleration, and other physical parameters (rosin build-up, string thickness, etc)  As a result of this exercise, I am also far more aware of my bow speed and am now using a small fraction of the rosin that I used to.

Handling the bow:

I recently had the opportunity to rehabilitate my bow hold.   Without going into the details, which in all likelihood don’t apply to your unique grip, I discovered that much of the issues of handling the bow with accuracy revolve around maintaining leverage.   You will notice this if you try the previously mentioned exercise of lifting bow off the string and slowly lowering back down again at various parts of the bow on either side of the balance point.  

Go ahead and try it right now both at the tip and at the frog.  Notice what is happening in your index and little finger when the bow is lifted.  Notice what happens to the angle of the wrist and any tension in your arm or hand.   Is the tip of the bow steady when you lift it?  Does it flop around a little when the hair leaves the string?   Does the grip seem to change when the bow is no longer supported by the string?  Does your hand lock up with tension when holding the bow in the air?   

By practicing raising and lowering the bow to the string at various lengths of the hair and paying special attention to how the weight is transferred between the string and the hand, you can discover exactly what a relaxed and steady bow hold requires.  So far, I have found that two things should be true of any bowhold: 1) it should be a relaxed and flexible grip with supple fingers, wrist and arm, and 2) it should be a steady grip that doesn’t collapse, shift, or wobble when you lift it slowly off the string.    These two traits will allow you to get a fuller undamped sound from your cello and give you the control necessary to alter the weight in fine increments and smoothly throughout the bow stroke (without bouncing).


The amount of bow weight you support and the direction of that support varies dramatically depending on which string you are playing on, the position of the note, and distance of the bow from the bridge.  All of this variation can make it difficult to make a consistent sound, however if the dynamics and color of your tone are being primarily steered by the variation in playing conditions, then we aren’t really in control of our tone.

One way to regain a measure of control is to try making a consistent tonal color and loudness regardless of contact point or which direction or part of the bow I am using.  As my teacher puts it, this is done by varying the bow speed & pressure so that the force the string sees remains constant regardless of the contact point.   Of course, the bow will seem much shorter near the fingerboard and nearly endless when playing near the bridge.  This consistency drill is an excellent way to work on bow dexterity with direct audio and tactile feedback, while training the ears to really hear these differences as well.

It is very easy when doing these kinds of exercises to get into the habit of using too much pressure, especially near the tip of the bow.  To correct these habits, simply start over by lifting the bow up and finding the minimum activation pressure again.  This is a relaxing reminder, and reassures the body of how little effort is actually needed to make a solid tone.

Slow and Low:

Continuing on the theme of consistency:  playing slow is a good idea for getting better accuracy and muscle memory, but it is also a way to improve the fluidity of your tone.  When you play slower, you are pretty much forced to move your bow down closer to the bridge just to maintain the same bowing patterns without running out of bow.  Playing near the bridge is generally more challenging than playing anywhere else because it requires both deep relaxation, reduced bow speed, and significantly more weight to activate the string in a clean tone.  As a result, any sudden changes in speed or pressure are immediately audible as hiccups or gaps in the sound.  This is an excellent way to put a microscope on your bowing technique and smooth out any rough spots in your stroke.

Developing the Ears:

The ears are the most important tools in a musician’s tool box.  Yet our minds are overwhelmed with so many technical aspects of creating sound that our ears are often neglected or ignored completely.   This presents a grave problem because playing the cello while focusing only on the visual aspects of your hand position is like driving on the freeway with your eyes squeezed shut.   This is because you “drive” the cello with your ears, and you can’t control what you can’t hear.  My teacher put it to me this way.  There are four progressive stages of acquiring any musical skill:  1) unconscious incompetence, 2) conscious incompetence, 3) conscious competence, and finally 4) unconscious competence.  While we move through four stages for any particular dexterity skill on the cello, the degree of consciousness that allows for this journey to take place depends entirely upon the ear’s ability to perceive the countless subtle nuances that become increasingly apparent as we develop musically.

The development of the ears depends entirely on how much we are actually relying on them.  It will not happen simply as a side effect of practice.  It requires intense concentration.  Human beings are primarily visual creatures, so it is not surprising that we often try to play the cello with our eyes: watching our hands or looking at a tuner.  However, when our eyes are busy watching our fingers or a dancing tuner needle, our ears are operating at a dramatically diminished capacity because the brain behind both of these sensory organs is effectively multitasking.  A study at the University of London showed that multitasking can lower your IQ by as much as 10 points.  This is a greater mental deficit than losing an entire nights sleep or from maintaining a prolonged cannabis habit. The logical inverse of this finding suggests that playing with your eyes closed could potentially focus the mind enough to effectively raise your “auditory IQ”.   This increased “auditory IQ”  can be used for both more accurate intonation and better tonal awareness.

My teacher has even recommended such drastic measures as playing in a pitch black room or while wearing a blind fold.  I am fairly clumsy even in a fully lit room, so I usually do these kind of sightless drills with my eyes simply closed.   When I do, I can hear so much more in the music.  It’s so mentally liberating that it’s almost as effective as listening to a recording of myself.  Almost

Record Your Best Sound (and then imagine a better one):

Owning and using a microphone is possibly the single greatest first step you can make to improve your sound.  Maybe I should have put this first on the list?  Well, if you don’t have a decent digital microphone like a Zoom HX series or an Apogee MiC, it is possibly the most worthwhile accessory purchase in your musical career besides maybe a metronome.   I cannot stress this enough.  Without it you might think you can hear how you sound, but you will be wrong.  Oh so wrong.   Trust me…  it’s always better to know.

The only downside of having a mic (and it’s a big one!) is the often crushing disappointment when you listen to the first recording of yourself after endless hours on work on a piece.   Pleasant surprises are few and far between whenever you hit the record button.  However, whatever you discover on the playback, it is simply information.  The objective reality is that information itself is neither good nor bad.  It is merely a crucial tool to start making adjustments and trying new approaches.   It is often during these exploratory adjustments that we can begin to start asking the right questions, so any initial pain or disappointment is well worth the cost in bravery or ego when staring down the red blinking record light.

In general, the more you use a mic, the more benefit you will get.  But there is a limit.  The human ego can be fragile thing when we open ourselves up to new experiences, and the feedback we get can occasionally be like having ice cold water dumped directly into the soul.   To ward against drowning  my  nascent cello ambitions in a bath of ice water, I also devote plenty of time to letting myself soar free of a microphone’s woeful ear, and imagine for several precious minutes that I sound more like Yo Yo Ma.  The illusion is tenuous and evaporates soon enough, but I think is a necessary white lie because these kinds of imaginings push me to aspire to things which are far beyond my current capability.   In a very real way, this kind of exercise opens a door of possibility that may have remained forever closed otherwise.   It also builds up the ego so that it can withstand a few solid doses of tough medicine from a callous microphone.

Beware of Bow Drift:

It is especially difficult for unseasoned cellists to keep the bow at a precise distance from the bridge.   This distance is often referred to as the “contact point”.   Intentionally changing the contact point during a bow stroke is usually done to get a certain tonal color or also during (de)crescendos within a bow stroke.   Unintentional changes in contact point tend to produce uneven tone, excessive string noise, and unintended dynamics and tonal color changes.   To a certain degree we begin controlling this distance by using our eyes, but as with ear training, we want to eventually graduate to using our other senses.   Learning how a steady controlled contact point feels and sounds is the ultimate goal so that we can eventually make subtle intentional dynamic and color changes even with our eyes closed.

Tenderizing the Wood:

The tone of your cello will depend to a certain extent on the amount of time it has been played, and more importantly which notes you have played the most.  The more you play certain notes on the cello, the more responsive, open, and resonant those notes will become.  This is part of the reason why older “vintage” instruments are so valuable: they have been played in every note in every position for generations.  The wood on your cello may look like it is motionless, but in reality it is alive and vibrating in what are called Chladni patterns:

Below you can see the outline of these Chaladni patterns created by the black dust sprinkled onto the wood that being vibrated mechanically at specific frequencies.    The places where the black dust gathers is where the wood is vibrating the least.  The empty spaces in between are areas where the wood is moving rapidly up and down between the nodes.  The pattern for each note and each octave is unique:

Perhaps you have noticed that the first time you play a note on the cello its sounds stuffier and feel less responsive than more commonly played notes?   This is because the cello has not vibrated in that specific Chladni pattern before.   The more you play that note, the clearer and more resonant it will sound as the wood relaxes like a soft old cotton shirt.   The process can take years.   If you are impatient, there is a device called a ToneRite that can more rapidly “mature” your instrument’s wood by subjecting it to intense vibrations while you are off doing other non-celloy things.  I cannot confirm the claims that it opens up your cello safely, however I can confirm that my own experiments with playing loudly into the bridge by hand have altered the overtones of my cello.

In general, the amount of resonance a cello has is directly linked to the bandwidth of resonant vibrations for that note and for the resonant frequencies of the wood itself.  That means that after years of playing with consistent intonation, those notes will sound more clear and defined when compared to out-of-tune notes, and the more you use techniques like vibrato and double stops, the more depth and warmth each individual note will have.  Playing the same note in a higher position (eg playing D3 on the C string) will encourage lower overtones and more depth and warmth in the sound when played in first and fourth positions.  Playing an open string D close to the bridge at very high volume will encourage the wood to vibrate with more clarity and with higher overtones. There is some debate as to how much of this effect is caused by the physical properties of the wood being altered, and how much is due to the ears of the musician growing and changing as the skill improves to draw more colors out of the cello.  After a grand total of two years and three months behind a cello, I am leaning towards the opinion that it is a good bit of both.  A relationship with a cello has been compared to a marriage of sorts, and the more you get to know your partner, the deeper the relationship grows.  To extend the analogy further, it is normal and expected that both partners in the relationship will grow and change over time.

On a related side note:  I just installed a Wolf Eliminator on my cello and I am finding that some of my tonal issues were the result of wrestling with a fairly strong Wolf on the F# that greatly altered the responsiveness of the cello on several adjacent notes and in almost every position.   Now my cello is much easier to play on any given note and the evenness of the response makes the notes sound and play much smoother.

Good Vibrations (1,126 Hours)

As much as I dream of owning a better instrument some day, I know from experience that the wide realm of possibilities that define a cellist’s expressiveness is more the result of mastering of the principles of technique rather than the pedigree of their equipment.  This has been made evident to me on the many occasions upon which my teacher has borrowed my humble student cello in order to demonstrate a new technique or to inspect my setup, and the quality of her tone retains the same “personality” and “sweetness” despite the instrument’s limitations.  While a higher quality and more resonant instrument (or bow) can be a great benefit in molding your talent and understanding of the cello, there are also some basic principles of physics that when applied to the cello playing (or purchasing) can aid in your personal search for that elusive rich & dulcet timbre.

Likely by now you have heard of such things as overtones, or upper partials when describing a certain quality of sound of string, bow, or instrument, and harmonics when describing the left hand technique of producing more ephemeral pure tones.  What you  may not have been aware of is that all of these terms are all synonyms describing the same types of vibrations on a string.    Hidden within the broad waving motion of each note are shorter and faster vibrations at specific fractional wavelengths (eg 1/2, 1/3, 1/4, 1/5, etc).  It can seem somewhat bizarre that a string can be vibrating simultaneously at so many frequencies at the same time (much like Schrodingers mysteriously bi-modal Cat).  Yet we know from experience that this is the case, because we can actively select each of these frequencies when we play harmonics or “false” harmonics  by isolating the individual overtones (and their octaves) by damping all the other vibrations with our finger tips:

The quality of a cello’s timbre is often described by a “color” as being warm, deep, mellow, clear, sweet, bright, rich, dull, round, metallic, rumbling or even harsh.   All of these terms are actually describing the strength and distribution of the overtones.   Warm, deep, mellow, pure or often what is generally referred to as “core” sound is actually describing weakness of overtones and stronger fundamental vibrations (eg all of the A’s ringing on the A string, 220hz, 440hz, 880hz, etc).  Rich, bright, metallic, rumbling, clear, or harsh is describing an increase in the strength of the overtones (eg all of the E’s, C’s, and G’s etc, which are also ringing on the open A string) compared to the strength of the fundamental vibrations.  Perhaps you’ve already noticed that occasionally when you play the open A string with a slightly harsh sounding technique, your tuner might register an E instead of an A.   This is because brighter sounds have stronger overtones, and the E is normally the strongest non-A overtone of the open A string!   As you will see later, it is no mere coincidence that the E and A sound so pleasing when played in harmony.

When a cello has a more core sound, it is easier to discern the intonation for that singular note.  However, when a cello is rich in overtones, it is easier to discern the relationship and intonation for the distance between notes.   Having more core sound vs rich overtones is something that you can alter by equipment selection and setup and also by bowing technique and fingering choice for enharmonics.  For example, playing with your bow closer to the bridge will produce stronger overtones, where as playing closer to the fingerboard will produce a more core or mellow sound.   In the case of enharmonics (ie equivalent pitches played on different strings) playing the same note closer to the bridge will reduce the strength of the overtones and produce a warmer sound, as I am sure you have noticed by now, playing the Open A string produces a much brighter (overtone rich) sound than playing the same note on the D string.   You can combine these techniques & setups to create various combinations of brightness and warmness.   Other factors that effect the richness of the overtones are the quality of the bow,  the gauge and tension of the strings, the suppleness of the bow hand/arm/shoulder, the shape of the bridge, the thickness/density/age of the wood, dryness/humidity, the quality and application of the varnish, and even the tension on the bow hair.   Generally speaking, the louder you play, and the more resonant your set up, the greater the component of overtones will be.  Some mutes will selectively dampen high or low frequencies, and depending on the note being played this will make the cello produce a dim rumble or a hollow squawk.

Though we do not hear them consciously as individual notes, overtones are what define our concept of harmony and dissonance.    This is because the part of the temporal lobe (auditory cortex) that is connected to our inner ear is designed to detect patterns and predict their significance.  For example. the simplest harmonic ratios between note frequencies are  2:3 (major 3rd), 3:4 (perfect 4th), or 4:5 (perfect 5th).  Because of the simplicity of their ratios, these notes share some of their strongest overtones, which means our brain has less work to do to detect the patterns involved, and this results in the general positive and uplifting association with these Major and Perfect intervals and this is what we perceive as “harmony”.  Not surprisingly, much of the earliest written music is based on the structure of these primal harmonies.   Other intervals have frequency ratios that share only weaker overtones (or upper partials) which means more work for the brain to decode that patterns, such as 5:6 (minor 3rd) 8:9 (major 2nd) or 8:15 (major 7th).   This extra load on our auditory cortex is more troubling to our psyche and leaves us with a feeling of discontent or unresolved tension (evidenced by the Riot of the Rite of Spring in 1913) and this what we call “dissonance”.   For better or worse, our brains are remarkably adaptable when it comes to learning new patterns and our sense of harmony is somewhat malleable & plastic both individually and as a society, which is why we enjoy music now (like Jazz and Heavy Metal) that likely would have wilted Mozart’s ears. 

The same is true when detecting and manipulating harmonic resonances on the cello.  Simple intervals create stronger sympathetic vibrations which is useful when trying to get better intonation by paying attention the resonance (ie “ringing”).   This is because the most resonant overtones are also the simplest ratios of frequencies.  As a general rule, the lower numbered overtones are stronger than the higher numbered ones even on setups with strong overtones. The strength of these basic overtones is why you can actually see your strings vibrating sympathetically when you play certain notes on the cello.  For weaker resonances, you will simply hear an increase in volume and texture of the sound and perhaps even feel your other strings vibrating by touching them with your finger tips.  Below is a map of the first 7 overtones on the cello (not counting the fundamental resonant frequency of the cello body itself which is usually F3 or F#3).  A complete map goes off the page to an infinite number of overtones, but these ones should be the most useful for checking intonation… remember, that even though the overtones are several octaves higher than the other open strings, every note is a strong overtone of the octave below it (eg G3 and G4 are strong overtones of the Open G2 string as well as the open C2 string).

Root 8va 5th 8va 3rd 5th m7 8va
1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8
C2 C3 G3 C4 E4 G4 Bb4 C5
G2 G3 D4 G4 B4 D5 F5 G5
D3 D4 A4 D5 F5 A5 C5 D5
A3 A4 E5 A5 C6 E6 G6 A6

What is truly amazing about this information is not only that it is useful for creating beautiful music, but that these mathematical relationships actually define what music is!!   This is why music is so fundamental to the human experience, and might even be universal to any life form with a sense of sound.   Or, as math-musician Vihart  puts it:  all sound is essentially music…

Reboot (959 Hours)

People respond to injuries in a number of ways. My own personal response has always been to get analytical and search for a solution. Sometimes it works, sometimes it’s just a waiting game. The general rule for injuries though is to avoid them at all costs. Injuries have a way of multiplying themselves. In fact the surest predictor of a future injury is having preexisting injuries. Whether this is due to a general lack of toughness or a consistent set of bad habits, I do not know. But I have come to learn to trust expert opinions on this topic rather experimenting with dynamite.

Given my recent bout of cello related injuries, my teacher proposed an idea that dropped a rope ladder down into the well in which my practice sessions have fallen. While she is pleased with my “rapid” progress, she also noted that I am her only student that suffers from these kinds of unusual injuries – which points to practice volume as a culprit.  To keep the proverbial “well” from becoming a “cliff”, she is suggesting stepping back from the 20+ hour practice week and dialing things down to a slower, steadier, and safer pace. Since bad form tends to exacerbate the injurious effects of overtraining, she also suggested that we spend a whole lesson breaking down my bow stroke to it’s elements. As it turns out, the list of things I was doing wrong is too long to post here in any detail, however I will post a brief list of the broad categories:

  1. Exaggerated Wrist flexion/extension at frog and tip
  2. Pinky Finger was resting on tip rather than the knuckle between the last two joints
  3. Fingers were too rigid rather than extending loosely near the tip and rolling in near the frog
  4. Joints were locking up during a bow stoke rather than flowing into the proper alignment
  5. Shoulder would elevate with the elbow
  6. Relying too heavily on the Pinky finger to unweight the bow
  7. General inconsistency in bow form, as opposed to using a specific bow grip, contact point, and bow section to get a specific tone color.

I have rather narrow long mirrors in my practice room, so I rearranged them to better see my right hand throughout the entire bow stroke. This was an eye opening experience and everything my teacher observed was confirmed during my two hour practice session. The upside is that even though my rehabilitated bow stroke was like an unfolding lawn chair, and bad habits persisted, there was little or no wrist pain during the entire practice session. I can only hope that I haven’t ingrained bad habits beyond the point of no return. I can already feel that there is a great deal of potential for increased control with the correct bow technique, but right now it almost feels like I’m holding the bow for the first time.

My teacher suggested I try these exercises to re-acclimate myself to the proper way to hold the bow.  I had originally worried that these exercises might have been the vehicle for my wrist injury, but no, it was simply a shoddy bow grip all along, and the medicine is also the diagnostic tool that determined there was a problem that need addressing.  Thanks to CelloDiary for posting these wonderful exercises!

The Secret Life of Etudes (947 Hours)

Even thinly disguised by the romantic French word for musical studies, my enthusiasm for Etudes has always mirrored my eagerness for “vegetables” or “homework.”  So whenever I find an etude that manages to straddle the border between the sensuously sweet and the densely nutritious, I savor the moments I have with it in the practice room.  This week I have found such a one in the Schröder etude 34 (aka Dotzauer 120, no 5), a beautiful meditation on double stops (two string harmonies).

 As you can see from the video above, double stops can be extremely lovely things when well executed.  They are also somewhat dreaded by new (and even mature) cellist because any intonation or bowing issues are magnified when you bring two strings into the equation.  For starters, being off by more than a few hair widths on either note will make the combination sound like two cats on a hot August night.  This is further complicated by the unique characteristics of each Cello (and the hands of the player) because parallel fingerings on adjacent strings are not precisely parallel, but rather can be staggered by game-changing millimeters.  This can be clearly observed when double stopping two strings with a single finger.   By now you may be realizing that the beginners tape on your fingerboard was really more of a general suggestion than a precise measurement!  If this weren’t enough, there is also the issue of the strings requiring different pressures to play cleanly (just as in string crossings) so you end up monitoring the pressure on the lighter string by pivoting on the heavier string as a fulcrum.  Going from tip to frog makes this even more interesting since uneven bow pressure can make the pitches waver even when the fingerings are accurate.

Yikes!  If this seems like quite a lot to think about, then you’re right.  It most definitely is.  Which is probably why double stops, despite their potential for beauty, are not all that common in cello music.  Why torture yourself by playing two strings when playing a duet is so much fun?   Well for one thing, the inherent difficulty of double stops makes them of tremendous educational value: ear training for intervals, fingerboard geography, intonation, hearing two distinct notes played simultaneously, enhanced bow sensitivity.  This is just the short list of stuff you can pick up in the early stages of learning them, and that by itself is a gold mine of tactile cello lore.

My “discovery” of this relatively simple Dotzauer etude reminds me of the story how the Bach Cello Suites almost disappeared into academic obscurity.  These jewels in the crown of cello repertoire were once regarded by those who knew of them as mere “etudes”, only played in the confinement of solitary practice rooms, until 1889 when a fateful young teenager named Pablo Casals discovered an old copy moldering in a thrift shop in Barcelona.  The first to perform them in public since their composition in (1717-1723), Casals transformed these studies into the international treasures that they are today, thus rescuing them from the dustbin of history.

I find this story compelling and inspirational because it challenges me to see the true beauty in what might otherwise be mistaken for the mundane.  I picked up this wonderfully singing instrument because I wanted to unlock a voice capable of expressing the part of myself that is beyond the articulation of mere words, and I see now that in order to do so I must first learn to tease out the beauty from the even the most unlikeliest of places.  Find ways to express even subtle moods where little or no emotional content is readily apparent: etudes, scales, even simple melodies and technical exercises.  Like the much maligned number Zero (upon which rests the creation of all modern Mathematics and thus Science) there is a Taoist saying that an empty vessel has the most potential for being filled.

I will end this entry with a selection from my favorite promoter of Etudes: Joshua Roman and his famous Popper Project with the spritely Etude No. 40.