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…


Back to the Basics (1083 Hours)

After I passed the 1000 hour mark, I decided to take some time to reevaluate the effectiveness of various practice techniques.  In the months while I was recovering from my recent injury, I was given the “opportunity” to test to the effectiveness of certain elements of my practice routine by virtue of their absence.   Doing too many repetitions would have aggravated my injury, and slow practice was also dangerous since any accidental tension is magnified when you hold on to it 4 to 5 times longer than during performance speed.   The lack of these two pillars in my routine manifested in increasingly poor technique and culminated in a lesson where my limbs became completely inarticulate and betrayed the 20 hours of practice I had put in during the prior week.   Luckily, my injury had sufficiently healed to resume a more rigorous practice routine, so I resolved to spend the week after my disappointing performance getting back to the basics. The resulting changes in confidence and reliability while under pressure were palpable, and one week after my most disappointing performance at a lesson, my teacher gave me the best compliment I’ve ever gotten while behind a cello.

To clarify what I mean by “basics” I will describe in detail the missing stages of my daily routine that seem to yield the best and most reliable results:

Slow Practice:

There are several methods of slow practice.  The simplest and most basic is to play a piece through in it’s entirety at half tempo.  This is like riding an obstacle course at a relaxed paced to look for trouble spots and start building up confidence in expressive techniques while still retaining the basic musicality. I find this tempo is most effectively used for an initial exploratory sight-reading and then for more routine practice once I am already familiar with the musical phrases and beginning to stitch the pieces together in context.  However, in order to first familiarize myself the building blocks of a piece I utilize the next type of slow practice: “super slow motion” where the metronome is set anywhere from 40 bpm all the way down to a tantric 6 beats per minute.   This is more like walking an obstacle course and examining each rock on the trail with a magnifying glass.   The great benefit of this technique is in the first phase of learning, when we are developing a solid base of muscle memory so every initial repetition is a good one.  A “good” repetition doesn’t mean perfection, it simply means that you can clearly identify what went wrong, and then address it on the next repetition.  This is key because it not only reduces the amount of unlearning you will have to do as you polish the piece, it also makes the learning you do in this piece more adaptable and generalized to other pieces though the magical effect of consistent reinforcement.  The “downside” of super slow practice is that it requires a substantial initial investment and can take several days just to finish an initial run through of a challenging piece.  It’s important to remember that while this may seem slower, it is actually much faster than rushing through a piece only to collect a series of unconscious and ingrained bad habits. By focusing on a smaller volume of music with deeper and more meaningful repetitions, you can become reasonably competent at a new piece in a fraction of the time it might take otherwise.

When first attempting a piece at these super slow speeds, its musicality changes completely to the point where the melodies can be virtually unrecognizable for a while, but this is actually a good thing because as your working memory adapts, you start to see the whole structure again and at a much deeper level.  Initially, it is also very difficult to play this slowly and retain your sense of rhythm.  There are two methods I know of for alleviating this hurdle:

1) Starting at half tempo and slowing down the metronome in a stepwise fashion.  For example, starting at 40 bpm and gradually dropping the metronome down 8 bpm.  Much like slow and deep stretching, this helps to retain a feel for the pulse of the rhythm as you slow down to the speed of a tree sipping water.

2) Play with multiple clicks per beat. For instance, if you’re playing in 4/4 time, you can do 4 clicks per quarter note at 60 bpm (or 16 beats per measure).  If you are encountering a mix of triplet and duplet rhythms, then its best to use the first method and set the metronome for the common downbeats.

In both cases, every nuanced flaw in bow technique and intonation will become exposed.   This phenomenon is in part because playing “really slow” requires more mental effort than playing “moderately slow”, but it is also because most of the flaws we hear when we play in slow motion (that seem to disappear when we play faster) were actually there all along and were manifested as “unsweet” tone.    One hint that really helped me was learning that in order to get the same feel of resistance in the bow: the slower I went, the closer I had to play to the bridge.   Also, in order to get the most out of this technique, it is practically essential to have a good recording that you can play along with and try to match intonation and expressiveness.  To do this, you will need a device that will slow the music down while maintaining the proper pitch.   Some examples of this technology are Audacity and Anytune the former works on pretty much any desktop platform and is absolutely free, the latter of which works on iOS devices and of course costs money.  While Audacity is a great boon for anyone with a full blown computer in their practice space, I find that a mobile platform with something like Anytune is much more user friendly, easier to access into a practice room, and integrates sources like youtube/iTunes/email attachments with a one-button-press simplicity that saves me precious time.   One especially nice feature is the ability to create and bookmark loops in the music to use for repetitions, and a stepwise tempo ramp function that can increase the speed of a repeated loop incrementally until you are playing at full speed.   When increasing the tempo, I like to use the stepwise ramp in sets (eg 3 sets of 10 loops from 25% to 75% performance tempo) .  Which brings us to my second favorite practice technique…


This practice technique is a bit of a double edged sword.  As has been said many times: practice doesn’t make perfect, practice only makes permanent.  If all repetitions were created equal, then you could point any kid (or adult) at an instrument and given enough time a musical genius would emerge.   However, when we begin learning an instrument, most initial repetitions are extremely rough estimates, and if we accumulate repetitions without really hearing what we are doing or without knowing how to improve it, these rough estimates become our unconscious technique.   Luckily, the other side of this coin is that good observations reinforced by good habits will also tend to give good results.   There is actually a school of thought that claims that musical “genius” is really just the “dumb luck” that happens when someone randomly does everything “right” the first time and then reinforces this success through good practice.  The astronomical unlikelihood of this occurring randomly could be the reason why there are so few musical geniuses.  However it could also be true that these “geniuses” had access to a slightly less rare creature:  a knowledgeable and observant teacher who kept them on the straight and narrow and identified bad habits before they could become a real problem.   As beginners, and especially for adults, it is of paramount importance that we learn to hear as much detail as possible to gain the sensitivity required to start make good repetitions as early as possible in our careers.   As mentioned above, the best way to ensure that we can hear everything we are doing is by going slow enough that our brains have time to register an error and process the feedback so that a correction can be made.

Of course, the “fastest” useful speed will vary dramatically by our familiarity with the requirements of the music.  We can temporarily reduce the requirements of the music by simplifying it in various ways:

  • using separate bowing for each note (ignoring ties and legato)
  • ignoring time values and simply practice the feeling the space between two notes
  • simpifying rythms (eg making notes all the same time value)
  • inserting rests between notes on difficult shifts or extensions
  • removing the left hand from the equation, and playing open strings on difficult/rapid string changes
  • ignoring dynamics, vibrato, and other expressive markings
  • creating exercises that combine multiple simplifications

When doing repetitions, I try to manage the complexities of the instrument by using the above simplifications in order to focus on a single aspect of technique.   There is a school of thought that each repetition should be identical so that when you are playing under stress, your hands will only remember one thing to do, and I think there is merit to this principle once the basic fundamentals of technique are fully mastered.  However, beginners like myself still have so much to learn, and the only way we can do it is by breaking up highly complex tasks into their components and focusing on ONE single aspect of technique at a time.  Of course, it’s also best to re-implement the originally written markings back in as soon as (comfortably) possible to avoid creating confusing muscle memories.  With my limited knowledge, the basic elements I work on separately when doing repetitions are:

(in order or precedence)

  1.  intonation/finger spacing (separate bowing)
  2.  bowing patterns (open strings)
  3. rhythm/pulse
  4. body awareness/tension
  5. tone/expressiveness

The most important thing to remember when doing repetitions is to start as small as possible.   If I am just learning a piece, I will start by doing super slow practice, and loop a motif or a short phrase, and add motifs and phrases as I gain comfort with each of the 5 focuses above.   Once I am familiar with the section, I will begin increasing the speed and reduce the number of notes in the loop, starting with only 2 notes, and adding one at a time until I am at the level of a motif, and then a phrase.  I usually go through these 5 aspects of technique in order though my attention will often shift to a different one when a glaring issue pops up.   Steps 2, 3, and 4 are especially important to focus on when increasing the tempo.  1, 4, and 5 are most significant when doing very slow practice and against a good recording to get instant feedback on intonation and expressiveness.  The goal is to get to the point where 1-4 are unconscious, require only maintenance and tweaking, so that you can place the bulk of your attention on tone and expressiveness even when doing bursts at full tempo and eventually play the whole piece without becoming tense or fatigued.

I hope you found this post helpful!  Please feel free to share any practice techniques that have worked for you in the comments section!!