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!

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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…

Repetition:

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!!

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.

Minimizing Discontinuities (953 Hours)

A few days ago I began developing the early stages of tendonitis in my right hand “bow” wrist. Having some experience with more vigorous training schedules, I know the reason for this hiccup in my practice schedule is my violation of a cardinal rule in training. Whenever you increase the intensity, it’s wise to simultaneously decrease the volume. Double Stops can be intense on the left hand, so I was keeping a close watch on it, relaxing and taking breaks as necessary. However, I neglected to observe what was happening in my right hand, and even spent my “rest breaks” doing bow dexterity exercises! I am currently remedying the muscle strain with problem with gentle shiatsu massages, stretching, ice packs, and sleeping wrist braces. To keep myself occupied during this period of reduced practicing, I would like to take a moment and write a post about the pitfalls of overtraining as a musician…

Shin’ichi Suzuki (1898-1998) once said that you only need to practice on the days that you eat. In this age of plenty, that’s likely to be 365 days a year. However, it has also been said that musicians are “athletes of the small muscles”. Any musician who intends to do serious training would profit from exploring the analogous training regimens for other athletic endeavors. Fortunately, in the process of training for triathlons in my 20s, I learned some valuable information about human anatomy & exercise physiology including balancing efficiency, intensity, nutrition, and rest. It is intuitive to imagine that training itself will increase your fitness, but this is not exactly what happens in the body. Exercise is a stressor which actually decreases fitness, first by using up the energy stored in your muscles (glycogen), then by depleting your other energy & electrolyte reserves, and finally by causing tiny tears in your muscle fibers. All of these effects combine to weaken the muscle’s ability to contract forcefully. If you continue beyond this point, your muscles will begin to tighten & then cramp up as a warning that further exertion will result in lasting injury (tendonitis, ligament tears, pulled muscles, etc). Increasing fitness is something that ONLY happens during rest periods (eg during sleep & days off). So the process for increasing fitness is cyclical in nature and has two components: the first is to break the body down (training), and the second is to build it up (rest). Neglect either one of these components and you could end up getting weaker, slower, clumsier, and more prone to serious injury.

Everyone’s body is different, and so the stress load involved in playing the cello (or any instrument) will be different for everyone. Even if you take all the proper precautions, there are no guarantees of avoiding an injury. That being said, I will list a few guide lines for body awareness that I use to avoid the precursors of injuries (tension, straining, and over exertion).

  1. Remember to Breathe – seems simple enough, but this is surprising easy to forget to do. This is also the first step in maintaining focused relaxation.
  2. Relax Your Thumbs – it’s virtually impossible to have tense hands when your thumb muscles are relaxed, and reducing excess tension will not only better your technique, it will also reduce the risk of injury.
  3. Use the Minimum Force – remember Newtons 2nd Law: Your instrument can’t push back on you any harder than you are squeezing on it
  4. Warm Up – stretching is not warming up. Take some time before your practice to get your blood pumping, jog in place, wiggle your fingers, do relaxed scales, bow dexterity drills, etc. Running your forearms under hot water is also an efficient way to prep your muscles for a work out.
  5. Stretch – gentle stretching is a great thing to do once your blood is flowing and your muscles are warm. It’s best to save “deeper” stretches after practice as a “cool-down.” However, stretching before a practice session with cold muscles can be dangerous and even introduce tension and strains.
  6. Take Plenty of Breaks – don’t wait until your muscles get tired and cramp up, take frequent mini breaks instead. Your brain and your hands will thank you. This is a good time to take in water and simple carbs to keep your energy and willpower up
  7. Pain Isn’t Normal – don’t ignore any burning, aching, pinching, tearing, throbbing, tingling, or numbness. Playing cello isn’t effortless, but it should never be painful. Stop playing immediately, and if you can’t figure out the problem without hurting yourself more, then wait till you can consult your teacher and/or a doctor. The earlier you stop & search for a solution, the more simple and quick that solution will be, the simplest being a good nights rest.
  8. Sleep – without adequate rest our brains and bodies cannot function properly for learning. In fact, not getting sufficient rest can put the same stress load on a body as a heavy workout. Chronic insomnia also has pretty nasty effects on memory formation, ability to focus, and can even decrease brain volume (ie cause dementia) if persistent.
  9. Balance Your Load – if you increase the intensity of your practice routine by introducing challenging new technique (extensions, double stops, energetic bowing techniques, etc), you should decrease the volume of your practice time to keep the overall physical stress load from spiking
  10. Ease Back Into It – in the event of an injury, don’t rush headlong back into your routine. Notch it up slowly and always, always, always, listen to your body.
  11. Rest on Your Rest Day – it’s typical in our busy multi-tasking lives to want to pack your rest time with activity to try and make up for any lost time on other priorities. If possible, try to make DOING NOTHING AT ALL a priority during your rest days. At least nothing that involves using your hands very much.
  12. Watch for Mental Fatigue – if at the end of a long practice you feel your passion for the cello waning, then you are probably suffering from ego-depletion and you are need of a rest day to avoid burnout and injury. This sensation is technically a form of temporary depression that is a direct result of overtraining. Take one Day off, and you will feel that siren song calling from your cello case again. You will also be more physically refreshed and mentally alert, and thus more efficient in the practice room.

Nothing will shorten your practice routine faster than holding on to excess tension, it is also the quickest road to injury. If you have a problem with relaxation, I recommend taking a class on yoga/tai chi or simply going for a nice walk. You might also find my post on inserting rest notes helpful since it is the most efficient route I’ve found toward ensuring relaxed playing for hours on end.

Embrace the Null Space (935 Hours)

There is a tendency when we look at a familiar piece of music to see it as a single contiguous object, rather than as a series of moments, each one flowing into the next. However when we look at a new piece of music, especially one with unfamiliar note transitions, something magical happens in our brains. We are forced to disengage our autopilot, slow down, and forge new neural pathways to an untilled plot of mental real estate. Once we find that note, even if the transition is not very clean or accurate, our instinct is to move forward and begin conquering to the next series of notes.

Unfortunately, if an awkward transition between any notes remains neglected, something rather untidy and unmagical begins to take root in our minds. Each time we play that passage, we accumulate a set of awkward sensations that get reinforced through repetition. This now predictable awkwardness turns into disconcerting thoughts, feelings, and judgements so we tune them out as best we can to “focus on the music” and in the process, the transition between the notes gets fuzzier and increasingly chaotic. The result of such practice habits can be disastrous during a performance where unconscious hiccups become magnified as tunnel vision kicks in and our instincts take over.

The best way that I’ve found to banish these subconscious gremlins is to insert a series of rest beats inbetween each note transition in a new piece, and put the section (usually just two notes) on a metronome loop, repeating the transitions over and over again. The rest beats are the key to this exercise because they give the mind time to calculate and the body time to relax and find a graceful path to the next note. Every mistake is an opportunity to examine what can go wrong, and then make a positive reinforcing correction on the next loop. Its important to avoid the temptation to fix the problem mid-loop, or else you’ll be ingraining “note hunting” habits. These are especially heinous because not only do they result in mealy technique, poor intonation, and messy bow-starts, but in a performance setting, the unsteady sounds they produce are often much more apparent to the audience than to the musician.

The reason this rest note exercise seems to work is very similar to the principles of micro muscle movements taught in tai chi. To go fast, you must first go slow. The slower you go, the more information your muscles and nerves have to work with, and the more time you have to declench that vulcan death grip on the fingerboard! Likewise, the more rest beats between the notes, the easier, smoother, and more relaxed your note transitions will ultimately be. I have gone as high as three rest notes. Try it on a short piece of unfamiliar music. You will be amazed when your fingers begin to be drawn, as if by magnetism, to the exact right spot with each metronome click. Once you experience this magical feeling, then you are only just beginning to get a benefit of repetition. To get the full benefit, you will need to wear a mental grove in that string by reinforcing the accurate motions on a daily basis.

This practice technique is so useful and effective that I now devote the first hour (or more) of my practice sessions to this kind of exercise. It’s essentially like scale work, but with an emphasis on accuracy rather than tone. There are similar exercises that I do for tone, but that will be for a future post!