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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11 thoughts on “Resonance, Tuning, Tone, and Intonation (Quick Update)

  1. Layla Fowler says:

    Thanks for sharing this! I’m a new cello student and needed a tuner, so the recommendation for Pitch Lab was very helpful! I’m about 25-30 hours into my 10,000 hours. 🙂

  2. I guess it was kind of a Pitch Lab commercial. But mostly, I just wanted to emphasize the importance of accurate tuning of the open strings.

    Good luck on your cello journey! If you start a blog, please let me know and I’ll link it here.

  3. Michael says:

    I found a bit of acoustic geekery when thinking about harmonic series over different notes. This specifically applies to the problem of tuning E. I thought you might appreciate it!

    http://www.willamette.edu/~hwu/article_engelstad.pdf

    • Thanks Michael! I certainly found the E on the D string difficult to tune for most of the first two years of playing. The malleability of it’s resonance in the first position makes it a bit tougher than some notes. That being said, the E turns out to be one of the easiest notes to do a rough check on the cello because it has a natural harmonic on the A string, and because it resonates mildly with the open C. Also, once you start working on double stops, the E harmonizes with both the open G (Maj 6th) and the open A (perfect 4th), and you can even try it against the open C (Maj 3rd) when played on the G string in 4th position. It does take a bit of practice to hear when they are tune, in part because the pitch of harmonization changes a little depending on which note you are harmonizing with. Hearing when any double stope is out of tune is quite easy though. So if the E sounds wrong when played with an open A, then keep adjusting it until it feels “less wrong”.

      If you are really interested in harmonic series and how notes vary between pythagorean tuning vs equal temperament, I would encourage you to google the “pythagorean comma”. This rabbit hole goes a bit deeper still and uncovers a glitch in the nature of sound, almost like the uncertain situation of Schrodinger’s cat, every note is simultaneously in tune and yet not in tune, depending on how you are observing it.

      • Michael says:

        It is indeed a rabbit hole. I remember when I first learned about ET and thought life is good now, with all notes being in geometric series. At that point,I put all these other tuning systems out of my head. I wasn’t playing cello then, though. I’m not really sure about your last point about being in-tune and not in-tune, but I am familiar with the various commas in tuning discussions.

        • That is a great question, Michael. As I’m sure you are aware, the ideal frequency of a note changes depending on which notes are played around it. This is because the overtones of each note don’t quite line up the rest of the notes in a key (unless they are the root of key, and there are only melodic concerns, and not harmonic ones). Since the strings are stuck in one tuning during a song and we are relying on their resonance to clue us in, then the usefulness of that resonance will depend on how close the overtones of the open strings are to the ideal frequencies of the notes in the scale of the music. This changes depending on the root of the key and also on whether we are using a melodic or a harmonic scale. On top of this, most music tends to dance between various melodic and harmonic key centers. So you can see that fixed value of string resonance can be a double edged sword. This is particularly true when playing Bach (who likes to make strong hints that the key you’re playing in isn’t always the one written on the page). This is probably also why intonation in the cello suites is often considered a matter of personal discretion (within the bounds of reason of course). You do have to make active choices in your intonation in Bach, and understand what harmonic or melodic compromises you are making and why.

          All of the above of course requires that you can hear that degree on intonation. Getting to this point requires a great deal of practice and focus, incremental refinement, and maintenance. It never really gets perfect, only better and better. Using the string resonance is an intermediate technique to get a ballpark sense of pitch. You can then refine this by playing it in a double stop with the note preceding and following it in three music to get a little further down the rabbit hole. Finally, you have to look at in the larger context on the musical structure and decide whether you are going to aim for a local or a more global consistency.

          I hope this helped!

  4. Pascal Soucy says:

    Wassup? It’s been a while 🙂

    • Hey Pascal! I have been having some health issues recently so I haven’t been able to practice as much lately (maybe 10 hours per week). I have also had to take a temporary break from lessons for the same reason. I do have some drafted posts that I will be publishing soon, hopefully with a demonstration video 🙂 Hope you are well!

  5. Daniel Kopp says:

    Hi mindful cellist! I think that this project you’re doing is amazing! I’m working on my master’s degree in cello performance and I do a lot of teaching. I want to give you a free skype lesson sometime. I’m just so impressed with your dedication and progress, and I’d love to help you reach greater heights on your cello journey. Let me know if you’re interested

  6. Henry Chen says:

    Thanks for writing this blog. It’s very helpful. Are you still learning cello? Would love to see an update!

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