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!