By Atar Arad

Not unlike the multitude of different calendars existing side by side with none claiming perfection (hence leap days and leap months), intonation systems come in different forms. Some are newer than others, and all are dealing, one way or another, with inherent imperfections imposed by the gods of music requiring us to continually explore and evolve, and never be entirely satisfied. With the variety of intonation systems invented through the ages, a modern string player has to be able to move from one to another as needed.

In childhood and through college I was taught to play with “expressive intonation.”  Leading tones had to be high for more pull to the tonic, major thirds had to be made sharper for the sake of brightness, and minor thirds had to be flattened for a darker sound. I have no recollection of needing to alter the intonation according to the kind of ensemble with which I was playing. We used the same intonation whether we played alone, with piano, or with other strings. There wasn’t any mention of a difference between listening horizontally or vertically either.

It took years of experience before I realized that when playing with piano, I should exercise some prudence before I let my intonation be “expressive” if I wanted to match the piano, and I usually do! I also learned that, when playing in a string ensemble, I may have to give up on the expressivity of my intervals for more harmonious-sounding chords.

Because of the diversity of choices in intonation, it should be evident that the tuning of our instruments should be subject to some different choices as well. Unfortunately many string players are still stuck today in a single way of tuning; they carefully tune all of their strings in perfect fifths regardless of the fact that using perfect fifths for tuning is not necessarily always the best choice!

Playing with Piano

A perfect fifth down from a perfectly tuned A gives you a D, which is lower than the D of the piano (by 1/12 of a Pythagorean comma, to be precise—the fifths of an equally tempered piano are slightly compressed). This small difference may require sharp ears for it to be noticeable. From this D, already lower than the piano D, you tune the G using another perfect fifth. This time the discrepancy of your two G’s is twice as large (1/6 of a comma) and is quite noticeable. From your now-very-low G, you tune down yet another fifth, and you arrive at a C, this time 1/4 of a comma flatter than that of the piano. The difference is not only noticeable—it is quite disturbing!

It is that simple and exactly that clear! Yet, there seems to be no desire to acknowledge this discrepancy of pitch. Many string players seem to be glad to have gotten used to it, continuing to tune the same way their predecessors did, the same way their fellow musicians do, dismissing the very reasonable idea of tuning each string separately to match the piano. I suggest that matching the piano string by string is a simple and necessary first step toward creating better intonation in harmony with the piano.

Let me ask violists to play the beginning of the fourth movement of Brahms’ Viola Sonata in F minor along with their pianist (Ex. 1, p 30). Tune your instrument in perfect fifths and listen to what happens in the sixth measure. The open C of your viola and the C of the piano hate each other! Now tune your strings to match the piano and play it again.  Do I see a smile on your face?

An even clearer example is Britten’s Lachrymae, Op. 48, which opens with the viola and the piano playing the exact same C. Ideally, the listener should hear one note, almost unaware that two different instruments are producing it. The same happens in the third measure (this time it’s a G) and yet again in the fifth measure with a common D. It is clear that tuning the viola with perfect fifths (as opposed to taking the C, G, and D from the piano) may result in a very disappointing opening.

The truth is that almost every piece you play with piano would offer a multitude of similar examples. Let’s face it: Every open C, G, or D you play requires tuning your strings to match the piano.

Violin pedagogue Mimi Zweig suggests an exercise that may advance the cause of tuning stringed instruments to match the piano, and enhance players’ desire to really play in tune with it. Open the lid of the piano and while your pianist presses down the right pedal get yourself as near to its strings as possible, placing your viola or violin (but no cello, please) under the lid. Play some slow, focused notes and adjust your pitch until you see the strings of the piano vibrate and hear them ringing sympathetically.

Playing in a String Ensemble 

When a string ensemble tunes their instruments in perfect fifths and then tries to use open strings to create a nice C-major chord, they do have to admit defeat. The C-major chord is far from perfect. That’s because the circle of fifths does not agree with the circle of thirds. As a result, the violin E sounds unbearably sharp alongside the viola or cello C. Since the interaction of the thirds is the most prominent factor in Classical and Romantic music, it may be advisable to sacrifice the open strings’ perfect fifths by tightening them, in favor of better thirds. Aiming for a pure major third between the open C and open E, or, for a pure major sixth, between the C and A, may facilitate the quest for better intonation.

This good news comes with a little caveat: The closer a group aims at a pure major third (or sixth) with open strings, the worse its fifths become. (A growing number of young quartets tune this way, making their lives easier and their intonation better. However, because of the bad fifths, some of them refrain from ever tuning onstage in front of an audience.)

Pure intonation in F-major movements is particularly difficult for a string ensemble to achieve with the strings tuned in perfect fifths. This is because the tonic F has to be placed differently to match either an occasional open C or an occasional open A. With your quartet, play the opening viola solo of the “American” Quartet, Op. 96, by Dvořák with your instruments tuned in perfect fifths (Ex. 2).

From the very beginning, the two violins have to match the second violin’s open A, and the violist has no choice but to match his or her initial F and all the remaining notes of the solo to this A. But wait a minute! There is one hopeless note with which you cannot do that: the prominent, repeated—accented!—open C in measure 5. This C is, of course, much too flat. Left as is, it could easily serve as inspiration for another viola joke! Now have your quartet tune the instruments compressing the fifths so that the C and A agree with each other. Violist, play the same solo and save the reputation of the viola community!

The same can be done with Beethoven’s String Quartet, Op. 59, No. 1, in F major (Ex. 3). You know by now that narrowing the fifths so that the open C matches the open A seems to be the right thing to do. But before you do that, take a look at measure 152 and the following six long measures of open C and G that you’ll have to hold. Should the purity of these six measures be sacrificed for the sake of the rest of the movement? Your choice . . .

There is a clearer decision, however, in the first movement of Dohnanyi’s Serenade, Op. 10, in the same key (Ex. 4). The viola’s stubborn fifths (mm. 22–28) surely dictate tuning the instruments with as perfect fifths as possible—with nothing to be done.

In order for you and your string ensemble to experience the possible advantage of tuning with narrow fifths, I would suggest the following: Choose a passage from your repertoire and play it with your strings tuned in perfect fifths. Do that again and again, gradually compressing the fifths. Take notice of the point at which the narrowed fifths allow you to play more easily in tune. Repeat this exercise, playing different passages in different tonalities.

You may even come to the conclusion that different tonalities actually benefit from different tuning.

Varying the type of tuning and intonation requires practice and to help you do that you can always download a tuning application from the web. These offer a surprisingly large number of tuning possibilities, of which equal temperament is but one. What should come first, however, is the desire to make your overtones love each other and to match the piano whenever appropriate. You should be able to program Dvořák’s “American” Quartet followed by his Piano Quintet, and tune differently for the two pieces. Your fingers are more intelligent than you give them credit for—or, perhaps it’s the brain. If you are discerning about what you hear and are capable of listening to your ensemble as one unit, your fingers will learn to oblige, regardless of what system you use.

At the risk of damaging my reputation as a teacher, I will say that practicing abstract scales is not ideal for an advanced player striving to be able to move from one type of intonation to another, and committing to tuning differently according to the tonality and type of ensemble. Instead, I recommend extracting scales from actual repertoire, allowing tuning and intonation choices to be based on the specific excerpt.

Just as how in sports all records are made to be broken, string players all must learn to expect the next generation to technically surpass their own. I have no doubt that up-and-coming string players will succeed in taking their intonation a step further with new tools and concepts. As a former member of the Cleveland Quartet, I am happy, and not at all embarrassed, to report that some young quartets play better in tune today than we did.

It is best to not resist that process but to encourage it, and in the case of tuning and intonation, to recognize that some habits and approaches may be slightly outdated. Remember, the gods of music call on us to continue to explore and evolve, and to never be entirely satisfied. 



Further Resources

I would recommend reading Ross W. Duffin’s How Equal Temperament Ruined Harmony (W.W. Norton & Company). It is interesting, remarkably instructive, pleasantly and humorously presented, and as engaging as a good detective story. (Did you know that in Mozart’s time there was a distinction between a major and a minor semitone? Did you know that at that time a G sharp was lower than an A flat?)