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As featured in The Harmonizer.

A quick lesson in physics teaches how to hear when you are totally locked in.

Barbershoppers are ear singers. We sing and tune by ear, so why do so many of us often sing out of tune? Perhaps a more pertinent question would be, “What does in tune actually mean?” Are we singing in tune with a piano? With our neighbor on the risers? With what we remember as “Do” that was blown 45 seconds ago?

The very concept of tuning requires a minimum of two sounding pitches. A solo voice cannot sing harmonically out of tune, because it is not being compared to any other source. Most amateur musicians can tell when an interval does not sound right, and we know intuitively when a sound is disagreeable or when it is pleasurable. If our goal is to sing in tune with another person, we need to know what it means to sing in or out of tune.

You don’t make overtones—they’re already there.

You’ve probably heard of overtones, or perhaps the overtone series. But did you know that we cannot “make” overtones? They are always there. Every note you sing, even every word you speak, contains an infinite number of pitches (overtones) above the one you are singing (fundamental). When you sing one note, you are actually singing many notes at the same time. The extra notes you are singing have a very specific order: the first pitch is one octave above the fundamental note you are singing, the second is a fifth higher, and then a fourth higher, and then a third higher, and so on until the overtones become so close together that we don’t have names for them. They eventually get so high in frequency that the human ear can no longer hear them.

But here’s where it gets interesting. These overtones exist in physics. We do not get to
choose at which intervals the overtones will sound. As an example, if you sing the note C, you will also be producing a C one octave above your fundamental. There is nothing you can do with your voice that will cause your first overtone (or any subsequent overtone) to be anything other than an octave.

The beats you don’t want to hear.

This is important because the intervals between the overtones reside in the most “in tune” place. In other words, overtones happen to exist where there are the fewest possible beats to create an interval. You hear examples of the overtone series in all music, especially on bugle calls like “Taps” and “Reveille.” These songs are a simply a brass player moving up and down on the overtone series, using no valves.

When you hear dissonance, you hear beats in the sound—-small fluttering disturbances in the sound that, if prominent enough, can make you cringe. The fewer beats you hear, the more in-tune you’ll perceive something to be. A great way to learn to hear beats is to sing against a fixed pitch: a pitch pipe works great. As you blow air through your pipe, hum the same note. Now, hum a little flat and hear how the beats are very obvious. Slowly bend the pitch back up, and when you finally match pitch, the sound will smooth out and the beats will go away.

The math of being in tune.

There is an easy mathematical solution to determine which set of pitches will be the most in tune. In a purely-tuned major third, the higher pitch will oscillate 5 times for every 4 times the lower pitch oscillates. This repeating pattern of 5:4 produces a harmony that the human ear finds pleasing and considers to be in tune. Not only is this because this tuning of a major third contains the fewest possible beats, but also because it is the exact interval between the 4th and 5th overtones in the overtone series. In other words, we constantly hear this interval in every note somebody sings and even in every word they speak.

By way of comparison, the major 3rd on a piano or electronic keyboard, which is equally
tempered and therefore slightly out of tune in every key, has a ratio of 15749:12500. In other words, for every 15,749 times the upper note oscillates, the lower note will oscillate 12,500 times. This ratio is so large that the pattern doesn’t repeat often enough for the ear to hear it as perfectly in tune. Beats are heard when a major third is played on these instruments, but this is the tricky piece: if we have grown up in Western music and heard this “out of tune” sound for a lifetime, we learn to accept it over time … it starts to sound right to our ears. That’s why getting away from the piano is critical for success in barbershop.

So let’s get really technical. We now know that physics determines which overtones are being produced. We also know that the overtones produced are the most perfectly in tune intervals possible. Third, we know that these intervals are produced in every note we sing. Thus, if Person One sings a C, he is unintentionally also producing an octave above that C, and then a fifth above that octave, which is a G. After that we get another C and then an E, and so on. That E, the fifth harmonic (or 4th overtone), does not match the E on a piano.

If Person Two sings an E against a Person One’s C, we find ourselves back to the first question: with what is Person Two supposed to sing in tune? If he or she sings in tune to the piano, this will not be the same E that Person One is already producing in his/her overtone series. Thus, they will be singing out of tune with each other. In order to avoid the beats of dissonance, Person Two must sing the same E that Person One is already producing via the overtone series of his/her C.

How is this done? With practice, we can tune our ears to hearing overtones. But more simply than that, listen for the beats. The fewer beats, the more in tune. Let your ears do the work. It is not about singing higher or lower; it is more about simply singing the “right” note. And that right note is the one that exists in physics, the one that has the fewest beats in the sound, and the one that is automatically produced in the overtone series of the person you’re singing with. When you hear beats, you’re hearing overtones not matching up in low ratios.

If you would like to learn more, search online for “just vs equal temperament” and you will find a wealth of information

Jay Dougherty Asst. Professor, Director of Choirs and Choral Activities Marietta College