Piano Tuning: The “Mysterious Art”
“I know a tuned piano when I hear one,” the customer often says, “but I have no idea how my tuner gets it that way . . . and why it doesn’t stay that way.”
In our line of work, we piano tuners meet extremely talented individuals from virtually every walk of life. Yet so often do we encounter a total lack of knowledge regarding our field, it seems helpful to put in simple terms the basic principles of what many have called a “mysterious art.” It is really not so mysterious (nor would many consider it so simple!)
The Vibrating String
A vibrating object such as a tuning fork or string that produces an audible tone is a phenomenon of acoustics. Although the object is itself vibrating, its tone travels through air via the compression and rareficaton of air molecules, at a rate which is equal to the vibration rate of the vibrating object. (I.e., a tuning fork vibrating at 440 vibrations per second will produce a compression-rarefication pattern of 440 vibrations per second.) If the air is removed from the area surrounding the vibrating object, the sound disappears (as is often demonstrated in science classes with a bell inside of a jar; as the air is removed from the jar, the sound fades away.) Most piano tuners will turn down your offer of a fan on a hot day; this is because the fan blows the air, which in turn distorts the sounds he is trying to hear.
String Tension and its Relation to Pitch
Most of us at one time or another have, probably unknowingly, simulated the phenomenon of a vibrating piano string by stretching a rubber band between two fingers and plucking it. You’ve noticed how, by pulling the fingers apart, the pitch or tone becomes higher as the band vibrates increasingly faster. Similarly, the piano string is stretched between two points and set vibrating by a felt-covered “hammer.” In the piano, however, the string is attatched at one end to a fixed pin (or “hitch pin”) and at the other end to a movable pin (or “tuning pin”) which, when tightened, increases the vibration of the string, thus raising its pitch. The process becomes a major undertaking when one considers that most pianos contain well over 200 strings and 20 tons of string tension, which must tamed and managed as the tuner works.
Tuning The Strings
The process of tuning, then, is the act of adjusting the pitch of all 200-plus strings in the piano (this takes slightly longer than tuning a rubber band). This is done, of course, one string at a time, with each string becoming the fixed pitch, or standard, for the next for the next string. But how, you ask, does he know what pitch is “correct” for each string? For a detailed answer, I would place before you Herman Hemholz’s brilliant scientific treatise, On The Sensations of Tone, published in 1885,which in my copy is 576 pages of scientific jargon and mathematical formulas. But because that book is beyond the reach of most normal people, myself included, the following is a very simplified explanation in layman’s terms.
The Phenomenon of Beats
Many tuners still tune “by ear.” This is not accomplished by some rare gift which gives the tuner some mysterious, inner sense of pitch. While some tuners do use electronic devices that actually measure the vibration rate of each string, most simply make use of a miracle of acoustics which they have trained their ear to hear: the phenomenon of sound beats.
Let’s assume we want to tune a string vibrating six times per second, or 6 Hz. (This is for illustration only: actually, even the lowest note on the piano would vibrate at 27 Hz). For our fixed standard, we have a tuning fork vibrating eight times per second, or 8 Hz. The string wave would be represented by the top wave, the tuning fork by the bottom wave:
Notice that twice within the one-second interval, the wave formations of fork and string are both in the same direction, or cresting, at the same time. This is called being in phase. (For you audio lovers, it’s the same principle as hooking up speakers in a stereo system.) In practice, each time the waves are “in phase,” it can be heard as a pulsation, or “beat,” which the tuner then utilizes to tune the string. In the example above, if the tuner lowers the pitch of the string by loosening it, the difference between the two vibration rates will become greater and the beats will get faster; if he raises the pitch by tightening the string, the beats will slow down as the string vibration rate approaches that of the tuning fork, and eventually will disappear. This overly-simplified explanation is complicated by the fact that strings have not only a primary vibration rate, called the first partial, but also subdivides itself into smaller portions which form a vibration rate of their own; thus, when we tune an octave, even though the high note is twice the vibration rate of the lower note, in practice we are able to tune it beatless. But dealing with that complication is for another article – maybe.
Setting the Temperament
Now, assuming your tuner knows the basics, he begins the gruelling process by establishing one octave in the middle of the piano as a foundation, or temperament octave (this is typically called “seting the temperament”). Most tuners use the octave F to F encompassing middle C, tuning the strings in this octave so they are in correct proportion to each other. But how, you ask, is this determined?
Here is where the laws of nature, and of nature’s God, have thrown us a curve. One would expect it to have been a fairly simple procedure to tune the notes of the scale so that the pianist could play any chord or combination of notes and find them perfectly in tune. Yet such is not the case, for we find that when we tune the scale to sound a perfect C-chord (C-E-G), some of these same notes are out of tune for playing a perfect E-chord (E-G-B) or an F-sharp-chord (F#-A#-D#). This is particulary a problem for keyboard instruments which do not allow musicians to “adjust” the pitch as they play, as can be done with fretless stringed instruments such as violins, violas, and cellos.
Keyboard musicians in days gone by adjusted for the problem by tuning the scale to allow for playing in simple key signatures (i.e., those having few sharps and flats, like C, G, D, etc.), and considering the other key signatures unusable — they called them “wolves.” The music they wrote generally reflected this reality. But eventually, musicians and composers wanted all chords and key signatures at their disposal, so they devised a compromised scale, or “temperament,” which leaves all the chords imperfectly tuned, but not so much as to be intolerable. This scale is called the Equal Temperament, and it is the method most used in modern music today. (Incidently, the number used to calculate this scale is 1.0594631 — i.e., the vibration rate of each note is multiplied by that number to arrive at the rate of the next note.)
For an excellent book on the topic of equal temperament, see Temperament: How Music Became a Battleground for the Great Minds of Western Civilization. Click here for a description of this book, a Q&A with its author, Stuart Isacoff, and audio examples. YOU WON’T BELIEVE HOW FAR-REACHING THE DEVELOPMENT OF EQUAL TEMPERAMENT WAS!
Tuning the Octaves and Unisons
Now we’ll assume the temperament octave has been properly tuned. This octave now becomes the foundation for tuning all the other octaves on the piano. In other words, with F to F having been tuned, along with all the notes in between, the tuner then proceeds to tune F-sharp to the F-sharp one octave below it, then G to the G one octave below it, and so on. When this is done properly, each succeeding F to F octave is a mirror image of the one below it.
At some point you may have noticed that most of the notes on the piano have three strings, each of which must be tuned to the same vibration rate. These groups of three are called unisons, and they are usually the tuner’s last consideration after he has tuned one string for each note on the piano. He now must go back and, for each note, tune the unison string(s) to the string he has already tuned.
This is why you may have noticed an array of “mutes,” such as thick felt strips or rubber wedges, which your tuner uses to block off strings he doesn’t want to hear so that he can hear only the strings he needs to hear.
When all of this has been accomplished, your tuner, as well as you, may breathe a sigh of relief and pause to appreciate (we hope) a job well done.