SINGING IN TUNE

TUNE AS YOU GO

       Of all the instruments, only the human voice can sing in perfect tune in all keys. Mother Nature has laid on musical instrument makers a tough situation.

SOME BASICS

       First, consider where we get the familar major scale (immortalized as the do-re-mi song in The Sound of Music ). It comes ultimately from nature. When we hear a sound - what we consider a single note - it is really made up of a combination of notes at various strengths. If a trumpet plays middle C {that is~ 256 vibrations/second), there are also present other notes ca11ed overtones, including the C an oc- tave above middle C, G above that, another C, then E above that, and many others. While these overtones are usually much less intense than middle C, they do include E and G, which, with the middle C, make up the C major chord. Unless you are playing a specially de- signed electronic instrument, there is no way to avoid this subtle major chord, even by playing only one note! If we next play G above middle C, we get another triad, G, B, and D. Notice that we now have found all the notes of the G major scale except F#, and that can be found by playing the note D (we get D, F#, and A). So far so good, so long as we do not stray far from the key of G major. Next~ we must think about what being in tune real1y means. First, each note - or pitch, to be more precise - is made up of vibrations. The more vibrations per second (which we call frequency), the higher the pitch. For middle C, the main - or lowest - or most prominent - frequency is 256 vibrations per second. If it is in perfect tune with middle C, the G above middle C will have 384 vibrations per sec- ond, or 1.5 times the frequency of middle c. Then the frequency of D above G wi]l be exactly 1.5 times the frequency of G, and so on. Here's the rub: if we tune G to exactly 1.5 times the frequency of C, then D to exactly 1.5 times the frequency of G, and go on through all twelve keys, we eventually can get back to middle C, but the frequency of that C is NOT 256 but 259.411 vibrations per second, and if you play both C's together it sounds BADLY OUT OF TUNE!

THE MAPMAKER'S DILEMMA

       Recall that the earth is basically a round ball some 8,000 miles in diameter. Imagine that you had a globe with a removable rubber surface, and that you wanted to cut out a piece that included the lower 48 states of the U.S.A. and make a flat map of it. To do that you would have to pull on the four corners (roughly Seattle, Boston, Miami, and San Diego) and stretch until the whole piece was now flat. The area around Kansas City would be quite accurate - for ex- ample the triangle from Kansas City to Topeka, KS, to Wichita, KS, back to Kansas City, would be closely representative of the real dis- tances. On the other hand, the distance from Boston, MA, to Seattle, WA, (remember the stretching?) would now be much larger than real. In short, the further away you got from the center of the 48 states the more distortion wou1d be introduced. Mapmakers have devised several ways to spread the distortion out, however, so that all areas of the map are - how to say it? - "close enough", or at worst equally distorted.

THE PIANO TUNER'S DILEMMA, OR WHY THE HUMAN
VOICE CAN SING IN PERFECT TUNE IN ALL KEYS -

       Unlike the human voice, which can be and is tuned at every note of a musical performance, the tuning of keyboard instruments is fixed by the tuner BEFORE the performance. That tuning can be done like the map obtained by stretching the corners, with the result that C major, G major, and F major will be in perfect tune, while the remoter keys (such as ab major, B major, and Db major) will sound so bad as to be unusable. This was the original way keyboards were tuned. As music evolved, composers began to write in the remoter keys (even Bach has some pieces in ab, B, and Db major), and today, after hun- dreds of schemes of tuning to resolve the dilemma, we use what is called equal temperament, which, like the mapmakers, uses compro- mise and spreads the distortion (or better, out-of-tuneness) around so that all keys are usable and equally pleasant. That's the good news. The bad news is that the main keyboard instrument, the piano, cannot play in any key in perfect tune. Further, when choirs sing to the accompaniment of a piano or organ, they sing in tune with the piano, so their voices become enslaved (at least pitch-wise) to an out-of-tune instrument. Now comes the good part. When the voices are freed from accompaniment, as in a capella singing, whether in madrigals, or in barbershop quartets, they now can sing in "perfect harmony" (to borrow a phrase ). If you have heard good barbershop singing, you may have felt the "WOW!" reaction that comes at the end of a piece when the quartet holds the final chord for several seconds, and has it really tuned up perfectly.

HYBRID INSTRUMENTS

       A few other instruments can play for the most part in perfect tune; while violins and related fretless bowed instruments do have four fixed pitches that are set when the instrument is tuned before a performance, other pitches can be adjusted by where the finger is put down. The slide trombone is similar, except that it has one fixed pitch (or three or four if you count the usable overtones).

BOTTOM LINE

       The key to playing or singing in pedect tune is, of course, careful listening. If you want to enjoy the rewards when when you hear a choir or quartet sing a capella, you must listen, too!

                                                                                                                       - Glenn A. Gentry

Reprinted from The Continuo, Vol 11 #2, January, 1999.