The piano, in all its innocence.

PHYSICS 101
So many of our problems arise when stubborn humans interact with a stubborn universe. "I WANT MY SUV AND I DON’T CARE HOW MUCH GAS IT USES!" or "I WANT MY NUCLEAR ARSENAL AND I DON’T CARE WHAT IT MAY DO TO THE PLANET!"

We wanted music, or at least our version of it, to be perfect. But the physical reality behind our kind of music required a certain imperfection. Which we wrestled with for centuries.

Unlike our reactions to certain of our other dealings with reality, the music problem isn’t going to hurt the planet, but it certainly does strange things to our ears and whatever parts of us our ears are connected to.

How? Why?

Not to get too technical, the problem goes like this:

Take a string. Stretch it. Pluck it. You hear a tone, which we’ll call A-1. Let’s say the string is vibrating 440 times per second. Take another string exactly half as long as the first one. Stretch it with the same tension and pluck it, the string vibrates exactly twice as fast (880 cycles per second). We’ll call this second tone A-2. You can pluck both strings at the same time and the two tones together, one low and one high, sound very pleasant. In the West, this interval, the aural distance between A-1 and A-2, is called an octave.

What has happened in the history of music, where many cultures discovered this property of strings, is that people came up with various ways of dividing up the possible sounds between those two notes. These ways of dividing the sounds are called scales.

In the West, we opted for dividing the basic scale into eight tones. (There are technical reasons for this choice that we don’t need to go into here.)

Starting with just those two notes, it’s possible to create a series of tones which go smoothly and perfectly from the lower tone to the higher tone. On a piano, you start at middle C and strike each white key sequentially to the right of middle C, and eight notes later you come to another C. You have played a scale in which you have smoothly gone from C-1 to C-2.

In an ideal universe, each note in that scale would increase by an exact, same number of vibrations per second.

The problem comes when you want to play a scale starting on a different note, a note other than C. Because: if you tune the strings for, say, the D scale perfectly, then it turns out you very slightly mess up the tuning for any strings that scale happens to share with the C scale. So now, if you go back and play the C scale, it sounds just a little different, a little "off". It’s no longer perfect.

What this meant in the history of Western music is that people had to figure out a way to fudge just a little bit ALL the tunings for all 12 possible scales. These different ways of tuning are called temperaments.

Until the 20^th century, pianos were tuned using many many different temperaments.

Bach was the first to popularize one method of tuning. He even wrote a major work, called "The Well-tempered Clavier," to demonstrate how well his particular set of fudgings worked.

Since then many other clever people have figured out many different ways to fudge the tuning.

Why, you ask, does this matter?

It turns out to matter a lot.

Our ears are so sensitive that, though we may not consciously realize it, we actually perceive these very subtle aural differences, these fudgings.

A C-chord that is tuned perfectly really does sound, well, pure, perfect, whole. But if you play, say, a G-sharp chord on that same piano, it has a very, very different aural quality, because the tuning had to be fudged so much to get that pure C-chord.

These differences are called timbre, or, sometimes, tonal color. Not only that, to our oh-so-clever little ears, these differences when used in complex music can have different (you ready?) emotional impact. Over the centuries, composers were aware of this and wrote their music accordingly.

If you play a simple piece on a piano where the C-scale is tuned perfectly it will sound one way. If you play the same piece on another piano where the C-scale has been fudged little bit, it will sound very different. It will have a different aural effect and even a different emotional effect.

OK, maybe you’re saying, this is more than I want to know, more than I need to know. All I know is that I like music. I like to listen to it. So what does this have to do with me?