Room 46--The notes in the cracks of the piano

Every sound is generally made from a fundamental pitch plus various harmonics. This is a very complex subject which you should investigate elsewhere. The harmonics are what give instruments and the human voice their special qualities which helps you distinguish them in the real world. It is the quality of harmonics which give the oboe its somewhat nasal tone quality and what allows you to tell the difference between that instrument and a clarinet.

If you want to hear how harmonics sound you can perform this demonstration on a grand piano. Take your forearm and press down the keys over a few octaves, but do it silently so that it doesn’t make a sound. Then several octaves below the keys you have depressed (this is so the dampers are lifted off the string) play a very loud staccato note. You should hear several of the strings which are not being dampened vibrate sympathetically from the loud note you played.

The modern piano is an interesting item because it uses a system of temperament which has been adjusted so that it sounds correct to the ear. Why the adjustment? Because if it were properly in tune according to the harmonic series, the upper pitches would be out of adjustment with the lower ones. For example, you can listen next to a synthesized version of the first 12 harmonics. Notice how when all the pitches sound together, it’s not too bad, but some of the upper ones are not exactly in tune. Listen! Next, listen to a scale in equal temperament, which approximates the way a piano is tuned. Listen!

Now see if you can hear how the pitches are not exactly the same in the system of just intonation. Listen!

Notice how the 3rd note in the just series seems lower than it should be. Go back and compare them again if you need to. Then, listen to what happens if you play both simultaneously. Then you can hear the beat frequencies caused by the differences in the two systems. Listen!

Let’s pose another question for thought. What about the pitches in between the ones represented by the piano keys? For example, there is a difference between a D# and an E-flat even though they’re the same key. That’s part of the adjustment that has been made to make the equal tempered scale sound correct to the ear.

One of the experiments that Charles Ives created was his Three Quarter-Tone Pieces, which are played by two-pianos tuned a quarter-step apart to effectively give possible chromatic scales of 24 pitches rather than the usual 12. It causes some unusual dissonances. Here is the second of the three pieces, so when as Ives might say, “When you’re ready to stand up and take your dissonance like a man--Listen!

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