There Is No Such Thing As "Perfectly In Tune"

Wow, I see I never had a "tuning" tag before. First I do want to just admit a small caveat: yes, given certain stipulations and an entirely digital environment with synthesized instruments, you can have everything perfectly in tune. But it will sound artificial--because it is. With acoustic musical instruments or with a mixture of acoustic and electronic instruments, perfect tuning is impossible.

But we hear things all the time that sound really in tune, don't we? Yes, but that is because our sensitivity to tuning is both conditioned by habitual listening and limited by our sensitivity. Some composers, like Harry Partch or Ben Johnston, seem to have an enormously greater sensitivity to small pitch differences than most people. For this reason they developed tuning systems that use smaller intervals than the usual ones.

The standard, at least since the late 18th century, system of tuning is called "equal temperament" and it divides the octave into twelve equal parts which enables the modulation to every possible key. Prior to this, with the more or less unequal tuning systems, all keys were not equally useable. But the cost of this usability was the loss of the purity of the intervals derived from the overtones of vibrating strings. Systems like Pythagorean tuning used perfect fifths, but this resulted in some very out-of-tune intervals. The meantone system tried to resolve this problem by making all the fifths a bit narrower, but there were still unusable intervals. The adoptation of equal temperament made all intervals equally usable, but the cost was that all intervals are, just slightly, out of tune!

Sometimes you might see a guitarist struggling with tuning the instrument. This comes from an ignorance of how equal temperament works. As your ear improves you start to notice that when you play an E major chord, the third string sounds out of tune. The reason for this is that on the guitar the sixth string overtone series is quite audible and way up there is a G# that is a Pythagorean interval which is flatter than an equal tempered G#. So the third string sounds sharp if you are playing an E major chord. So you adjust the tuning of the third string a bit. But when you play a C major chord the third string open G natural sounds flat! So you go back and forth and typically end up somewhere in the middle, in effect, tempering the tuning a bit. The solution? Never tune with an E major chord, use E minor instead.

But the same problem exists in more complex environments as well. Piano tuners have to ignore the overtones from the lower strings when tuning the higher ones. Bowed instrument players often adjust the tuning of notes to make them more pure (or perhaps sometimes less pure) according to the context. Singers do the same. Wind instruments also make these kinds of adjustments. If you listen just to a certain point of sensitivity it all sounds perfectly in tune, but the closer you listen the more you get the feeling that everything is just slightly out of tune. Which it is.

Here is the Pachelbel Canon three different tuning systems: Just intonation, meantone and equal temperament. Can you hear the difference?