Article from Making Music, April 1987
The DX7 II fiddles with it, lots of music is based on an equal one, but the thing is, what is it?
LAST MONTH I fell inside a DX7 II and found something very strange. Did you know you can tune every note on the keyboard individually? Yes, said Yamaha, we designed it that way so you can fix your own temperaments. Wassat? Quite.
One trip to the library later and Making Music is in the position to tell you. The western way of sorting out a scale is to take an octave and split it into 12 slices. Arrange it on a keyboard and you have your familiar black and white notes. Unfortunately, when the ancients first did this they found it was a lot more difficult to get a scale to agree with itself than they thought.
How can this be? Well, logic told them that the simplest way of tuning an organ or piano would be via the circle of fifths: eg start on the C and play it alongside its fifth, a G. Tune the G so it's 'pure', ie spot on with no beating. Now play the G and its fifth, the D, and repeat the process. Keep going and you'll come back to C but an octave higher than the original, with all the notes in between covered and timed up.
Except that you won't. Those two Cs finish some way out of kilter, because music is not like that. The physics of frequencies may be immutable but our decision to hack an octave into 12 is arbitrary - other cultures pick other numbers. So there's nothing which says that just because two of our notes are perfectly in tune with each other they both ought to agree with a third, and that with a fourth, and so on...
In practice what you have to do is detune certain of those notes, some sharp, some flat by tiny amounts so nothing sounds really awful. In other words (ie not mine): "Tunings of the scale in which most or all of the concords are made slightly impure in order that few or none will be left distastefully so." And that is a temperament.
These days we use Equal Temperaments - the impurities are shared out so nothing gets really awful. This is far more significant than it sounds because the idea of sitting at one keyboard and being able to play without any keys being out of bounds would be more remarkable to early composers than your 16k cat-being-sick-in-a-bucket sample. Honest.
To get the circle of fifths to agree at both ends involves tweaking each note by about two cents (two hundredths of a semi-tone), and in general fourths go up and fifths go down. It was not always thus. In the 17th and 18th centuries before equality gained recognition, players fixed temperaments where certain keys were good (pure) and others were... er... to be avoided. They preferred the "extra diversity of intonational shading". Oh yeah.
Another popular choice (and one to be found in the DX7 II's temperament presets) is Mean Tone where all major thirds are pure. This invariably produces one particularly appalling fifth known as a 'wolf. In the late 17th and early 18th century a group of German Musical Theorists (brilliant name) became interested in Equal Temperament. Principle amongst their number was Herr Werckmeister and though he was by no means the first to propound the scheme, it gained acceptance from then on and his name became attached.
Gear in this article:
Feature by Paul Colbert
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