Musique Non-Stop

Last night's forum was a quiet success. I was a bit harsh when I said the speaker was a pompous buffoon - he's just rather...portentious. Which, given the subject matter of 'Murder by Assembly Line: Capitalism and the Holocaust', seems justified.

Two new people turned up - young sociology students who grasped the roots and contradictions of racism immidiately and firmly. Which is more than can be said for most sociologists. I think we'll be seeing them again.


After that, I spent most of the night trying to work out the ratios involved in musical harmony. It gets complex, but boils down to this:

Imagine a vibrating string. Prevent one half (say the left half) vibrating, and the tone goes up by one octave. Seeing as we're concerned only with intevals less than one octave, we can ignore the right side of the string, which always vibrates. Of the right side, there are simple fractions describing how much of it does *not* vibrate.

Unison: 0
Minor 2nd: 1/24
Major 2nd: 1/8
Minor 3rd: 1/5
Major 3rd: 1/4
4th: 1/3
Diminished 5th: 2/5
5th: 1/2
Minor 6th: 3/5
Major 6th: 2/3
Minor 7th: 4/5
Major 7th: 7/8
Octave: 1

Three points. First, this is not the usual way of representing the ratios, but I find it clearer. Second, this describes the 'Just Temprement' system, which is not the system actually used in the modern world - we use an approximation called 'Equal Temprement'.

Third, other ratios are possible. There is no 3/4, which would go somewhere between the Major 6th and the Minor 7th. There is no Augmented 4th, which is slightly lower than the Diminished 5th. In fact there are many unused ratios in that range.

So why am I doing this? Well, it seems to me, that the practical problems involved in Just Temprement, which led to the adoption of Equal Temprement, do not apply to computer generated music. Just Temprement requires the complete retuning of the instrument for a key change - but a computer can calculate retunings in milliseconds.

Equal Temprement means that all keys are 'equally' out of tune. Now that the reasons for it's adoption can be circumvented, we can go back to the earlier system, and have perfectly in tune music, if we wish.

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