RE 88CET

I do not mean to disparage Gary's 88CET compositions. It may
well be that one of his pieces is worth more than all my efforts
put together.

I do think I have the lead on quantity, however. He puts his
output at about half a CD. I suppose that is between 20 and 25
minutes.

I just did a census of my hard disk and counted 745 files with a
total playing time of about 45 hours. Some of these are
duplicates, and some are definitely not worth listening to. But
most are finished compositions, and some have even received
favorable review by esteemed members of this list. Probably
somewhat more than half of them are my "improvisations", but the
rest are arrangements of other peoples compositions.

I used 145 different scales.

Am I losing something by committing to all this automation?
Certainly. But I am also gaining other things. As they say in
the programming world, I can work at a higher level and let the
computer take care of the details. I think it is like the
difference between writing novels with a quill pen and a word
processor. Instead of a spell checker, I use a harmony checker.

But transcendental and irrational tunings can't be subjected to
this form of analysis unless they are first approximated in JI
terms. I think it's simpler just to work within a JI framework
to start with.

Put in it's most fundamental terms, instrumental music is an
attempt to make machines sing. In the realm of mechanical
musical instruments, Temperament was the easy way. That was
then. This is the electronic age. Temperament is
computationally difficult, and Just Intonation is easy.

Marion

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The algorithm for calculating a root is actually not so difficult.
This calculates a square root:

Answer := Of_Number;
loop
Delta := (Of_Number / Answer) - Answer;
if abs Delta <= Answer * Epsilon then
return Answer;
end if;
Answer := Answer + 0.5 * Delta;
end loop;

Epsilon indicates the required precision and is the smallest number that
makes a difference.
I suppose that modifying this to do the twelfth root of 2 is easy.
It converges very rapidly so it's doable by hand. It's very elementary
so it must have been known for a very long time.

Manuel Op de Coul coul@ezh.nl

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> most
> of the fascination with the twelfth root of two was in the problem
> of actually calculating these numbers. It was a considerable task that
> required strange algorithms to give approximations.

Of course, all you need to calculate these things to arbitrary precision is
ln(x), e^x, multiplication, and division. Anybody know when the Chinese
discovered the Taylor series (or the equivalent) for ln(x) and e^x?


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