THE generating function

Hi Manuel,

We must be misunderstanding each other. Let me be more clear about what I
was trying to say by providing a simple example:

Suppose you want to create a function that takes the integers 1, 2, and three
as inputs and gives 5, 7, and 11 and outputs. Unless my spreadsheet has lead
me totally astray, two simple examples of such functions are f1(n)=n*n-7n+1
and f2(n)=6/x-x+5. I could provide you with as many more as you would like.

Now to guess what you might be trying to say:

If you analyze a series of integers using some particular method you will get
a particular generating function.

I got my distaste for this kind of phraseology from sweating over those
Junior High School tests that require you to provide the next number in a
series. Later, I came to realize that there are an infinite number of ways
to analyze any particular set of data, and that this "teaching method" has
more to do with helping the teacher to maintain control of the class than a
real study of methods of analysis, as does much of what is taught in schools.

When it comes to analyzing data, I have found it better not to be so
monoTHEsistic.

Marion


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Haverstick again...once again, pardon me if I'm wrong, but did not
Partch himself, in several places in his book, get rather indignant
at those folks who had possession of microtonal keyboards (such as
Universities), but kept them under glass, so to speak, and would not
allow access to them by interested parties? And rightfully so...
Jon Szanto's comment to me in the last digest about respecting a
person's wishes as to how they want their music performed, referring
to Partch, was OK by me...but, again, I must state that music, once
brought into the physical world, belongs to no one (except in a legal
sense, to prevent them from getting ripped off)...since I did not know
Partch, I am at somewhat of a disadvantage here...but, I see no sensible
reason why his music should not be performed by whoever wants to, on
whatever instruments they want to use. Of course, one should respect
another's wishes...however, I think being selfish with one's art is
unacceptable on a deep level...sorry...Hstick

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