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
Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 27 Jul 1996 08:32 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id XAA15974; Fri, 26 Jul 1996 23:32:14 -0700 Date: Fri, 26 Jul 1996 23:32:14 -0700 Message-Id: <199607270631.AAA04816@freenet.uchsc.EDU> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu
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
Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 27 Jul 1996 19:23 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA21195; Sat, 27 Jul 1996 10:23:18 -0700 Date: Sat, 27 Jul 1996 10:23:18 -0700 Message-Id: <199607271721.LAA18998@freenet.uchsc.EDU> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu