Finite JI = periodicity block

> [Paul Erlich, TD 465.6]
> all JI scales involve a sort-of-arbitrary decision of
> where to stop. What I've shown is, this decision is not
> completely arbitrary, it almost always seems to conform
> to a periodicity-block construction.

BINGO !!

Paul, you are brilliant. This statement expresses
precisely the idea that I was groping towards a year ago
when I formulated my concepts of bridging and finity.

(Which, I found out earlier this year, were formulated
by Fokker decades ago...)

Thanks for cleaning up my work for me!

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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I wrote,

>> all JI scales involve a sort-of-arbitrary decision of
>> where to stop. What I've shown is, this decision is not
>> completely arbitrary, it almost always seems to conform
>> to a periodicity-block construction.

Joe Monzo wrote,

>BINGO !!

>Paul, you are brilliant. This statement expresses
>precisely the idea that I was groping towards a year ago
>when I formulated my concepts of bridging and finity.

>(Which, I found out earlier this year, were formulated
>by Fokker decades ago...)

>Thanks for cleaning up my work for me!

Joe, the entire body of work I've put into this subject was specifically
aimed at you. When you came to visit me at my house, you described your
interest in the finity concept to me and I told you that the closest thing I
had heard of was Fokker's PD work. I knew very little about it at the time,
but due to your interest I dug into it and found many interesting things,
thus all my posts on the subject. I'm personally more interested in
temperament, since it seems like the next logical step -- once you've found
your periodicity block, distibute the unison vectors over the generating
intervals so that there is no sudden "break" at the edge of the block --
you're liberated and can represent an infinite expanse in the lattice with a
finite number of notes. Even if you want to keep the simultaneities in JI,
if you're using a computer you can use the temperament as the basis for an
adaptive JI scheme. There are other reasons I like temperament too. But for
you, Joe, I've focused on strict JI structures -- hope you've found them
valuable.