Re: [tuning-math] Digest Number 859

Paul Hj. wrote:

>> I'm elsewhere now and the file is unavailable to me, but I'm positive
>> there were some Z-related groups of size 12 in there. Not sure why our
>> tallies don't match--do you want to apply your newfound knowledge and
>> see what Mr. Polya has to say about the matter, or should I?
>>
> Can you? A couple things - my error - 56822 is correct. Also, the
> above tally adds up to 56822. Definitely did not see 12 in your file
> (I scrolled all the way through it). 25253 is prime, which is a
> disappointment, oh well. I'm betting 25253 is right.
> (How would Polya calculate that?)

There are definitely 3 Z-related groups of size 12 in that file (I just
checked)--look for lines that start with "12". Maybe Excel counted them as
lines that started with "1"?

Polya would calculate it as in my earlier post for 12-tet: just do the
cycles for Z24 instead of 12, and look for the coefficient of x^12 in the
resulting polynomial...

--Jon

Gene wrote:

> It seems to me the simplest definition would be to say it is the
> smallest number among the orbit of sets if we take the sets to be
> numbers base 2--that is, the sum 2^i for i in I.

Yes, this is the way John Rahn puts it, iirc. Forte's prime forms disagree
on 3 hexachords: he uses [013689] instead of [023679], [013589] instead of
[014579], and one other I can't think of. His ordering is also a mess--he
gives labels like 6-1, 6-2 etc for hexachords, but it's based on an old
ordering that reduced for the Z-relation, so it doesn't make any sense any
more. I wish we could lose that ordering and just use the natural ordering
of binary representations instead. That's obviously the way any fast
computer implementation is going to do it.

--- In tuning-math@yahoogroups.com, jon wild <wild@f...> wrote:
>
> There are definitely 3 Z-related groups of size 12 in that file (I
just checked)--look for lines that start with "12". Maybe Excel
counted them as lines that started with "1"?
> --Jon

I checked the raw file up and down. (I unzipped it again). I cannot
find one "12". Could you give me line numbers?

Paul