Re: The Prime Number Series as Generator (part 2):

Hi Paul,

Yes, you're right, that's the explanation of why it works.

I was looking for too complicated an explanation.

Well, it's good for us to know the reason. Perhaps I mightn't be the
only one whose been puzzling over it!

Thanks!

In fact, then, could get some prime ratios quite far apart
that will also work.

Clearly denom. and denum. have to be even
to produce primes

For 4/3, the closest ones will be to either side of
8/6

Try: 9/7 above, and 7/5 below.

9 isn't prime, so if one is particularly interested in primes,
double the numbers again, and you get 15/11 and 17/13,
and:

7/5 and 17/13 will work with each other, and all those other
numbers.

For 3/2, -> 6/4 -> 7/5 and 5/3 work.

However, I do think large primes are a valid method of exploration, as
valid as any other.

You can't hear that an interval is an e.t. one as distinct from
a large prime one, or a large ratio rational intonation one.

So seems to me, all the methods are equally valid, so long
as one makes no extraordinary claims to be able to hear
whether an interval is one or the other.

Mathematicians have long been fascinated by the gapiness
of the distribution of primes, and in some ways it is still
little understood.

Perhaps that fascination can be explored in music, or
inspire music and scale construction, or even, who ever knows
what the future may turn up, in some way something may
lead back the other way from scale construction and music
to prime number theory.

Robert

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_18204.html#18204

> Mathematicians have long been fascinated by the gapiness
> of the distribution of primes, and in some ways it is still
> little understood.
>
> Perhaps that fascination can be explored in music, or
> inspire music and scale construction, or even, who ever knows
> what the future may turn up, in some way something may
> lead back the other way from scale construction and music
> to prime number theory.

Exactly what I've had in mind all along!!

-monz
http://www.monz.org
"All roads lead to n^0"

Robert Walker wrote,

<<Perhaps that fascination can be explored in music, or inspire music
and scale construction, or even, who ever knows what the future may
turn up, in some way something may lead back the other way from scale
construction and music to prime number theory.>>

As a general rule, or natural enough way of going about things, I very
much agree with this sentiment/approach... thanks Robert!

--Dan Stearns

Robert Walker:
> > Mathematicians have long been fascinated by the gapiness
> > of the distribution of primes, and in some ways it is still
> > little understood.

For anyone on the list interested in gaps in the prime number sequence,
there's a very interesting article in the December 2000 Scientific American
about the size of the gaps and so on. Some people are just obsessed with
prime numbers (as we have seen! :).

Todd