microtonal music here....

http://artists.mp3s.com/artists/433/carlos_sampaio.html
Thanks
:)

I am trying to understand the lattices.

Can somebody remind the Fundamental theorem of arithmetic to me ?

I should pay more attention when I was in highschool...

Thanks

hi Alexandros,

> From: "Alexandros Papadopoulos" <Alexmoog@otenet.gr>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, September 14, 2002 3:22 PM
> Subject: [tuning] Fundamental theorem of arithmetic
>
>
> I am trying to understand the lattices.
>
> Can somebody remind the Fundamental theorem of arithmetic to me ?
>
> I should pay more attention when I was in highschool...
>
> Thanks

try this definition:

http://www.ixpres.com/interval/dict/fundo.htm

and this explanation:

http://www.ixpres.com/interval/monzo/article/article.htm#prime

-monz
"All roads lead to n^0"

hi again Alexandros,

> try this definition:
>
> http://www.ixpres.com/interval/dict/fundo.htm

i thought that in case you don't have web access,
here's the main part of my definition:

>> A mathematical rule which states that any number
>> can be described as the product of its prime-factors,
>> with each prime in the series raised to various
>> exponents, 0 or positive.
>>
>> By extension, this method can also be used to
>> factor rational proportions into the series of
>> primes or odd-numbers, with 0, positive, or
>>*negative* exponents, the negative exponents
>> representing the denominator of the ratio.

BTW, you mathematicians, isn't the first part of
my definition incorrect? ... shouldn't it say
"any *integer* (or whole-number?) can be described
as ..." etc., ?

-monz
"all roads lead to n^0"

--- In tuning@y..., "monz" <monz@a...> wrote:

> BTW, you mathematicians, isn't the first part of
> my definition incorrect? ... shouldn't it say
> "any *integer* (or whole-number?) can be described
> as ..." etc., ?

I suppose you're supposed to figure it out by context.

You could say: Any integer N>1 is represented uniquely by a product p1^e1 p2^e2 ... pk^ek, where the the pn are primes, written in ascending order so that n<m ==>pn<pm, and the exponents en are positive integers.

hi Gene,

> From: "Gene Ward Smith" <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, September 14, 2002 10:01 PM
> Subject: [tuning] Re: Fundamental theorem of arithmetic
>

> --- In tuning@y..., "monz" <monz@a...> wrote:
>
> > BTW, you mathematicians, isn't the first part of
> > my definition incorrect? ... shouldn't it say
> > "any *integer* (or whole-number?) can be described
> > as ..." etc., ?
>
> I suppose you're supposed to figure it out by context.
>
> You could say: Any integer N>1 is represented uniquely
> by a product p1^e1 p2^e2 ... pk^ek, where the the pn are
> primes, written in ascending order so that n<m ==>pn<pm,
> and the exponents en are positive integers.

YIKES! is *that* what i need to put in my definition?!

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:

> YIKES! is *that* what i need to put in my definition?!

Not really. What about "The factorization of any integer N>1 into prime factors is unique aside from the order of the factors"?