something completely different

Here's something a bit off the wall

2 + 4 + 8... 0.333 = 1/3
3 + 9 + 27... 0.125 = 1/8
4 + 16 + 64... 0.0666 = 1/15
5 + 25 + 125... 0.0416 = 1/24

inf.
Sigma n^(-i) = 1/(n^2 - 1)
i=1

The sum of these series for natural numbers > 1 is 0.75.

The sum of these series for the primes is... 5/9?
First 100 Primes = 0.5514386377736781
First 1,000 Primes = 0.551680596677039
First 10,000 Primes = 0.5516925343579381

Sorry if that doesn't make any sense.

-Carl

Carl Lumma wrote:
> Here's something a bit off the wall
> > 2 + 4 + 8... 0.333 = 1/3
> 3 + 9 + 27... 0.125 = 1/8
> 4 + 16 + 64... 0.0666 = 1/15
> 5 + 25 + 125... 0.0416 = 1/24
> > inf.
> Sigma n^(-i) = 1/(n^2 - 1)
> i=1
> > The sum of these series for natural numbers > 1 is 0.75.
> > The sum of these series for the primes is... 5/9?
> First 100 Primes = 0.5514386377736781
> First 1,000 Primes = 0.551680596677039
> First 10,000 Primes = 0.5516925343579381
> > > Sorry if that doesn't make any sense.
> > -Carl

This is the "tuning-math" group, not the "math-that-has-nothing-to-do-with-tuning" group.

Is someone forging Carl's email?

>> 2 + 4 + 8... 0.333 = 1/3
>> 3 + 9 + 27... 0.125 = 1/8
>> 4 + 16 + 64... 0.0666 = 1/15
>> 5 + 25 + 125... 0.0416 = 1/24
>>
>> inf.
>> Sigma n^(-i) = 1/(n^2 - 1)
>> i=1
>>
>> The sum of these series for natural numbers > 1 is 0.75.
>>
>> The sum of these series for the primes is... 5/9?
>> First 100 Primes = 0.5514386377736781
>> First 1,000 Primes = 0.551680596677039
>> First 10,000 Primes = 0.5516925343579381
>>
>> Sorry if that doesn't make any sense.
>>
>> -Carl
>
>This is the "tuning-math" group, not the
>"math-that-has-nothing-to-do-with-tuning" group.
>
>Is someone forging Carl's email?

No, that was me. Would you like me to delete it? It
was tuning-motivated and I was planning to come back
to it later, but I agree it was a bit of a stretch
without more detail.

-Carl

Carl Lumma wrote:
>> Is someone forging Carl's email?
> > No, that was me. Would you like me to delete it? It
> was tuning-motivated and I was planning to come back
> to it later, but I agree it was a bit of a stretch
> without more detail.
> > -Carl

No need to delete it; I'll take your word that it's tuning-related (though I don't see how). The figures look wrong, though. Surely the sum of 2^(-i) for all i from 1 to infinity is 1, not 1/3.

Herman wrote...

>> No, that was me. Would you like me to delete it? It
>> was tuning-motivated and I was planning to come back
>> to it later, but I agree it was a bit of a stretch
>> without more detail.
>>
>> -Carl
>
>No need to delete it; I'll take your word that it's tuning-related
>(though I don't see how). The figures look wrong, though. Surely the sum
>of 2^(-i) for all i from 1 to infinity is 1, not 1/3.
>

Whoops, you're right. Typo. Should have been

>> inf.
>> Sigma n^(-i) = 1/(n^2 - 1)
>> i=2

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Herman wrote...
>
> >> No, that was me. Would you like me to delete it? It
> >> was tuning-motivated and I was planning to come back
> >> to it later, but I agree it was a bit of a stretch
> >> without more detail.
> >>
> >> -Carl
> >
> >No need to delete it; I'll take your word that it's tuning-related
> >(though I don't see how). The figures look wrong, though. Surely
the sum
> >of 2^(-i) for all i from 1 to infinity is 1, not 1/3.
> >
>
> Whoops, you're right. Typo. Should have been
>
> >> inf.
> >> Sigma n^(-i) = 1/(n^2 - 1)
> >> i=2
>
> -Carl
>

Actually it is powers of 1/4 that add to 1/3. Powers of 1/5 add to
1/4 etc. Your sum above merely equals 1/2, not 1/3, for n=2.

inf.
Sigma n^(-1) = 1/(n-1)
i=2

I think is what you want.

i=1

All right! I have almost been outdone for irrelevant math on tuning-
math! I hope I am not a bad influence. Just kidding. Actually, I'd
like to see the scope increase some, even though admittedly I was
too far out was many of my posts.

PGH

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
> >
> > Herman wrote...
> >
> > >> No, that was me. Would you like me to delete it? It
> > >> was tuning-motivated and I was planning to come back
> > >> to it later, but I agree it was a bit of a stretch
> > >> without more detail.
> > >>
> > >> -Carl
> > >
> > >No need to delete it; I'll take your word that it's tuning-
related
> > >(though I don't see how). The figures look wrong, though. Surely
> the sum
> > >of 2^(-i) for all i from 1 to infinity is 1, not 1/3.
> > >
> >
> > Whoops, you're right. Typo. Should have been
> >
> > >> inf.
> > >> Sigma n^(-i) = 1/(n^2 - 1)
> > >> i=2
> >
> > -Carl
> >
>
> Actually it is powers of 1/4 that add to 1/3. Powers of 1/5 add to
> 1/4 etc. Your sum above merely equals 1/2, not 1/3, for n=2.
>
> inf.
> Sigma n^(-1) = 1/(n-1)
> i=2
>
> I think is what you want.
>
> i=1
>
> All right! I have almost been outdone for irrelevant math on tuning-
> math! I hope I am not a bad influence. Just kidding. Actually, I'd
> like to see the scope increase some, even though admittedly I was
> too far out with many of my posts.
>
> PGH
>

Talk about typos sorry

inf.
Sigma n^(-1) = 1/(n-1)
i=1

>> Whoops, you're right. Typo. Should have been
>>
>> >> inf.
>> >> Sigma n^(-i) = 1/(n^2 - 1)
>> >> i=2
>>
>> -Carl
>
>Actually it is powers of 1/4 that add to 1/3. Powers of 1/5 add to
>1/4 etc. Your sum above merely equals 1/2, not 1/3, for n=2.

Yeah, I wrote the sum wrongly. Sorry everybody. -Carl

I think I see what Carl's getting at. Your question is what that
interval would sound like? The one that is the sum of all primes?

On Tue, May 27, 2008 at 12:55 PM, Carl Lumma <carl@lumma.org> wrote:
>>> Whoops, you're right. Typo. Should have been
>>>
>>> >> inf.
>>> >> Sigma n^(-i) = 1/(n^2 - 1)
>>> >> i=2
>>>
>>> -Carl
>>
>>Actually it is powers of 1/4 that add to 1/3. Powers of 1/5 add to
>>1/4 etc. Your sum above merely equals 1/2, not 1/3, for n=2.
>
> Yeah, I wrote the sum wrongly. Sorry everybody. -Carl
>
>

--- In tuning-math@yahoogroups.com, "Mike Battaglia" wrote:
> I think I see what Carl's getting at. Your question is what that
> interval would sound like? The one that is the sum of all primes?

Actually I was playing with different kinds of
error weighting based on the notion of the human
voice as an ideal timbre. It didn't work out
terribly well and then I posted with several
typos. Sorry everyone, please disregard.

-Carl

Be careful when trying to calculate the sum of a series where, for each
term, the next term is ALWAYS bigger. It doesn't actually converge.
Could you refine the search?

________________________________

From: tuning-math@yahoogroups.com [mailto:tuning-math@yahoogroups.com]
On Behalf Of Mike Battaglia
Sent: Tuesday, May 27, 2008 3:23 PM
To: tuning-math@yahoogroups.com
Subject: Re: [tuning-math] Re: something completely different

I think I see what Carl's getting at. Your question is what that
interval would sound like? The one that is the sum of all primes?

On Tue, May 27, 2008 at 12:55 PM, Carl Lumma <carl@lumma.org
<mailto:carl%40lumma.org> > wrote:
>>> Whoops, you're right. Typo. Should have been
>>>
>>> >> inf.
>>> >> Sigma n^(-i) = 1/(n^2 - 1)
>>> >> i=2
>>>
>>> -Carl
>>
>>Actually it is powers of 1/4 that add to 1/3. Powers of 1/5 add to
>>1/4 etc. Your sum above merely equals 1/2, not 1/3, for n=2.
>
> Yeah, I wrote the sum wrongly. Sorry everybody. -Carl
>
>