Re: [tuning] Digest Number 727

Regarding the Fibonnaci Series thread. Am I missing the point or just
dense?- I keep seeing the sequence 5 - 7 - 12 -19, etc.

I thought the series was 1 - 2 - 3 - 5 - 8 - 13 - 21 - etc. Each number
being the sum of the previous two numbers - so how does 7 follow 5? can
someone educate me?

Cheers-

Allen Strange

Allen Strange wrote,

>Regarding the Fibonnaci Series thread. Am I missing the point or just
>dense?- I keep seeing the sequence 5 - 7 - 12 -19, etc.

>I thought the series was 1 - 2 - 3 - 5 - 8 - 13 - 21 - etc. Each number
>being the sum of the previous two numbers - so how does 7 follow 5? can
>someone educate me?

Allen,

The Fibonacci sequence is indeed 1 - 2 - 3 - 5 - 8 - 13 - 21, and we've been
talking about a generator (2^phi) which gives scales of these sizes. We've
also been talking about Kornerup's golden fifth of 696.21 cents, which gives
scales in Yasser's sequence of 2, 5, 7, 12, 19, 31, 50, . . . notes. Also,
we observed that in both sequences, each number is the sum of the previous
two numbers. I've touched upon the mathematical reasons for these patterns
-- I can go into more depth off-list if you're interested.

Perhaps you are confused because Spud duBoise referred to the
Kornerup/Yasser series as a Fibonacci sequence. Well, it does have the
property that each number is the sum of the previous two numbers, but there
are many such sequences, such as the Lucas sequence:

1, 3, 4, 7, 11, 18, 29, . . .

So I guess, strictly speaking, he was mistaken to call it "Fibonacci", but
at least that clues you in to the property by which the sequence is
constructed iteratively.

-Paul

Paul!
It has always been my understanding that the other series can be considered "reseeded"
fibonacci series as the the final convergence proportion between adjacent terms will still be
1.618.......

"Paul H. Erlich" wrote:

> Allen Strange wrote,
>
> >Regarding the Fibonnaci Series thread. Am I missing the point or just
> >dense?- I keep seeing the sequence 5 - 7 - 12 -19, etc.
>
> >I thought the series was 1 - 2 - 3 - 5 - 8 - 13 - 21 - etc. Each number
> >being the sum of the previous two numbers - so how does 7 follow 5? can
> >someone educate me?
>
> Allen,
>
> The Fibonacci sequence is indeed 1 - 2 - 3 - 5 - 8 - 13 - 21, and we've been
> talking about a generator (2^phi) which gives scales of these sizes. We've
> also been talking about Kornerup's golden fifth of 696.21 cents, which gives
> scales in Yasser's sequence of 2, 5, 7, 12, 19, 31, 50, . . . notes. Also,
> we observed that in both sequences, each number is the sum of the previous
> two numbers. I've touched upon the mathematical reasons for these patterns
> -- I can go into more depth off-list if you're interested.
>
> Perhaps you are confused because Spud duBoise referred to the
> Kornerup/Yasser series as a Fibonacci sequence. Well, it does have the
> property that each number is the sum of the previous two numbers, but there
> are many such sequences, such as the Lucas sequence:
>
> 1, 3, 4, 7, 11, 18, 29, . . .
>
> So I guess, strictly speaking, he was mistaken to call it "Fibonacci", but
> at least that clues you in to the property by which the sequence is
> constructed iteratively.
>
> -Paul
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Kraig wrote,

>It has always been my understanding that the other series can be considered
"reseeded" fibonacci series as the the final >convergence proportion between
adjacent terms will still be 1.618.......

Exactly right -- see my recent posts.