The golden ratio- Basic stamp question

Archiver

I am trying to figure out how to program the basic stamp to use the
number phi (1.61803398874989484820...) or (5 + 1)/2.
What I am doing is creating a complex sine wave with an infinately
complex series of tones created by using the number phi as a
constant. I have heard it said that this number is what we percieve
as beauty. I am not sure exactly what this means, but I want to
check it out. I am using the freqout function with two piezo
buzzers. I want to make them give off a tone of a number times
phi. I am having trouble programming in complex equations into the
stamp. Any suggestions?

Archiver

The BASIC Stamp uses integer math, but there is a trick you can do to
multiply by fractional values -- though nothing to the resolution of
your golden number. You can multiply by units of 1/65536 (0.000015259)
by using the ** operator. To multiply by your number you would do this:

myNewValue = myOldValue + (myOldValue ** 40503)

If you work backwards, this is the same as

myNewValue = myOldValue x 1.618026733

and is about as close as you're going to get. That said, you're going
to end up with a whole number ... so this may not work out for you in
the end.

-- Jon Williams
-- Applications Engineer, Parallax
-- Dallas Office

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Original Message

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From: wilcowannabe [noparse]/noparse]mailto:[url=http://forums.parallaxinc.com/group/basicstamps/post?postID=PJD_P9M1xdbOjLk0n8BoapzTAvHNMdB0G-PoKSoMoDjFYZ1JpaGmfp1PKw3BaWpzVZCuyd50C7kkC8sX]wilcowannabe@y...[/url
Sent: Friday, June 25, 2004 5:09 AM
To: basicstamps@yahoogroups.com
Subject: [noparse][[/noparse]basicstamps] The golden ratio- Basic stamp question


I am trying to figure out how to program the basic stamp to use the
number phi (1.61803398874989484820...) or (5 + 1)/2.
What I am doing is creating a complex sine wave with an infinately
complex series of tones created by using the number phi as a
constant. I have heard it said that this number is what we percieve
as beauty. I am not sure exactly what this means, but I want to
check it out. I am using the freqout function with two piezo
buzzers. I want to make them give off a tone of a number times
phi. I am having trouble programming in complex equations into the
stamp. Any suggestions?

Archiver

Hi Wilcowannabe,

Here is a similar notion and a tutorial about
using the ** operator to create fractions at this
URL:
<http://www.emesystems.com/BS2math1.htm#musical>

That shows how to use the ratio,
1.059463
to create an even-tempered ascending major
musical scale using the Stamp and a speaker. And
the ratio,
0.943874
to generate a descending minor scale.

(By the way, nothing played on piezo buzzer or
speaker is ever going to meet a standard of
beauty, for anyone, anywhere, anytime. Well,
granted, there has to be an exception!)

There is an accumulation of integer round-off
errors as a program applies the multiplier again
and again. If you really want to experiment with
higher precision and want to dig deeper into the
math, try this
http://www.emesystems.com/BS2math6.htm#multiplication
That shows how to carry the same logic out to 24
or 32 bits. There is an example with
multiplication by a constant 3.7305512 to 8
decimal places precision.

-- Tracy


‰
>I am trying to figure out how to program the basic stamp to use the
>number phi (1.61803398874989484820...) or (5 + 1)/2.
>What I am doing is creating a complex sine wave with an infinately
>complex series of tones created by using the number phi as a
>constant. I have heard it said that this number is what we percieve
>as beauty. I am not sure exactly what this means, but I want to
>check it out. I am using the freqout function with two piezo
>buzzers. I want to make them give off a tone of a number times
>phi. I am having trouble programming in complex equations into the
>stamp. Any suggestions?