- I´d like to share a little concept for ACCOUSTICAL FACTORIZATION by
using the relation between tones and overtones on strings, many
guitarplayers might be familiar with: Maybe its useful for someone of you?
Imagine a string swinging in the fundamental frequency. You can
theoretically create additional overtones for example on a guitar by
touching the string slightly at any point you wish.(Practicaly only
overtones with high amplitudes might be hearable by ear, so the number
of playable Overtones is limited; see also
An Overtone is created by dividing the fundamental Oscillation of the
string in a bunch of standing waves with the same wavelenght each.
What does it have to do with Factorization?
Explanation by example:
1. Add to the fundamental oscillation of a string an oscillation of
187 standing waves by creating an Overtone with wavelenght of 1/187
2. Try to create as much additional overtones you can with the
IMPORTANT PREMISE, that you search these Overtones only by touching
the allready existing wavenodes. (So touch the string at 1/187, 2/187,
3/187, but NOT for example at 2,5/187)
3. You will find out that under these circumstances the string allows
only the following three Overtones:
Overtone with wavelenght 1/187 (187 standing waves)
Overtone with wavelenght 11/187 (17 standing waves)
Overtone with wavelenght 17/187 (11 standing waves)
4. Interpreting this result in mathematical terms will wake you up,
Surely it works in theory with any possible "Overtone-Composite", as
long as the Premise mentioned above is taken into account.
Anyway, the search for overtones in that way still works like trying
out every divisor of 187, so it doesnt seem to be spectacular and is a
slow way of factorization.
5. More intersting might be the following way:
-Create the Overtone 1/187 first by external stimulation, DONT start
with the fundamental resonance.
-Now "shake" the whole string and add in that way so much energy, that
at some point the absorption of energy within the amplitude of the
allready existing standing wave comes to its limits
-Now the string will try to "swing" in all other possible frequencys,
while the allready existing wavenodes are the most stable and the
wavemaxima are the most vulnerable parts of the string regarding
-Guess what additional Overtones will arise first...
Sorry to bother you with so much text, I hope I get some replys
nonetheless. Is it intersting? Does it fit in any formula? Do you have
hints for me where to read further or something like that?
In case have an additional look at
- PHYSICS: Factoring Numbers with Waves
Science 27 April 2007: 554-555
A wise man hears one word and understands two.
[Non-text portions of this message have been removed]
Thank You for the hint, IÂ´ll have a look at it soon as I get free
--- In firstname.lastname@example.org, "scolnik" <scolnik@...> wrote:
> PHYSICS: Factoring Numbers with Waves
> Science 27 April 2007: 554-555
> DOI: 10.1126/science.1140915
> Hugo Scolnik