Thought for the Day => Golden Ratio

[uncloned]

The golden ratio found in nano scale quantum constructs

"Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618..., which is the golden ratio famous from art and architecture."

http://esciencenews.com/articles/2010/01/07/golden.ratio.discovered.a.quantum.world

[Sam_Zen]

One can find (or apply) the golden ratio in many things, so it's pitch as well..

[psishock]

+1 to Sam

[uncloned]

yes, however, I didn't expect it on a quantum level where probability rules every movement and state of matter.

essentially a string of atoms, really energy fields expressed as probabilities, have a vibrational relationship of PHI - and not say, two - is to me astounding - at least at this time it is not obvious as to why this should be.

If you consider that the harmonics of a string (and most instruments) are a ratio of 2 - a ratio of 1.618... is rather counter intuitive.


Though this did re-spark my interest in my phi based scale - which I hope to play with tonight.

[Sam_Zen]

What's counter intuitive ?
The ratio of 2 is based on octaves, so it derives its own scales and harmonics.
But if 2 is inverted one gets 0.5, and if 1.618... is inverted one gets 0.618... Quite unique and elegant.

Another article :
http://esciencenews.com/articles/2009/12/21/mystery.golden.ratio.explained

There's a Dutch 'academic' composer of electronic music, Jan Boerman, who used the golden ratio in many works.

[uncloned]

Well, perhaps its me - factor of 2 seems fairly straight forward.

It is easy to find that on say a guitar string - but try to find 0.618?

Now, here is a thought. Computers use binary - a language built on a factor of two. PHI is irrational, but I'd think it not impossible to use a numbering system base PHI, just like base two or base 10. After all, even though PHI is irrational if you take a ruler PHI still has a mark just like 1 or 2. So it should be possible.

I wonder (since this math is beyond me [I think]) what relationships would become obvious in a base PHI system that isn't apparent now.

[Sam_Zen]

Very nice ! That's what I thought , as a system base, a factor.

a ruler PHI still has a mark just like 1 or 2

It sure should have, because it's a remarkable number. The only inversion with a difference of exactly 1.
In fact, there are 2 numbers to use : 1.618 and 0.618.
The first causing an ascending order of higher values, the second one a descending order of lower values as an order.

It is easy to find that on say a guitar string - but try to find 0.618?

A matter of relocating the frets on the guitar I suppose, measuring the positions, as with the octave tuning.

[maleek]

The golden ratio and the mandelbrot fractal is two very fascinating which could perhaps even be described as mysterious subjects.

[uncloned]

the point about the ruler is that PHI is an irrational number



so technically you never can get *exactly* the right spot on a ruler or a guitar.

The idea though of using two tunings, one ascending (1.618) and one descending (0.618) is interesting - I wonder if it is possible to implement.

Now - I sort of used it as a base in that 12th root of PHI piece I posted at www.notonlymusic.com


makes me wonder about things like if the recession of the galaxies are multiples of PHI - if PHI and Plancks constant are related...


BUT - here is an argument I made in the microtonal tuning list....

PHI is irrational in BASE 10!!

It would not necessarily be irrational in every counting system - say... BASE PI - again I do not have the math to prove or disprove this conjecture but it "feels" right to me.


@maleek - hmm phi based fractals? that could be interesting

[Sam_Zen]

At least one can use PHI as a variable while rendering a fractal.