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JBL37
01-09-2010, 08:27 PM
Does anyone use the GOLDEN RATIO in their work? Jim

http://www.dailykos.com/story/2010/1/8/823188/-Golden-Ratio-Discovered-in-Quantum-World

lakeside53
01-09-2010, 08:32 PM
Only when I'm in the bathroom :D

I did make some windows in that ratio... 1.618 IIRC - SWMBO... but I must admit, they did look "right"...

01-09-2010, 08:47 PM
Yes, in damn near everything I do, In any artistic endeavor I try to stress 3,5 and 7s as they are more interesting the 2,4 and 6 as I believe it is human nature to try to make sence of everything you observe. If it's 2,4 or 6 you can divide it up the middle and cast it off. The odd numbers cause you to trip up. If you look for it you will find the numbers 3,5 and 7 in everything interesting that you find pleasing.

darryl
01-09-2010, 08:59 PM
Used to use those ratios when building speaker cabinets. I used to look at rooms in new houses and marvel at the sizes they were laid out in, and the acoustics they presented. Some were basically cubic- not comfortable. Even with an 8 ft ceiling and one other dimension at 8 ft - it was not something I cared for.

If I was building a front panel for a piece of equipment, I'd try to stagger the dimensions to fit odd numbers. It just looks better.

Evan
01-09-2010, 10:04 PM
The Golden Ratio, Golden Mean, Phi...

It is a very interesting number. It is a fractal number. It is described by the Fibonacci series: 0, 1, 1, 2, 3, 5, 8, 13 ...

What number comes next?

The sequence is very special and not all of it's characteristics have been discovered. For instance, Any Fibonacci number that is prime Fn has a prime index (n) which is prime, with the exception of F4 = 3. However, not all Fibonacci primes are indices for Fibonacci primes. It isn't known if there are an infinite number of Fibonacci primes.

The golden rectangle has the ratio of 1/1.618... This is very important to the design of structures that must deal with resonant phenomena. A golden rectangle may be divided into a square which then leave another smaller golden rectangle. It may be divided into a square and of course another golden rectangle, ad infinitum. What this means is that there is no wavelength of vibration that has a fundamental and a harmonic that share the x and y axes of the shape.

For example, a rectangle with a 2-1 ratio can support a standing wave in one axis and the 2nd harmonic in it's other. This makes possible an infinite series of resonance frequencies that such a shape can respond to.

A golden rectangle on the other hand has no such resonances which makes it a desirable shape for speaker cabinets and machine components.

Alexander Slocum, Professor of Mechanical Engineering at MIT recommends using the golden rectangle when possible as the basis for many parts of machines. A specific example is the spacing of the sliding bearings for a lathe or milling machine carriage. The centres of the linear bearings should be placed on the corners of a golden rectangle if possible. This makes binding due to cocking impossible and eliminates many possible resonances.

If parts are designed that each have the shape of different size golden rectangles is is axiomatic that neither will share any resonant frequencies.

If a golden rectangle is designed with a prime ratio then it has no resonant frequencies in common with any other regular polygon other than itself.

I took advantage of these principles when I designed my milling machine.

nheng
01-09-2010, 10:25 PM
Evan, Alex is a friend of mine and we were on a First robotics team with our kids several years ago. He's put a lot of good stuff in open access ... which I guess MIT has done in general.

Too many things to think about these days but the Golden ratio is going to climb up the list ... at least where resonances are a concern.

Have you thought about introducing it into machine tooling and workholding accessories? Although in those cases, the tools or parts being fixtured would probably become part of the final ratio.

Den

Astronowanabe
01-10-2010, 03:14 AM
it's inverse is itself -1
squared it is itself +1

I call it an additive sequence, that is,
0, 1,1,2,3,5,8,13,21,34,55,89,144 ...
is but a particular additive sequence that has the property successive terms tend to Phi. the truth is they all do.

that is pick any two numbers, and yes I do mean any.
positive, negative, integer, fraction, decimal ...
and start adding the the last two to get the next

every once and a while as to go, divide the last by the one before
and sure as sh*t they are going to go to 1.61803...

and just this week ...they just found in all the way
down at the quantum level

Golden ratio discovered in a quantum world
Researchers from the German Helmholtz-Zentrum Berlin f¸r Materialien und Energie, in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio.

darryl
01-10-2010, 04:18 AM
I seem to recall reading about music, the tones used being related to the golden mean-

Maybe I'm off base, but it was pretty interesting reading. What else was involved- the Mozart effect-

Charles P
01-10-2010, 04:27 AM
A number of composers appear to have used it (Barktok, Debussy and Satie are usually cited - not Mozart). Whether they planned it that way or it's just a post compositional observation is unknown.
There's another more modern (to my ears tune-less) composer who used it but I can't recall which at the moment. It does however seem to suggest that the use doesn't confer listenability

Charles

beanbag
01-10-2010, 05:46 AM
Musical notes are about as ratio-ed and proportional and interval-ed as you can get. The golden ratio is like the opposite

01-10-2010, 07:37 AM
.......................There's another more modern (to my ears tune-less) composer who used it but I can't recall which at the moment. It does however seem to suggest that the use doesn't confer listenability

Charles

If it was used accurately I would expect the music to sound without evidence of hand and therefore sterile. Likely sound worse then elevator music.

Evan
01-10-2010, 09:30 AM
If it was used accurately I would expect the music to sound without evidence of hand and therefore sterile.

Hmm. It should sound atonal in that the frequencies will be non harmonic. That isn't necessarily evidence of "lack of hand". The 12 tone scale we use for music is not the only scale people find pleasing. It is very mathematically defined in case of the equally tempered scale. Each note is at an interval equal to the twelfth root of two. Each octave is a doubling of frequency.

Computer programs exist that will generate music based on the mathematical properties of the equally tempered scale. The music so generated can be surprisingly "listenable". I will supply an example later. It seems that there is something more basic going on that determines whether music is appealing or not.

The equally tempered scale is a compromise that was evolved from the necessity of tuning an orchestra to play in concert with the one instrument that can't be retuned in use, the piano. The tuning of a piano is in
itself a compromise mandated by the physics of vibrating strings and the way that humans perceive sound. It is also necessary to prevent the dissonances that will occur if a "just" or "perfect" tuned instrument is made to play in a different key than it's tuning.

By far the biggest contributor to the "evidence of hand" in music is the imperfect timing of music played by a real hand. Even the most skilled artist cannot completely remove the small variations in timing that make the music sound "alive".

Any ham radio operator that is proficient in code can attest that it is easy to recognize a particular person on the radio by the sound of their "fist" when they transmit code using a hand key. It's a characteristic timing of the elements of the code that each person develops, usually inadvertantly, and is almost like an affectation of speech.

Music without these small timing variations sounds sterile and by definition it is since only a mechanical or electronic machine can play with perfect timing.

01-10-2010, 11:38 AM
The muscal scales we are used to today are "tempered" that is the twelve tones have the incremental ratio of 2^(1/12) that is 1.059545... per semi-tone. Before Bach and the standardization of the frequency of "A" European music tonality was almost chaotic. The progression of musical pitches were ratios attainable only by fretless instruments and the human voice. Anything with keys or valves were forced into compromise when playing in key other than what they were made for.

It all appeared to be hair splitting in 2010 but in the Rennaisance the subtle (and sometimes jarring) tonal dissonances drove the musicians of the day bananas. If you sit at a well tuned piano in a quiet room and play pairs of notes together you will hear some intervals seem to "waver" lightly (if that's the word.) These are "beats" indicating the inevitable error between a tempered scale and a true scale. Most errors are small but to anyone with a good sense of perfect pitch they are very distracting.

Oddly, the very thing that sounds so sour from a kid orchestra (bad pitch) is the very thing that sounds so pleasing on a much smaller scale of error in an orchestra or chorus. If all the voices and nstrument were in perfect tune they would seem lifeless.

And that about exhausts my knowledge on this topic.

Getting back to the Golden Rectangle, the proportion (I always rounded t to 1 5/8:1) is often what make or breaks the impact of a stage set to the audience. Richard and I would brainstorm over a set design for hours tweaking it here and there wasting acres of paper until it suddenly gels. Later in buildng the set while scaling up the rough pencil sketch I often found the last few details settled had the Golden Rectangle involved in it somewhere. It wasn't a conscious decision; it was a "looks right" decision.

beanbag
01-10-2010, 05:51 PM
Just to add a few musical blurbs:

Dynamics can also make a huge difference in whether music passes the Turing test. On types of instrument that does not have (continuously variable) dynamic range, like a harpsicord or organ, where all the notes are equal volume, the performer has no choice but to throw in timing variations on purpose.

On the other hand, dynamic range control, the initial impulse and trailing off of notes, is what makes or breaks vocal or midi music in sounding human. Another example is Bach's keyboard works played on piano. They can be played with perfect timing and sound very "alive" with good dynamic modulation.

Also, I learned from Peter Schikele that in a pentatonic scale, no note is a wrong note. I.e. Every note sounds fine followed by any other note. You can randomly mash the black keys on a piano and it will sound ok.

01-10-2010, 08:24 PM
................................Oddly, the very thing that sounds so sour from a kid orchestra (bad pitch) is the very thing that sounds so pleasing on a much smaller scale of error in an orchestra or chorus. If all the voices and nstrument were in perfect tune they would seem lifeless.
.......................................

That is exactly the point I was trying to make but failed to make it as elequently as Forrest.

hornluv
01-10-2010, 08:47 PM
I had no idea there were so many musically minded folks here. I first learned about the golden ratio when I was a music student. In analysis of most music written in the Sonata-Allegro form (one of many musical forms, but the one most often used as the first movement of symphonies, concertos, and sonatas), it has been noticed that it tends to basically follow the golden ratio, but it's a really rough conformation. If you describe it as part A is to part B as B is to A+B, then it's pretty close, but nobody thinks for a minute that composers did it on purpose. Just another instance of musicologists and theorists trying to pigeonhole stuff into a particular set of rules.

Evan
01-10-2010, 08:55 PM
What Forrest suggests may well be true but it isn't possible to tune all the instruments to perfect tuning. The strings are no problem but brasses and woodwinds are tuned by the placement of the valves and finger holes. As far as I know nobody has ever put together an entire orchestra to play with perfect tuned instruments. As long as all play in the single key the instruments are tuned for it should sound fine but extremely limited in scope.

The piano is the master instrument to which all the others are tuned in an orchestra. Piano tuning is an art and a science that requires an intimate knowledge of the physics of oscillatory phenomena and how it pertains to metal wires under tension. It also requires knowledge of how we perceive sound as musical notes. The upper octaves of a piano are stretched by tuning them sharp to account for the reduced response of the human ear at high frequencies. In order to properly tune a piano the tuner must have either perfect pitch or very close to it. Technical instruments alone can't replace the subjective response of the ear and brain.

Here is the small piece of computer generated music that I promised. It was generated by an old program called Automid. It's a 15k midi file which will play on most computers.

http://ixian.ca/server/ewmidi04.mid

beanbag
01-10-2010, 09:53 PM
The upper octaves of a piano are stretched by tuning them sharp to account for the reduced response of the human ear at high frequencies. In order to properly tune a piano the tuner must have either perfect pitch or very close to it. Technical instruments alone can't replace the subjective response of the ear and brain.

thanks for the info about piano tuning. This little bit caught my attention, as I know that the ear has reduced amplitude response at high frequencies, but I didn't know what that has to do with frequency. I read a bit about piano tuning here
http://www.precisionstrobe.com/apps/pianotemp/temper.html

and it mentions that one reason for this octave stretching is due how a vibrating strings harmonics aren't exactly an integer multiple of the fundamental. Thus the amount of stretch has to do with a particular piano. You can also tweak the note spacings/stretch for different temperaments.

I found a good thread that discusses this, especially the last response.

People have been tweaking with this stuff for hundreds of years.

Tony Ennis
01-10-2010, 10:42 PM
Typo in your URL Evan. The piece is interesting enough.

darryl
01-10-2010, 10:49 PM
What is it that your brain is comparing the notes you hear to? Is it something you picked up as you progressed through infanthood, then childhood, etc- or is it something which began at your conception and continued through that first nine months- is it something which came before that- say from the very particles you were eventually going to be made from-

I don't know- I must have picked up some musical ability, or at least appreciation, from my mom and dad, who both played guitar. I would have heard music in the womb- but it seems there is a deeper connection than that.

gwilson
01-10-2010, 10:51 PM
When I was Master Musical Instrument Maker in Colonial Williamsburg,I had to tune the harpsichords. They were tuned in the old mean tone system as we represented an earlier era than the tempered scale.

The gut tied on frets of lutes and other early fretted instruments were so made because they could be slid about for playing more perfectly in tune in different keys. The development of tempered scales eliminated the need for movable frets.

After 16 years,I was persuaded to become Master Toolmaker,and make anything needed in the historic trades shops. It had been noticed that I had made many of the tools in my shop.

Pete F
01-10-2010, 11:54 PM
When I was Master Musical Instrument Maker in Colonial Williamsburg,I had to tune the harpsichords. They were tuned in the old mean tone system as we represented an earlier era than the tempered scale.

The gut tied on frets of lutes and other early fretted instruments were so made because they could be slid about for playing more perfectly in tune in different keys. The development of tempered scales eliminated the need for movable frets.

After 16 years,I was persuaded to become Master Toolmaker,and make anything needed in the historic trades shops. It had been noticed that I had made many of the tools in my shop.

Now that is one of your more unusual careers. Did you happen to know Michael Brophy? He was a silversmith there for many years, although it was some time ago.

-Pete

Evan
01-11-2010, 01:32 AM
The reason for the perceived downward frequency shift at the high end of the range is a sort of aliasing that takes place in the chochlea of the ear. At high frequencies the neurons of the hair cells cannot fire at the same rate as the stimulus which produces a flat response. By sharpening the actual tone it compensates for this response and the brain receives the correct number of impulses per second to produce the subjective experience of the expected notes.

As mentioned, the physics of vibrating strings also play a major part.

deeman
01-11-2010, 04:30 AM
If anyone here plays slide guitar you can tune your instrument to any tuning you want however you become the "nut" on the neck moving it to whatever tone in the range you want.Since you are not limited you play by ear and many times find notes anywhere between full notes.Duane Allman was brilliant for demonstrating his ability to play by ear and not just playing over a fret but also anywhere between them and have it sound better to the ear.

Pete F
01-11-2010, 10:08 AM
I used to practice slide in the dark for just this reason. I never let anyone hear it, though :p

Jack Bruce (of Cream) said he started playing fretless bass because he didn't want to have to look down to see where the right fret was while singing. Fretless, he could just plop his finger down and slide up (or down, I suppose) to the right note.

-Pete

gwilson
01-11-2010, 08:33 PM
The name Michael Brophy sounds familiar,but I can't recall him by now. I have always been able to remember faces,but not so good with names.