The Golden Ratio

[Gopi Passiflora]

First, take a look at this article about the Golden Ratio:

https://en.wikipedia.org/wiki/Golden_ratio

Using the definition of the golden ratio in terms of x and y:

x/y = (x + y)/x

...I created some plots based around the equations related to the definition:



I then added a plot to the graph for y/x = (x + y)/y



It looked like a pinwheel (sort of), tilted with the spokes having slopes equal to the golden ratio or its inverse, so I thought I wanted to share.

[Madelaine McMasters]

Though the science is sketchy, the Golden Ratio also shows up in the violins of Antonio Stradivari and has captured the imagination of countless audiophiles. My father built a set of bookshelf speakers when I was young, and explained to me their golden ratio proportions, which he carefully designed (both the proportions and the story) to make people think they sounded good. Those speakers are now in the possession of my emergency backup kid, who is a violinist and claims the speakers actually very good, not because of any golden ratio, but because they were built by my father. I couldn't agree more.

[Arduenn Schwartzman]

[ChinRey]

3 hours ago, Madelaine McMasters said:

Though the science is sketchy

The scienctific aspect is solid enough, it's a fairly simple equation and math doesn't need any reason. The "magic" properties on the other hand, is pseudoscience and you can find just about any mathematical relationship you like in just about any relatively complex object.

It's still very useful for visuals though since it's a quick and easy way to come up with a balance between too square and too stretched:

I use it a lot in my builds for that reason.

I know there are a few forumites who for some weird reason aren't math geeks and don't feel comfortable with the formulas Gopi and Arduenn posted. There is a much easier way to approach the golden ratio, the Fibonacci series. Each number in the series is simply the sum of the previous two:

0 1 1 2 3 5 8 13 21 34 etc.

The further you go out in the series, the closer the ratio between two neighbour numbers is to the golden ratio. 5:8 is probably close enough, 8:13 (the one I used for the golden ratio rectangle above) certainly is.

 

4 hours ago, Madelaine McMasters said:

the Golden Ratio also shows up in the violins of Antonio Stradivari

Numerology was a very important part of renaissance philosophy so it's quite possible the Cremonese violin makers used deliberately. Don't credit Stradivari for it though. His design wasn't very different from that of his master, Nicola Amati.

 

4 hours ago, Madelaine McMasters said:

My father built a set of bookshelf speakers when I was young, and explained to me their golden ratio proportions

Believe it or not, that too actually make sense. You don't want too simple ratios between the dimensions along the various axises in an acoustic space because it is likely to cause problems with uneven frequency response and even standing waves. The golden ratio (or rather the Fibonacci series) is a good tool to achieve the irregularities we want without the need for too complex calculations.

[Ted McGregor]

double post .. forum software .. sorry ..

Edited October 16, 2021 by TDD123

[Ted McGregor]

4 hours ago, ChinRey said:

 The "magic" properties on the other hand, is pseudoscience and you can find just about any mathematical relationship you like in just about any relatively complex object.

There is a much easier way to approach the golden ratio, the Fibonacci series.

The golden ratio (or rather the Fibonacci series) is a good tool to achieve the irregularities we want without the need for too complex calculations.

Ik
leef
op de
grens van de
toekomstige tijd
die me steeds een stapje voor blijft
terwijl het verleden mij achtervolgt als een droom.

Source of poem

Edited October 16, 2021 by TDD123

[Madelaine McMasters]

8 hours ago, ChinRey said:

The scientific aspect is solid enough

I was referring to the use of the golden ratio to explain some magical acoustic advantage in Stradivari's violins or speaker enclosures. Those explanations are rubbish, as other confounding factors dwarf any advantage the golden ratio might provide. In fact, there have been at least two small double blind violin trials in which Strads were shown to possess no "magic" at all. I've a good friend who's a luthier and thinks that the golden ratio is more expectation than explanation. Phrenology again comes to mind.

https://www.npr.org/sections/deceptivecadence/2012/01/02/144482863/double-blind-violin-test-can-you-pick-the-strad
https://www.science.org/content/article/million-dollar-strads-fall-modern-violins-blind-sound-check

My father designed an anechoic chamber back in the 1960s, and became familiar with "room dynamics". He was curious about golden ratio claims, so built both sphere and golden ratio speakers using the same components. Their internal volumes were identical, but the spherical speaker had fewer resonances and sounded better in the chamber. The resonances of the golden ratio speaker were primarily due to wall flexure. The spheres, though lighter, were more rigid. Because Mom found them ugly, they didn't survive. I'd now give anything to have them, they'd be so retro-cool. I do keep my eyes open for spherical objects that might be repurposed.

Dad often opined about the nonsense of designing a listening room to any specific ratio, then subsequently filling it with random objects of various acoustical characteristics. My theater room sound system seems to agree, as it contains a microphone I place in my expected listening position before doing a room calibration. I can cause the calibration to change substantially by rearranging the furniture. My emergency backup kid studied acoustics during the pursuit of his music degree and was exposed to the golden ratio there, and how it's a distracting consideration, given all the other confounding factors. Sound absorbing treatments are the method of choice for tuning rooms and reducing reflections inside speakers. Ultimately, with help from Mom, he concluded that "good looks help".

Meanwhile, as the result of my father's further explanation of the Fibonacci sequence, I see it everywhere in nature, including in the plants in my yard (pinecones!) and every head of cauliflower I get from the market. It's also "apparent" in nautilus shells (actually no) and the Whirlpool Galaxy. Nevertheless, I do wonder how hard people work to fit the patterns they see onto the Fibonacci sequence.

http://www.eniscuola.net/en/2016/06/27/the-numbers-of-nature-the-fibonacci-sequence/
https://www.goldennumber.net/spirals/

Nature seems to have pretty good understanding of the utility of the Fibonacci sequence. Humans might be over extending it. I find it curious that the golden ratio figures so prominently in discussions of visual beauty and photographic composition, but photographic film, digital image sensors, photo print paper, TV and movie screens don't use it. You can find movies and photographs which are claimed to use golden ratio composition, but they're displayed in non golden ratio formats on non golden ratio screens. The same thing happens when you frame a photographic print. If the frame is uniform, either the print or the frame must be non golden ratio.

If you want to cut a sheet of paper into smaller versions of itself, the square root of two is the perfect aspect ratio. In printing circles, this is the "Lichtenberg Ratio" and is the foundation of European "A" series paper sizes. Cutting in half a sheet of paper with a 1.41:1 aspect ratio produces two sheets with the same ratio. This is pretty convenient when you want to scale something up or down.

https://www.cl.cam.ac.uk/~mgk25/iso-paper.html

As an example of just how far we'll go to find Fibonacci in nature, there's this...
https://www.sunnysports.com/blog/5-examples-of-the-fibonacci-sequence-in-plants/

In which we find this image...

And this nonsense claim...
Although we all usually see trees everywhere in our day to day, how often do we really look at them for patterns. In trees, the Fibonacci begins in the growth of the trunk and then spirals outward as the tree gets larger and taller.

 Tree rings do not spiral out.
At all.
They're concentric.

If the intention was to describe the branching patterns of trees as having some Fibonacci relation, this didn't pass muster.

Edited October 16, 2021 by Madelaine McMasters

[ChinRey]

24 minutes ago, Madelaine McMasters said:

In fact, there have been at least two small double blind violin trials in which Strads were shown to possess no "magic" at all.

Oh, there have been far more than two such blind tests. I have a fairly large collection of 19th and early 20th Century books about violins by various experts of that time. Nearly all of them speak about how the Stradivarius tone can't be imitated. Then, almost in the next sentence they go into detail how Vuillaume or some other 19th C maker produced violins that could not be distinguished from a Strad. Not one of them seem to realize how they contradict themselves. (Poidras is the only exception I can think of but he doesn't buy the Strad uniqueness myth at all.) It's not as if Stradivarius' workshop ever made Strad anyway, not the way we think of Strads that is. Not only have they changed a lot with age, they have also been heavily modified and don't sound anything like they originaly did.

[Ted McGregor]

40 minutes ago, Madelaine McMasters said:

Nevertheless, I do wonder how hard people work to fit the patterns they see onto the Fibonacci sequence.

... it' s because we are pattern seeking mamals .. it' s inate in us ... leading us to many false conclusions as you described.

[Arduenn Schwartzman]

I'm not even remotely considering using the Golden Ratio in my latest build. Just my Golden Rules: (i) will it snap to grid and (ii) will it conveniently split into <10m chunks?

[Ted McGregor]

1 hour ago, ChinRey said:

Nearly all of them speak about how the Stradivarius tone can't be imitated. Then, almost in the next sentence they go into detail how Vuillaume or some other 19th C maker produced violins that could not be distinguished from a Strad. Not one of them seem to realize how they contradict themselves.  

This reminds me a lot of the everlasting discussion amongst audiophiles about analog versus digital. Even now when the full bandwith and spectrum of noise can be digitally captured and compressed loslessly, analogue enthusiasts still claim the better quality in sound. 

Edited October 16, 2021 by TDD123

[Arduenn Schwartzman]

1 minute ago, TDD123 said:

analog versus digital

Come on now, who in their right mind would have an artist put their autograph on a plastic CD case?

[Ted McGregor]

10 minutes ago, Arduenn Schwartzman said:

Come on now, who in their right mind would have an artist put their autograph on a plastic CD case?

.. but we're digressing here..

 

Edited October 16, 2021 by TDD123
speeling

[Maryanne Solo]

Analogue, fibonacci, music etc lol.
What is borne out with the advent of CD's & digital audio tape beforehand is that people & sound engineers didn't, (and still don't), realise that with digital you
have to create the entirety of a sound. Meaning its atmosphere, space, timbre & weight.
Most early digital recordings, CD's for example, sound absolutely disgusting where analogue was always warm and thumpy.
Compare vinyl masters with modern .flac files on an outstanding system or top shelf, (not Audiophile model),
Somethingheiser headphones. It's almost enough to make you cry with joy how beautiful things can sound.
A good example of understanding digital space is the Line 6 Variax guitar.
(I have an original parker fly carbon fibre galaxy worth three times the price of a Variax and 1/16th of its abilties).
I'm getting a Variax asap lol.  

[Myth Valeska]

No

[Doris Johnsky]

WHAAAAT?

[Maryanne Solo]

Analogue Golden Ratio 😂