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Old 2nd May 2013, 09:07 AM   #41
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Default Where is the golden ratio?

To take this just a tiny bit seriously:

Hi Stee, I fail to see the golden ratio in your proposition.
"dB" is a logarithmic system (as someone pointed out) so linear mathematics aren't quite applicable.

40 dB = 10 000
24 dB = 256

ergo: 40 dB / 24 dB = 39,0625 (which incidentally is equal to 16 dB)

Yes, you see when you divide logarithmic functions you simply subtract the denominator from the numerator. Easy as pie! However, you can not divide them with each other (well, I suppose you could, but it will give you no meaningful answer)..

I don't recall either 39-something or 16 to be even close to the golden ratio..
By the way, 40/24 is EXACTLY 5/3 which (in my eyes) is a bit more elegantly written (always use primes if you can) but a VERY coarse approximation of Phi (which is the greek letter associated with the golden ratio).

An Italian guy named Leonardo Pisano Bigollo (aka "Leonardo of Pisa" or "Fibonacci") showed this back in 1202, You may have heard of him

If I understand you correctly, you are trying to find a relation within amplifier construction that correlates to Phi. I cannot see it, so please explain how you find the golden ratio in the numbers you have provided.
If I have misunderstood something, please enlighten me.
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Old 2nd May 2013, 10:27 AM   #42
SY is offline SY  United States
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Quote:
Originally Posted by nakamoomin View Post
However, you can not divide them with each other (well, I suppose you could, but it will give you no meaningful answer)..
Exponentiation.
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Old 2nd May 2013, 12:41 PM   #43
Stee is offline Stee  Italy
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Old 2nd May 2013, 01:07 PM   #44
Bonsai is offline Bonsai  Taiwan
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40 dB = 10 000
24 dB = 256

Really?
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Old 2nd May 2013, 03:17 PM   #45
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Hmm. That's true, I suppose exponential ratios are as good as any.

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Old 2nd May 2013, 04:58 PM   #46
JMFahey is offline JMFahey  Argentina
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Quote:
Originally Posted by Bonsai View Post
40 dB = 10 000
24 dB = 256

Really?
Really.

It's expressing Power ratios.

As in: to make a speaker sound 40 dB louder, you need to multiply applied power by 10000X .

EDIT: so if we are analyzing the "Ratio" , it means 10000/256=39.0625 .... far from the "Golden Ratio"

And even if we were analyzing Voltage ratio, it would be 100/16=6.25 ... still very far from the classic Artistic Golden Ratio .

Which one is chosen does not matter much, anyway, as far as *none* even resembles Stee's idea.

Last edited by JMFahey; 2nd May 2013 at 05:04 PM. Reason: Putting things in perspective
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Old 6th May 2013, 12:30 PM   #47
oshifis is offline oshifis  Hungary
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Stee,
The golden ratio is based on the ratios found in the nature (like the proportions of human body), and this is the reason we find it pleasant.
Remember that an amplifier's internal construction can not be directly perceived, so adhering to the golden ratio as gain ratio does not make sense.
Of course you can make an amplifier with "golden" geometric ratios of its front panel, and it will look aesthetically pleasant...
Not to mention that (as others also pointed out) the gain is measured logarithmically, and the golden ratio is a linear relation... For example:
Zero dB amplification is an unity gain, frequently used but you can not relate it to the golden ratio.
On the other hand, you can play with the numbers as you like, and it still won't sound "golden", because there are so many other factors.
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Old 6th May 2013, 02:42 PM   #48
Stee is offline Stee  Italy
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Old 6th May 2013, 04:34 PM   #49
hpeter is offline hpeter  Europe
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Quote:
Originally Posted by Bonsai View Post
40 dB = 10 000
24 dB = 256

Really?
if he talks about power ratio it is ok, but should be
24dB - 251,2
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Old 6th May 2013, 06:32 PM   #50
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Yes, I rounded the numbers after the 3dB=2 rule of thumb.. Thanks for correcting it.

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