I think I see what Victor is saying, 
dB is a relative relationship power ratio between two power levels.

I was taught that it is a "log" scale, because the linear scale 
version of that was too difficult to graph, so logrithmic graphing 
was used so it would all fit on the graph paper used back then.
A Bel is a small increment based on a given power level ratio.
A Deci-Bel required a huge graph paper to graph it, too cumbersome,
so a logrithmic scale was used to better graph it.
That's the history as I recall it (please correct as needed).

It's applicable to Volts, Watts, gain and as well as acoustical SPL
and pretty much any other powers ratio if memory serves. It's a power
level relationship relative to another power level.

So, Victor, that about sum it up?  BTW: Saw the correction in the 
December issue of JAES regarding that Taylor Series problem.  :-)

-Partev



==================================================================================================




--- richarddobson@blueyonder.co.uk wrote:

From: Richard Dobson 
To: csound@lists.bath.ac.uk
Subject: [Csnd] Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: dynamic range
Date: Wed, 07 Jan 2009 10:11:55 +0000

victor wrote:
> Again, I don't agree, I'm sorry. Ampdb() does not express
> amplitudes in any system, as far as I can see, but just converts
> a ratio into the SPL scale (which is expressed as 20log10(ratio)).
> This can be applied to any input.
> 


It's simply a matter of the range, and the reference value.

20. *  log10(32767) ~= 90.3

Except that  "by convention" 32767 was defined as Csound's maximum 
positive value before clipping; i.e. it posits a 16bit sample range 
(which is why some people still seem to thiunk Csound is somehow a 16bit 
system).  Whereas the global audio industry standard is to define that 
as 0dBFS. If we therefor want to express a level in industry terms of 
-6dB,  we know that would be 16384;  but the formula above gives it as 
84.2.  That is how the usage was defined in the original manual.

Hence  the ampdbfs pair, to express all levels relative to digital peak 
= 0dBFS. And subsequently the 0dbfs opcode itself, intended finally to 
render the old 16bit representation obsolete and (ideally) deprecated. 
The mathematics is not in question; the choice of reference level is. 
The new opcodes  simply enabled Csound to express itself in a way 
exactly compatible with industry practice.

Richard Dobson



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_____________________________________________________________
Netscape.  Just the Net You Need.

Just for the record ....
A decibel is 1/10 of a bel not the other way around.
And the reason its a logarithmic scale is has little to do with the  
size of graph paper -
it's because changes in the physical phnomenon called amplitude, is  
heard as the psychophysical phenomenon called  loudness, and the  
relationship between them is logarithmic. i.e we hear logarithmically.

for a simple intro, see: http://www.avatar.com.au/courses/PPofM/intensity/Intensity1.html

D.

On 14/02/2009, at 10:36 AM, Partev Barr Sarkissian wrote:

> I think I see what Victor is saying,
> dB is a relative relationship power ratio between two power levels.
>
> I was taught that it is a "log" scale, because the linear scale
> version of that was too difficult to graph, so logrithmic graphing
> was used so it would all fit on the graph paper used back then.
> A Bel is a small increment based on a given power level ratio.
> A Deci-Bel required a huge graph paper to graph it, too cumbersome,
> so a logrithmic scale was used to better graph it.
> That's the history as I recall it (please correct as needed).
>
> It's applicable to Volts, Watts, gain and as well as acoustical SPL
> and pretty much any other powers ratio if memory serves. It's a power
> level relationship relative to another power level.
>
> So, Victor, that about sum it up?  BTW: Saw the correction in the
> December issue of JAES regarding that Taylor Series problem.  :-)
>
> -Partev
>
>
>
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> = 
> ======================================================================
>
>
>
>
> --- richarddobson@blueyonder.co.uk wrote:
>
> From: Richard Dobson 
> To: csound@lists.bath.ac.uk
> Subject: [Csnd] Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re:  
> dynamic range
> Date: Wed, 07 Jan 2009 10:11:55 +0000
>
> victor wrote:
>> Again, I don't agree, I'm sorry. Ampdb() does not express
>> amplitudes in any system, as far as I can see, but just converts
>> a ratio into the SPL scale (which is expressed as 20log10(ratio)).
>> This can be applied to any input.
>>
>
>
> It's simply a matter of the range, and the reference value.
>
> 20. *  log10(32767) ~= 90.3
>
> Except that  "by convention" 32767 was defined as Csound's maximum
> positive value before clipping; i.e. it posits a 16bit sample range
> (which is why some people still seem to thiunk Csound is somehow a  
> 16bit
> system).  Whereas the global audio industry standard is to define that
> as 0dBFS. If we therefor want to express a level in industry terms of
> -6dB,  we know that would be 16384;  but the formula above gives it as
> 84.2.  That is how the usage was defined in the original manual.
>
> Hence  the ampdbfs pair, to express all levels relative to digital  
> peak
> = 0dBFS. And subsequently the 0dbfs opcode itself, intended finally to
> render the old 16bit representation obsolete and (ideally) deprecated.
> The mathematics is not in question; the choice of reference level is.
> The new opcodes  simply enabled Csound to express itself in a way
> exactly compatible with industry practice.
>
> Richard Dobson
>