[LAD] twice as loud

[lieven moors]

On 07/24/2010 10:31 PM, fons at kokkinizita.net wrote:
> On Sat, Jul 24, 2010 at 02:58:36PM +0200, lieven moors wrote:
>
>   
>> On 07/23/2010 10:23 PM, fons at kokkinizita.net wrote:
>>     
>>> On Fri, Jul 23, 2010 at 06:42:11PM +0200, lieven moors wrote:
>>>
>>>   
>>>       
>>>> On 07/23/2010 06:29 PM, fons at kokkinizita.net wrote:
>>>>
>>>>     
>>>>         
>>>>> Transporting this to the audio domain, given two similar
>>>>> sounds A and B with a B having a higher level than A, you
>>>>> could adjust a third one X so it appears to be 'halfway'
>>>>> between A and B. If you do this with A much smaller than
>>>>> B, would you expect X to be close to 'half a loud as B' ?
>>>>>
>>>>>   
>>>>>       
>>>>>           
>>>> If A would be very close to silence, yes.
>>>>     
>>>>         
>>> I'd be *very* surprised if that would turn out to be true.
>>>
>>> I bet that if B is A + 40 dB, X would turn out to be
>>> close to A + 20 dB. And if B is A + 60 dB, X will be
>>> close to A + 30 dB. In both cases A is very small 
>>> conpared to B (at most 1/10000 in power).
>>>
>>> Ciao,
>>>
>>>   
>>>       
>> Let's put it differently. If you only had sound B, and you
>> were asked to position a similar sound X halfway between
>> total silence, and the level of sound B, wouldn't that be the
>> same as asking that sound X has half the loudness of sound
>> B, or as asking that sound B has double the loudness of
>> sound X?
>>     
> So with e.g. A = B - 60 dB we could end up with X at
> B - 30 dB (two steps of 30dB which are supposed to be
> near equal subjectively), 
That is assuming that our experience of loudness
corresponds to the continuous logarithmic scale
with which we measure SPL's. I suspect that this
is not the case. Our ears have minimum and
maximum SPL values they can observe/tolerate,
and I think that this range is the 'unconscious'
reference for measurement of loudness.
So we might have to adapt the 'steepness' of the
logarithmic curve to that range.
> while with A = silence we would
> have X somewhere between -6 and -10 dB relative to B
> (these are the extremes of common values for 'twice as
> loud'). How low can A be before this inconsistency turns
> up ? Or more important: how reliable is such an idea of
> 'halfway' ?
>   
I would say it's the only reliable thing in this context,
because it's the very thing we want to measure.
> The simple fact is that on a logarithmic scale the whole
> concept of 'half' or 'double' is **meaningless**. That is 
> because such a scale depends on an arbitrary reference
> value, and changing that value shifts the whole scale by
> a constant amount without changing the underlying reality.
> Two levels that are e.g. 10 and 20 on one scale (hence the
> second is 'double' the first) could be as well be 80 and 90
> just by changing the reference value for the log scale.
>   
Yes, but changing the base does change the underlying
reality.
> Of course half/double still makes sense in the original
> domain. But if the perceptual scale is logarithmic, they
> are perceived as a constant difference, not as a ratio.
>   
I think we are aware of the original domain, in de sense
we are approaching the limits of our hearing. What
we interpret as half/double as loud depends on the
position within that range.

regards,

Lieven