3db per octave slope?

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Bubbagump
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Joined: Wed Aug 06, 2008 3:48 pm

3db per octave slope?

Post by Bubbagump »

I loaded a file of white noise and it seems there is a ~3db per octave slope to the graph. Is this true? What is the reasoning behind this?
HarBal
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Re: 3db per octave slope?

Post by HarBal »

Yes that is true, both in the context of what Har-Bal displays, and what it should be mathematically. Put white noise through a conventional hardware RTA and you will get the same behaviour!

Why? Because white noise has uniform power spectral density, meaning for a fixed bandwidth the power within that band is constant irrespective of the centre frequency. Har-Bal displays the spectrum in (sub)octave band weighted form as this is closer to the way we hear than a conventional power spectrum plot. Now an octave corresponds to a ratio of 2:1 in frequency. If you have an octave band resolution and Fl is the low cutoff and Fh is the high cutoff then Fh = 2 * Fl and the bandwidth is Fh-Fl = Fl. Hence, the power in an octave band is proportional to frequency because the band increases proportional with the centre frequency. It just so happens that the the same proportionality applies to sub-octave band filters but I didn't bother doing the maths as it looks ugly in plain text.

If you want to see a flat line in Har-Bal for a noise input you need pink noise, which is also why pink noise is used for room calibration when monitoring through RTA's. Have you noticed how "hard", "bright" and uncomfortable white noise sounds to the ear? That's because our ears process in approximately 1/3 octave band filters so when listening to white noise the top end is very strong. As an aside, white noise at high volume will not only damage your ears but your speakers as well as the high frequency drivers have a much lower voice coil rating than the low frequency ones but with white noise the HF drivers are driven equally hard.

Cheers,


Paavo.
Bubbagump
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Re: 3db per octave slope?

Post by Bubbagump »

That is very interesting. Thanks for the info. I had always looked at an equal loudness contour and it doesn't really look like a -3db slope as it peaks at ~1.5khz and 10khz... but I suppose as a trend it does have a -3db/oct character.
HarBal
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Re: 3db per octave slope?

Post by HarBal »

ISO Equal loudness contours are constructed with pure tone tests (ie. a single frequency at a time) and there are also Equal loudness contours conducted with noise but typically octave band filtered noise.

With sinusoidal testing the loudness contours are roughly flat from 1kHz to 5kHz (apart from the peaks and troughs cause by the pinnae) but you need to remember that the perceived loudness is a weighted sum of the intensity of sound in each critical band in the ear. A critical band is approximately 1/3 of an octave for frequencies above about 500Hz so if you happen to use white noise instead then the perceived loudness will increase with frequency (~3dB per octave) because the sum of energy within the critical bands increases with centre frequency of the critical band.

The breakdown of the 1/3 of an octave approximation for critical bandwidths below 500Hz is the reason why a complex chord played high on the piano can sound consonant but when played in a low register sounds dissonant. The wider critical bandwidths below 500Hz makes beating more pronounced.

Regards,


Paavo.
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