Feel free to ask questions. I'll do my best to answer.

Saturday, March 5, 2011

Hearing Beyond Haas

Below 300-500Hz in a listening room the frequency domain is the most relevant acoustic metric to our perception.  Above there, it's the the loudspeaker's anechoic response. I'll do my best to offer an explanation.

Brush up on this first: Haas Effect
Haas Demonstrations

The cochlea's operation varies with frequency and has been mapped.  This is part of the place theory of pitch perception.

from Encyclopedia Britannica.  The place theory is not perfect b/c you can play a note, remove the fundamental, and still have the same pitch perception.  (Schouten, 1940)  Other issues that cannot be explained by place theory:
  • the fine degree of accuracy observed in human pitch perception,
  • pitch perception of sounds whose frequency components are not resolved by the place mechanism,
  • the pitch perceived for some sounds which have continuous (non-harmonic) spectra, or
  • pitch perception for sounds with an f0 less than 50 Hz. . . .
Taken from Acoustics and Psychoacoustics by David Howard and Jamie Angus.

Then there is the temporal theory--the timing of neural firing.  At low frequency, neurons can fire as fast as the frequency to around 300 Hz.  Above there they cannot keep up so pitch detection becomes progressively more by location of the firing on the basal ganglia with it being essentially by "place" at 5 kHz(some experts say 4 kHz and some as low as 1kHz). Below 1-5 kHz and above 300 Hz, the nerve firings are phase locked but fire in an almost random fashion.   All this combined with ear canal resonance and pinna modifications above 2 kHz mostly explains the equal loudness curves as number of nerve firings is approximately equal perceived volume.  We become naturally less sensitive to low frequency sounds as less nerves are firing.

We have very good freq detection below 300-500Hz because the neurons can fire at  similar speeds as the wave forming.  The question is "Why poor time resolution?"  I'd say it's because the wavelengths are huge and take a lot of time to form.  Simple physics.  This fortunately falls into the range of where the room goes modal for the very same reason and decay times likely rise.  Above there our time resolution is comparatively good barring ear canal resonances, but pitch detection less so as we'll see.

Let's look at Haas for another second, but not as it relates to directional hearing.  We don't hear reflections as a separate event until at least 30ms according to the Haas Effect(which only looked at speech signals and ultimately depends on level as seen below).
(Toole, Sound Reproduction)

It takes a 50 Hz wave about 20 ms to even form, but only 2 ms for 500 Hz, and 0.2 ms for 5,000.  The number of listens or complete cycles it takes for our ear to distinctly perceive a pitch varies with frequency as graphed below.

Log Frequency (Hz)
(Rossing, 1989)

To recognize a definitive pitch at 50 Hz it takes approx 2.5 cycles or 50 ms.  You can see Haas's effect cannot operate here as it does for smaller frequencies.  You can't hear an echo or a smudging of something that you can not perceive as a distinct pitch.  At 500 Hz it takes closer to 8 cycles or 16 ms which is just inside the Haas limit.   So at 5,000 Hz, it takes approx 80 cycles to hear a definite distinct pitch or 1.6 ms.  

So what does this mean for the studio engineer, audiophile or home theater enthusiast? Below 300-500Hz, an EQ can be used to largely correct audible errors at the listening position provided the null frequencies are not too deep.  The deeper in frequency, the more you can be sure the measured response will be more audibly accurate.  Bass measurements need to be taken at the listening position(s) as the bass builds up before we hear it clearly, the measurement is shorter than the integration time of the ear, and the visible graph is steady state in the room.   You can think of it as existing around us instead of moving from front to back and is part of the reason we don't hear our subwoofer's location.   Theoretically we may not hear 'fast' bass, though I'd bet we can still feel it.  Think of it this way; straight EQ doesn't function in the time domain, only the frequency domain. Since we have poor time resolution in the bass but great frequency resolution, an EQ can trim the peaks(but boosting deep nulls is a bad idea in a moderately powerful sound system).  Placement of the subwoofer(s) and listener(s) is of primary consideration to avoid nulls.  A cancellation cannot be fixed by EQ. Bass damping can help all aspects of bass reproduction, but a couple bass traps are no where near as effective as good placement. Room correcting software should be calibrated after trapping is installed and placement is at its best to remove listening position nulls.  This paper from Genelec seems to agree experimentally.  Perhaps we can say that an EQ will absolutely work for your subwoofer.

Here's the graph of the data from that paper:

Above there, 300-500 Hz, the speaker needs to have a flat anechoic response with a smooth off axis to reproduce the recording with a smooth off axis response and cannot be EQed by the 'in room response' d/t the ear's time resolution, the Haas Effect, and all the reflections contaminating the "in room" graph.  For more information, see this.