Why "Flat" is Inaccurate

[DDF]

I’ve been thinking about something lately. What I’m proposing here is an explanation, based in science (for those who demand such things), for why a gently tailing top end response is perceptually more accurate than a flat on axis frequency response. Remember you read it here first!

There’s a school of thought that rigidly prescribes to the target of a flat frequency response as the ideal for any loudspeaker. Minor variations are sometimes accommodated: long high frequency reverb decay times are “allowed” some high end tailoring, to tilt down the top end. Voicing my own personal designs over the years, I’ve never been able to accept this over-all approach.

For example, take your standard two-way with 4th order acoustic Linkwitz Riley xovers: you get a beautiful graph. However, for me, this approach never sounded completely accurate. Over time, in differing rooms, I tend to hear this as excess energy centered around 5 kHz, even with a flat on-axis response. I tend to tip the top end down a bit, sometimes allowing it back up after 10 kHz. I know I’m not the only one that favours this tailored on-axis target.

I can finally explain why this is a more accurate approach (in fidelity, not preference).

Imagine typical stereo creating a phantom center image with speakers set at some angle of incidence to the head. Well, the speaker playing at the right, into the right ear, projects more treble into the right ear than a real center sound source would. Ditto for the left ear.

The only place where the tonal balance is really correct is for an image right at one of the speakers.

To get an idea of the phantom center tonal error, see this head related transfer function (HRTF) graph (averaged over a small population), scanned from a 1966 JASA article by Edgar Shaw:
http://www3.sympatico.ca/dalfarra/HRTF.jpg

For an equilateral triangle set up, a speaker would be at 30 degrees trying to replicate a phantom in the center. The perceived artificial boost at 7 kHz is on the order 3 to 4 dB, with a gently rising characteristic starting at 2 kHz, peaking at around 7kHz, then reaching equality again above 10 kHz. There it is, the dreaded subjective high-end hotness with flat on axis designs.

By compensating using a gentle high-end roll off, our center phantom image perceptually sounds tonally correct again. Of course 3 to 4 dB compensation at 7 kHz adds the inverse error for images at the speakers, so a compromise of, say, 2 dB at 7 kHz sounds completely reasonable. Using a tweeter with some rise after 10 kHz then brings the difference back, and everyone is happy.

Of course this is tricky, as everyone’s HRTF is as unique as his or her fingerprint. However, it’s a very reasonable assumption that everyone will hear more treble from a source 30 degrees incident than 0 degrees. Tailor to taste.

The repercussions of this effect are wide ranging. For example, the HRTF at 30 degrees is also hotter from 200Hz to 1 kHz than the response at 0 degree (note: all curves converge below 100Hz, as the head becomes small in relation to the wavelength and head diffraction effects minimize). Perhaps there should also be less baffle diffraction compensation than a flat measure would indicate. Indeed, many voice to 4 or 5 dB, even for nominally flat acoustic power designs.

It would also result in perceived tonal changes with changes in speaker placement geometry that are independent of room effect and speaker toe-in. Different angles, different perceived phantom image error.

The difference between stereo and single speaker mono was always ascribed to the inherent picket fencing and crosstalk error inherent in stereo. I’d wager that the HRTF difference for phantom image generation is also a large factor.

Finally, and I know Lynn will love this last one as it’ll dovetail nicely with his far eastern philosophies. This effect explains why different people hear different tonal balances from the same speaker/room, and why there is objectively no one “right” frequency response across the population. Everyone needs a response tailored after their own HRTFs, if phantom images are to sound tonally correct to them.

To me, this is a “very big deal”. Almost makes me want to run out and buy Etymotic in-ear mics and get the HRTF characterized.

Cheers,
Dave Dal Farra

[Pano]

That's why you need a center speaker, Dave.

[sqlkev]

interesting approach, I just dialed some DEQ according to the diagram that you linked to and what you suggested. My dipoles now have slight better separation of left and right and voicing is a tad better. Am i hearing things?

:edit: playing around with toeing a bit more, now I'm not sure what to make of this
the speakers did so well earlier, now it doesn't do the disappearing act anymore.

[CeramicMan]

Nah, if the 0 degree angle of incidence is used as a reference and normalized to a straight line, the peak around 2kHz would practically disappear and the peak around 5~7kHz would also be reduced. I agree that everyones hearing is different, but that's beside the point. A clarinet wouldn't be equalized in real life.

And the other thing is: why should a phantom image be only in the centre? I agree that a lot of multimedia sounds are monophonic, but there's no 'standard' listening position, so there are other factors to consider such as the off-axis speaker response, reverberation of the room, and the polar patterns of the microphones used for the recordings.

[oshifis]

If you set up the speakers so that not directed to the listener but parallel to the center line, then the frequency dependent directional polar diagram will make sure the high frequencies will not be emphasized.

I remember that the legendary Celestion SL-6 had 1.5 dB/octave rolloff over most of its frequency range and I read somewhere that its optimal setup is not tilted towards the listener.

[Pano]

If sounds straight in front of the head have a different FR than those off to the sides, the phantom image may, indeed, sound odd.

But to EQ the phantom center properly you would need more than simple EQ. The EQ would need to track how common to center the sound is. Sort of like the simple Dolby matrix stuff. Apply the head function EQ most heavily to sound sthat are common to left and right - the center.. The EQ would need to change as the sounds become less common.

A good setup would allow you to dial in the angle of the speakers and maybe other things.

That's not to say that you couldn't fake it a simpler EQ.

Does this mean that the Binaural recordings done with a dummy head should have a better center phantom image? Because the HRTF is built in?

[Svante]

You are right in that stereo reproduction of a centered sound image requires a frequency response correction due to the HRTF. You are not the first to realize this, though... Correct me if I am wrong, but didn't the "BBC dip" have an explanation like that?

[Kensai]

Would a Polk SDA-like arrangement of drivers be useful for clearing this up with minimal effort?

Kensai

[catapult]

For an equilateral triangle set up, a speaker would be at 30 degrees trying to replicate a phantom in the center. The perceived artificial boost at 7 kHz is on the order 3 to 4 dB, with a gently rising characteristic starting at 2 kHz, peaking at around 7kHz, then reaching equality again above 10 kHz. There it is, the dreaded subjective high-end hotness with flat on axis designs.

Interesting idea, Dave. The problem I see with it is both ears are hearing sounds from both speakers, not just right-speaker, right-ear. Your graph doesn't show 30 degrees so let's take 45 instead. What the ear would hear would be a sum of the 45 and 315 curves. And the power spectrum reaching the ear would be even less than a linear addition of the curves because the short wavelengths make the signals uncorellated. Given all that, I think any boost would be MUCH smaller.

[rdf]

While that's true catapult the magnitude difference of the direct first arrivals between 315 and 45 is on the order of 15 dB, too wide for much cancellation or summation even with phase co-operating fully. Regarding the diffuse/power field, it's an interesting question but those signals would also be much reduced in level for a non-pathological speaker setup. Their impact would seem to me hinges on how the ear weighs the delay and directionality above and beyond straight frequency tailoring.