I want to bring back the subject of which equalization method that's the ideal for equalizing speakers with non-ideal directivity.
In 2008, Sean Olive et al. published the paper
Comparison of Loudspeaker-Room Equalization Preference for Multichannel, Stereo, and Mono Reproductions: Are Listeners More Discriminating in Mono?. 9 trained listeners were given the task of ranking 4 'EQ methods' (PIR, no EQ, in-situ, direct) using 3 'playback modes' (mono, stereo, surround). Listeners were more discriminating when listening in mono, which is consistent with prior research.
Below is a spinorama of the speaker model that was used. It was the front right speaker in the loudspeaker setup.
The direct sound in the midrange is fairly flat up until 600 Hz where there's a small-medium resonance followed by a shallow (but fairly wide) dip, which is followed by another small-medium resonance at 1.2 kHz, which is also immediately followed by a dip. Unlike the first dip, this one is deep and narrow. At the beginning of the treble, there's a broad low-amplitude resonance from 2 to 4 kHz. This resonance is followed by very broad and moderately deep shelf, which essentially covers the rest of the treble response.
The ERDI also shows a lot of messiness in the midrange with a jagged, and too steep, rise towards 2 kHz. In the treble, there's a broad dip centered around 3 kHz, adding more intensity to the 2-4 kHz resonance, thus turning it into a broad medium-high amplitude resonance in the ER and PIR curves.
Overall a poorly performing speaker.
For the listening tests, it was crossed over at 125 Hz with 4 subwoofers that were equalized flat (in-situ) down to 25 Hz.
Let's take a look at how the spinoramas looked post-EQ and how the listeners rated them.
(a) is 'No EQ', (b) is 'PIR', (c) is 'Direct', and (d) is 'Insitu'.
These spins are averages of all 5 speakers used in the test. The 1.5 kHz dip is noticeably wider. It also seems like there has been a bit of smoothing applied to these curves.
PIR, in-room, and direct were all placed in a statistical tie. Listener neither liked nor disliked the sound of these EQs, but it was preferred significantly more than the unequalized sound, which they disliked:
Why were (b), (c), and (d) preferred over (a)? They all got rid of the 2-4 kHz resonance in the direct sound, even going so far as to create a dip in the cases of (b) and (d). The 600 Hz peak and 1.5 kHz dip were also corrected, to differing degrees, for all 3 EQ methods. Still, the equalized spins vary widely.
Although all EQ methods were statistically tied, PIR pulled ahead with a preference score that was about 0.5 higher than the direct and in-room EQs. I'll now ignore the confidence intervals and reinterpret the spins with the assumption that PIR EQ is superior.
- (b): The PIR based EQ effectively gets rid of all resonances, both on-axis and off-axis, but due to the directivity error around 3 kHz, the shelving in the direct sound is extended from ~4 kHz down to covering almost the entire treble response. Fortunately, a lack of sound pressure is much more audibly benign than an excess of sound pressure.
- (c): The direct sound based EQ does have quite a flat direct sound. There's a couple of broad dips in the treble, but since they're at the same level as the tonality baseline in the lower mids, it's arguably the upper mids that are a bit peaky. However, the main issue with this EQ is how the 3 kHz ERDI dip creates a low Q resonance in the ER curve.
- (d): As expected, the in-room EQ turns the direct sound into a mess - or at least does a poor job at cleaning up the mess that was there to begin with. The 1.2 kHz resonance is made slightly bigger, the 600 Hz and and 3 kHz peaks have been turned into dips, and the following treble shelf has been neglected. It's thought-provoking how this roller coaster spin was equally preferred to the direct sound spin, but the explanation is simple: the in-room based EQ managed to deal with the broad 3 kHz resonance both on-axis and off-axis, and the listeners appreciated it, because the rest of the problems are minor in comparison.
To sum it up: (d) only deals with the largest problem and leaves many minor ones unsolved. (c), on the other hand, solves all the minor problems but not the major one. (b) solves the major problem and some of the minor ones, too. (b)>(c)=(d).
It has been argued that "we don't hear PIR". That's true. We don't hear the listening window either, since it is an average of several angles covering an area much larger than our ears. Yet we base our EQs on the LW instead of the on-axis, even for a single listener, and we do so for a good reason. In many speakers, the on-axis has certain quirks that don't show up in the rest of the spinorama curves. Kali IN-8 has already been used to illustrate this point, so I'll use Fostex PM0.3 instead:
ON, LW, ER, and SP all generally share the same shape up to 5 kHz where the on-axis dips all the way past the LW and ER and touches the SP. If one were to EQ out this dip, it would create a peak in the 3 other curves. The resulting peak in SP would be inconsequential. The peak in LW means that moving your head just slightly away from the on-axis would result in the resonance possibly becoming objectionable. The peak in ER means that the reflected sound would be tonally different from the direct sound, likely degrading the overall sound quality.
Instead of equalizing the on-axis, the listening window can be equalized to get a very flat on-axis response without messing up the early reflections. Likewise, the predicted in-room response can be used as a proxy for equalizing the actual in-room response without messing up the direct sound.
It's worth noting that Olive et al. could have achieved a much more accurate direct sound for their PIR EQ by having used a shallower target slope. It's also desirable to use a slope when equalizing the LW in order to avoid making the on-axis too bright. For a well-behaved speaker, with a gradually increasing ON-LW gap, a slope of -0.1 dB/oct. per 0.5 dB of gap at 10 kHz should be used. Hence a 1 dB gap should be equalized with a -0.2 dB/oct. slope, a 1.5 dB gap should be equalized with a -0.3 dB/oct. slope, etc.
You might be wondering why I'm explaining how to make a proper LW EQ while seemingly arguing in favor of PIR EQ. That's because there's another variable than the spinorama to consider: listening distance.
As the listening distance increase, so does the ratio of reflected sound to direct sound. The best graph I could find to show this relationship was Figure 10.8 from Sound Reproduction by Floyd Toole:
The direct sound drops by -6 dB/dd (inverse-square law), but the combination of direct and reflected sound doesn't drop nearly as rapidly. It can be concluded that the reflected sound alone also does not drop by the same magnitude per double distance as the direct sound.
BYRTT made this animation, using the Neumann KH 80 spin, which shows the same relationship:
The difference in SPL between the direct sound and the early reflections increases as the head moves closer to the speaker.
So the farther the listener is positioned from the speaker, the more the early reflections contribute to the combined sound. It can then be concluded that the longer the listening distance, the more favorable a PIR based EQ becomes.
"ER ≠ PIR", one might argue. Again, that's true, but they're almost identical for all speaker models except a for few with horrible directivity indices. For all practical purposes, they are interchangeable. PIR exists because it's very slightly better at predicting the in-room response than ER is, just like ON is slightly better at determining the direct sound than the LW is.
The listening distance, used for the listening tests described in the
EQ preference paper, was 2.9 m:
A listening distance of ~3 m was also used for the listening tests that Olive's model for the predicted preference ratings of loudspeakers is based on.
Let's have a look at the relevant variables of the model along with their weights:
- NBD_ON: 31.5%
- NBD_PIR: 20.5%
- SM_PIR: 17.5%
Ignoring NBD and SM, it can be rewritten as:
Or in other words: PIR was given more weight than the on-axis response by a substantial margin.
It's then safe to assume that the early reflections were also assigned greater importance than the direct sound.
How is it determined how far people sit from their speakers? Isn't that entirely up to the individual listener? No. At least not entirely. There is a minimum listening distance, which must be considered, and it depends on the particular geometry of the loudspeaker.
Chapter 10.5.1 in Toole's book deals with the issue of sound energy distribution of ideal point sources versus real loudspeakers. He explains that since a complex source, like a loudspeaker, doesn't radiate sound from an infinitely small point, what is heard at different frequencies is different at short distances and long distances. "In the near field, as shown in Figure 10.9b, the sound level at any frequency is uncertain.":
"Figure 10.9c shows estimated distances at which far-field conditions should prevail for a loudspeaker system and for its components. This would be the minimum distance at which [...] listeners should sit in order to have a predictable experience.":
These calculations, for this hypothetical speaker, are based on Beranek (1986) who states that the far field begins at a distance of 3 to 10 times the largest dimension of the sound source.
Below is same calculation for a handful of actual speakers. Instead of the 3-10 interval, I have used the integer 6. This number was chosen because it is close to the average (6.5) and because it brings some realism to the results.
Dynaudio LYD 5: 260 mm * 6 = 1560 mm ≈ 1.6 m
Adam S2V: 346 mm * 6 = 2076 mm ≈ 2.1 m
ELAC DBR-62: 358.902 mm * 6 = 2153.412 mm ≈ 2.2 m
B&W 805S: 418 mm * 6 = 2508 mm ≈ 2.5 m
Infinity R253: 1019 mm * 6 = 6114 mm ≈ 6.1 m
And now for the whole purpose of this post.
My recommendations for the optimal EQ method as determined by the listening distance:
- <2 m: LW
- 2-3 m: LW/PIR (depending on which reduces resonances the most)
- >3 m: PIR
- Outdoor speaker at any distance: LW
DISCLAIMER: This approach, like the LW-only and PIR-only approaches, is founded on speculation due to insufficient information. The above value ranges are qualified guesses, nothing else.
Finally, let's see how the 5 speakers should be equalized using this approach, assuming the minimum far field listening distance is also the actual listening distance.
LYD 5: Listening distance is under 2 m, so LW EQ should be used. The peakiness from 800 Hz to 4 kHz in the ERDI creates a few dips in the ER that are unimportant.
The current EQ profile (seen above) has an on-axis resonance centered around 6 kHz. A steeper slope, with a value of ~-0.5/dB/oct., should be used.
S2V: This speaker is in the 2-3 m category, so the ERDI needs to be examined to decide the EQ method. A wide peak from 0.5 to 2.5 kHz can be seen. That means LW EQ should be used. The flat LW gets traded for a dip in the ER.
Unfortunately, the LW is too flat in the current EQ profile. A slope of -0.3 dB/oct. should be used to get rid of the excess treble energy in the on-axis.
DBR-62: This is a tricky speaker. It also falls into the 2-3 m category, so again the ERDI has to be taken into account. The ERDI rises towards 2 kHz, before it starts dropping to create a dip, which reaches its minimum at 3.8 kHz. It's followed by a rapid rise up to 4.7 kHz, where the curve gets to the same level it was at before it started dropping. To prevent the 3.8 kHz dip from creating what would otherwise become a peak in the ER, PIR EQ should be used.
Here are the spins both pre-EQ and post-EQ:
The midrange is nicely cleaned up and is practically flawless. The treble is more or less unchanged and is still a little too recessed, but using a shallower PIR slope would create an unwanted resonance in the upper midrange. There is nothing about this EQ profile that I would change.
805S: Minimum listening distance is 2.5 m. This speaker has a great ERDI except for the dip around 1 kHz. A peak in the ER can be avoided by using PIR EQ so that the ERDI dip also turns into a dip in the LW.
The current LW EQ profile doesn't make use of a steep enough slope to deal with the on-axis peaking around 4 kHz. Instead, a PIR EQ with a ~-1.1 dB/oct. slope should be used.
R253: Like with all floorstanders, the far field of the R253 starts way past 3 m and it's therefore necessary to use PIR EQ. Current EQ profile:
With PIR EQ, the problematic peak in the ER gets exchanged for a benign dip in the direct sound. A slope of ~-0.7 dB/oct. should be used.
