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Speaker Off Axis: Understanding the effect of Speaker Toe-In

This article provides a conceptual basis for understanding speaker toe-in and how it relates to the subject of speaker off axis response.

Speaker toe-in has a significant effect on the sound – in terms of soundstaging, imaging and tonal balance – and we think it is important to understand some of the facts and data behind why the sound changes when you alter speaker toe.

Altering toe-in fundamentally changes the relationship of the direct and reflected sounds in the room. More toe-in reduces the level of early reflected sounds from the lateral side walls. Less toe-in increases the level of reflections. Toe in also changes the amount of high frequency energy above about 4kHz in the direct sound.

How you perceive sound

When you listen in a home recording studio, home theater or stereo listening room what you perceive as sound is a combination of many things. We can conceptually break down the sonic contributors into three parts:

  1. The direct sound
  2. The early reflections
  3. The late reflections

For definitions and more discussion see our article speaker off axis response: psychoacoustic and subjective importance.

Speaker pointed at the listening position

A speaker that is fully toed-in is one that points directly at the listening position. The direct sound is therefore described by the 0 degree, on axis frequency response. The on axis sound generally contains the most high frequency energy. All speakers except omnidirectionals have decreasing high frequency energy as you move off axis.

Toe

In the hypothetical room shown above the first lateral side wall reflection will be at 86 degrees. Note that this angle will vary from room-to-room, but is nearly always above 70 degrees. This is significantly off axis, and most speakers will have a distinctly non-flat response at this off axis angle.

An overly simplistic way to look at the psychoacoustic effect of reflections would be to simply add the direct and reflected sound together. Your brain does something like this but it is not a straight mathematical addition. It gives some clues however as to what is going on inside the brain.

The vast majority of speakers show a tapering off in high frequency energy above about 4kHz as the tweeter becomes directional. This is because the tweeter starts to get acoustically large relative to the wavelengths being reproduced. The exact frequency at which the response starts tapering off is therefore mathematically related to the acoustical size of the driver (see here for more discussion on this).

Frequency response measurements at 0 degrees (on axis) and 90 degrees. These are very similar off axis angles as the example presented above for a speaker toed-in directly at the listening position. Measurements taken from the ATC SCM19 speaker. The A+B trace shows the 0 and 90 degree traces added together...and you can see the slowly decreasing dispersion as frequency increases.
Frequency response measurements at 0 degrees (on axis) and 90 degrees. These are very similar off axis angles as the example presented above for a speaker toed-in directly at the listening position. Measurements taken from the ATC SCM19 speaker. The A+B trace shows the 0 and 90 degree traces added together…and you can see the slowly decreasing dispersion as frequency increases.

You can see that the frequency response of the combined direct + reflected response is very close to that of the direct response by itself. The direct sound is significantly higher in level than the reflected sound, showing that the reflected sound is not that important in terms of what you hear. Also note that the reflected sound contains less high frequency energy than the direct sound above 5kHz.

Speaker “brightness”

Some loudspeaker designers expressly design around a non-flat on axis response. Often they design in a rising high frequency response, the idea being that this accounts for tweeter directionality and provides a flatter response at the listening position.

Take a look at the response below, from a Dynaudio speaker. Listened to on axis (0 degrees), this would be a very “bright” speaker! Presumably a better angle to listen to this speaker at would be around 45 degrees off axis.

Speaker lateral off axis response, Dynaudio Confidence C4.
Speaker lateral off axis response, Dynaudio Confidence C4.

Speaker pointed straight ahead

When the speaker is pointed straight ahead there is actually much more of a similarity in the level of the direct and reflected sounds. Psychoacoustically this will increase the width of the soundstage.No_ToeFor a wide dispersion speaker the response at 30 and 60 degrees off axis will be virtually identical through the midrange up to the point at which the tweeter starts becoming directional. This is clearly shown in the example response below.

30_60
Response at 23 and 68 degrees off axis for an ATC SCM19.

In this example the combined response of the direct and reflected sounds is significantly higher than either individual response. The reflection is much higher in level than when the speaker is pointed straight ahead and so will be more psychoacoustically significant.

It’s important to realize that reflections are not necessarily bad. There is a lot of research (collated in places like Floyd Toole’s Sound Reproduction book) that shows people like strong lateral reflections, as they increase perceived soundstage width and envelopment.

The problem with speakers that have a rising on axis response is that you have to point them straight ahead if you do not want an excessively bright sound, and so have to deal with the lateral side wall reflection being higher in level. Speakers designed around a flat on axis response give you more choices.

Conclusions

When you toe-in a loudspeaker you are altering:

  • The tonal balance of the direct sound – more toe-in equals more high frequency energy since tweeters becoming directional at higher frequencies.
  • The level of the lateral side wall reflection
  • The relationship between the direct and early reflected sounds. More toe-in minimizes the effect of reflections because the reflections are lower in level. Note the more toe-in the more spectral dissimilarity between the direct and reflected sound.

15 thoughts on “Speaker Off Axis: Understanding the effect of Speaker Toe-In”

  1. “so more toe-in equals more high frequency roll off.”

    Nyal, surely a speaker that is heavily toed-in to point directly at the main listening position will mean the listener receives an on-axis tweeter response and hence less high frequency roll-off versus no toe-in whereby the listening position is very off-axis.

  2. There’s a third option, advocated by Earl Geddes (and embraced by yours truly), which is to use very aggressive toe-in such that the axes criss-cross in front of the listening position. With the right type of speakers, this offers three advantages:

    1. The listener is off-axis by maybe 15-20 degrees, which mitigates the spectral discrepancy that you made note of between the first-arrival and early reflected sounds.

    2. The first significant sidewall reflection from the left speaker is actually taking the long bounce off the right-side wall (and vice-versa), so it has good spectral content, a relatively long time delay (which is desirable), and it arrives at the opposite ear from that speaker’s first-arrival sound, which promotes a sense of envelopment without negative side-effects.

    3. For off-centerline listeners, the soundstaging tends to hold up remarkably well. This is because the ear/brain system’s two localization mechanisms – arrival time and intensity – somewhat cancel one another out. The near speaker obviously “wins” arrival time., but the far-side speaker “wins” intensity because the listener is pretty much on-axis of that speaker but well off-axis of the near speaker. The key to this working well is, the near speaker’s output must fall off smoothly and fairly rapidly as we move off-axis, a 90-degree (6 dB limits) radiation pattern being the theoretical ideal according to Geddes. I’ve had customers sell their center-channel speakers after switching to this type of set-up for their dual-role music/HT systems.

    1. this is exactly what we try to achieve in car audio since every listener is very close to 1 speaker and very far from another. essentially nobody is in a sweet spot. by aiming the left speaker at the right person and the right speaker at the left person (or close to it) you accomplish a much more balanced soundstage in such a lousy environment. I like your wording of which speaker “wins” and why as far as your brain interprets.

  3. I wonder if the author or other commentators could shed light on my strange experiences of using my floorstanders? My room is 12 ft w x 26 ft d x 9 ft H. Speakers placed with drivers facing the longer side of the room. I tried two positionings:

    1) The speakers are placed 212cm, around 7ft apart, 5 ft from the front wall. Each speakers are only 73 cm (the edge of the speakers) from the two sidewalls. My listening position is 240cm away, around 8 ft. TOTAL TOE IN. I barely see the speaker panels.

    2) All things almost identical to (1) But now, NO TOTAL IN. Or very slight toe in.

    I did option 1 since many people suggest toe-in reduce the effect of ‘side wall’ reflections. But my experience in my setting is that option 1 seem to offer more auditory (bad sounding) side-wall reflections than option 2.

    The test is simple:
    1. I use my hands to hold two small pillows in front of my head, and actually also slightly over my head. The pillows are positioned in such a way so my eyes could see the tweeters, but not the side walls and some parts of the ceiling. It means the pillows behind held this way block most early reflections from the side walls (and some parts of the ceiling) entering my ears. When I put the pillows down, I could immediately know how those early reflections contribute to the overall sound.

    2. I did the pillow exercise for option 1 and 2.

    3. Strangely enough, option 1 shows the GREATEST discrepancy between the pillows on / off. With pillows, the sound is much less aggressive and piercing. Without the pillows, the overall sound is harsh. For option 2, with or without pillow doesn’t have such a drastic difference.

    The result does surprise me a bit since many manuals say maximum toe-in could ‘reduce’ the effects of side-wall reflections. My case turns out to be the opposite. I wonder why it is so. One possible explanation may be:

    1. My speakers has bad off-axis responses, so maximum toe-in actually INCREASE the spectral differences between the direct on axis and indirect off axis responses. The differences contribute to sonic disharmony.

    2. So with only slight toe in, the direct and indirect sound in my setting actually has more sonic similarity. In this scenario, it’s TOTAL TOE OUT that reduces the effects of side wall reflections.

    I hope some experts could shed some light on my experiences and educated guess.

      1. I am using ProAc EBS tower produced in the late 1980s. I guess I have new findings based on a switch of another speaker cable, which requires me to qualify my previous ‘findings’.

        Simply put, the previous situation is valid when I used a pair of old Audio Research cables which is known to have a tendency to taming the high. That will affect the off axis response I guess. If the ProAc off axis isn’t particularly brilliant. Cables may worsen / influence the off-axis to give unpredictable results like mine.

        A switch to Belden 8471 doesn’t lead to my previous findings. Off-axis is more audible for both toe-in and toe-out. I used ordinary conductors.

        Anyway, audio reproduction is so complicated that one variable introduced to the loop of things discussed here may give opposite results. Both funny and painful πŸ™‚

        1. Hi Charles

          If you measure your room acoustics with the old cables and the new cables I’d be surprised if you see any difference in the frequency response! That’s even more interesting!

  4. I also use the aggressive toe-in strategy advocated by Duke and Earl (who suggests it works best for 2-way speakers). I’m not sure why it works but it does provide a much more immersive experience with much fuller lower midrange and upper bass, and a much greater depth illusion.

  5. I am using aggressive toe in with my B&W 686s2 speakers and the result is excellent. Use them with a Quadl-ite sub. A very special combination.
    Interesting discussion…thanks to all.

    1. Am also getting excellent results with aggressive toe in: equilateral triangle listening position with 45 degree toe in. So 15 degrees off axis. Huge sweet spot: if you’re a bit closer to left speaker than right speaker, then you are more off axis to the left speaker and less off axis to the now-further-away right speaker. And vice versa. (Pair of Geithain RL906 actives.)

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