Speaker off axis: constant directivity horn waveguide speakers

This blog article is the fourth in a series on speaker directivity and off axis response. This article will consider the off axis response of constant directivity speakers and consequences for acoustic design. Previous articles in the series established the psychoacoustic as well as subjective importance of speaker off axis response, different ways to measure speaker directivity and the off axis characteristics of waveguided and non-waveguided forward firing cone / dome speakers.

Many speakers are labeled "constant directivity" because the term seems have become cool in recent years. True constant directivity (I'll use the abbreviation CD from now on), however, would mean that the directivity of the speaker does not change from the lowest frequency all the way to the highest frequency. It would also mean that the directivity is constant in the horizontal and vertical planes. The only true constant directivity speaker would be a full range, point source hemispherically radiating speaker, something that does not exist in reality.

So what we have left are quasi-CD speakers. We'll look at the two way designs that have become popular in home theater recently in this article and look at other design approaches such as Constant Bandwidth Transducers (CBTs) and dipoles in future articles.


Constant directivity speakers using waveguides

The design of these speakers takes the form of a woofer with a horn loaded tweeter. The tweeter is generally a compression driver, but does not have to be. There are a few different types of horns, but the one we are interested in is the constant directivity horn. This type of horn is actually often called a waveguide and is just a larger version of those found on forward firing cone / dome speakers. Geddes has written a nice paper that explains what a waveguide is and how it differs in theory from a horn.

The larger the waveguide the lower in frequency the directional control extends to. These speakers are often two ways with a relatively large woofer. The woofer is run up much higher than it would be in a cone/dome speaker and is purposely used to the point at which its response beams. The narrowed response is then matched to the controlled directivity provided by the waveguided compression driver. The theoretical directivity design model for this kind of speaker is wide directivity at low frequencies that narrows as the woofer starts to beam and then stays constant throughout the rest of the frequency range.

Procella P8 - a good example of the CD breed

Procella P8 - a good example of the CD breed

These types of speakers have found their niche in high performance home theater. The compression driver used in the waveguide provides very high sensitivity and therefore does not need to dissipate a lot of power to hit cinema SPLs. For Acoustic Frontiers high performance home theater at this point equals constant directivity compression driver based speakers. That really narrows down the list of manufacturers! Companies that design speakers like this are Pro Audio Technology (formerly Professional Home Cinema), Procella (the brand we love and recommend) and the JTR Noesis line. If you want to DIY check out DIYSoundGroup, who provide flat packs and SEOS CD horns. Seaton speakers do use compression drivers but they don't use true waveguides (they fit into the coaxial driver category).

SPL vs frequency vs lateral off axis angle plot for the Geddes Abbey 12. The black line is the -6dB line. You can see the basic characteristics I referred to earlier - directivity narrows as the woofer starts to beam then stays constant from 1.5kHz through 10kHz.

SPL vs frequency vs lateral off axis angle plot for the Geddes Abbey 12. The black line is the -6dB line. You can see the basic characteristics I referred to earlier - directivity narrows as the woofer starts to beam then stays constant from 1.5kHz through 10kHz.

With these types of speakers the larger the woofer, the larger the waveguide and the lower down in frequency directional control extends. Another example of a well executed CD speaker is JBL's M2 speaker featuring their strangely shaped Image Control Waveguide. Mix Magazine published an article about the story behind the M2 that is worth reading.

JBL's image control waveguide, as featured in the M2 and Studio line.

JBL's image control waveguide, as featured in the M2 and Studio line.

We published this graph earlier, but here it is again: the JBL M2 off axis measurements. You can see by the shape of the off axis curves that the crossover to the waveguide is around 800Hz. Above this frequency the directivity, and therefore off axis spectral balance, is constant through 8kHz or so.

Off axis measurements for JBL's M2

Off axis measurements for JBL's M2


Room acoustic implications of constant directivity waveguided speakers

CD waveguided speakers, like the JBL M2 and Procella P8, have some important implications for room acoustics. The off axis sound, at least in the range the waveguide is working, has similar spectral content but it lower in level than the direct sound. Reflections from major boundaries in the room are therefore lower in level than they would be with a wide directivity speaker such as a cone/dome speaker and have fewer perceptual effects. Below the waveguide transition frequency the spectral content of the reflected sound will have a different composition to the direct sound, which may cause unwanted effects. However Floyd Toole's research shows that image shift, source broadening and timbral coloration from reflections are primarily related to frequencies above 1kHz so maybe the CD design is solid if large enough to provide control down to a low enough frequency.

We would expect the frequency response at the listening position to exhibit a slope from bass frequencies to the point at which the waveguide takes over at which point it should flatten out. This kind of frequency response will look very different to that from a cone / dome speaker. Automated room correction routines that attempt to correct to an arbitrary target curve do not take differing speaker directivities into account, and this is a good reason not to use them unless you can manually draw the target curve. If you find one that lets you set the target curve, such as Dirac Live, a good approach is to measure the uncorrected speakers, use a high level of smoothing such as one octave to show the shape of the frequency response at the listening position, and then fit the room correction target curve to this.

60x40 coverage CD horn (18Sound XR1464).

60x40 coverage CD horn (18Sound XR1464).

One negative of CD speakers is coverage. Some speakers, such as the JTR Noesis are using very narrow coverage waveguides, with only 60 degrees coverage to the -6dB point (i.e. 30 degrees laterally off axis). When used as screen channel speakers in a home theater this means that at minimum the speakers need to be toed in to provide consistent mid / high frequencies across a row of seats in a home theater.  In some wider home theaters the speakers may not have wide enough coverage. When used as surround speakers each row generally needs its own speaker due to narrow coverage. This limitation can be worked around, but needs proper coverage analysis during theater layout. Other speakers use much wider dispersion waveguides, such as the apparent 120 degrees in the M2, or the 90 degrees in the Procella P6.

In future articles we'll look at other speaker designs such as coaxials, dipoles and CBTs!

Speaker off axis response: forward firing cone / dome speakers

This blog article is the third in a series on speaker directivity and off axis response. Previous articles in the series established the psychoacoustic as well as subjective importance of speaker off axis response and looked at different ways to measure speaker directivity.  Today we will look at the directivity characteristics of forward firing cone / dome speakers. This category of speaker design represents the vast majority of speakers manufactured today and what most people own. These speakers are comprised of two or more forward facing drivers with cones for the reproduction of low to mid frequencies and domes for the high frequencies. Variations on this approach such as dome midranges, ring radiator tweeters and the like all have similar issues. Future articles will examine other speaker designs including co-axial, dipole, dipolar hybrids and horns.


The basic cone / dome speaker: nearly always flawed lateral off axis responses

This type of speaker typically has an off axis response that deviates from the on axis response. The classic issue is mismatch of drive unit directivity at the crossover point between the midrange and tweeter. Typically what you will see is that the midrange driver starts to beam (i.e. the directivity narrows) as the frequency is increased. Yet when the tweeter is brought in its response is very wide. On axis things look good but off axis analysis reveals a lack of energy due to midrange beaming. These issues are most pronounced in speakers using 5"+ midrange drivers with 1" tweeters.

A couple of examples are shown below. The left hand graph, from a StereoPhile review of the Vienna Acoustics Mahler is particularly bad. Even at relatively shallow off axis angles such as 30 degrees there is an obvious ridge at 3kHz. The right hand graph, from a StereoPhile review of the B&W Nautilus 805, is well behaved with a quite consistent off axis response to angles of around 30 degrees, after which the lack of off axis energy from the midrange becomes visible in the overall shape of the graph.

From a room acoustic treatment perspective speakers with off axis performance like this force the designer's hand. The speaker on the left, the Vienna Acoustics, will sound better with the lateral reflections fully absorbed in all but the largest rooms where the speakers and listener are far from boundaries and hence reflections are low in level relative to the direct sound. In most rooms leaving the lateral early reflection points untreated would create an obviously colored sound, particularly in the region from 1-4kHz due to the significant variation in the off axis frequency response. We have more flexibility with the speaker on the right (the B&W) but leaving the lateral reflection points untreated at angles over 30 degrees would still lead to timbral coloration in the 1-4kHz range.

Normalized off axis response, Vienna Acoustics Mahler

Normalized off axis response, Vienna Acoustics Mahler

Normalized off axis response, B&W Nautilus 805

Normalized off axis response, B&W Nautilus 805


The waveguided cone / dome speaker: potentially superb lateral off axis responses

More advanced cone / dome speakers nearly always use a waveguide on the tweeter in order to better match the directivity to the midrange driver at the crossover point.

Below are a couple of examples of waveguided tweeters, the left from Revel's M105 and the right from YG's Carmel. In both cases you can clearly see the shallow depression around the tweeter. This depression shapes the dispersion of energy from the tweeter essentially making it radiate like that of a driver with a larger diameter in the lower frequencies.

Revel M105

Revel M105

YG Carmel

YG Carmel


Now let's take a look at some measurements of waveguided speakers to see how this approach works in terms of it's ability to shape the off axis response.

Below is the YG Anat, from this StereoPhile review. Your guess is as good as mine as to where the crossover point is between the midrange and the tweeter! This is a very well designed speaker with no obvious off axis issues due to mismatched midrange / tweeter directivities. The waveguide has clearly done it's job!

This type of speaker gives a skilled acoustic designer huge flexibility in how they treat the room. The room's early and late reflected contributions to the measured and perceived sound can be shaped to the client's subjective preference. Early lateral reflection points can be left reflective for maximum soundstage width and envelopment or can be absorbed for more precise imaging.  In the right room, where the listener is relatively far from boundaries, diffusion can be used to break up and redirect reflections.

YG Anat III lateral off axis response

YG Anat III lateral off axis response


Vertical off axis

All speakers with vertically arranged tweeter / midrange drivers will have some nulls in their vertical off axis response. These nulls are caused by phase cancellation due to differences in the length of the sound path between the two drivers and the measurement location. There is a mathematical relationship between the path length difference and the cancellation frequency. A 1" difference, for example, will cause a cancellation null at 6780Hz and a 2" difference 3390Hz. Even in a speaker as well engineered as the YG Anat, which has exceptional lateral off axis response, looks messy in the vertical domain. The graph below only goes out to 45 degrees off axis, compared to 90 degrees for the lateral off axis graph above, yet clear nulls exist in the off axis response at angles beyond 25 degrees.

YG Anat III vertical off axis response

YG Anat III vertical off axis response

For the acoustic designer these off axis nulls, present in all forward firing vertically arranged cone / dome speakers, represent reflections with a distorted spectral balance that can contaminate the potentially very well behaved sound arriving from early lateral reflections. The two boundaries which must be considered are the floor and ceiling.

The floor is always a challenge as rarely is it possible to design in a 3"+ fiberglass absorber into the floor for consistent absorption down to below the room's transition frequency (although it has been done in some home theaters, with a heavy grate over the top and then carpet over that!). The solution generally revolves around using a thick carpet, typically made of wool or natural fibers, with a thick jute or woven fiber rug underneath. This approach provides relatively consistent absorption down to 500Hz or so.

There are more options with the ceiling. In rooms with high ceilings the reflection is at a lower level relative to the direct sound due to the spherical way in which sound expands and loses energy at 6dB per doubling of distance. With high ceilings any treatment we use at early reflection points is also further away from the listener and there are therefore less issues with using engineered diffusers which are generally required to be no less than 3x the wavelength of the lowest diffused frequency (in order that the listener is in the diffusers farfield). This allows us to use either absorbers or diffusors, or some combination of the two. In rooms with lower ceilings absorption at ceiling reflection points is generally the recommended option, though it is possible to use geometric diffusors which do not have the same minimum distance as their engineered brethren.

Hopefully this article has been educational, please leave your thoughts via the add a comment function below! In future articles we will look at the off axis response characteristics of other speaker types such as single driver / coaxial, panel dipoles and horns.

Speaker off axis response: psychoacoustic and subjective importance

This article focuses on why speaker directivity and off axis response is important to the quality of sound reproduction that we get in our home theaters, two channel listening rooms and project studios. It is the second in a mini-series of articles - the first article covered the theory of speaker directivity and different ways to measure it. We will be following up this blog post in the coming weeks with further posts looking at the directivity characteristics of different types of speakers and examples of good and bad design.


Why off axis is important: the psychoacoustic angle

When we listen to a loudspeaker in a room what we hear is a combination of three things:

  • Direct sound
  • Early reflections
  • Late reflections

The ear / brain system combines the sound information from the direct sound, early reflections and late reflections and hears them as if they were a single entity.

The direct sound is the signal which leaves the loudspeaker and travels straight to the ears of the listener without hitting any boundaries such as the floor, ceiling or side walls. It is typically considered as the on axis or axial frequency response of the loudspeaker, although many use the 'listening window' instead since it is rare to be sat directly on axis with the speaker both horizontally and vertically! The listening window is an average of a number of speaker measurements taken at small off axis angles. There is little doubt that most modern speaker designers target a flat on axis response, with some variation from designer to designer for 'voicing' purposes.

The early reflected sound leaves the loudspeaker and then bounces once off the major boundaries in the room before reaching the ears of the listener. The speaker's contribution to the early reflected sound is the frequency response at the off axis angles that represent the sound path from loudspeaker to boundary to listener. The fittings and furnishings of the room at the locations of the reflections change the spectral content of this sound on its way to the listener because objects like acoustic panels, carpet, ceiling tiles are all frequency dependent absorbers.

Late reflected sounds are those that arrive at the listener's ears after multiple reflections. The speaker and room both contribute to what we hear as late reflected sounds. The speaker's contribution is termed sound power. The room contributes it's decay properties, both at mid-to-high frequencies (reverberation) and low frequencies (room resonances).

Direct, early reflected and late reflected sounds, from this Harman paper, page 12.

Direct, early reflected and late reflected sounds, from this Harman paper, page 12.

From the above paragraphs it is clear that only the direct sound is unchanged by the room. The 'acoustics' of the room in which the loudspeaker is placed change both the early and late reflected sounds and therefore what we hear. The first four paragraphs of my article Listening Room Reflections and the ETC provide some more in depth reading on the subject. I often use the following quote from Arthur Benade because I think it is very good at explaining what is going on!

“The auditory system combines the information contained a set of reduplicated sound sequences (my note – i.e. the direct sound and its reflections) and hears them as if they were a single entity, provided:

a. that these sequences are reasonably similar in their spectral and temporal patterns,


b. that most of them arrive within a time interval of 40 ms following the arrival of the first member of the set.

The singly perceived composite entity represents the accumulated information about the acoustical features (tone color, articulation, etc) shared by the set of signals. It is heard as though all the later arrivals were piled upon the first one without any delay.

Interestingly enough, Harman research shows that the frequency response at the listening position above the room's transition frequency can be predicted from the anechoic measurements of the speaker by combining the data together as follows: 14% direct sound + 44% early reflected sound + 44% late reflected sound.

Let's wrap this paragraph up with a few conclusions:

  • The direct sound's contribution to the frequency response as measured at the listening position is far less than that of the early and late reflected sound.
  • The speaker's contribution to early and late reflected sounds is all off axis sound, at various angles, some very far off axis (up to 70 or 80 degrees laterally off axis in the case of the side wall reflection).
  • The early and late reflected sounds are modified by what is in the room - acoustic panels, carpets, drapes, furniture, everything.
  • What is placed at the small surface area of the room's early reflection points on ceiling, floor, side walls, front / back walls is as important to the frequency response at the listening position as everything else on every other surface in the room combined.


Why off axis is important: the subjective preference angle

Floyd Toole's research at the National Research Council in the 1980s started to conclusively link objective speaker measurements to subjective preferences using double blind tests with trained listeners. His findings were that listeners prefer speakers with smooth flat on axial frequency responses and well behaved off axis performance. Speakers with these characteristics were scored higher in listening tests than those with off axis issues. This conclusion was bolstered by further tests throughout the 1990s and into the modern era and holds true with both trained and untrained listeners. The story is well summarized in this blog article by Sean Olive, current Research Director at Harman.

The conclusions from this research are as follows:

  • A flat on axis response is important
  • Both on and off axis response must be similar in shape. If this is true then this means the early reflected and late reflected sound as heard in room will be similar in spectral balance to the direct sound.
  • Smoothness of the on and off axis curves - i..e absence of resonances - leads to higher subjective preference scores

 The chart below reveals the clear link between subjective and objective measurements as found through the Harman research.

Listener subjective preference vs Harman processed anechoic speaker response data.

Listener subjective preference vs Harman processed anechoic speaker response data.

The Harman research has in fact reached the point where the subjective preference of a listener can be predicted from a speaker's anechoic measurements!


Watch this video & read this book!

Here's a great video that features Sean Olive, Head of Research at Harman talking about speaker testing and listening tests.


Floyd Toole's excellent book Sound Reproduction, Loudspeakers and Rooms provides a huge amount of information about psychoacoustics and the link between objective speaker measurements and subjective preferences. It is required reading for anyone interested in deepening their knowledge about loudspeakers and rooms and how they interact.

Thanks for reading and let me know about your thoughts on the link between off axis response and subjective preferences via the add a comment function!