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Discussion: How important is smooth vertical directivity?

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See the following diagrams of a very typical 18cm/2.8cm 2 way I just simulated with a crossover at 1.8 khz. Note also how crossover slope affects how smoothly the drivers are combined off axis. The vertical response is always a mess, however. A waveguide helps a lot to widen the vertical window but you will always have cancellation. A small midrange driver also helps a great deal.

LR2 Horizontal: LR2 horizontal.png
LR2 Vertical:LR2 vertical.png
LR4 Horizontal: LR4 horizontal.png
LR4 Vertical:LR4 vertical.png

I would contend what you're hearing between crossover slopes is the dip in power response around Fc, but beaming sound with a huge notch in it to your ceiling is not exactly great either.

Note that I adjusted the Z offset of the woofer so that it is as close to the tweeter in that axis as possible. Normally on a flat baffle, the acoustic center of the woofer is behind the tweeter, which tilts the most in-phase axis downwards if the tweeter is on top. This is why you often see speakers with baffles that slope back, and highlights another nice bonus of a waveguide - it places the tweeter acoustic center right over the woofer acoustic center.
 

oivavoi

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See the following diagrams of a very typical 18cm/2.8cm 2 way I just simulated with a crossover at 1.8 khz. Note also how crossover slope affects how smoothly the drivers are combined off axis. The vertical response is always a mess, however. A waveguide helps a lot to widen the vertical window but you will always have cancellation. A small midrange driver also helps a great deal.

LR2 Horizontal: View attachment 38246
LR2 Vertical:View attachment 38247
LR4 Horizontal: View attachment 38245
LR4 Vertical:View attachment 38249

I would contend what you're hearing between crossover slopes is the dip in power response around Fc, but beaming sound with a huge notch in it to your ceiling is not exactly great either.

Note that I adjusted the Z offset of the woofer so that it is as close to the tweeter in that axis as possible. Normally on a flat baffle, the acoustic center of the woofer is behind the tweeter, which tilts the most in-phase axis downwards if the tweeter is on top. This is why you often see speakers with baffles that slope back, and highlights another nice bonus of a waveguide - it places the tweeter acoustic center right over the woofer acoustic center.

This was very interesting! You learn something new every day, at this forum at least... Thanks!

So there's apparently a trade-off between more even off-axis response (which is good) and steeper crossover slopes (which is usually also good, I think)?

EDIT: Thinking further, this indicates to me that loudspeakers are ideally designed for different use cases. For nearfield listening - optimize on-axis response, maybe steeper slopes, if possible. For farfield listening, off-axis listening in the home, etc - optimize off-axis response, maybe shallower slopes. At least given this crossover point and such a driver configuration.
 

617

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This was very interesting! You learn something new every day, at this forum at least... Thanks!

So there's apparently a trade-off between more even off-axis response (which is good) with steeper crossover slopes (which is usually also good, I think)?

Yes. The more gradually the speakers cross-over, the more their directivity characteristics 'blend' together. Notice how the LR2 horizontal response looks like one blob but the LR4 looks like it is wearing a tight belt. This corresponds to less of this frequency in the reverberant field of the room.

There are two reasons for steep crossover slopes:
1. Stop drivers from operating out of their comfort zone w.r.t. distortion
2. Limit the bandwidth of poorly integrated speakers

If you're designing on a flat baffle, your drivers will have different Z offset (into/out of the baffle). The easiest way to deal with this is to simply limit how much bandwidth this error occurs over. Not an ideal approach, but if you're starting in speaker design for fun it's not a bad compromise; if you manage to get the drivers in phase at the crossover it does guarantee that any crap off axis is a dip rather than a peak.

If you're using drivers which are matched well in terms of directivity, steeper slopes make less of a difference, but if you're going between disparate driver sizes (6" to 1" for example) a fourth order crossover will not 'blend' the shapes of the response very well. See the horizontal responses to see what that looks like.

On flat baffle speakers for normal far field use I always try to do a second order crossover between tweeter and mid unless it's a small mid, and even then you might as well. This requires the tweeter be set back somehow, however, using a sloped baffle, a waveguide or a felt lined cavity or something.
 

oivavoi

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Yes. The more gradually the speakers cross-over, the more their directivity characteristics 'blend' together. Notice how the LR2 horizontal response looks like one blob but the LR4 looks like it is wearing a tight belt. This corresponds to less of this frequency in the reverberant field of the room.

There are two reasons for steep crossover slopes:
1. Stop drivers from operating out of their comfort zone w.r.t. distortion
2. Limit the bandwidth of poorly integrated speakers

If you're designing on a flat baffle, your drivers will have different Z offset (into/out of the baffle). The easiest way to deal with this is to simply limit how much bandwidth this error occurs over. Not an ideal approach, but if you're starting in speaker design for fun it's not a bad compromise; if you manage to get the drivers in phase at the crossover it does guarantee that any crap off axis is a dip rather than a peak.

If you're using drivers which are matched well in terms of directivity, steeper slopes make less of a difference, but if you're going between disparate driver sizes (6" to 1" for example) a fourth order crossover will not 'blend' the shapes of the response very well. See the horizontal responses to see what that looks like.

On flat baffle speakers for normal far field use I always try to do a second order crossover between tweeter and mid unless it's a small mid, and even then you might as well. This requires the tweeter be set back somehow, however, using a sloped baffle, a waveguide or a felt lined cavity or something.

Very interesting. Thanks. How come I've been interested in audio and reading lots about it for 5-6 years, and only now I get to understand these fairly important issues when it comes to speaker design?

My own subjective impression is that active monitors with steep crossover slopes can sound very good in the near-field, possibly because distortion is reduced, or that any break-up modes are more or less completely suppressed. But they can indeed sound fairly uneven off-axis.
 

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Very interesting. Thanks. How come I've been interested in audio and reading lots about it for 5-6 years, and only now I get to understand these fairly important issues when it comes to speaker design?

My own subjective impression is that active monitors with steep crossover slopes can sound very good in the near-field, possibly because distortion is reduced, or that any break-up modes are more or less completely suppressed. But they can indeed sound fairly uneven off-axis.

They sound good in the nearfield because when you listen to speakers up close you hear more of the direct sound and less of the sound from the room, proportionally, so the dip in the power response , or any off axis issue, is less apparent. Basically big headphones at that point.
 

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Impressive preservation of top octave, but 15 degrees isn't much. +/- 30-40 is where I tend to see the big nulls.

Yeah, that's where I run into physical issues (e.g., mike too close to the floor). For small speakers, I could conceivably turn them sideways, but I've been too lazy to do so. Nonetheless, take a look at the +/-15 degree plots of most other multi-driver speakers that Stereophile has published- they usually look pretty ugly even by 15 degrees.
 

MediumRare

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Two related questions for the techies:

- How could the difference in ideal headphone and loudspeaker FR help us deduce the role of the room and reflections in preference?
- Is recorded music mastered primarily for loudspeakers or headphones, or does that not make any difference?
 

DDF

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On flat baffle speakers for normal far field use I always try to do a second order crossover between tweeter and mid unless it's a small mid, and even then you might as well. This requires the tweeter be set back somehow, however, using a sloped baffle, a waveguide or a felt lined cavity or something.

I prefer 3rd order acoustic, offset xover points and with gentle roll off through xover ("low Q" of second order part). You get better out of band roll off for distortion reduction plus "blend" through xover close to 1st order, if done right, that provides better off axis. George Short of North Creek fame independently came to the same conclusion (we briefly discussed on a board years ago)
 
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617

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I prefer 3rd order acoustic, offset xover points and with gentle roll off through xover ("low Q" of second order part). You get better out of band roll off for distortion reduction plus "blend" through xover close to 1st order, if done right, that provides better off axis. George Short of North Creek fame independently came to the same conclusion (we briefly discussed on a board years ago)

That actually describes my approach well - close to Fc it's more like 2nd order and as you get further away from Fc it gets steeper. For a lot of drivers it's difficult to actually get 12db/octave deep into the stop band - your filter might give you 12db/octave but the driver itself might be rolling off for another six = 18db. I feel like at some point with a metal cone midwoofer I've even added another component to get a really steep roll off up high just to completely clear breakup. Frankly I like the idea of fourth order low passes on woofer/mid networks, but you rarely see that.

I used to fret about crossover slopes because a lot of people used to describe them like they had an intrinsic sound, but it's really more of a spectrum, and your slopes are only even symmetrical if your drivers are aligned well. VituixCAD has been a game changer for me since it actually shows me what's going on off axis while I'm trying to get on-axis flat. The 'average window' response is great as well.
 

pozz

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Two related questions for the techies:

- How could the difference in ideal headphone and loudspeaker FR help us deduce the role of the room and reflections in preference?
- Is recorded music mastered primarily for loudspeakers or headphones, or does that not make any difference?
The first question is pretty complicated. I'm not sure what you mean or how to answer in the context of the discussion, so I'll start from scratch.

Ideally the transduction of an electrical signal to its acoustic counterpart would show no difference at all when measured. Frequency response should therefore be flat, i.e., show no deviations in amplitude. This should be the case for both loudspeakers and headphones, but it isn't because speakers play in a room and headphones are worn on your head.

When you talk about reflections, what you're referring to is time-domain behaviour and the way the acoustic signal propagates in its surroudings since there's a delay between the speaker firing and the wavefront hitting your eardrum (your body, really, since your torso, head and ear shape influence what ends up at your eardrum, with bass rattling the rest). Same thing for the headphones and IEMs but on a smaller scale. Headphone manufacturers have to account for the resonances of the entire circum/supra-aural cup, for example.

So again, ideally by the time the wavefront hits you, there should be no change in amplitude at all. But there will always be some difference because, by the time you hear it, given the speed of propagation, you're perceiving multiple slightly delayed versions of same wave. The hearing system works according to a time-based averaging function which will take into account the interference patterns of the multiple arriving wavefronts within a small window. Think of it as the time required for your ears to go through their own mechanical to electrical transduction.

The reasons why the preferred curve is different for headphones and loudspeaker is due to the physical difference in listening situations.

The discussion in this thread is about the effects of vertical reflections on listening with speakers. Assuming a boxlike geometry, vertical reflections from the floor and ceiling will arrive at your ears at the same time. This means whatever effect they have will be perceived the same way, and will be far less noticeable than that of left/right sidewall reflections, which will arrive at slightly different times and cause slightly different interference patterns at each ear.

Since loudspeakers aren't perfect transducers and incur energy losses, and are also of a certain size and shape, the discussion turned to the effects of multiple driver crossovers on vertical polarity, which will affect FR according to the height of your listening position. Smooth vertical polarity, like smooth horizontal polarity, will ensure minimal differences between different listening positions. Actually getting smooth polar response means solving an extremely difficult design problem.

Reflections in themselves are just multiplied versions of the direct sound from your speakers. They serve to increase the amount of apparent source locations. Given a well-designed speaker with flat FR and smooth off-axis response, the content of reflections won't differ significantly from the speaker's direct sound. Any abrupt on-axis or off-axis FR anomalies will emphasize certain areas of the spectrum and cause you to limit the listening position to a smaller range of locations or outright change what you end up hearing. It's worth thinking about the multiplication of apparent sources and the connection to reverberation and perceived spaciousness. Too many reflections and perceived sound will be indistinct. Too few, and the sound will shrink to pinpoints on a line situated between your speakers (only under anechoic conditions; no amount of acoustic panels in your living room will even come close to what this is like, although you can screw up balance by relying too much on one kind of absorber, like foam).

With headphones, the above set of issues occurs in the small distance between the driver and your ear. All of the same things happen, but on a small scale. The main thing to consider here is that preference is much harder to establish because of the individual dimensions of your ear. There's no one way to tailor a headphone such that it compensates perfectly for everyone's ears, although the goal is more or less clear: flat FR. Still, just as the circumstances have shrunk, so has the perceived sound shrunk to the distance between the two drivers. The best headphones have managed to minimize the effects at best, though the flipside is that many other problems that loudspeakers have are obviated.

With mastering, the workflow is pretty archaic. The basic assumption is that mastered music at end of the process will sound good on any medium. This is a roundabout way of saying that most mastering engineers will use both speakers and headphones, audition their mixes in a number of environments, and then make adjustments. There are very few studios that are interested in the acoustical differences between headphones and speakers. From a methodological, scientific perspective, the methods are random and haphazard. But then so are most listening circumstances, so it works out.

Some have created specifically binaural music for headphones. Chesky Records have created a set of filters to replicate the experience with speakers. It's not an active area by any means.

These days signal processing is cheap, and some of the issues of stereo sound and hardware limits have been addressed with DSP and software. When this area gets really good, hardware will likely only be required to hit a basic set of necessary parameters (like maximally flat FR) and the digital side will take care of the rest.
 

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That actually describes my approach well - close to Fc it's more like 2nd order and as you get further away from Fc it gets steeper. For a lot of drivers it's difficult to actually get 12db/octave deep into the stop band - your filter might give you 12db/octave but the driver itself might be rolling off for another six = 18db. I feel like at some point with a metal cone midwoofer I've even added another component to get a really steep roll off up high just to completely clear breakup. Frankly I like the idea of fourth order low passes on woofer/mid networks, but you rarely see that.

I used to fret about crossover slopes because a lot of people used to describe them like they had an intrinsic sound, but it's really more of a spectrum, and your slopes are only even symmetrical if your drivers are aligned well. VituixCAD has been a game changer for me since it actually shows me what's going on off axis while I'm trying to get on-axis flat. The 'average window' response is great as well.

I agree there's no magic to particular slopes. Whatever works to simultaneously control distortion, give best response on and off axis and eradicate cone and surround resonance.

Many drivers have a cone resonance peak center frequency and width that varies significantly with angle of observation. These require steep low pass. I try to avoid drivers like this and prefer to use one that can be deallt with using a notch filter at all angles.

I've been using simultaneous on and off axis sim off measurements since CALSOD in the 80s, I agree its mandatory for a good system design.
 

MediumRare

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- How could the difference in ideal headphone and loudspeaker FR help us deduce the role of the room and reflections in preference?
Here's a little more explanation of my (vague) question:

- We know that the ideal anechoic FR for a speaker is essentially flat and that many speakers can achieve that.
- Yet, headphones, including, but not only, IEMs are very far from producing that FR.

For example, this see this FR for a highly regarded IEM, where some HF drops by 25 dB or more.
Screen Shot 2019-11-10 at 8.39.50 AM.png
https://www.innerfidelity.com/images/EtymoticER4XR.pdf

And this article discusses measurement of ultra-high-end over the ear headphones and shows the radically different FR of them versus "flat".
https://www.innerfidelity.com/conte...nar-magnetic-headphone-manufacturers-comments

- Thus, I deduce that in-room FR of loudspeakers (including all reflections) should be closer to what these headphone FRs are rather than flat - and that's why we don't want to listen to music in an anechoic room (or solely nearfield?) - it sounds all wrong without the transformation of the signal due to differential reflections. https://www.br-so.com/sound-and-space/klang-ohne-raum-akustik-im-reflexionsarmen-raum/

SO: What do all you acoustics and psychoacoustics experts have to say about that? And @amirm, since you have done a deep dive into speaker measurement, I'd value especially your comments, too.
 
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pozz

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Here's a little more explanation of my (vague) question:

- We know that the ideal anechoic FR for a speaker is essentially flat with some downward slope, and that many speakers can achieve that.
- Yet, IEMs are very far from producing that FR. For example, this see this FR for a highly regarded IEM, where some HF drops by 25 dB or more.
View attachment 38403
https://www.innerfidelity.com/images/EtymoticER4XR.pdf

- This article discusses measurement of ultra-high-end over the ear headphones and shows the radically different FR of them versus "flat".
https://www.innerfidelity.com/conte...nar-magnetic-headphone-manufacturers-comments

- Thus, I deduce that in-room FR of loudspeakers (including all reflections) should be closer to what these headphone FRs are rather than flat - and that's why we don't want to listen to music in an anechoic room (or solely nearfield?) - it sounds all wrong without the transformation of the signal due to differential reflections.

SO: What do all you acoustics and psychoacoustics experts have to say about that? And @amirm, since you have done a deep dive into speaker measurement, I'd value especially your comments, too.
Ideal FR for speakers in an anechoic space is flat. The preferred downward FR slope you're talking about refers to the same speakers being measured in a small reflective room, like a living room, with the changes due room response (speaker boundary interference response or SBIR, also called "room gain").

Speakers should measure flat so that our ear system can do the pre-emphasis itself (gain between 2kHz and 7kHz, peaking around 3kHz, sharply dipping around 8kHz; fairly different responses can be expected from person to person but the shape will be same) before the wavefront hits the eardrum. If you craft that response into the speaker, you'll be doubling the effects.

IEMs are designed to compensate specifically for ear canal resonance. Depending on insertion depth and canal shape, the differences can be as much as 35dB IIRC. Some of the pre-emphasis due to the concha and pinna coupling to the air of the room is bypassed (in fact the entire outer ear is shaped like a horn, with the ear canal wider at the entrance than at the eardrum), so IEM target curves will be different from those of headphone curves.

You don't want to listen to music in an anechoic chamber mainly because the environment is uncomfortably quiet. You'd hear the music mixing with your own somatic sounds. The precision though would be unparalleled. The speakers would be solely responsible for reproducing the timing and amplitude cues we rely on for a sense of distance and envelopment, which are hard to achieve stereophonically.

The research into preferred response has also been about understanding how the room contributes to perceived sound, one of the streams of which is the question of how it can augment stereo to the benefit of listeners; the resulting answer was that early reflections add beneficially to the sound produced by the speakers when it comes to spaciousness, but to the detriment of FR accuracy---the relative tradeoffs here are a matter of argument, and my perspective is that of someone who mixes music, though not for a living.

I'm pretty interested in control room design, which has run the gamut from the non-environment (which mimics a free field by absorbing everything in the sidewalls and ceiling, but keeping the floor reflective for mids and highs to provide some sense of spaciousness) to the maximally diffusive. Given that the most interesting solutions require specialized facilities and megadollars, this is largely an academic matter for me at the moment.
 
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MediumRare

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@pozz Thanks, I'll edit my question. I appreciate your explanation; maybe some others will reply as well.
 

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@MediumRare Have you had a chance to take a look at Tyll Hertsen's test at Harman's reference listen room with his HATS, and his posts on his development of his headphone target curves? He took his headphone measurement rig to Harman to measure the response from a pair of M2? I think that was how he and Harman initially get started with their very first headphone FR target curves (I may be totally wrong on this). There are a lot of nuances to those type of testings, and the interpretation and subsequent processing of the data aren't entirely straightforward. In headphone listening, you don't have your body receiving (feeling) the sound energy, especially the bass, like when you are listening to loudspeakers. This accounts for some of the deviations between the speaker and the headphone curves. And there are others (e.g. cross talk between channels with speakers, but not with headphones, etc.). Here is a link to one of Tyll's posts.
https://www.innerfidelity.com/content/initial-results-head-acoustics-hats-measurements-harman
 

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Twelvetone

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An old-time hack (from an old hack...) is to have an assistant hold a shaving mirror on the ceiling while you're in the MLP, and slide it around till you can see the tweeters (or tweeter-mid junctions, or whatever you judge to be the forward-lobe origin point, MOL) of both speakers, and then mark that patch of ceiling. Treat that area with something (a potatoes string bag full of old sweaters, 4x), and then listen. I've heard it make decided improvements.
 

QMuse

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Treat that area with something (a potatoes string bag full of old sweaters, 4x), and then listen. I've heard it make decided improvements.

I certainly hope it would improve SQ because it is pretty obvious it will make relation with ones wife much worse. :D

P.S. Is it important that sweaters are clean washed and dried or it doesn't matter? :)
 
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