Geddes on Waveguides

Facts:

2a) Operation of a compression driver at and below system resonance is contraindicated, due to the attendant increase in distortion products in this region.
Fact: nonlinear distortion in a compression driver is inaudible - see my AES papers on this.
2b) To reduce driver diaphragm displacement with a decline in frequency requires a high pass filter slope > 12 dB per octave.
To "reduce it" correct, but the 6 dB downward slope does dramatically reduce the excursion requirements. In home use excursion below resonance is not an issue at all.
2c) Driver loading (or the absence thereof) provided by a loudspeaker enclosure (horn included) is not a matter of mythology. In conical horns, as well as those asymptotically conical, the early decline of driver loading and the absence of a material [Fc] are well known and understood.

3) Under these conditions, a minimum of a 3-way partition of the audible spectrum is needed; e.g., 20-200, 200-2000, 2000-20,000 Hz. This fact is particularly relevant for an all-horn system.

Thats not the way I see and I am not disatisfied with the results. But these aren't "facts" they are opinions.

Facts:
3...
Facts 3 ... are opinions offerd with no substantiation.
4) To mitigate beaming at the upper limit (determined almost entirely by the perimeter size and geometry of the effective piston radiating area), dispersive elements must be introduced such as an acoustic lens, passage bifurcation, or other beam spreading mechanisms. All drivers, horn loaded or not, exhibit high frequency beaming. This occurs when signal wave length approaches or becomes smaller than radiator dimensions.

Once again, this is untrue and proven by the data for the Summa shown on my website which has a constant DI up to 20 kHz for a 1" aperature, which should, according to your claims, beam like crazy.

Facts:

4a) The laws of acoustics dictate the beaming; unless of course, you mitigate it. In your case, this is achieved by introducing a foam acoustic lens and a geometric discontinuity in the horn neck. In the later case flare curvature increases rapidly from the compression driver exit and then steadily declines as a cone asymptote is approached. To mitigate the inevitable reflectance at the mouth, a toroidal surface of arbitrary dimensions is introduced. Here curvature abruptly increases again.

Again untrue - the foam has no effect on directivity, and if it did (think about it!!) the foam would narrow the directivity because it is a convergent lense! And I also have data to prove that.

I first tried to affect the directivity with the foam, but to widen the directivity would have required a concave surface NOT a convex one. But the fact is that there was very little change in directivity. So I opted to use a convex outer surface, which, if it does anything, makes the directivity narrower, not wider.

I think you have the physics wrong.

There are many ways to design a loudspeaker system. We differ in approach and as to what is important when doing that.

Regards,
WHG

Different approaches is fine, but quoting falsehoods as "facts" is not. If you want to argue the math and physics then bring it on. You'll not win that one.

Even Don Keele got the directivity at HFs wrong and simply could not understand how the Summa waveguide was able to do what it does. That's because he too misunderstood the physics.

Beaming from a source is happens when the source is flat and in an infinite baffle. A flat disk at the end of a waveguide is NOT an infinite baffle and DOES NOT have to beam according to the physics. At the mouth the wavefront is not flat any longer and will not beam when placed in in a baflle or otherwise. However, If the waveguide is not precsiely an OS then the wavefront at the mouth will not be a sufficiently coherent spherical section to radiate properly and it will beam. Only an OS countour will allow this effect for a circular wavefront. - Thats the physics and the data proves it.

I didn't get a 4.0 average in my Physics PhD by sleeping in class.
 
Its also nice to place that dip on axis away from the listening area ;)

If they were designed to be listened to on axis then there wouldn't be a dip, there would be peaks off axis.

Histoirically the Summa had only a very small dip and I did EQ this out. But then I found that the power response was better if I did not do this, so I stopped.

In the Abbey the dip was much worse - it's taken me a long time to figure out why that happened - EQing for the axial response would have been a disaster. There is actually a power response peak at the same frequency as the axial dip (a clue to why the dip is so pronounced). So I actually drive the dip deeper with the EQ to make the power response and the DI off axis better.
 
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Fact: nonlinear distortion in a compression driver is inaudible - see my AES papers on this.

I've seen your papers but I've also heard the distortion. At least on sweeps. Does there have to be masking by music to make this distortion inaudible?

FWIW, every horn + driver combo I've measured shows a rapid rise in distortion below a frequency who's wavelength is directly related to the diameter of a round horn mouth or the hypotenuse of a rectangular one. Easy to hear on sweeps, in music I'm not so sure.
 
2b) To reduce driver diaphragm displacement with a decline in frequency requires a high pass filter slope > 12 dB per octave.
Only if the high pass filter is well above the mechanical resonance of the driver. Below the mechanical resonance the excursion is already constant with frequency before application of a high pass filter, so any high pass slope will reduce excursion as frequency goes down.

From the sound of it the driver resonance is 1.5Khz and is operated lower through EQ so this would be the case in this design.

Facts:

3a) Bifurcation of the frequency range, where speech and most instrument fundamentals exist, is not particularly desirable.
I do agree that dividing the midrange in half is not ideal (I prefer to keep crossovers out of the 300-3000Hz range, and have as much as possible if not all of the midrange produced by the same driver) however I wouldn't call it a "fact", more of a subjective opinion.
3c) Above 10k Hz, signals from cymbals, triangles and other like instruments are audible and important.
I also agree that 10Khz and above is still important and shouldn't be written off as unimportant. I've been recently experimenting with small amounts of EQ to flatten the top end from 8Khz upwards, and its quite surprising just how noticeable a 0.5dB shelf reduction from 10Khz upwards is on an otherwise flat response. More so than I would have expected.
 
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I've seen your papers but I've also heard the distortion. At least on sweeps. Does there have to be masking by music to make this distortion inaudible?


We only tested with music.

Be careful - I have never claimed that there weren't audible artifacts in Horn/driver systems, I've heard them myself, but they are not "nonlinear" effects in the driver itself. All attempts at showing that they were have failed.

Lidia and I did a follow up paper showing that group delay effects were audible with an increasing audibilty with SPL level - in other words, the effect was nonlinear. BUT, this is a nonlinearity in our "perception", not in the system, because group delay is linear. Wrap your head arround that one for a minute.

This is not a simple subject, but I will say that the more I dug into it, and that has been extensive, the less I found that it was what the classic dogma said it was and the less intuitive it was. In other words, I don't believe much of what people claim is the problem. None of what I had thought or what others have claimed has turned out to be true. Its just not that simple.
 
I do agree that dividing the midrange in half is not ideal (I prefer to keep crossovers out of the 300-3000Hz range, and have as much as possible if not all of the midrange produced by the same driver) however I wouldn't call it a "fact", more of a subjective opinion.

No crossovers would be best, except thats not possible.

The ear is the most accute from 1 kHz to 6 kHz. So if I have to have a crossover I don't want it in this range. I'd much rather do one at 800 Hz than be forced to have two, especially if one of those is between 1 kHz and 6 kHz. So since I CAN reach from 800 Hz to 16 kHz with no degradation, this seems to me to be the optimum.

Our ears acuteness peaks at about 2 -3 kHz - the worst possible place to put a crossover.
 
Lidia and I did a follow up paper showing that group delay effects were audible with an increasing audibilty with SPL level - in other words, the effect was nonlinear. BUT, this is a nonlinearity in our "perception", not in the system, because group delay is linear. Wrap your head arround that one for a minute.

Very interesting. I've heard people say in the past that they feel 3/4 ways seem to fall apart at higher SPLs, and I wonder if this has anything to do with it.

But don't Digital/FIR/ etc filters behave differently in these respects??? :confused:
 
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OK, I understand the group delay thing, I've read that before in your lit. But not hearing harmonic distortion is hard for me to understand because I hear it plain as can be on sweeps. When the horn/driver is swept at frequencies under its distortion point it's easy to hear.

I don't know that it's audible in music, but why wouldn't it be? I will admit, I don't hear the amount of distortion in music that I hear on the sweeps. At least I don't think I do. But it's so obvious on the sweeps that it seems hard to imagine it's having no audible effect on program material.
 
OK, I understand the group delay thing, I've read that before in your lit. But not hearing harmonic distortion is hard for me to understand because I hear it plain as can be on sweeps. When the horn/driver is swept at frequencies under its distortion point it's easy to hear.

I don't know that it's audible in music, but why wouldn't it be? I will admit, I don't hear the amount of distortion in music that I hear on the sweeps. At least I don't think I do. But it's so obvious on the sweeps that it seems hard to imagine it's having no audible effect on program material.

Harmonic distortion is audible, but I think what happens is that each instrument/sound has its own harmonic signature, and it goes something like

Fundamental + 2nd harmonic + 3rd harmonic etc

where those harmonics are MUCH higher in level than HD IRL

So if the driver's harmonic signature has harmonic distortion what you get is 2nd/3rd harmonic distortions that mimic or even subcede the level of natural harmonics at the same frequency, and then when you take the harmonic distortion of the harmonics, the SPL drops, and so forth. Only when there's higher order harmonics do they become audible because that's not part of the harmonic signature of the real life sound so we can recognize the driver adding it.

Am I correct? Logically, it's a masking effect only because real life sound is full of ever present harmonics, and test sweeps are fundamental only.

That said, i'd say it makes things very dependant on WHAT instrument/real life sound is being reproduced.
 
Harmonic distortion is audible, but I think what happens is that each instrument/sound has its own harmonic signature, and it goes something like

Fundamental + 2nd harmonic + 3rd harmonic etc

where those harmonics are MUCH higher in level than HD IRL

So if the driver's harmonic signature has harmonic distortion what you get is 2nd/3rd harmonic distortions that mimic or even subcede the level of natural harmonics at the same frequency, and then when you take the harmonic distortion of the harmonics, the SPL drops, and so forth.
That's something I've wondered myself. Harmonic distortion on tone sweeps is quite audible in the midrange even at quite low distortion levels, probably because a pure tone has no harmonics of its own, but in music most instruments already have 2nd and 3rd harmonics which are far greater in magnitude than those generated by the driver distortion, so may be somewhat masked.

At most you're changing the timbre of the instrument slightly by changing the relative proportions of pre-existing harmonics. (Richening the timbre)

However what this "instruments already have harmonics" theory does not take into account is intermodulation distortion products which are sum and difference frequencies. These have no natural counterpart in the music content itself and are totally foreign to the original instruments. If of sufficient amplitude I fail to see how intermodulation couldn't be audible.
Only when there's higher order harmonics do they become audible because that's not part of the harmonic signature of the real life sound so we can recognize the driver adding it.
What makes you think high order harmonics are not part of "real life sound" ? Have you looked at many instruments individually on a spectrum analyzer ? There are plenty that have high order harmonics beyond 2nd and 3rd.
 
Maybe that part was wrong/lazily added.

However what this "instruments already have harmonics" theory does not take into account is intermodulation distortion products which are sum and difference frequencies. These have no natural counterpart in the music content itself and are totally foreign to the original instruments. If of sufficient amplitude I fail to see how intermodulation couldn't be audible.

I think IMD is audible but i'm no researcher. It's a result mostly of poor flux control isn't it? According to zaph, high order harmonic distortions are an indicator of high IMD.

So maybe you're right that high order harmonics themselves would be masked as well, but drivers with high order HD will have high IMD??
 
No crossovers would be best, except thats not possible.

The ear is the most accute from 1 kHz to 6 kHz. So if I have to have a crossover I don't want it in this range. I'd much rather do one at 800 Hz than be forced to have two, especially if one of those is between 1 kHz and 6 kHz. So since I CAN reach from 800 Hz to 16 kHz with no degradation, this seems to me to be the optimum.

Our ears acuteness peaks at about 2 -3 kHz - the worst possible place to put a crossover.
1-6Khz now ? A few posts ago you said the ear was most acute at 1-4Khz and crossovers should be avoided in that region.

I'm not sure that its quite as simple as "the ear is most acute in this frequency range, therefore we should not put a crossover there". Do you have any basis other than this for deciding what frequency range to avoid for crossovers ?

If the goal is to have a convincingly "coherent" image, as you would get from a single full range (or coaxial) driver, then you really have to take into consideration the psycho-acoustic effect of each frequency range on localisation - dividing the spectrum at different points doesn't have the same effect on localisation of images, more so if the drivers are widely spaced, and different crossover frequencies will cause differing degrees of loss of coherence compared to the ideal of a single concentric driver.

(Something that can be tested by crossing over two identical vertically spaced full range drivers, where the only difference is variations in the crossover frequency between them)

I agree 2-3Khz is not a good place for a crossover, in fact its almost certainly the worst possible, but once you get to 4Khz and above it seems to work very well.
 
I think IMD is audible but i'm no researcher. It's a result mostly of poor flux control isn't it? According to zaph, high order harmonic distortions are an indicator of high IMD.

So maybe you're right that high order harmonics themselves would be masked as well, but drivers with high order HD will have high IMD??
IM distortion has orders just like harmonic distortion.

A non-linearity that causes 2nd order harmonic distortion also produces 2nd order intermodulation distortion when two or more tones are present.

I don't really see the connection between high order harmonic distortion and intermodulation distortion in general...
 
The ear is the most accute from 1 kHz to 6 kHz. So if I have to have a crossover I don't want it in this range. I'd much rather do one at 800 Hz than be forced to have two, especially if one of those is between 1 kHz and 6 kHz. So since I CAN reach from 800 Hz to 16 kHz with no degradation, this seems to me to be the optimum.

Where is this info coming from? It's a comment often heard on audio forums without a reference and I'm wondering how it is determined and in what way the ear is more actute in that range. Obviously we all know the equal loudness curves, but are we also talking about ability to detect time domain abberations?

What I also start to wonder is whether the problems can now be mitigated to the extent that the actual crossover point becomes non critical in these terms. Let's suppose we first place the crossover where it can best optimise directivity, so we have a nice polar response, a smooth transition and you can't pick the crossover point. Now let's say we also go with a sophisticated DSP crossover that can even correct for group delay. Now let's also say that we have a point source arrangement. Could it be that we now have removed the problems related to the crossover and it now ceases to be something we need to worry about?

Or to put it another way, what problems do we have left that are related to having a crossover?
 
What I also start to wonder is whether the problems can now be mitigated to the extent that the actual crossover point becomes non critical in these terms. Let's suppose we first place the crossover where it can best optimise directivity, so we have a nice polar response, a smooth transition and you can't pick the crossover point. Now let's say we also go with a sophisticated DSP crossover that can even correct for group delay. Now let's also say that we have a point source arrangement. Could it be that we now have removed the problems related to the crossover and it now ceases to be something we need to worry about?

Or to put it another way, what problems do we have left that are related to having a crossover?
I think you've eliminated one too many flaws (of practical speakers) in your hypothetical situation to make it meaningful.

The biggest single perceptual difference between different crossover frequencies IMHO is due to non-coincident drivers, with the attendant lobing and interference patterns between the drivers, as well as the fact that some frequencies are coming from one location in space and some are coming from elsewhere, which may or may not interfere with our sense of source location, depending on crossover frequency.

Design a co-incident driver and that goes away, so the majority of issues surrounding a crossover and the crossover frequency choice also go away. Most practical implementations of coaxial drivers also inherently match directivity at the crossover frequency as well - for example a tweeter mounted in the middle of a woofer inherently has its directivity controlled by the cone of the woofer, matching the directivity of the small active portion of the middle of the woofer cone at the top end of its range.

Factors like group delay, linear phase etc aren't nearly so important as this at making the crossover "disappear" IMHO.
 
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I've been recently experimenting with small amounts of EQ to flatten the top end from 8Khz upwards, and its quite surprising just how noticeable a 0.5dB shelf reduction from 10Khz upwards is on an otherwise flat response.

I went here a couple of days ago and can agree with your assessment. I also recall the opinions that CD should be presented with a rolloff at the top. I haven't come across anything to suggest how much but it would be good to find something to read on the subject.
 
Where is this info coming from? It's a comment often heard on audio forums without a reference and I'm wondering how it is determined and in what way the ear is more actute in that range.

It comes from a paper by Brian Moore in the AES where he studied the audibility of group delay and found that the ears sensitivity to this peaked at 2 kHz. It dropped quickly below 1 kHz and above something like 6 kHz. We know that the ear is most sensitive to SPL levels around 3 kHz. There was also a recent ASA paper on what constitutes an annoying sound - like nails on a chalk board - and found that it was sounds in the range of 2-5 kHz that we are most annoyed by.

Does this mean that everything is most sensitive in this range - no, but I know of no data that says otherwise.
 
IM distortion has orders just like harmonic distortion.

A non-linearity that causes 2nd order harmonic distortion also produces 2nd order intermodulation distortion when two or more tones are present.

I don't really see the connection between high order harmonic distortion and intermodulation distortion in general...

I think that everyone should read our papers on the perception of nonlinear distortion, because there are a lot of misconceptions being reiterated here.

Everyone that I know of who has done "real" experiments in this regard has come to the same conclusion. Its only those people who do the "I can hear it" tests that remain unconvinced. The scientifc data ALL says otherwise.

And please note that none of this research says that I cannot create a situation where it is audible, only that it is not a primary consideration in most cases. The issues with loudspeakers has to do with "order" of the nonlinearity. Higher orders are not typical in mechanical systems because they require high forces. Low order distortion is not audible for music. maybe it is for pure tones, but thats not a "realistic" test.
 
I think you've eliminated one too many flaws (of practical speakers) in your hypothetical situation to make it meaningful.

At the recent Australian Hifi show, one of the best speakers was a Cabasse point source 4 way coaxial with a DSP crossover. The most recent speaker I have built is a point source coax horn which has CD performance all the way down to below 300 Hz. Then it crosses to an offset woofer near the Shroeder frequency. There is a crossover at 900 Hz and 230 Hz. So to me this issue is meaningful!

...

Thanks Earle. When I first started measuring speakers as a teenager, I recall measuring 103 dB @ 3.5k out of my first speakers. Outch! Even to teenager ears that was nasty!

My interest in GD has increased after a demo in which a DSP crossover switched GD correction in and out with an instant switch. Frequency response was matched in both profiles fairly closely, a demo set up by a friend with a digital active system. The difference was quite surprising, including both the bass and a significant change in the size of the sound stage. It was enough for me to want to set up another demo and look into it further.