Ideal Tweeter Crossover Frequency

[LARRY]

There has been a lot of discussion on the crossover frequency for the mid range horn (300 hz, etc.) in a three way horn system, but very little on the tweeter crossover frequency.

What would be the 'ideal' crossover frequency for the tweeter in a three way horn system? There are drivers available that have useable frequency response on the low end to approximately 800 hz and respond to 18000 hz and above. There are horns, waveguides, etc. that also cover this frequency range. For optimum reproduction should a crossover frequency in the 1000 hz, 3000 hz, 5000 hz ? or some higher frequency be chosen?

The Khorn, Lascala, and Belle have a limitation due to their cabinet structure, but the Jubilee, Jamboree and others have no limitation, so this would allow for large high frequency horns that could crossover at lower frequencies.

This forum has may knowledgeable people and I would appreciate discussion of what frequency is 'ideal'.

Thanks, Larry

[Chris A]

My initial answer is "don't use a tweeter...". But if you've got to have one, then put the crossover somewhere where the ear is least sensitive. The following Fletcher-Munson curves show where the ear is most sensitive - i.e. avoid where the curves' lowest SPL points are:

[Al Klappenberger]

Larry,

I don't think there is an "ideal" crossover frequency. From what I hear from others, the place to cross over is where the beam-width of the two horns are nearly the same. This makes for a smooth distribution of sound at the crossover. The frequency range of the horns and drivers chosen factors into it too.

Al K.

[WMcD]

It is my understanding that PWK wanted to avoid a crossover point of 3500 Hz on the theory that the FM curves show it is where the ear is "most sensitive." This is what Cask is sayng. So he favored 6000 Hz once he had mid horns and drivers which which could continue in performace up to 6000 Hz.

But let me suggest that is the best place to put the crossover freq for the same reason. The two drivers will be sounding at the crossover freq and thus there will be constructive and distructive interference. Basically with constuctive interference combination there is 3 dB or so gain. But with distructive interference the combination can go to nothing -- rather than just a -3 dB gain. But in the real world, the combination goes low toward the inaudible.

My reasoning is that we want to be able to hear the signal despite destructive interference. Therefore, it is best to put the crossover point where our ears can still hear the signal. PWK would be correct if there were added freqs like harmonics or IM being caused at the crossover freq but that does not seem to be the situation.

Looking at the FM curves, it appears to me that both PWK's theory and mine don't hold much water. We're only talking about a few phons difference between the two freqs. Therefore, as Al points out, it is better to look at other parameters which have to be optimized.

Wm McD

[Guest David H]

There has been a lot of discussion on the crossover frequency for the mid range horn (300 hz, etc.) in a three way horn system, but very little on the tweeter crossover frequency.

What would be the 'ideal' crossover frequency for the tweeter in a three way horn system? There are drivers available that have useable frequency response on the low end to approximately 800 hz and respond to 18000 hz and above. There are horns, waveguides, etc. that also cover this frequency range. For optimum reproduction should a crossover frequency in the 1000 hz, 3000 hz, 5000 hz ? or some higher frequency be chosen?

The Khorn, Lascala, and Belle have a limitation due to their cabinet structure, but the Jubilee, Jamboree and others have no limitation, so this would allow for large high frequency horns that could crossover at lower frequencies.

This forum has may knowledgeable people and I would appreciate discussion of what frequency is 'ideal'.

Thanks, Larry

Excellent question, and I don't have a good answer. I try and choose drivers that allow me to cross the tweeters outside of the vocals.

Dave.

[Chris A]

Looking at the FM curves, it appears to me that both PWK's theory and mine don't hold much water. We're only talking about a few phons difference between the two freqs. Therefore, as Al points out, it is better to look at other parameters which have to be optimized.

Actually Gil, I think it gets messier. The issue is complex polar response due to the crossing drivers (the reason why Roy and others like me advocate steep crossover filters). I remember the now-famous review by Richard Heyser on the Khorn talking about this issue and the tweeter/midrange crossover effect had on the listening experience. Pianos and female vocals were affected (in addition to the cabinet diffraction on the tweeter response and the uncorrected delay between the Khorn midrange and tweeter). Driver delay mismatch is a really big problem for the crossover region, IMHO. I can hear its effect.

All this adds up to a lot of trouble. My solution (and Roy's, BTW): just go to active crossovers and two-way design (i.e., dump the tweeter). It's a top-notch engineering trade that works for me (i.e., I invested in it). That is a large factor in why I believe the K-402 Jubilee sounds so much better than the Khorn (IMHO), along with the physics of controlled polars in the K-402 at the low crossover frequency.

There is a lot to share in this area. But maybe 'one bite at a time" is a better approach.

Chris

[WMcD]

Chris,

My major point was that PWK's demand that the crossover point be moved well up out of the 3.5 kHz range appears to me to be unfounded -- at least to the extent it is founded on the fact that this is where the ear is most sensitive. This is because we have to ask, "Sensitive to what?"

I certainly agree with the messiness of it all.

Wm McD

[DrWho]

For a 3 way design that covers the audible range (20-20k), I like xover points of 20-80, 80-800, and 800-20k. This puts a decade of bandwidth into the top two drivers, and then just 2 octaves for the sub where the system will tend to be less efficient (narrower bandwidth will have lower distortion).

[Chris A]

For a 3 way design that covers the audible range (20-20k), I like xover points of 20-80, 80-800, and 800-20k. This puts a decade of bandwidth into the top two drivers, and then just 2 octaves for the sub where the system will tend to be less efficient (narrower bandwidth will have lower distortion).

Mike, I concur with one variation: there is an advantage to crossing at-or-below 500 Hz rather than 800 Hz due to human hearing physics: my "3-way system" is crossed at 55 and ~400 Hz. If you are using direct radiating rather than horn-loaded in any of your drivers, then your chosen crossover points make more sense.

Years ago there was similar rationale: the rule of thumb was that each driver should take approximately equal share of the total 9+ "hearing octaves", dictating ~3 octaves/driver: crossings were considered at ~240 Hz and ~2 kHz.

Today's view is different in the horn-loaded speaker world due in no small part to the availability of Ti- and Be-diaphragm neodymium-magnet compression drivers and active digital crossovers. Full-range drivers were not well regarded back then due to technology limitations in commercially available drivers.

Chris

[DrWho]

Do the Fletcher-Munson curves really tell us where accuracy is more important in the bandwidth?

It's my belief that the sound on the recording already has the influences of the Fletcher-Munson curve applied since the studio engineer was using his/her ears while mixing. An accurate reproduction system will then maintain the intended perception of the music...

I guess I'm not convinced that we're going to more readily hear the artifacts of an imperfect crossover when it is located at frequencies that don't need as much SPL to be perceived at the same loudness. Maybe if these artifacts were near the noise floor, but all the artifacts I know about exist at the same SPL as the music. With that in mind, I would suggest that what matters more is the actual source material itself, and trying to divide the spectrum in such a manner that the timbre of individual instruments stays as consistent as possible.

I tried to find some plots of the spectral density of common music, but I can't seem to find anything readily available online, but I know they exist. There is very little music energy above 8kHz for example, and a ton below 80Hz depending on the source material. It's basically like a tipped scale. Trying to divide the spectrum such that the music energy is as equal as possible across drive units is going to minimize the overall distortion of the system. I'd be curious to understand why F-M curves might tell us that the lower distortion is less important than the audibility of the xover artifacts (I guess I'm suggesting that the artifacts are equally audible regardless of the actual xover frequency...assuming of course that things like polars and distortion are lined up fairly close).

Thoughts?

[Chris A]

It's my belief that the sound on the recording already has the influences of the Fletcher-Munson curve applied

I concur.

I guess I'm not convinced that we're going to more readily hear the artifacts of an imperfect crossover when it is located at frequencies that don't need as much SPL to be perceived at the same loudness.

Perfectly understandable. If you consider why the ear is most sensitive at certain frequencies, and you understand the physics of tuned pipes, then the question is, "what are the properties of human hearing acuity?" For me, I'm fairly convinced that sensitivity is also correlated to aural acuity. But I've not seen proof of that.

...I would suggest that what matters more is the actual source material itself, and trying to divide the spectrum in such a manner that the timbre of individual instruments stays as consistent as possible.

Yes, but the problem is still the crossover region where two drivers of different design characteristics are both emitting acoustic energy.

Trying to divide the spectrum such that the music energy is as equal as possible across drive units is going to minimize the overall distortion of the system.

If you are talking about IMD, then I'd agree with some reservations.

I'd be curious to understand why F-M curves might tell us that the lower distortion is less important than the audibility of the xover artifacts (I guess I'm suggesting that the artifacts are equally audible regardless of the actual xover frequency

Human perception of distortion is another subject of interest. PWK showed us that we can hear distortion at low frequencies. I don't recall seeing an article on distortion detection thresholds vs. frequency band (as mentioned above). I'd guess that it follows the F-M curves, but there are clearly studies done since we all seem to know about increased odd-harmonic distortion vs. even-harmonic distortion "dissatisfaction" in human hearing. Maybe PrestonTom can help out here?

Chris

[Rudy81]

For a 3 way design that covers the audible range (20-20k), I like xover points of 20-80, 80-800, and 800-20k. This puts a decade of bandwidth into the top two drivers, and then just 2 octaves for the sub where the system will tend to be less efficient (narrower bandwidth will have lower distortion).

This is what I am trying to do with the build of the DBB and the use of the P. Audio horn and driver. The sub, RSW-15 can easily cover the bottom. We will see how it sounds.

[DrWho]

For me, I'm fairly convinced that sensitivity
is also correlated to aural acuity. But I've not seen proof of
that.

That's a great way to put it and is exactly the question I'm asking. I wonder if there's existing research on the subject?

Maybe
to take it a step further, do you think the artifacts of an imperfect
xover are small enough that aural acuity is going to be a limitation on
their perception? I would say most of the artifacts I'm aware of are
readily audible.

If you are talking about IMD, then I'd agree with some reservations.

I
was actually thinking of every type of nonlinearity, but I'm curious
what your reservations might be. What I was referring to was the fact
that the excursion and power requirements increase as you widen the
bandwidth (even if you only extend it higher in frequency). Hoffman's
Iron Law also dictates a reduction in sensitivity with increasing
bandwidth as well, so it ends up being a double hit to the power
requirements...

[Chris A]

I wonder if there's existing research on the subject?

I would think that there is, but I'm not familiar with it.

...do you think the artifacts of an imperfect
xover are small enough that aural acuity is going to be a limitation on
their perception? I would say most of the artifacts I'm aware of are
readily audible.

Well, certainly, there are things that we can measure but really cannot hear (for instance, phase information under steady state signal conditions). The polar problems of diffracting signals from two drivers - these effects probably are audible, down to a threshold amount (whatever that happens to be, and at whatever frequency we are talking about).

I
was actually thinking of every type of nonlinearity, but I'm curious
what your reservations might be.

"Minimizing distortion", at least to me, should really be "minimizing aurally detectable distortion". The ear is a tuned closed-ended tube with a membrane, associated connecting hardware to a cochlea, which is, in fact another tuned tube of tapered design that is doing transformation into the frequency domain. Detectors inside the cochlea relay amplitude, but apparently the phase information (detector to detector) is not sensitive to relative phase within a certain window of time. So we are now looking at a "blind spot" for aural perception--distortion that can easily be measured with engineering instruments but not heard.

Additionally, as we proceed away from the most sensitive detection frequencies toward the bottom and top ends of the ear's detection capability, some interesting things are happening: the tube that is amplifying the signal (ear canal) is losing its effectiveness and is now shifting the burden to other body perception mechanisms, the amplitude of the ear's "unit loudness" is increasing so that the signal must be louder for us to detect and perceive a signal (relative to the most sensitive portion of the ear's tuned passband). This "distortion perception threshold" is increasing as the frequency continues to move away from the center tuned frequency of the aural system. So now we are not talking about minimizing total distortion, but total perceived distortion, etc.

I think you can fill in the blanks on where this discussion is leading: we detect distortion as a function of frequencies involved. If I were going to do engineering trades on loudspeaker system design (using multiple drivers crossing over to faithfully reproduce the full aural detection spectrum) then I'd say that frequencies around the center aural frequency are most difficult to reproduce in a way that keeps the ear from detecting "distortion" (i.e., a thresholding problem). So this implies that not all hearing octaves are created equal. Minimizing total aurally detectable distortion may mean that we can get away with more IMD up very high or very low before we can detect it. Dividing up the power spectrum across the drivers, then, may not be a evenly divided logarithmic or power-band scale, but another scale that uses the response of the ear to modify the breakpoints.

There are many types of distortion. I feel that our ears hear crossover distortion phenomena (i.e., non-TMD distortion) more readily at frequencies around the 3.5 kHz than it does TMD distortion of a single diaphragm that is trying to faithfully reproduce multiple frequencies of differing phases simultaneously, even close to 3.5 kHz. Why does the ear hear odd harmonic distortion more easily than even harmonics? My answer: because the ear has developed over time from the standpoint of the needs of its environment (...not linear systems theory...). Assumptions about design criteria need to be made in light of how the ear perceives distortion and "fidelity".

Pretty long answer to a simple question, but one that is necessary to voice the underlying assumptions of what we are trying to achieve.

Chris

[sunnysal]

Pick the crossovers to match as closely as possible the limits in frequency range of the instruments you wish to reproduce.

http://gallery.audioasylum.com/cgi/gi.mpl?u=7080&f=musrange.gif

[Chris A]

Pick the crossovers to match as closely as possible the limits in frequency range of the instruments you wish to reproduce.

http://gallery.audioasylum.com/cgi/gi.mpl?u=7080&f=musrange.gif

Exactly. That figure illustrates the problem very well. Understand that the harmonics (above the fundamental frequencies shown in this chart) are what gives each instrument its characteristic sound, and when there are any irregularities to the reproduction of harmonics (magnitude and polars), the speaker system winds up sounding "off".

This is also why I recommend minimizing the number of crossovers and that any crossing occur at 500 Hz and below--where human hearing is much less sensitive to directivity changes due to crossover diffraction effects. This is the famous "polar control" problem.

This also illustrates why I believe the K402 two-way Jub sounds as good as it does, at least from the standpoint of crossover/driver-staging design. Constant coverage (i.e., minimizing polar coverage change vs. frequency) is a big deal for the soundstage as well as faithful reproduction of each instrument, including human voice.

[DrWho]

Why does the ear hear odd harmonic distortion more easily than even harmonics?

Does it? I would suggest that the issue of masking is a totally separate phenomenon and isn't directly related to aural acuity...

...I'd say that frequencies around the center aural frequency are most difficult to reproduce in a way that keeps the ear from detecting "distortion" (i.e., a thresholding problem).

Let's pick 80phons on your first chart as an example...at 200Hz and 2kHz, you're looking at about 78dB SPL for both. The second and third harmonic of 200Hz will land you at 400Hz and 600Hz, which are both about 75dB SPL for 80 phons. The second and third harmonic for 2kHz is 4kHz and 6kHz which respectively puts you at about 70dB SPL and 75dB SPL for 80 phons.

Are you saying the distortion will be more readily perceived at 200Hz, or at 2kHz? Or will it be the same?

Now do the same comparison at 500Hz and 4kHz. Which do you think will be easier to perceive distortion?

And then do you think the relative perceptibility changes based on the source material? If so, why?

[4tay]

A lot of this overlooks driver charactaristics. For example: Some tweeters are really poor below 10K while others are comfortable down to 7K. Some mids are magnificent to 5-6K while others can deal with 7-9K.

It seems that there needs to be a crossover point that is respective of the FR and accuracy of the drivers in the enclosure, and not some pre-determined curve or frequency.

[Chris A]

I would suggest that the issue of masking is a totally separate phenomenon and isn't directly related to aural acuity...

I think we just diverged on the definition of "acuity". I'm not sure how to proceed.

Let's pick 80phons on your first chart as an example...at 200Hz and 2kHz, you're looking at about 78dB SPL for both. The second and third harmonic of 200Hz will land you at 400Hz and 600Hz, which are both about 75dB SPL for 80 phons. The second and third harmonic for 2kHz is 4kHz and 6kHz which respectively puts you at about 70dB SPL and 75dB SPL for 80 phons.

I think you are going into "harmonic distortion" - something that PWK once stated that he wasn't that concerned about.

I was really thinking about the other types of distortion, chiefly IMD or perhaps FMD.These are more difficult to agree upon and to visualize, but the ear's "acuity" to these types of distortion are now well known (PWK's writings and other authors).

I think the issue here once was: "where do you put the crossover frequencies?". I'm still of the opinion that one should avoid putting crossovers near the "tuned pipe" frequency of the human ear canal and eardrum. All other things being equal (...as they never are...), putting the crossover regions away from this center frequency region has always resulted in a smoother and better sounding speaker design, IMHO and IME. [:^)]

Chris

[pzannucci]

There are many factors but you should always try to keep any anomalies in a speaker system, be it crossover between drivers or peaks/depressions in response out of the area where the ear is most sensitive.

Other factors come up also such as:

Being able to tell the difference in two types of driver materials from the change in the sound at crossover

Time domain problems. If time alignment was not really needed why does everyone think that their k-horns sould better time aligned or Jub's for that matter.

Associated resonances and distortions of the driver at particular frequencies

Dispersion characteristings of the driver

Doppler effect generated by cone movement relative to crossover frequency

Other oddness due to crossover acoustic slope and driver overlap

You can minimize much of the above by being critical of your driver, crossover, and baffle alignment choices, You can put the crossover in a hearing sensitive area by being mindful of the possible tradeoffs of doing that and trying to minimize the effect.

Add horns to equation and it gets much harder. Due to the size and typical limited bandwidth, it becomes hard to minimize many of the issues unless you use electronic manipulation. If you can get your crossover relatively low (almost full-range from 500/600 up), use eq/time alignment,and/or run two-way, then you probably want to stay away from the ear's sensitive frequencies.