First order vs. First order time-aligned and a dilemma

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Vertical displacement is the prerequisite, then phase offset determines the exact geometry of the XO-induced lobing.
Phase offset determines only the tilt of the lobe, not its size.

At least we have symmetric lobing and at no angle the response is louder than on-axis.
What if we want louder to go over our head and contribute to the hole in the reverberant power created by lobing?
 
Phase offset determines only the tilt of the lobe, not its size.
Both of which are geometric properties.
What if we want louder to go over our head and contribute to the hole in the reverberant power created by lobing?
We may do so, but only if all other directivity discontinuities are fixed -- eg the "christmas tree" directivity of the typical 2-way without proper waveguide on the tweeter. If the direcitivity of the tweeter is wider than that of the woofer at the XO, then it is a good idea to keep the hole from the XO to get a flatter overal power response. The less directional tweeter already fills in more than enough at and above XO.
 
Phase offset determines only the tilt of the lobe, not its size.

What if we want louder to go over our head and contribute to the hole in the reverberant power created by lobing?
For speaker drivers that don't have an unusually narrow beam width (i.e. horns), you will get more or less the same power response regardless of which direction the main lobe is pointing because there will still be the same number of lobes radiated into the room in all cases - i.e. even if you point a null directly at the listener.

The main lobe doesn't necessarily need to point horizontally ahead however it should point in the direction of the intended listening axis. I.e. it might be valid for the lobe to point at a slight incline if designing a speaker for stadium seating, however the measurement mic should be placed on the same incline when making measurements to design the crossover. The same applies for a speaker with a tilted baffle.

A problem arises when you take measurements in the listening axis, and design for flat response in the listening axis but the phase is not aligned. This means that you are compensating for a amplitude dip in the listening axis (due to partial destructive interference, due to phase misalignment) by raising the amplitude of the drivers. Therefore a hump appears in the power response at the crossover frequency. It will also raise your non-linear distortion slightly as the drivers each have to work harder to produce the same system output level compared to being perfectly phase aligned. As previously mentioned it is also less desirable for the phase in the listening position to be non-zero because the amplitude changes more rapidly as the listener moves away from the design axis.
 
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For speaker drivers that don't have an unusually narrow beam width (i.e. horns), you will get more or less the same power response regardless of which direction the main lobe is pointing because there will still be the same number of lobes radiated into the room in all cases - i.e. even if you point a null directly at the listener.
So, let's assume that all reflected energy contributes evenly toward the reverberant field. This makes the discussion more relevant. In a well designed speaker in my opinion, this will be close to reality in that there will be fewer early reflections and a more homogenous reverberant field.
A problem arises when you take measurements in the listening axis, and design for flat response in the listening axis but the phase is not aligned. This means that you are compensating for a amplitude dip in the listening axis (due to partial destructive interference, due to phase misalignment) by raising the amplitude of the drivers. Therefore a hump appears in the power response at the crossover frequency.
This is the point. It changes the ratio of power to listening axis response (DI). Both should be smooth. Where there is destructive interference in the wider pattern due to the physical source offset, there will be a reduction in power compared to more complete summation. By reducing the apparent response with a phase offset by an equivalent amount, power and response can be EQed together back to where they are wanted.

I have done this by measurement alone and was rewarded for it. Again, it matters that the nature of the reflections are even-handed as discussed above or there will be an unknown quantity to compensate for.
It will also raise your non-linear distortion slightly as the drivers each have to work harder to produce the same system output level compared to being perfectly phase aligned.
DI smoothness is more important to me than HD, so if that's what is required to supply the correct power into the room, so be it. The drivers will have to be up to the task.
As previously mentioned it is also less desirable for the phase in the listening position to be non-zero because the amplitude changes more rapidly as the listener moves away from the design axis.
If the (whole) speaker has been designed for directivity and wavefront summation first, it shouldn't be necessary to sit at the edge of the lobe. Besides, pointing the lobe straight ahead may increase floor interaction and reduce power even more, compounding the issue.
 
Let's talk about "sounding musical". I've been mouthing for better or worse about the "musical sounding" of lower order filter specifically 1st vs. higher order filter. Why does 1st order sound more musical? I don’t mean this posting as a proof or definition of what is musical since our hearing is just too complex for that but I just want to touch only one aspect, being humble person, but hopefully it may open a door here and there.
There is a saying “one big c leads to another”, well actually the official version of this quote is “one stands on shoulders of giants”. Before I start I want to allude to an article of a review of a Quad preamp that might shed some light to why certain type of sound is interpreted as “musical”. The reviewer touched on a subject that back then I never knew even existed in audiophile and something I didn’t really know first hand being dead poor not able to have any decent equipment, and something I didn’t fully understand until I started listening to my own 1st speakers. To make a long story short, something I wish a few people could learn a thing or two, he said that there is a “continuous of music” that only a few components could reproduce. That few certain high end equipment are capable to possess this quality. He went on and said the Quad preamp which costs only $500 at the time (more like $5000 now) was one of those component.
You may say this is kind of audiophile BS but I think most people “hear” this when they switch from a solid state amplifier to a good tube amplifier. I mean tube amplifier has the ability to sound musical although sometimes it’s hard to put our fingers on it. But if you listen carefully or at least when I listen carefully, things sound more continuous. The leading edge followed by the trailing edge and I didn’t feel like the music was skipping. There is a more complete flow more natural as most people would put it. You then want to analyze why. Naturally when the charge flows in the solid state device, there are impurity, obstacles which impede the electron movement, therefore the electrons will experience inductive and capacitive phase shift however small but it is enough for our ears to notice. And due to this phase shift, it’s like the electrons are constantly experience higher order filter however minute in these time scale maybe. On the other hand, the space charge in tubes don’t have this problem or at least not to the same magnitude since they travel in a complete vacuum.
Back to the topic of first order filter speakers, since the phase shift is a constant 90 for both woofer and tweeter, the summation is more predictable. On the other hands, higher order filters have higher rate of phase shift so the summation has more of a probability of “skipping” at least that is the layman term.
I am more than convinced ever that first order filter in its inherent nature has a more airy, more complete, more spacious, more palpable, more continuous sound because of a more predictable phase shift. Ironically, I think higher order often been given the benefit of sounding cleaner, just as solid state is more cleaner vs. tube, because of this “skipping” for lack of a better word. Kind of interesting. Something bad that turns out good.
 
I think the confusion comes about due to the fact that there is no generally agreed upon definition of time aligned. And since it’s difficult to define what is “time aligned”, the only way to prove a speaker is time aligned is that it can produce perfect step response. There is really no other way. From what I’ve heard, in order to advertise that your commercial speakers are time-aligned (and I think it’s a patented term), you have to be able to prove that your speakers can produce a perfect step response. Based on information from Stereophile magazine, there are only a handful of them that can make that claim and you can pretty count them with ten fingers. So you can see how hard it is to design time aligned speakers.
Also phase aligned is a subset of time aligned. That is if you’re time aligned, then it means you’re also phase aligned. But it you’re phase aligned, it does not necessarily mean you’re time aligned.
With a true 1st order Butterworth, assuming the drivers contribute zero acoustic roll-off and no phase shifts on their own, wouldn't the tweeter and the midrange be 90 degrees out of phase at the crossover point? If so what is the point of time alignment? (Except to offset the drivers to exactly cancel out the said 90 degree phase shift, but then it would have been phase alignment not time alignment.)
That is true, but 1st order time aligned speaker designer can delay the response of the tweeter so the tweeter phase can match that of the woofer. But it’s difficult and whoever knows it probably won’t share it with you. I guess you could place the tweeter further behind the woofer but that would only aligned at the cross over frequency but at the lower frequency the phase align might be worse. So it’s kind of a compromise you have to make. The DSP folks claim that DSP can align anything and can perform a perfect step response. But personally I think DSP introduces another set of issue of phase shift of its own so it’s just another compromise that you have to consider.
(Except to offset the drivers to exactly cancel out the said 90 degree phase shift, but then it would have been phase alignment not time alignment.)
The easy way is to invert the polarity of the tweeter to get it phase aligned but it’s no longer time aligned. So in this case you’re phase aligned but not time aligned.

I have always thought that, conceptually, only even-order (2nd, 4th) crossovers (total electrical+acoustic) can be time-aligned. Correct me if my concept is wrong.
The 4th order may phase aligned without having to invert the polarity, but the phase shift could be 360 degree so it’s not time aligned. It’s the equivalent of inverting the polarity of the driver but in this case you do it electrically.

So the only way to get time-aligned is at minimum you have to have 1st order to get a constant phase shift of both the tweeter and woofer. But in most cases you have a 180 at xover frequency. So the trick here is how to align the tweeter phase without having to invert the tweeter polarity. Well if I knew the answer then I probably wouldn’t be here.
 
FTR, I have heard both Vandersteens and Thiels and ... meh. I really didn't like the Thiel's bright/harsh top end, and Vandersteens, though exceptionally well engineered haver never seduced me.

So, while I'd like to be fascinated by the perfect step response of these speakers, they just don't do it for me. As Bill Waslo often points out, they're only perfect at 1 point in space. Move your head and you have other issues.

In general, if I was going to get serious about this idea, I'd probably go with something more like a woofer-assisted-wideband. At least above the crossover frequency, you have perfect phase and time alignment, plus no crossover in the mid/treble ranges.
 
A widebander should be considered as a midrange in a 3 way system.
[ 3 wayyy ? ]
No problems in crossing with 1st order a wideband driver ( I see in other threads the request of some thin inductors to add Re...that might be useful for a midrange as it would "substitute" for a resistor often found in midrange path)
Is the Satori tweeter with ferrofluid ? Again, no problems in crossing it with a cap ( resistor required here, too ).
Then there's the woofer, so BIG problem with all the problems associated with height, positioning, rear wave attenuation etc.
 
In general, if I was going to get serious about this idea, I'd probably go with something more like a woofer-assisted-wideband. At least above the crossover frequency, you have perfect phase and time alignment, plus no crossover in the mid/treble ranges.

Wide band drivers don't have the sound quality. It compromises sound quality for wide band. Another reason I do 1st order because it's challenging. I mean I can whip up a 24db or even 12db like in my sleep. For example I designed the xover for the SBA poly using a quasi - 12db roll off and got it right the first time without even having to fine tune while the 1st order took me weeks.
 
So what wideband driver who you consider up to the task erik.......?

C.M

I don't really know. I have seen a few DIY designs, plus at least one commercial offering that takes this approach. I haven't thought about it that far. I was just thinking about the idea of getting a perfect impulse or step response.

If I was willing to let go of "perfect" in the lower octaves, then this seems like a reasonable compromise.
 
Let's talk about "sounding musical". I've been mouthing for better or worse about the "musical sounding" of lower order filter specifically 1st vs. higher order filter. Why does 1st order sound more musical? I don’t mean this posting as a proof or definition of what is musical since our hearing is just too complex for that but I just want to touch only one aspect, being humble person, but hopefully it may open a door here and there.
There is a saying “one big c leads to another”, well actually the official version of this quote is “one stands on shoulders of giants”. Before I start I want to allude to an article of a review of a Quad preamp that might shed some light to why certain type of sound is interpreted as “musical”. The reviewer touched on a subject that back then I never knew even existed in audiophile and something I didn’t really know first hand being dead poor not able to have any decent equipment, and something I didn’t fully understand until I started listening to my own 1st speakers. To make a long story short, something I wish a few people could learn a thing or two, he said that there is a “continuous of music” that only a few components could reproduce. That few certain high end equipment are capable to possess this quality. He went on and said the Quad preamp which costs only $500 at the time (more like $5000 now) was one of those component.
You may say this is kind of audiophile BS but I think most people “hear” this when they switch from a solid state amplifier to a good tube amplifier. I mean tube amplifier has the ability to sound musical although sometimes it’s hard to put our fingers on it. But if you listen carefully or at least when I listen carefully, things sound more continuous. The leading edge followed by the trailing edge and I didn’t feel like the music was skipping. There is a more complete flow more natural as most people would put it. You then want to analyze why. Naturally when the charge flows in the solid state device, there are impurity, obstacles which impede the electron movement, therefore the electrons will experience inductive and capacitive phase shift however small but it is enough for our ears to notice. And due to this phase shift, it’s like the electrons are constantly experience higher order filter however minute in these time scale maybe. On the other hand, the space charge in tubes don’t have this problem or at least not to the same magnitude since they travel in a complete vacuum.
Back to the topic of first order filter speakers, since the phase shift is a constant 90 for both woofer and tweeter, the summation is more predictable. On the other hands, higher order filters have higher rate of phase shift so the summation has more of a probability of “skipping” at least that is the layman term.
I am more than convinced ever that first order filter in its inherent nature has a more airy, more complete, more spacious, more palpable, more continuous sound because of a more predictable phase shift. Ironically, I think higher order often been given the benefit of sounding cleaner, just as solid state is more cleaner vs. tube, because of this “skipping” for lack of a better word. Kind of interesting. Something bad that turns out good.

So I left my previous post touching on the phenomenal called "skipping" which is responsible for making higher order filter although sounding "clear" but somewhat dry and sterile. What is this "skipping"? Is it another
of My BS? Well I don't work for the marketing department so I better at least have some explanation for it.
Right or wrong at least I tried.

Let's start at a high level.
Let's say when a signal in a time domain makes a sudden (relatively) jump or dip, it creates extra high frequency components that are not there in the first place or you could say the high frequency contents are not part of
the original signal. But why would "skipping" makes higher order filter sounding "clear"? Well usually when you tune your speakers to have a lift in the treble region or a lift in the high frequency, the sound does have a perceived clearer sound but whether accurate or not well that's another matter but I thing we all can agree that bright sounding speakers for better or worse do have a "clearer" sound compared to darker or more euphoric sounding speakers.
OK, but why do we percieve "skipping" or more accurately the extra high frequency contents are "skipping"? That is why does the sound that has more extra high frequency contents appeared to be "skipping"? I think it has to do with how our hearing evolved. And it has to do with the dopler affect. As things coming straight at you, the sound has higher pitch and when things going away from you the sound has lower pitch or the frequency is lower.
So thousands of years ago when we were hunters and gatherers, our hearing has to be pretty accute to guard for danger. Higher pitch sounds mean something coming at you while lower pictch means something going away from you. I am sure our hearing evolves all the way back to leopards and tigers and who knows and those animals have to use their hearing to
protect themselves. So when we hear music with these extra high frequency contents, we can't help it due to our evolution that our hearing has to divert our attention to these higher frequency contents which are being interjected
into the musical stream. So our hearing has to switch back and forther hence the percieved "skipping".
OK, so I explained how these periodic high freq. contents appeared as "skipping". But you ask what does it have to do with 6db vs. 12db vs. 24db. roll off? So here is why I think higher order filter create more "skipping"
vs. lower filter. Before explaining, let's look at an analogy.
Let's say you drive at 50mhp on the highway. Now the highway has bumps and dips. So you notice these bumps and dips which makes your ride somewhat uncomfortable. Now you decides to speed up to 80mph. Since you go faster, the bumps and dips come at you a lot faster so you feel a lot more bumpier. You see it's the same car, the same road but the speed causes more bumpiness.
Now back to your speakers, your left and right woofers are not going to move at exactly the same time, just as your tweeter and woofer are not going to move at the exact theoretical moment as you want. They going to have some minor delta. Now if you have a 6db slope, your phase shift is more gradual so there will be less skipping just like when you go at 50mph. But as you going faster at 80 mph for example at 24db slope, the minor variation from your tweeter and woofer, get exaggerated. When the minor variations added up, they will have sudden jump in time domain which introduces unwanted higher frequency contents which results in "skipping" which I said eariler. What I said above implies that first order filter also has this "skipping" but it is just less than higher order filter everything else being equal. What I said also implies that even with 24db, you can reduce "skipping" by having really good components with good tolerance (like making the road less bumpy). But if you have Toyota drivers, well good luck.

Anyway, that's what I think.
 
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