well, that diffraction behaves the way you suggest Dr Geddes i can't agree with entirely.
i've heard diffraction effects from horns that do not follow the increase with volume you suggest (linear relationship) and some that are only audible when the spl is decreased (unmasked)
their perception is indeed often confused with non linear distortion.
but i still view non linear distortion as a by product that stems from a linear system being "not so linear".
i've heard diffraction effects from horns that do not follow the increase with volume you suggest (linear relationship) and some that are only audible when the spl is decreased (unmasked)
their perception is indeed often confused with non linear distortion.
but i still view non linear distortion as a by product that stems from a linear system being "not so linear".
No disagreement about the importance of understanding linear systems, and also discrete-time systems nowadays.
It's just that there have been too many times I have heard people say time delays or timing jitter corresponding to a frequency greater than 20kHz cannot possibly in any way have an audible effect because humans can't hear anything above 20kHz. Or, anybody who does not have at least a normal audiogram from an audiologist couldn't possibly hear distortion less than .01% because their hearing isn't even up to normal. Some people say these things with supreme confidence, and I am including some engineers who understand linear systems very well.
It's just that there have been too many times I have heard people say time delays or timing jitter corresponding to a frequency greater than 20kHz cannot possibly in any way have an audible effect because humans can't hear anything above 20kHz. Or, anybody who does not have at least a normal audiogram from an audiologist couldn't possibly hear distortion less than .01% because their hearing isn't even up to normal. Some people say these things with supreme confidence, and I am including some engineers who understand linear systems very well.
The fact that hearing is not linear surely has no bearing on the requirement for a reproduction system to be linear?
What about if you say humans can only hear frequencies and are deaf to phase, so will ignore phase issues in the design? Or that humans can't hear less than .5% or .1% THD and so we won't worry if any THD at all is above that? Some engineers have said things like that, including in this very forum.
So sure, if you require a reproduction system to be linear, great. But if you can find one that really is, I hope you can afford it. Of course most people don't listen all that carefully or care if a their system is highly linear. People who do care a lot are people like mastering engineers who (1) are highly skilled listeners, and (2) are using their system as instrumentation that they want to be as accurate at possible.
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I was thinking more from the engineers point of view when it came to system design, which is what this thread seems to be about. I listen to the music and if it sounds good to me I don't care so much about the rest
A great point ... and one that seems to be a source of endless confusion. Human hearing may very well have a multitude of non-linear mechanisms ... but that in no way argues against the need for linearity in our electro-mechanical reproduction systems.
Certainly, economics must play some role in our audio reproduction systems, which means that we are motivated to understand LIMITS of human hearing ... bandwidth, distortion, magnitude vs phase sensitivity, etc ... but none of this argues against the fact that we strive to make our reproduction systems quite linear, and regularly use linear system theory to explore and understand them. Analyzing one of those systems, is indeed what this thread has been about 🙂
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Thanks 😉, the maths is well over my head and when 4th dimensions and gravity waves were mentioned it started getting a bit twilight zone for me 😱🙂
There is only scant evidence that phase is a significant factor, but overwhelming evidence that frequency response is. It's a matter of degree, it's not black and white.
As far as the audibility of THD we did a test once with THD as high as 20% and the test results said that this was not significant in the perception of that device. Basically THD is a meaningless metric to use for sound quality. It doesn't correlate with perception. .1% can be audible and terrible and 20% can be insignificant - how can one use a metric like that.
That's a typical, but simplistic, point of view since it doesn't help a designer to improve his designs in any way. To do that one needs to understand how the masses perceive things, not how one individual does. And what engineering specifications correlate to what they perceive - it is far from an easy task that can simply be brushed away with a phrase like "Wellll - it sounds good to me!"
Is a designer then forced to go down the one-size-fits-all route and aim for highly directional speakers?
I am understanding SOME of your work. It has been my understanding that a line array (in room) that is at least nearly floor to ceiling, will not have first order reflections on those surfaces, but rather the floor and ceiling extend the line array.
This is why I built mine in this fashion and subjectively, it seems to fit.
Does what you are saying support this or have I fooled myself? 🙂
A line array that extends from a (reflective) floor to a (reflective) ceiling WILL have first order reflections from the floor and ceiling ... but those reflections are EXACTLY what would be produced from an extended array. By USING reflections, we are EXTENDING the array.
Imagine holding a long pole, and pointing it at a mirror. Push that pole right up against a mirror. See how the reflection makes the pole "look" twice as long? We used a REFLECTION to EXTEND the length of the pole 🙂
Now imagine a pole placed, length-wise, between TWO mirrors ... so that the small ends of the pole are right up against the mirrors. The pole is suspended, length-wise, between the mirrors (if you will). If you can stick your head between those mirrors, how long does the pole look now? Did we somehow "avoid" reflections ... or "use" them to our advantage? 😉
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That makes sense. Thanks for explaining it to me. There must be less time difference on those reflections so they reinforce the sound rather than compete with a detectable, competing reflection.
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We are always taught that reflections are "bad". We are always taught that everything goes south, when sounds of the same frequency radiate from more than one "point". But these rules are often too simple.
A reflective surface can be analyzed by eliminating it altogether, and replacing it with an "image", or "virtual source" that resides behind the reflective surface. This holds for ANY source, of ANY orientation. Often, this second source is indeed bad 🙁 But in the case of line arrays ... positioned right up against the surface ... that image is nothing more than an EXTENSION of the array. The reflective surface is GONE ... in ALL ways ... and the line array is simply EXTENDED. This simple analysis HOLDS for all frequencies, all time delays, all signals, etc etc. The reflective surface is gone ... it's been replaced by an "image" source. In the case of line arrays, that "image" serves a very useful purpose: it EXTENDS the length of the array ... nothing more, nothing less 🙂
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perhaps some more clarification ...
Let's compare an infinite line source, to a finite line extended fully between two perfectly reflecting surfaces.
Those reflecting surfaces are causing all kinds of bounces, reflections, and reflections of reflections ... all conspiring somehow with different delays, different amplitudes ... maddening !!! How can we possibly analyze that complexity? That must be nothing but pure BAD!!
What if i were to tell you a super-simple way to analyze ALL of it? What if i were to tell you that the two cases ... an infinite line, and a finite line between 2 reflective surfaces ... were absolutely, in ALL measurable ways for ALL measurable signals for ALL points ANYWHERE between the planes ... EXACTLY IDENTICAL?
Well that's exactly the case 🙂 Replace the reflecting surfaces with virtual images or sources, and you've comprehended ALL signals for ALL points in space. That's not an approximation, only good for a millisecond or two ... that's not an approximation, that only works if you're kinda close or kinda far ... it's exact, for all points, all times, all frequencies.
(of course, there are no "perfectly" reflecting surfaces ... but we can get reasonably close, over a satisfying range of frequencies)
Let's compare an infinite line source, to a finite line extended fully between two perfectly reflecting surfaces.
Those reflecting surfaces are causing all kinds of bounces, reflections, and reflections of reflections ... all conspiring somehow with different delays, different amplitudes ... maddening !!! How can we possibly analyze that complexity? That must be nothing but pure BAD!!
What if i were to tell you a super-simple way to analyze ALL of it? What if i were to tell you that the two cases ... an infinite line, and a finite line between 2 reflective surfaces ... were absolutely, in ALL measurable ways for ALL measurable signals for ALL points ANYWHERE between the planes ... EXACTLY IDENTICAL?
Well that's exactly the case 🙂 Replace the reflecting surfaces with virtual images or sources, and you've comprehended ALL signals for ALL points in space. That's not an approximation, only good for a millisecond or two ... that's not an approximation, that only works if you're kinda close or kinda far ... it's exact, for all points, all times, all frequencies.
(of course, there are no "perfectly" reflecting surfaces ... but we can get reasonably close, over a satisfying range of frequencies)
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Earl,
What would be a good measure of (perceptible) distortion? Given that lower harmonics are less offensive and higher ones are more, wouldn't some sort of weighing scheme work to correlate strongly with distortion perception. What do you think?
Thanks
Thank you for putting it in simple terms. 🙂 I completely agree, partly due to my own experience with my first home line array build. Compared to the average person I could be called an audiophile, but compared to most enthusiasts I'm likely a tin ear. However, when I roughed in crossover points/slopes etc. and powered up the arrays for the first time it was startling what I was hearing.
What you describe (far better than I) is many things but my minds eye made two things stand out. My room is very live but at least my rig is on a very long wall. Gone were the distracting reflections from the ceiling and floor. Instead, the floor and ceiling are now an asset. Okay, I know that's really one thing but it makes a negative turn into a welcome positive.
I always recommend to folks building a short array for their home to consider a full length array. In many ways it's simpler to design, and brings additional rewards. Unfortunately at this point, I'm not sure I'd ever be able to depart from a full array for my main system. Maybe that's a good thing! 😉
What you describe (far better than I) is many things but my minds eye made two things stand out. My room is very live but at least my rig is on a very long wall. Gone were the distracting reflections from the ceiling and floor. Instead, the floor and ceiling are now an asset. Okay, I know that's really one thing but it makes a negative turn into a welcome positive.
I always recommend to folks building a short array for their home to consider a full length array. In many ways it's simpler to design, and brings additional rewards. Unfortunately at this point, I'm not sure I'd ever be able to depart from a full array for my main system. Maybe that's a good thing! 😉
This is precisely what Lidia and I did in our papers back in the late 90's (available on my website.) We showed that IMD had almost no correlation to perception - about .2, THD had a slightly larger correlation at -.3 - yea, negative, meaning that people liked some THD. The metric that we developed we called the GedLee metric which had a correlation of > .9, which is pretty good. But this metric is much harder to calculate than THD or IMD and so nobody bothered. Seems people prefer easy to meaningful.
Earl, I looked though some of the papers on your website, but it's not quite clear to me how you are calculating the GedLee Metric. It looks like some equations show it as a function of f and x, or only of x, but in the latter case partial derivatives are being taken of T(x), so the presence of f may be implied. Also, what you are representing with the variable x could be more explicitly stated. It looks like it might be instantaneous normalized amplitude?