The main benefit of FF over APS-C isn't image quality, it's lenses

If there is no IQ benefit, then there's no reason for anyone to move from crop to FF.
Mostly true, but then there is the viewfinder. ;)
As an EVF user, I keep getting shocked at how uselessly bad the viewfinders are whenever I pick up an entry-level dSLR. I pick up full frame dSLRs much more often than D3300-class cameras, and I always forget about this until I try shooting with one...
 
The FF will also deliver better resolution, unless the APS-C lens is 150% as good resolution wise in linear terms.
This is observably false. From Imaging Resource:

Sony A7 Measured Resolution (no aliasing):
2,900 lph horizontal
2,850 lph vertical

Sony A7 Measured Resolution (extinction):
3,600 lph both

Sony A6000 Measured Resolution (no aliasing):
2,900 lph horizontal
2,800 lph vertical

Sony A6000 Measured Resolution (extinction):
3,500 lph both (the article actually says 3,500 - 3,600 lph)

There will be a small difference in sharpness. This is due to the fact that for a given FoV the details are being projected unto a smaller imaging circle, and lens sharpness is correlated with the size of the projected detail. At ISOs where noise is a non-issue, this difference is easily eliminated in post processing.

In theory there should also be a difference in extinction resolution that is larger than what we see above (<3%). But neither sensor is any where near the pixel density for that to be a factor.
 
"Good enough" meaning about 2/3 as good as an APS-C lens or half as good as a MFT lens, in linear resolution terms, for equal performance.
This is observably false. See my reply "Resolution is pretty much the same" up above.

I've heard people say this before, but it is a myth and it is not grounded in the science of optics or imaging at all.
Resolution is in lines or line pairs per mm, and the smaller the format, the less mm you have to work with - which means you'll need sharper lenses on smaller formats.
Smaller format digital sensors have higher pixel densities. Even lenses that are just OK can comfortably out resolve the pixel densities we're dealing with today on crop and m43.

You can still see the difference between an OK lens and a great lens because while they are related, resolution and sharpness are two different things. And a good lens will have greater contrast at a given lpmm test resolution. This was visible even in the early days of DSLRs with 3 MP and 6 MP sensors.

But even with today's 20 MP m43, 24 MP APS-C, and 50 MP FF sensors we are not actually out resolving the lenses themselves in the center. (On some lenses we do at the edges and corners when shot wide open. Or for a poor lens even when stopped down.)
 
Thoughts? Is there really any benefit from a FF base kit over a crop base kit? I'm thinking not in any meaningful way IQ wise.
Yes.

Given, at base ISO, tripod shot, 16X20 prints, maybe not so much difference IQ wise.

Once you save up the cash, you can add a 35, 50 or 85 f1.4 prime to a 42 meg pixel FF camera base kit and shoot under almost any lighting condition and have pixel peeping sharpness even at ISO 6000.

I am coming to the conclusion that FF with an f1.4 or f2.0 prime is the sweet spot for shooting under almost any lighting condition with good IQ.
 
Thoughts? Is there really any benefit from a FF base kit over a crop base kit? I'm thinking not in any meaningful way IQ wise.
Yes.

Given, at base ISO, tripod shot, 16X20 prints, maybe not so much difference IQ wise.
That's a situation where you have more than enough time to gather sufficient light. A cell phone camera (with sufficient resolution and DR) would suffice.
Once you save up the cash, you can add a 35, 50 or 85 f1.4 prime to a 42 meg pixel FF camera base kit and shoot under almost any lighting condition and have pixel peeping sharpness even at ISO 6000.
I added a 50/1.4 to my crop camera for low light shots. It helped, but moving to FF helped even more. I then got a 24/2, 35/1.4, and 85/1.4 and now I can handle just about any of the dark environs I encounter. I also added a old 58/1.2 :)
I am coming to the conclusion that FF with an f1.4 or f2.0 prime is the sweet spot for shooting under almost any lighting condition with good IQ.
For me it is!
 
Excellent post and great photos from all formats used! Vision trumps gear - unless the gear is one of those old cardboard film cameras you used to get outside tourist spots (anyone remember those....?)

In your earlier post a few pages back where you had a flikr link to both your APC-S shots and FF shots, I personally thought / felt (and I hope you don't mind me saying so) your NEX 7 shots were much, much better and also more inspired than your FF shots.

Kind of proves the point.
 
That's a technical description. I was more hoping to understand what inspired that photo, or how you thought of the composition. (Or if it was luck, but I suspect not)

I'm perfectly capable of recreating that photo. I'd have a very hard time coming up with it.

It's very pretty.
Well you did ask for a little bit more of the process which went into taking that photo. And my description was the physical process. :)

As for the thought process....well I just saw there was an image there somewhere. In that parking lot walking around I saw the puddle with some fall leaves in the water. It was bright so the reflections were prominent. I just got that feeling that I am sure a lot of photographers get when you can sense there is something lining up. I tried some shots from a few different angles, from different sides. But when I put the camera down low, facing into the sun, and the added the leaf...well that was it. I had to shoot this several times for the composition to come out right.

But I guess it was just that feeling. I think subconsciously you eventually see things in a way where its sorta like a spider sense tingling. You mind is processing things that you conscious mind hasn't quite put together yet. This happens to me a lot. Not all the time, but fairly frequently. Its most noticeable when I see a prominent play of light. Like when interesting shadows are made or when something like a leaf is back lit and translucent. But it can be any number of things. I will see something and it just feels like a photo is in there, then I go find it.

This is actually a pretty good description of most of my photography.
 
Excellent post and great photos from all formats used! Vision trumps gear - unless the gear is one of those old cardboard film cameras you used to get outside tourist spots (anyone remember those....?)

In your earlier post a few pages back where you had a flikr link to both your APC-S shots and FF shots, I personally thought / felt (and I hope you don't mind me saying so) your NEX 7 shots were much, much better and also more inspired than your FF shots.

Kind of proves the point.
Thanks Easy. And its entirely believable you like one over the other. Art and imagery are intensely personal things. I was at a different time in my life when most of the APSC shots were taken and I am sure my style was not quite the same as it is now. I also processed differently back then. So there could be any number of reasons you prefer one group over the other.
 
So show some basic analysis of what vertical vibrations are traversed to the floor for a horizontally oscillating speaker
Why would the speaker be horizontally vibrating? Only the drivers are. The whole box resonates. Actually, the box is more or less the whole point. The sides vibrate in directions perpendicularly to them. The bottom vibrates up and down, and so does the top. Just place a light object on the top of a speaker with strong bass and watch it.
The horizontally oscillating speaker is obviously the driver. If you think the box itself is resonating significantly then again show the analysis. That's what we do in science.
Very simple. When I wonder if my subwoofer is still alive (it died a few years ago and I had to order some part), I place my hand on the top of the box. If I feel vibrations, the speaker is still alive. I do the same experiment with my central speaker, which has a subwoofer in it. Very scientific, I must assure you.
or why you would want hard contact with the floor as opposed to sitting on a carpet.
You may or you may not. The point here was that there is a difference.
I asked why or why not. If you have a reason in mind then please state it.
I might like one over the other. Remember, audiophiles do not care about the reason. As long as differences exist, they want to exploit them for full satisfaction.
Or how a box will resonate differently. Without any analysis at all this is all in the realm of myth.
Fortunately, resonance effects are well studied but not completely understood. I have quite a few publications on the topic and there is still a lot left to do.
Please link those which have any relevance to loudspeakers.
The beauty of the analysis I am doing is that it applies to a large variety of phenomena: from sound in speakers to quantum mechanics.
Furthermore, the absence of ridiculous couplings (look, I stopped the floorboards from buzzing!) is not what the audiophile community is claiming for the benefits.
It could be one of them. But the contact affects the floor and the vibrating system itself.
So show the analysis, even in back-of-the-envelope form.
It is in any book on differential equations. The simplest case is a spring mass system (google it). It is a very simple case. The analysis of more complex systems is based on PDEs instead of ODEs and is much more delicate.
Because the differences may be due to different placements.
A truly rigorous double-blind test would move the speakers immediately. This has been done by the way.
I am all ears. Move to how many positions? I have experimented with quite a few. And then - turned to face the listener or parallel to each other? I am sure thy did all that and gave the listeners weeks in each position.
The first step is obviously to substitute the speakers in the same position. If differences are noticed over a short period of time then it doesn't seem necessary to continue the experiment over weeks.
Wrong, a short period of time is very misleading. Unless you are musically deaf, the differences would be "in your face" (unless you use a second pair of the same brand but them some manufacturers match the speakers in the pair). The point is if the second pair could be improved with a different placement, and you need time for that.
It doesn't matter how one "creates" the analog signal? Shannon-Nyquist guarantees perfect band limited reconstruction. If there are differences between reconstructions then at least one of the methods does not live up to that standard.
None does. You cannot do perfect SN interpolation with audio even theoretically (casualty); not to mention in practice - to create repeating wave fronts with that shape. Oversampling would help a lot but unfortunately, we are stuck with the "redbook" CDs.
So show, even in rudimentary form, what you think is the difference between ideal reconstruction and the various methods that you think are different.
Same as in imaging. The ideal reconstruction involves the sinc functions. They live forever and your tune is never band-limited (unless it never ends and it started before the Bing Band). Instead, one could use some kind of interpolation.
It should be if it were linear and time invariant (convolution) but it is not.
But it is largely so for DACs and amplifiers.
For amps - no. Too much power there.
If we are running into the DR limits then we are talking about clipping.
Or compression before clipping.
Numbers.
Nonlinear response is usually supposed to be quite low, except in the clipping case.
"Supposed"? By whom?
By people who design amplifiers to be linear.
You have natural constraints.
frequency dependent phase shifts,
Part of spectral response.
Not really, it could be a linear transformation but not a convolution anymore. "Spectral response" does not describe it then.
Linear, frequency dependent phase shift has a well defined Fourier transform corresponding to a convolution and spectral response and all that.
I read this sentence three times and I noticed a few inconsistencies. Phase shifts, etc., is a transform (an operator). It does not have a FT per se (unless you take the kernel). It can very well be a non-convolution.
And? How does this answer the question in boldface above?
The sound field would be different, so now you have a direction to explore why the speakers sound different at a particular listening location.
There is no problem to measure that they would sound different. The question is - which of those differences matter? They are too many, how to choose a few metrics which would tell is if a speaker A is better than a speaker B? IMO, there is no such thing. Last time I was shopping for speakers, the usual suspects did not sound good to me. What I really liked was a pair of McIntosh speakers - not cheap at all but that brand is better known for their tube amps, preamps, etc. I am pretty sure that they would show a higher degree of harmonic distortions that the usual ones.
 
I challenge you to propose any physical mechanism whatsoever that explains how any of those factors could produce an audible result.
They're not unmeasurable, they're just unmeasured. It's pretty insensitive to linear effects. Amplitude and phase matter only a little bit. Acoustics of a room, or simply taking a step over a few inches, can really change frequency response and we don't notice. On the other hand, the ear is a frequency-domain device with an extreme dynamic range -- over 100dB. What's that mean? Intermodulation distortion is a Really Big Deal. On the other hand, do you ever see that in an audio data sheet? No. It's frequency response and occasionally harmonic distortion.

Where do effects come from?

Jitter is, and continues to be, a big deal. Audio systems are misengineered, and the clock comes from the audio source. You phase lock to it. Do the math, and you'll see little bits of jitter add audible error.

Components like capacitors are sufficiently nonlinear to give audible distortion in the signal path. Of course, most audio equipment is badly enough misengineered that insufficient feedback and nonlinear gain also give errors. That's easy enough to fix. None of this is rocket science.

Things like power rails couple in. As you go pro, you put more and more capacitance there. However, in many real (expensive) amplifier, audio engineers are not quite clever enough to regulate the rails.

The speaker wire acts like an antenna. And a capacitor. And an inductor. It's easy to make a good for five bucks one, but a bad one will actually introduce badness.

And a million other places.

Could they all be solved with 2016 technology, or at least brought down an order of magnitude? Indubitably. Do people do it? As far as I can tell, no. A little bit on the real amateur stuff. The audiophile-grade stuff?
 
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I challenge you to propose any physical mechanism whatsoever that explains how any of those factors could produce an audible result.
They're not unmeasurable, they're just unmeasured. It's pretty insensitive to linear effects. Amplitude and phase matter only a little bit. Acoustics of a room, or simply taking a step over a few inches, can really change frequency response and we don't notice. On the other hand, the ear is a frequency-domain device with an extreme dynamic range -- over 100dB. What's that mean? Intermodulation distortion is a Really Big Deal. On the other hand, do you ever see that in an audio data sheet? No. It's frequency response and occasionally harmonic distortion.

Where do effects come from?

Jitter is, and continues to be, a big deal. Audio systems are misengineered, and the clock comes from the audio source. You phase lock to it. Do the math, and you'll see little bits of jitter add audible error.

Components like capacitors are sufficiently nonlinear to give audible distortion in the signal path. Of course, most audio equipment is badly enough misengineered that insufficient feedback and nonlinear gain also give errors. That's easy enough to fix. None of this is rocket science.

Things like power rails couple in. As you go pro, you put more and more capacitance there. However, in many real (expensive) amplifier, audio engineers are not quite clever enough to regulate the rails.
This reminds me of the importance of the power block (transformer and such).
The speaker wire acts like an antenna. And a capacitor. And an inductor. It's easy to make a good for five bucks one, but a bad one will actually introduce badness.

And a million other places.

Could they all be solved with 2016 technology, or at least brought down an order of magnitude? Indubitably. Do people do it? As far as I can tell, no. A little bit on the real amateur stuff. The audiophile-grade stuff?
 
So show some basic analysis of what vertical vibrations are traversed to the floor for a horizontally oscillating speaker
Why would the speaker be horizontally vibrating? Only the drivers are. The whole box resonates. Actually, the box is more or less the whole point. The sides vibrate in directions perpendicularly to them. The bottom vibrates up and down, and so does the top. Just place a light object on the top of a speaker with strong bass and watch it.
The horizontally oscillating speaker is obviously the driver. If you think the box itself is resonating significantly then again show the analysis. That's what we do in science.
Very simple. When I wonder if my subwoofer is still alive (it died a few years ago and I had to order some part), I place my hand on the top of the box. If I feel vibrations, the speaker is still alive. I do the same experiment with my central speaker, which has a subwoofer in it. Very scientific, I must assure you.
The question was whether devices such as spikes or cone-shaped feet can produce an audible difference and if so, why. There was never any question of whether the box sides could be felt to be vibrating, although, if you think about, it's kind of humorous that you had to check for the sub's operation by touching its side instead of just listening.
or why you would want hard contact with the floor as opposed to sitting on a carpet.
You may or you may not. The point here was that there is a difference.
I asked why or why not. If you have a reason in mind then please state it.
I might like one over the other. Remember, audiophiles do not care about the reason. As long as differences exist, they want to exploit them for full satisfaction.
You continue to define audiophiles as people who don't care about reasons. No true Scotsmen fallacy aside, it does kind of put a damper on reasoned discussion.

It would be no less false to claim that serious photographers don't care about the reasons why certain equipment or techniques seem to produce different-looking images.
Fortunately, resonance effects are well studied but not completely understood. I have quite a few publications on the topic and there is still a lot left to do.
Please link those which have any relevance to loudspeakers.
The beauty of the analysis I am doing is that it applies to a large variety of phenomena: from sound in speakers to quantum mechanics.
I'll take your word for it.
The first step is obviously to substitute the speakers in the same position. If differences are noticed over a short period of time then it doesn't seem necessary to continue the experiment over weeks.
Wrong, a short period of time is very misleading. Unless you are musically deaf, the differences would be "in your face" (unless you use a second pair of the same brand but them some manufacturers match the speakers in the pair). The point is if the second pair could be improved with a different placement, and you need time for that.
If you have already determined that there is a difference between two speakers, then the null hypothesis that two speakers are not distinguishable to the listener has been disproved. It follows that this particular experiment can end.
It doesn't matter how one "creates" the analog signal? Shannon-Nyquist guarantees perfect band limited reconstruction. If there are differences between reconstructions then at least one of the methods does not live up to that standard.
None does. You cannot do perfect SN interpolation with audio even theoretically (casualty); not to mention in practice - to create repeating wave fronts with that shape. Oversampling would help a lot but unfortunately, we are stuck with the "redbook" CDs.
Repeating wave fronts with what shape?
So show, even in rudimentary form, what you think is the difference between ideal reconstruction and the various methods that you think are different.
Same as in imaging. The ideal reconstruction involves the sinc functions. They live forever and your tune is never band-limited (unless it never ends and it started before the Bing Band). Instead, one could use some kind of interpolation.
We don't need a signal that started before the Big Bang to make an audibly perfect reconstruction. The question is again how long of a signal is needed to be perfect by an audible (or any other) standard.
It should be if it were linear and time invariant (convolution) but it is not.
But it is largely so for DACs and amplifiers.
For amps - no. Too much power there.
As you surely know, decently-performing amplifiers are very close to linear over a huge range of output power, certainly covering the dynamic range of CD audio.
frequency dependent phase shifts,
Part of spectral response.
Not really, it could be a linear transformation but not a convolution anymore. "Spectral response" does not describe it then.
Linear, frequency dependent phase shift has a well defined Fourier transform corresponding to a convolution and spectral response and all that.
I read this sentence three times and I noticed a few inconsistencies. Phase shifts, etc., is a transform (an operator). It does not have a FT per se (unless you take the kernel). It can very well be a non-convolution.
"Frequency dependent phase shifts," which I take to mean a phase shift operator which can be expressed as function of frequency, e.g., tau(f), associated with multiplication in the frequency domain by exp(i tau(f)), which is a Fourier transform of a particular kernel. I think you knew all this.
The sound field would be different, so now you have a direction to explore why the speakers sound different at a particular listening location.
There is no problem to measure that they would sound different. The question is - which of those differences matter?
Well, at least we are able to reach an agreement that the audible differences are measurable in some way.
They are too many, how to choose a few metrics which would tell is if a speaker A is better than a speaker B?
The first step is demonstrating via double blind test that audible differences even exist. The second is relating those audible differences to measurable quantities. Subjective judgments of "better" are way beyond the scope of anything I've said.
 
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Things like power rails couple in. As you go pro, you put more and more capacitance there. However, in many real (expensive) amplifier, audio engineers are not quite clever enough to regulate the rails.
This reminds me of the importance of the power block (transformer and such).
Which is just dumb, in 2016. In 1970, you build a power block by getting a giant transformer, and then you needed big capacitors which could source 100W for 1/120 second without dropping too much. Circa 1985, you could put in a switching power supply, but which introduced a lot of switching noise which was a little hard to manage. In 2016, a modern digital switching power supply works brilliantly. It's cheap, and it outputs smooth, clean, beautiful power.

But the audio industry buys giant transformers and capacitors, because they look fancy. And goodness knows, they sure were important a half-century ago. Plus, they're easy to engineer with. A freshman can build a simply linear power supply.
 
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I challenge you to propose any physical mechanism whatsoever that explains how any of those factors could produce an audible result.
They're not unmeasurable, they're just unmeasured. It's pretty insensitive to linear effects.
Please clarify what you mean.
Amplitude and phase matter only a little bit.
Not sure what you mean here, either. Amplitude is kind of the overwhelming thing that we perceive as listeners.
Acoustics of a room, or simply taking a step over a few inches, can really change frequency response and we don't notice.
Maybe some people don't notice. Others seem to. Certainly the response in the room is measurable (and tends to be pretty huge).
On the other hand, the ear is a frequency-domain device with an extreme dynamic range -- over 100dB. What's that mean? Intermodulation distortion is a Really Big Deal.
Intermodulation distortion in the speakers, in the amp, or in your ear/head (and here I don't mean imaginary stuff, I mean real processing in your ear/head).
On the other hand, do you ever see that in an audio data sheet? No. It's frequency response and occasionally harmonic distortion.

Where do effects come from?

Jitter is, and continues to be, a big deal. Audio systems are misengineered, and the clock comes from the audio source. You phase lock to it. Do the math, and you'll see little bits of jitter add audible error.
Math isn't sufficient to show us what is audible. The combination of some perceptual acoustics knowledge and the math might suggest, however, when the jitter might become audible.
Components like capacitors are sufficiently nonlinear to give audible distortion in the signal path. Of course, most audio equipment is badly enough misengineered that insufficient feedback and nonlinear gain also give errors. That's easy enough to fix. None of this is rocket science.
But it is electrical engineering, so we can examine this systematically. We can also do tests to determine, at the end of the day, whether any of it is actually audible.
Things like power rails couple in. As you go pro, you put more and more capacitance there. However, in many real (expensive) amplifier, audio engineers are not quite clever enough to regulate the rails.
Let's skip, for the moment, what bad audiophile designs do and focus on competent examples.
The speaker wire acts like an antenna. And a capacitor. And an inductor. It's easy to make a good for five bucks one, but a bad one will actually introduce badness.
Antenna theory is pretty well studied. How about some rough numbers on what the speaker wire is likely to pick up and/or on what is going to come out the other end. Again, without such numbers all this falls within the realm of the anecdotal. Not disproven, mind you, but anecdotal.
And a million other places.

Could they all be solved with 2016 technology, or at least brought down an order of magnitude? Indubitably. Do people do it? As far as I can tell, no. A little bit on the real amateur stuff. The audiophile-grade stuff?
 
Not sure what you mean here, either. Amplitude is kind of the overwhelming thing that we perceive as listeners.
Turns out that's not true. It takes pretty big changes in linear amplitude response before we notice, and smaller changes in phase, but even phase we're a lot less sensitive to than a spike where there shouldn't be a sound. Intermod gives that.
Acoustics of a room, or simply taking a step over a few inches, can really change frequency response and we don't notice.
Maybe some people don't notice. Others seem to. Certainly the response in the room is measurable (and tends to be pretty huge).
That's kind of the point. A null in a room might be several times quieter than a peak point. And you barely notice -- some people will and others won't. Sure, bass is louder in the back of a concert hall, and you can tell that, but as you pointed out, it's a huge difference there.

In comparison, the differences of the type you might see in an audio system are really really tiny, and imperceptible.
On the other hand, the ear is a frequency-domain device with an extreme dynamic range -- over 100dB. What's that mean? Intermodulation distortion is a Really Big Deal.
Intermodulation distortion in the speakers, in the amp, or in your ear/head (and here I don't mean imaginary stuff, I mean real processing in your ear/head).
Amplifier and speakers. Basically, anything nonlinear will cause intermod. The ears are a frequency-domain device. If you have two tones coming in, intermod will cause a third tone. The ear will completely pick up on that. An oscilloscope generally will have a much harder time.

Your ear/head is frequency-domain and won't
Math isn't sufficient to show us what is audible. The combination of some perceptual acoustics knowledge and the math might suggest, however, when the jitter might become audible.
I've worked through the math, many years ago, and won't repeat it right now. Sufficient to say, jitter is very, very noticeable.
Components like capacitors are sufficiently nonlinear to give audible distortion in the signal path. Of course, most audio equipment is badly enough misengineered that insufficient feedback and nonlinear gain also give errors. That's easy enough to fix. None of this is rocket science.
But it is electrical engineering, so we can examine this systematically. We can also do tests to determine, at the end of the day, whether any of it is actually audible.
Yes. Such test have been done. I don't have good references, but I've seen plots, and it is audible. One of the major developments which had gone unnoticed when I last looked were NG0 capacitors. Audio engineers presume ceramics are useless, but ceramic technology has come a long, long ways in the past 50 years. I've never seen a comparison of a modern ceramic to a polystyrene film. Large C0G/NG0 capacitors are nothing like the ceramics of old.

A capacitor here might be a microfarad. People then presume e.g. nonlinear capacitance in signal wires matters. Back-of-the-envelope numbers suggest it's so hopelessly low that it has no chance to do so. But that's one of the places you get $5000 wires.
Let's skip, for the moment, what bad audiophile designs do and focus on competent examples.
I can't discuss a null. To the best of my knowledge, no such examples exist.
Antenna theory is pretty well studied.
But not well understood. But that's hardly relevant to the conversation.
How about some rough numbers on what the speaker wire is likely to pick up and/or on what is going to come out the other end. Again, without such numbers all this falls within the realm of the anecdotal. Not disproven, mind you, but anecdotal.
That's actually very hard to do. Incredibly hard to do. A lot of analog is anecdotal. The best way to look at this is:
  1. Little loops of wire, as in a circuit built on a protoboard, commonly pick up noticeable signals in the 100MHz FM range.
  2. This is a much bigger antenna.
  3. It's inside of the feedback loop.
  4. Generally, having 100MHz all over a circuit causes slight bits of wonkiness. Slew rate limitations and that kind of thing.
It's a little bit of analog voodoo, in that hard numbers are hard to come by, since (1) antennas are not well-understood and (2) the size of the effect can vary by many orders of magnitude based on how you happen to position your speaker wires, how close you are to a radio station, etc.

As a sidenote, I don't work in this field, and I'm more competent than 99+% of the high-end audio engineers out there. This isn't praise or a testament to my competence. Virtually no one competent goes into that field.
 
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So show some basic analysis of what vertical vibrations are traversed to the floor for a horizontally oscillating speaker
Why would the speaker be horizontally vibrating? Only the drivers are. The whole box resonates. Actually, the box is more or less the whole point. The sides vibrate in directions perpendicularly to them. The bottom vibrates up and down, and so does the top. Just place a light object on the top of a speaker with strong bass and watch it.
The horizontally oscillating speaker is obviously the driver. If you think the box itself is resonating significantly then again show the analysis. That's what we do in science.
Very simple. When I wonder if my subwoofer is still alive (it died a few years ago and I had to order some part), I place my hand on the top of the box. If I feel vibrations, the speaker is still alive. I do the same experiment with my central speaker, which has a subwoofer in it. Very scientific, I must assure you.
The question was whether devices such as spikes or cone-shaped feet can produce an audible difference and if so, why.
No, the question was what physical effect could possibly cause a difference.
There was never any question of whether the box sides could be felt to be vibrating,
It is in boldface above.
although, if you think about, it's kind of humorous that you had to check for the sub's operation by touching its side instead of just listening.
Not at all. I have a HT system with a sub in the center as well and decent L/R ones. When there is no significant bass, it is hard to say where it comes from. Everything I watch goes through it, Weather Channel included. Actually, I am not even sure that my TV speakers work.
or why you would want hard contact with the floor as opposed to sitting on a carpet.
You may or you may not. The point here was that there is a difference.
I asked why or why not. If you have a reason in mind then please state it.
I might like one over the other. Remember, audiophiles do not care about the reason. As long as differences exist, they want to exploit them for full satisfaction.
You continue to define audiophiles as people who don't care about reasons. No true Scotsmen fallacy aside, it does kind of put a damper on further discussion.
I guess some still believe Elvis is alive. Yes, you cannot generalize like that. I said before something like there is a big group, etc., but I got tired of repeating it.
Fortunately, resonance effects are well studied but not completely understood. I have quite a few publications on the topic and there is still a lot left to do.
Please link those which have any relevance to loudspeakers.
The beauty of the analysis I am doing is that it applies to a large variety of phenomena: from sound in speakers to quantum mechanics.
I'll take your word for it.
Thank you.
The first step is obviously to substitute the speakers in the same position. If differences are noticed over a short period of time then it doesn't seem necessary to continue the experiment over weeks.
Wrong, a short period of time is very misleading. Unless you are musically deaf, the differences would be "in your face" (unless you use a second pair of the same brand but them some manufacturers match the speakers in the pair). The point is if the second pair could be improved with a different placement, and you need time for that.
If you have already determined that there is a difference between two speakers, then the null hypothesis that two speakers are not distinguishable to the listener has been disproved. It follows that this particular experiment can end.
I am not trying to disprove such a hypothesis. I know that two brands/models sound different. The question is which one sounds better to me.
It doesn't matter how one "creates" the analog signal? Shannon-Nyquist guarantees perfect band limited reconstruction. If there are differences between reconstructions then at least one of the methods does not live up to that standard.
None does. You cannot do perfect SN interpolation with audio even theoretically (casualty); not to mention in practice - to create repeating wave fronts with that shape. Oversampling would help a lot but unfortunately, we are stuck with the "redbook" CDs.
Repeating wave fronts with what shape?
sinc
So show, even in rudimentary form, what you think is the difference between ideal reconstruction and the various methods that you think are different.
Same as in imaging. The ideal reconstruction involves the sinc functions. They live forever and your tune is never band-limited (unless it never ends and it started before the Bing Band). Instead, one could use some kind of interpolation.
We don't need a signal that started before the Big Bang to make an audibly perfect reconstruction.
Nice try to insert the word "audibly". He said "perfect".
The question is again how long of a signal is needed to be perfect by an audible (or any other) standard.
That is your question, not his. He insisted that there is only one way, it is perfect, therefore, no difference. I replied that there are many other, and you agreed with me but did not want to admit it.
It should be if it were linear and time invariant (convolution) but it is not.
But it is largely so for DACs and amplifiers.
For amps - no. Too much power there.
As you surely know, decently-performing amplifiers are very close to linear over a huge range of output power, certainly covering the dynamic range of CD audio.
I know but my wife will divorce me if I buy one of those. Wait, I have to buy five (mono blocks). On a second thought, the rear one can be hooked up to a stereo one.
frequency dependent phase shifts,
Part of spectral response.
Not really, it could be a linear transformation but not a convolution anymore. "Spectral response" does not describe it then.
Linear, frequency dependent phase shift has a well defined Fourier transform corresponding to a convolution and spectral response and all that.
I read this sentence three times and I noticed a few inconsistencies. Phase shifts, etc., is a transform (an operator). It does not have a FT per se (unless you take the kernel). It can very well be a non-convolution.
"Frequency dependent phase shifts," which I take to mean a phase shift operator which can be expressed as function of frequency, e.g., tau(f), associated with multiplication in the frequency domain by exp(i tau(f)), which is a Fourier transform of a particular kernel. I think you knew all this.
The key word was "can". Yes, I happen to know something about that. I gave a graduate course last year about the theory of such operators.

BTW, the power spectrum (modulus of the FT of that multiplier) is 1 (for tau real), and in particular independent of tau. What does it tell you about its "spectral response"? Compare it with a convolution with a gaussian like function, which FT (its modulus) does tell you about the spectral response of the system.
The sound field would be different, so now you have a direction to explore why the speakers sound different at a particular listening location.
There is no problem to measure that they would sound different. The question is - which of those differences matter?
Well, at least we are able to reach an agreement that the audible differences are measurable in some way.
When did we disagree on that? The problem is that they are buried in too much "noise". There is too much data and we do not even know what to look for.
They are too many, how to choose a few metrics which would tell is if a speaker A is better than a speaker B?
The first step is demonstrating via double blind test that audible differences even exist. The second is relating those audible differences to measurable quantities.
I am willing to take a part of such an experiment. I need 3 months with each pair of speakers. The I will leave it to you to find out what measurements make me like some particular pair.
Subjective judgments of "better" are way beyond the scope of anything I've said.
Again, I got tired of writing "to me".
 
Not sure what you mean here, either. Amplitude is kind of the overwhelming thing that we perceive as listeners.
Turns out that's not true. It takes pretty big changes in linear amplitude response before we notice, and smaller changes in phase, but even phase we're a lot less sensitive to than a spike where there shouldn't be a sound. Intermod gives that.
It seems to be fairly well established that, given two sources in a double blind test, people seem to rate favorably the source that is louder, i.e., has larger amplitude.

However, you now seem to be talking about amplitude response. Do you mean amplitude response as a function of frequency?
Acoustics of a room, or simply taking a step over a few inches, can really change frequency response and we don't notice.
Maybe some people don't notice. Others seem to. Certainly the response in the room is measurable (and tends to be pretty huge).
That's kind of the point. A null in a room might be several times quieter than a peak point. And you barely notice -- some people will and others won't. Sure, bass is louder in the back of a concert hall, and you can tell that, but as you pointed out, it's a huge difference there.

In comparison, the differences of the type you might see in an audio system are really really tiny, and imperceptible.
But a few inches can make a pretty big difference in a typical living room.
On the other hand, the ear is a frequency-domain device with an extreme dynamic range -- over 100dB. What's that mean? Intermodulation distortion is a Really Big Deal.
Intermodulation distortion in the speakers, in the amp, or in your ear/head (and here I don't mean imaginary stuff, I mean real processing in your ear/head).
Amplifier and speakers. Basically, anything nonlinear will cause intermod. The ears are a frequency-domain device. If you have two tones coming in, intermod will cause a third tone. The ear will completely pick up on that. An oscilloscope generally will have a much harder time.
The ear/head is known to do a tremendous amount of nonlinear processing. For example, we can perceive beats when a tone is piped in one ear and another tone from the other ear. One would need to weigh the nonlinear response of the ear relative to the intermod in the amp and speakers.
Your ear/head is frequency-domain and won't
?
Math isn't sufficient to show us what is audible. The combination of some perceptual acoustics knowledge and the math might suggest, however, when the jitter might become audible.
I've worked through the math, many years ago, and won't repeat it right now. Sufficient to say, jitter is very, very noticeable.
That doesn't tell us very much. How much jitter, and is that an amount that is likely to be found in today's sources? That's the general form of the question.
 
I have an Adcom GFA 555 II for sale. You can be jamming to music, unplug the amp from the wall, and it will still play for about 8 seconds.

Its a beast.
 
The question was whether devices such as spikes or cone-shaped feet can produce an audible difference and if so, why.
No, the question was what physical effect could possibly cause a difference.
Yes, what physical effect could possibly cause an audible difference.
although, if you think about, it's kind of humorous that you had to check for the sub's operation by touching its side instead of just listening.
Not at all. I have a HT system with a sub in the center as well and decent L/R ones. When there is no significant bass, it is hard to say where it comes from. Everything I watch goes through it, Weather Channel included. Actually, I am not even sure that my TV speakers work.
So much for the golden ears. (Joking.)
I might like one over the other. Remember, audiophiles do not care about the reason. As long as differences exist, they want to exploit them for full satisfaction.
You continue to define audiophiles as people who don't care about reasons. No true Scotsmen fallacy aside, it does kind of put a damper on further discussion.
I guess some still believe Elvis is alive. Yes, you cannot generalize like that. I said before something like there is a big group, etc., but I got tired of repeating it.
Point of fact, your generalization ranged from audiophiles to "serious" audiophiles, none of which supposedly care about measurements. I realize it was an overgeneralization, but then why say it?
If you have already determined that there is a difference between two speakers, then the null hypothesis that two speakers are not distinguishable to the listener has been disproved. It follows that this particular experiment can end.
I am not trying to disprove such a hypothesis. I know that two brands/models sound different. The question is which one sounds better to me.
The original question was the value of proving the existence of (audible) differences by double blind testing. You have changed the question to what sounds better among components with known audible differences, even though is irrelevant to the original point.
It doesn't matter how one "creates" the analog signal? Shannon-Nyquist guarantees perfect band limited reconstruction. If there are differences between reconstructions then at least one of the methods does not live up to that standard.
None does. You cannot do perfect SN interpolation with audio even theoretically (casualty); not to mention in practice - to create repeating wave fronts with that shape. Oversampling would help a lot but unfortunately, we are stuck with the "redbook" CDs.
Repeating wave fronts with what shape?
sinc
What is a sinc wave front?
So show, even in rudimentary form, what you think is the difference between ideal reconstruction and the various methods that you think are different.
Same as in imaging. The ideal reconstruction involves the sinc functions. They live forever and your tune is never band-limited (unless it never ends and it started before the Bing Band). Instead, one could use some kind of interpolation.
We don't need a signal that started before the Big Bang to make an audibly perfect reconstruction.
Nice try to insert the word "audibly". He said "perfect".
I said perfect re: Shannon-Nyquist. Within real world limitations we can approach the conditions to some given standard. If you prefer better than audible standards, that could and perhaps should be considered as well.
The question is again how long of a signal is needed to be perfect by an audible (or any other) standard.
That is your question, not his. He insisted that there is only one way, it is perfect, therefore, no difference. I replied that there are many other, and you agreed with me but did not want to admit it.
Not sure what it is I am not wanting to admit, but okay.
It should be if it were linear and time invariant (convolution) but it is not.
But it is largely so for DACs and amplifiers.
For amps - no. Too much power there.
As you surely know, decently-performing amplifiers are very close to linear over a huge range of output power, certainly covering the dynamic range of CD audio.
I know but my wife will divorce me if I buy one of those. Wait, I have to buy five (mono blocks). On a second thought, the rear one can be hooked up to a stereo one.
You honestly do not find any amplifier which is decently performing over ~96 dB dynamic range that won't cause your wife to divorce you over?

I recommend double-blind testing. You might find some cheap Yamaha (crowd favorite) that actually fulfills all your requirements aside from the audiophile ego.
"Frequency dependent phase shifts," which I take to mean a phase shift operator which can be expressed as function of frequency, e.g., tau(f), associated with multiplication in the frequency domain by exp(i tau(f)), which is a Fourier transform of a particular kernel. I think you knew all this.
The key word was "can". Yes, I happen to know something about that. I gave a graduate course last year about the theory of such operators.
Accepting that you have expertise in the area, why did you profess confusion when you knew perfectly well what I was talking about?
BTW, the power spectrum (modulus of the FT of that multiplier) is 1 (for tau real), and in particular independent of tau. What does it tell you about its "spectral response"?
You are right. I assumed that the Fourier transform would have be known to get the spectral response, but properly speaking the power spectrum doesn't contain the phase. But again I think you knew perfectly well what I was talking about.
When did we disagree on that? The problem is that they are buried in too much "noise". There is too much data and we do not even know what to look for.
Which is why we start with a double-blind test. If the two sources are not distinguishable, noise and all, then we can focus our effort on something else that does seem to cause a perceptible difference.
 
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And it's telling that what's considered one of the best pieces of audio equipment is more than two decades old. It's as if people were claiming the Throwback Tuesday cameras had a certain je ne sais quoi to them making them the best cameras ever, and Canon and Nikon both made 6 megapixel sensor cameras, throwing as much lead weight into the body as possible to stabilize the camera for motion artifacts.
 

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