Yes, there most definitely is a 0.1Hz fundamental. The periodicity assumption underlies everything to do with Fourier analysis.
Simply put, Fourier analysis only works on waveforms that repeat forever with a definite period. When you use a FFT analyser, you grab an arbitrary chunk of the signal and implicitly assume that this is the repeating unit. This can lead to some interesting errors if the real period of the signal is different or it is not periodic at all.
Simply put, Fourier analysis only works on waveforms that repeat forever with a definite period. When you use a FFT analyser, you grab an arbitrary chunk of the signal and implicitly assume that this is the repeating unit. This can lead to some interesting errors if the real period of the signal is different or it is not periodic at all.
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You and others are claiming that the "silence" we hear between the notes is actually a long period fundamental that is exactly canceled by the harmonics of the struck note (clock, piano etc) in phase and level from a short duration pulse.
I find that impossible to believe.
Now, as for a mathematical process that requires certain conditions to be applicable and that this processing "proves" that the silence is actually lots of harmonics with a long period fundamental that equals exactly silence is a mathematical model.
To me, that maths and it's conclusion proves the model is wrong.
I find that impossible to believe.
Now, as for a mathematical process that requires certain conditions to be applicable and that this processing "proves" that the silence is actually lots of harmonics with a long period fundamental that equals exactly silence is a mathematical model.
To me, that maths and it's conclusion proves the model is wrong.
There is a fundamental (no pun intended) difference between cross-over distortion and things like piano keys and clock ticks.
With cross-over distortion, each time there is a cross-over, the waveshape traversed is exactly the same. And there is no resonance phenomena. The fundamental of the distortion is the same frequency as the input signal.
With piano notes and expecially with clock ticks, the waveshape on each note/click is not the same. At each note or click, resonances of various sorts are excited. There really no fundamental at a frequency of the tick rate, but fourier analysis will force you to assign a fundamenal corresponding to the analysis interval - which you must arbitarily assign.
When analysing the behaviour of systems, there is the right tool for the job. And an unsuitable tool for the job. If you want to drive a nail into wood, a hammer is a good tool to use. If you want to drive a coach screw into wood, well, you can use a hammer. But it will work vastly better if you use a spanner.
Similarly, if a wave repeats exactly the same each each time a precise time interval passes, fourier analysis is the right tool to use.
But clock ticks don't repeat exactly the same each tick. Firstly, due to mechanical slop, each tick does not occur at the same interval. At when the tick begins, the resonances that you hear thus start at a random phase. So, with a nominal tick rate of 1 second, the fundamental IS NOT 1 Hz. There really is no fundamental, but if we did the fourier calculation over 100 ticks, the apparent fundamental would be 0.01 Hz. And there would be harmonics at 0.01 HZ intervals right up to and well past 1 Hz. Each at a very tiny level. Not a very usefull way to understand or characterise clock ticks, but mathematically valid. Do that and you'd likely conclude you can't hear a clock tick - all those harmonics below the amplitude and frequency thresholds of hearing. About as valid as hitting a threaded coach screw with a hammer, and hey, the wood split and we've got no strength.
It's far better to use fourier analysis by considering the sub- 1 second (5 milisecond perhaps) on a typical click (ignoring for the moment that real clock ticks have three distinct parts. Clockmakers call it locking, unlocking, and release as I recall. The 3 parts come from when the fork driving tine hits the pin, the pin leaves the tine, and then the pin hits the fork recovery tine).
If the fork in a typical clock movement resonates at say 400 Hz, it's better to analyse it on that basis. Then its easy to understand why we can hear it.
A 4-stroke engine is somewhat similar. Say its running at 600 RPM. We can certainly hear the exhaust. Firing is at half crank speed, 300 firings/min - that's 5 Hz. So, one might expect fourier to tell us that the exhaust not consists of a fundamental at 5 Hz, and harmonics at 5 Hz intervals. That's mathematically valid, but not terribly useful. We're using the wrong tool, or using the tool incorrectly again. Its far better to say the exhasust system resonance (at say 150 Hz) is shocked into action every 200 mSec. And do the fourier analyis based on one cycle of teh resonance (6.67 mSec). That will characterise the sound we hear. No one hears engines emitting 5 Hz.
Now, let's get back to establishing whether anyone wants a blameless engineering treatment of a tube amplifier. I think it would be a good intelectual exercise, and very interesting, but I'm thinking no one actually wants it in the sense that they would use it for anything.
With cross-over distortion, each time there is a cross-over, the waveshape traversed is exactly the same. And there is no resonance phenomena. The fundamental of the distortion is the same frequency as the input signal.
With piano notes and expecially with clock ticks, the waveshape on each note/click is not the same. At each note or click, resonances of various sorts are excited. There really no fundamental at a frequency of the tick rate, but fourier analysis will force you to assign a fundamenal corresponding to the analysis interval - which you must arbitarily assign.
When analysing the behaviour of systems, there is the right tool for the job. And an unsuitable tool for the job. If you want to drive a nail into wood, a hammer is a good tool to use. If you want to drive a coach screw into wood, well, you can use a hammer. But it will work vastly better if you use a spanner.
Similarly, if a wave repeats exactly the same each each time a precise time interval passes, fourier analysis is the right tool to use.
But clock ticks don't repeat exactly the same each tick. Firstly, due to mechanical slop, each tick does not occur at the same interval. At when the tick begins, the resonances that you hear thus start at a random phase. So, with a nominal tick rate of 1 second, the fundamental IS NOT 1 Hz. There really is no fundamental, but if we did the fourier calculation over 100 ticks, the apparent fundamental would be 0.01 Hz. And there would be harmonics at 0.01 HZ intervals right up to and well past 1 Hz. Each at a very tiny level. Not a very usefull way to understand or characterise clock ticks, but mathematically valid. Do that and you'd likely conclude you can't hear a clock tick - all those harmonics below the amplitude and frequency thresholds of hearing. About as valid as hitting a threaded coach screw with a hammer, and hey, the wood split and we've got no strength.
It's far better to use fourier analysis by considering the sub- 1 second (5 milisecond perhaps) on a typical click (ignoring for the moment that real clock ticks have three distinct parts. Clockmakers call it locking, unlocking, and release as I recall. The 3 parts come from when the fork driving tine hits the pin, the pin leaves the tine, and then the pin hits the fork recovery tine).
If the fork in a typical clock movement resonates at say 400 Hz, it's better to analyse it on that basis. Then its easy to understand why we can hear it.
A 4-stroke engine is somewhat similar. Say its running at 600 RPM. We can certainly hear the exhaust. Firing is at half crank speed, 300 firings/min - that's 5 Hz. So, one might expect fourier to tell us that the exhaust not consists of a fundamental at 5 Hz, and harmonics at 5 Hz intervals. That's mathematically valid, but not terribly useful. We're using the wrong tool, or using the tool incorrectly again. Its far better to say the exhasust system resonance (at say 150 Hz) is shocked into action every 200 mSec. And do the fourier analyis based on one cycle of teh resonance (6.67 mSec). That will characterise the sound we hear. No one hears engines emitting 5 Hz.
Now, let's get back to establishing whether anyone wants a blameless engineering treatment of a tube amplifier. I think it would be a good intelectual exercise, and very interesting, but I'm thinking no one actually wants it in the sense that they would use it for anything.
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I have an experiment in the lab with a 12 nanosecond pulse that repeats at 100Hz. We use it to calibrate our EMI receivers. I have verified by experiment countless times (it is part of the calibration process) that the spectrum of the pulse is as predicted by figure 13-10 here for a duty cycle of 0.0000012. The Fourier Series
It has Fourier components at 100Hz, 200Hz, etc, and so on up to almost 1GHz. When these are added together, they do indeed cancel out to zero everywhere except the 12ns pulse duration.
A clock tick is no different, it has Fourier components at 1Hz, 2Hz, 3Hz and so on throughout the whole audio band, and these sum to zero except during the period of the tick.
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Fourier tells you what is appropriate to your lab experiment. It is like cross-over distortion in that at each 10 mSe, the waveform is a simple pulse, exactly the same each time.
For a 1 per seond clock tick, the fundamental corrsponds to the time period at which the waveform repeats indentically. That is NOT 1 second. It's not 1 second, it's much longer, because the timing & phase of the tick frequencies varies randomly. In fact. for a purely random phase in each tick, the fourier period is infinity and there is NO fundamental.
And even if it's not random, then sure the fundamental is then 1 Hz. Is that useful to know. For your lab experiment, I guess it is, but what would a clockmaker's view be? I reckon he'd say "What a lot of tosh! Boffins should stop reading math books and get a real clock."
Use the right tool for the job. Fourier analysis assigning a fundamental to the tick rate is the wrong tool for the job.
Yet you have seen it more often than you can count.
Look at a square wave of 1Hz. You actually see almost 1/2 second of absolutely flat line, generated by the exact cancellation of all the odd harmonics.
jan
Every periodic signal can be represented by a Fourier series. Whether it should be in practice is a completely different issue.
Exactly right. And not all signals are periodic anyway. Some are random in some way.
Now, can we please get back to whether there is any value in doing a blameless treatment for a tube amplifier?
Nevertheless, it is true. Who said that truth always has to be intuitively obvious?AndrewT said:
Getting back to blameless valve amplifiers, it seems to me that one snag is that valves have rather large sample variations. Of course a good design can cope with likely variations but the end result will still be more variable than typical SS designs.
Not a problem. Ever looked at the parameter variations in bipolar transistors? Of FETs? In gain, strays like interelectrode capacitances, and carrier storage time, there's MUCH more variation in solid state devices.
What IS perhaps an issue is that with transistors, manaufacturers tell you, either up front in datasheets, or you can ask their factory applications engineers, just what the max and min variation in parameters that matter actually are.
With tubes, there was usually a lot less info in datasheets. And the tube manufacturer applications engineers are all gone, with the factories. You've got buckly's chance of getting good info out of Chinese factories. Russian manufactuers might be a bit better.
Still, if you asume +,- 10% variation in any given parameter not specified in the tube datasheet, you won't go far wrong.
Another possible issue is that gradual change in tube characteristics is to be expected due to wearout mechanisms. Except for power transistors worked very hard, gradual change over life in solid state is negligible. But even with tubes, this is more of a SPICE simulation isue than a real problem in end use.
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OK, let's get rid of practicalities: imagine you digitally record one clock tick during one second and you play it endlessly.
You will still hear the tick of a clock, but this time we are sure the sound is composed of a 1Hz fundamental and its harmonics. Now, rearrange randomly all the phases of all the harmonics and play it: do you think you will still hear a clock ticking?
Assume a fundamental of 100Hz..... strawman goes down in flames.
Done that. I've also done it's mate: mono to two amps and listen to the stereo field resulting. Especially via headphones. Particularly interesting at very low and very high signal levels.
While I agree that THD is (mostly) meaningless I disagree with the your comments on sensitivity - the "hiss" is exactly the problem area which leads to comments on "blackness" or "fatigue".
<anecdote>
I am personally quite sensitive to higher order harmonics - but I have a musical background so I'm probably not "normal".
</anecdote>
I'd also point out the danger of invoking "competently designed" - the value in Self's work (the point of this thread) is that it explicitly examines "incompetence".
The various reviews from the sixties and seventies on the classic PP-pentode-with-feedback provide some launching points - eg. issues of stability, insufficient gain, inadequate initial linearity.
As I said earlier, a summary of the existing literature would be a really useful starting point. (No, I'm not going to do it now - my time is going elsewhere for the next two years)
Generally agree with your comments here. No-one wants to know. It won't sell more boxes. But getting THX certification, that's a different matter
If the phases are truely randomised, no you won't. It will sound very different. But the fourier spectrum that represents the randomised repeating 1 clock tick period is different to the spectrum of the original clock tick. But this process you have made the click traverse the exact same waveshpe each time, which is not what a ticking clock does.
The phased randomised version of a single repeated clock tick will have a fundamental of 1 Hz (for a 1second tick) and harmonics at exactly separated by 1 Hz. That isn't what a natural clock tick has. Because each tick traverses a different waveform each time, a long term fourier spectrum has components at frequencies very much less than 1 Hz apart.
In this case the 9th harmonic is 900 Hz and the ear at that frequency has about 20 to 25 dB more gain over the fundamental. So the 9th should be percieved at only 50 to 45 dB down. So the "straw man" is looking at least a bit singed.
But wait, there's another factor....
Harry Olson showed by very carefully constructed tests in the 1930's, that harmonic distortion less than 1% (40 dB down) was not detected by ear. Sensitivity to distortion was investigated again in the 1950's by Philips. They got much the same answer, and it was the basis of an early German consumer protection spec that said in order to be sold as "Hi Fi" an audio system had to have less than 1% THD at any level below clipping. (it was an end to end spec, not just the power amp, so it's a tougher spec than you might think)
These days, we have much better source material on CD's, and even on 1970's and 1980's vinyl. And amplifier system evolution has long passed the point where 0.1% THD is ho hum. Speaker are MUCH better (except for efficiency). We've all got used to high quality sound. So I think that if the Olson test/survey was done again today, we would turn out to be much more sensitive. But it is difficult to imagine that we would detect lower than about 0.2% or so (54 dB down).
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Thus, you think that the relative phases of harmonics have an audible impact in the case of truly harmonic signals, but not when the spectral components (not necessarily harmonically related) are time-shifted relative to each other.
You thus imply that the relative phases of harmonics have to be audible in the case of crossover distortion.
This could be tested relatively easily.
There is no implication that the phases of harmonics in cross-over distortion, or any sort of harmonic distortion, matters, for the following reasons:-
When the harmonic structure is such that the fundamental is in the audio range, the ear is insensitive to phase. But if the spectra is such that the harmonics come together as a peak at intervals around 0.2 second or longer (5 Hz or lower), our ears are sensitive to the timing.
The fact that the ear is insensitive to phase is very well known and docuumented. The process of passing music through analogue studio-transmitter links, radio transmitters and radio receivers, makes a complete mess of the phasing. Nobody cares, except in so far as both channels in a stereo system must have roughly the same messing, or the spacial imaging will be affected.
When I was a teenager starting out in the electronics game, I was like many others. It didn't take long to realise that altering the phase of harmonics makes a VERY obvious difference to the waveform shape on a CRO. But, suprisingly (back then), a change completely inaudible. As you would expect from studying the way the ear actually works.
I should perhaps clarify why a series of clock ticks containing random phases of tick components is very different, audibly and mathematically to a single sampled tick repeated endlessly with the harmonic phases randonly altered.
The first is a series of ticks, each one unique containing a burst of resonnce frequences random in phase with respect to all preceding and following ticks. You hear the ticks because there is a burst of energy each second. If you alter the phases, it makes no audible difference - you still get a burst of energy once per second.
The second example comprises a coarser set of harmonics that come together in a peak once per second, and are in the same phase for all ticks. So if you alter the phases they won't come together in a peak once per second.
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Things are not that clear-cut: the ear remains sensitive to the time-domain for frequencies well above 20Hz
It has indeed been the doctrine for a number of decades, but the subject is being revisited and nowadays it isn't an absolute truth anymore
The "burst of energy" concept is probably what matters: even for a non-coherent signal there will be such a burst, simply because many of the components will have a harmonic or near harmonic structure.
If you could perfectly mimic the spectral content of the ticking clock (the real, imperfect one) using magnitude information only, the result would be a somewhat colored random noise, no perceptible ticking.
What makes the sound characteristic is the fact that at certain time instants, all the components harmonic or not coincide to create a burst.
I suspect that something similar plays a role in the perception of crossover distortion, at least for a certain frequency range.
As I said, this shouldn't be too difficult to test in reality, and I will give it a try one these days.
some "experts" should get educated, read a real, modern psychoacoutics textbook
simply flat out wrong on the basics of harmonic phase audibility:
better:
"Ohm's acoustic law", harmonic's "phase inaudibility" actually was an overreach even 150 years ago
Ohm's acoustic law - Wikipedia, the free encyclopedia
August Seebeck - Wikipedia, the free encyclopedia
psychoacoustic researcher's human listening test have shown DBT discrimination, timbre or even pitch change sensation with relative polarity of harmonics that give asymmetric waveforms
those stuck on the issue try to fight a retreat with the "its just the distortions in the playback system that make harmonic relative phase audible" - but that position is wrong too
http://www.diyaudio.com/forums/loun...st-speakers-what-does-tell-4.html#post3904960
http://www.diyaudio.com/forums/everything-else/54596-audibility-absolute-phase-5.html
Jan and Sy I believe have reported DBT AB/X of music files with added midrange phase shift
others have shown listeners can train to hear the amount of phase shift in a LR4 XO even with music
test signals and headphone listening give the highest resolution, easiest demonstration of harmonic relative phase sensitivity - the lower sensitivity with speakers/room and real music is probably why phase shift is often ignored, audibility denied
simply flat out wrong on the basics of harmonic phase audibility:
better:
"Ohm's acoustic law", harmonic's "phase inaudibility" actually was an overreach even 150 years ago
Ohm's acoustic law - Wikipedia, the free encyclopedia
August Seebeck - Wikipedia, the free encyclopedia
psychoacoustic researcher's human listening test have shown DBT discrimination, timbre or even pitch change sensation with relative polarity of harmonics that give asymmetric waveforms
those stuck on the issue try to fight a retreat with the "its just the distortions in the playback system that make harmonic relative phase audible" - but that position is wrong too
http://www.diyaudio.com/forums/loun...st-speakers-what-does-tell-4.html#post3904960
http://www.diyaudio.com/forums/everything-else/54596-audibility-absolute-phase-5.html
Jan and Sy I believe have reported DBT AB/X of music files with added midrange phase shift
others have shown listeners can train to hear the amount of phase shift in a LR4 XO even with music
test signals and headphone listening give the highest resolution, easiest demonstration of harmonic relative phase sensitivity - the lower sensitivity with speakers/room and real music is probably why phase shift is often ignored, audibility denied
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