| Sine and square waves percieved pitch, why? - Click HERE for Original Thread |
| baggystevo82 |
Hello,
I have this question as part of my digital audio module coursework, and would very much appreciate some help! heres the question:| quote: | | d) Quite difficult: you will need to do this with a neighbouring group. Tune one sig-gen to a frequency close to the lower end of your hearing range, giving sine waves. Use the other sig-gen to give square waves and alter the frequency so that you can hear within that sound a sound which is the same as the first sig-gen is giving. What is the frequency on the meter of the second sig-gen? What is the ratio of the two frequencies? Tune both sig-gens to higher frequencies and see if you can repeat the test. What is the ratio of the two new frequencies? Do you have an explanation? |
and here's the graph of my results. It seems a bit strange that there's a sudden changeover in characteristics of the graphs and I'm confused....help....:xeye:
Cheers,
Steve |
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| janneman |
Well,
From the way that the question was framed, it looks like you should EXPECT something irregular, so your curve may be quite alright. As for an explanation, I don't have one, but I would google things like pitch perception or pitch shift with frequency.
Jan Didden |
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| baggystevo82 |
Hi,
Cheers, yeh that's what I thought. I think my lecturer just wanted us to do a very low frequency, and one high one, but I got curious and homed in on the area around which the change occurs. It's just the almost instant change that surprised me, within 1/4 of a Hz or so, seems like there's some strange phenomenon I don't know of, besides harmonics of square waves etc that's causing it....hmmmmm.....ponder ponder....
Thanks,
Steve |
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| janneman |
Yes, the sharpness of the change IS funny, mother nature seldom builds something like that. Hmmm....
Jan Didden |
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| KBK |
The human ear works as a 'diode' and only hears the leading edge of a given note. perhaps, if you played withthe DUTY CYCLE of the given sqare waves, the percieved answer may alter itself in some manner, compared to the original observations.
Also, the ear is timing and transient sensitive, which should be a logical extrapolation (follow the logic trail) of the statement that the ear works as a diode. This means, harmonics, timing (time related components surrounding the transient information) and amplitiue of the transient components are critical for human Observation.
If the 10% and the 90% points of the square wave (as normally considered) are cleaned up, via a small dose of inductance, the answer may pop out in a more clear fashion.
The fact that the human ear is capable of resolving transient information down to less than 100,000th of a second (timing issues, not frequency) is interesting. This is due to the timing of arrival of signals between each ear for spatial recognition of information, at the very least, and is a known human skill and phenomena,
This means, clocking of digital systems and the like, due to nyquist, must exceend 225khz sampling in extreme accuracy, to meet the minimum requirement for exceeding human resolving capacites, as recognized ---at this time---. Who knows, that figure may have to be revises YET AGAIN....and again..as it has been over the years.
I suspect you are hearing simple negative or postive edges of the given waveform, and the brain 'mixes up' the leading edge, depending on the phase transition at a given frequency. This may be why a low frequency was specified, so the area of frequential overlap between the two frequencies is as large as possible.
What I mean, is the time factors involved as an issue, at the transition point for both the square and sine are enlarged, at the lower frequencies,and the phenomena may be easier to resolve, or confuse the mind-brain, at the lower frequency. Simple signal ear-brain phasing issues. We recognise the transient, not the phase of it. Low frequencies create negative and positive rarefraction-compression of the air, regardless of the frequency of the signal, that can be easily recognised, even with the pahse being reversed. Otherwise, signals would be more garbled when they are, when they are wired out of pahse with regard to your speakers and speaker systems.
Some people, like me, due to exposure in the world of design on a very regular basis, have taught ourselves to recognise these issues and resolve (with listening, and completing large numbers of 'single cause analysis' experiments) them to a very high level, simply due to a larger understanding of what I am hearing when I listen to audio signals, in any fashion. Many experiments, many correlations, etc. It puts me one step ahead of the next guy who is designing audio gear. |
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| janneman |
Man, you should get published in some scientific journal, this is sensational! Your insight and knowledge is what we all have been waiting for. The ear as diode, wow, who would have thought that??
Jan Didden |
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| baggystevo82 |
Cheers for that! It was kinda what I was thinking I think, Ill have to have a good think about that one.
Cheers,
Steve |
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| KBK |
The ear, 'as a diode' has been known for quite some time. The human voice is single-sided, as in the fact that the entire human voice is a positve pressure front, with transient timing and amplitude as the founding components of intelligibility. Same thing behind the human behaviour of 'clapping' of hands.
Our hearing has evolved around these considerations.
Note that horn speakers would not work if this were not true, as they make the negative component of the waveform resemble total garbage, if it is measured.
There is incredibly high distortion the negative components of a horn speakers's acoustical signal, yet most percieve horn signals as beng more intelligible.
There is nothing new in these statements. It is all old and well covered work. Possibly not well considered, or well connected, but the parts of the solution and answers are all well known.
All these things follow through to being essential understandings in the art of electronics design. First you must understand how people hear things. Then you can design electronics. Forget about measuring anything, or designing and building it. These considerations are the most major points of consideration, and belong at the top of "page one, chapter one", of designing audio gear, of any kind. Whatever the case may be.
And just about no-one in the entire industy undertands these things, it seems. For example, electronic feedback networks introduce phase or time skewed transient components, so they inherently sound like **** to the human ear. This is simple extrapolation of the above related facts.
Yet....no-one seems to 'get it'.
So I'll do exactly what I usually do. I'll say it quietly, and nicely in some small backwater or corner like this one here...and sooner or later, people will pick it up, and it will enter the lexicon of design in the realm of logical analysis in electronics design. Heck, you might end up seeing such information as part of an article in Stereophile 2-3 years from now or something similar to that. And, no-one seems to know where such information comes from, or where it originated. Some guy will be applauded and complemented on his work, how smart he is, etc, and it won't be me. I suspect the JAES magazine has had similar articles, but not all the perinent info in one spot, at one time, so people can connect the dots. For once. (involving this particular application of logic concerning this exact subject) Please and thank you......
This is one of my favorite games, and I've played it dozens of times. Seeding. Who cares, really, as long as they eventually figure it out. |
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| MBK |
KBK,
almost namesake ;)
Love your seeding approach - I often have the same kind of thoughts. Not that I necessarily have much to seed, in DIY audio at least. Reminds me of Jorge Luis Borges' publication of single very short book concepts - he didn't feel like actually writing the book :D As a special pun to Pass one could mention the title of one of Borges' books - The Aleph.
Anyway , I once started a dicussion with relevant info here, the single ended nature of things .
About the ear, not only does it appear to work as a single ended detection device with highest sensitivity at the zero crossing, it also has active, highly nonlinear amplification mechanisms. This was first suspected in the 60's, then disregarded for decades, and recently well demonstrated. See here for example:
Inner Ear Amplifiers . Poor Gerbils.
All this explains the apparent insensitivity to high levels of certain distortion, such as low harmonics distortion, and high sensitivity to other forms of distortion, such as crossover distortion, or high order distortion components.
Many other references exist ... somewhere... |
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| baggystevo82 |
All brilliant stuff! If you're trying to influence me for the future its working, hehe.
Thanks again!
Steve |
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| janneman |
| quote: | Originally posted by KBK
[snip] The human voice is single-sided, as in the fact that the entire human voice is a positive pressure front, [snip] |
Ahhh!. That must be the reason that the world pressure rises and rises with all that talking! So much hot air, maybe we found the real source of global warming!
Jan Didden |
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| sam9 |
| Is this related to why lossey compression works even if it offends my sense or order? I'm thinking of masking where a sharp loud shound will mask what follows for a few mS. MP3 uses this and I think DTS may as well. Would this period where masking occurs be analogous to the recovery periode of a diode? |
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| baggystevo82 |
Isn't that where a muscle tightens up in your ear in response to a loud sound to stop it vibrating too far and too violently? I remember a surgeon on Tomorrows World tested to see if this ear implant thingy worked by stimulating it and seeing if that muscle tightened up.
Steve |
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| sam9 |
Thet example I can cite is why "click and pop removers" from the days of vinyl were/are often unsatisfactory. I had one way back when and while it worked sometimes, sometimes it just turned a loud pop into a dull thump. What was wierdwas that years later software inteded to do the same thing to for LPs trancfered to CD would sometimes display the same behavior. This hints that it is not the pop-removal that is the problem.
Using software that let me zoom in to the actual wave form revealed what was happening. First the pop was bing removed and no artifacts added. What was going on was that the pop was followed by dampened ringing. This turned out to have nothing to do with the LP either since it could be reduced but not eliminated by using a different stylus. The thump was there alol along but the initial pop masked it. remove the pop and the tump/ringing was revealed. You could sometimes get rid of the thump, too by lowering the threashold of the remover (hardware or software type).
Anyway the point is that I'm completely convinced of the reality of the masking effect of an initial stong inpulse because of my experienxe tracking down "thumps". |
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| Sch3mat1c |
Of course... mind you... that would suggest that voices would sound "upside-down" if I played them 180 degrees out of phase (i.e., reversed terminals). They do not.
Explain?
Tim |
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| baggystevo82 |
I guess what was being talked about earlier just means that ears are more responsive to compressions than rarefactions? Wouldn't that just mean that the ear was non-linear in response relative to drum excursion or air pressure on the drum? That being the case I cant think of an explanation, unless it's something to do with it being a longitudinal wave....dunno...:xeye:
Steve |
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| dnsey |
Looking at it in a simpler way (within my understanding!), it seems clear that below the 'crossover' point, the square wave frequency approximates f/2 within experimental error. (Note the part of the question referring to ratio). It therefore seems likely that the first harmonic of the sq wave is more easily perceived than the fundemental frequency. At the crossover point, the ear/brain begins to perceive the fundemental directly. Is this not due simply to the ear's non-linear frequency response - i.e. more LF enregy than HF is required to perceive a particular (subjective) amplitude?
Apologies if this amounts to what's already been said, but my simplistic mind sees it more easily that way:-)
I'd also note that both generators should be set to produce the same output, as perceived pitch varies with amplitude, and this might muddy the waters. I would be interested to know if the crossover point also changes with amplitude, or indeed with individual listeners. |
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| baggystevo82 |
yes that was what I was thinking, that at low frequencies the ear/brain can percieve the seperate up and down parts of the wave (which occur at a rate of 2f) and then at higher frequencies the ear/brain loses that ability and sees the overall shape, rather than the seperate transients...if that makes sense. I still have a bit of a problem with the suddenness of it though, I certainly would be interested in other peoples observations on this! If anyone wants to give it a go, I used the attatched signal generator (opening 2 instances at the same time). I used 0dB gain for the sine wave, and -20dB for the square for reference.
Cheers,
Steve |
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| sam9 |
Express the transition point as a wave length rather than frequency. Then consider if the wave length (or half or quarter wave) corresponds to any typical human dimension shuch distance between ears, length/radius of auditory canals or other hearing structures.
I'm just taking a shot in the dark (i.e., this is not one of those exersizes where I already know the answer), but virtually all wave behavior has some relationship to the physical dimension of the objects with which it interacts. |
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| Mr Evil |
| quote: | Originally posted by baggystevo82
yes that was what I was thinking, that at low frequencies the ear/brain can percieve the seperate up and down parts of the wave (which occur at a rate of 2f) and then at higher frequencies the ear/brain loses that ability and sees the overall shape, rather than the seperate transients... |
If that is so, then you can test it by performing the experiment on people with different hearing bandwidths (i.e. people of varying ages). If the transition frequency shows no correlation to age, then the theory is false. |
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| KBK |
When you have a square wave at low frequency, there is time for the system (ear brain-air) to re-stabilize at the either positive DC point or the negative one. The 'change' in the signal, at this point, becomes the 'crossover' component, the 'zero crossover' point. Thus, for a given low frequency square wave, the single cycle, or frequency, has multiple points where the ear-brain can hear it as a frequency, or 'transient change' point. Whereas, a sine wave only has the two. That likely would be the more plausible answer, on analysis of the situation. As you increase the frequency of the square wave, this phenomena of the air re-stabilizing, masking effects, etc..all cease to have as large an influence, and you would slowly change over to a singular frequency recognition with the ear-brain system of signal recognition, on that given square wave 'cycle'.(as it increases in frequency of cycles) It might be more correct to say that the air re-stabilization effect is still there, obviously, but we have passed through the frequency and pressure area where the eair-brain's air pressure sensitivity (as a system) have altered in their understanding on how they interpret this phenomena.
As for the sound of a signal being audible, even if the wiring of a speaker is reveresed, some folks, like me, and many, many audiophiles, have learned to recognise 'reverse phase' signals very easily,and find them to be disturbing. It almost feels like the brain and ear are turned 'inside out'. I would liken it to seeing a mirror image, as in when you look at a mirror.
Make sense? |
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| phn |
| I can only second KBK. Before designing audio we should know what we can hear. Thankfully there are tons of academic books on the human senses out there. But my favourite by far is Diane Ackerman's A Natural History of the Senses. There's no tech talk. Just a very well written, easily read and entertaining book. You will not find this a chore. The engineers here may prefer books with figures and graphs and stuff. But if you visit any library you should find enough of those to last you a couple of years reading. |
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| Enzo |
All the preceding discussion has just assumed this is an artifact of the human ear. What you havevn't done is considered the way the sound was delivered to the test subjects. What speaker did you use? What was the listening environment? We can probably assume the amplifier had response well below the 100Hz, but we don't know how well it responds.
Speakers that don't have low end response can be fooled. We often bump a bit at maybe 250 to fool the ear into thinking there was more bottom than there is.
Your speaker may have some resonances that interfere. If it is a multidriver speaker system, then there may be interaction between the drivers or in the crossover. The sine will be all fundamental and will come out hte woofer, but the square wave has high freq components that will come out the tweeter or midrange, and there may be phase differnces between them that affect the perceived sound. Sum and difference signals would then confuse the ear.
And the response of most speakers is not linear. The impedance of the speaker varies with freq as well.
Room acoustics matter, resonances and standing waves can alter perceptions. Reverberations or sound reflections may be frequency dependent. Was this sound presented through a stereo setup? Or one speaker? And what about the room around it. Try your experiment in another setting and with different equipment before drawing firm conclusions.
If you want to test the ear in this experiment, should you not do it in an anechoic chamber?
ANother thing is level. SPL can alter the perceived freq in some circumstances. Look up the FLetcher Munson curves. At lower levels your ear has a reduced response range, so as you get louder, yuo can hear deeper tones. This might be involved.
You might pick up the test sound with a calibrated microphone and analyze for any phase aberations or intermodulation artifacts.
It is an interesting experiment, but don't jump to conclusions. |
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| Enzo |
| What I meant by level considerations was that if the sine and square signals were not absolutely matched in level, it will hit the ear different. and the 200Hz transition migh tbe where the FM curves were crossed in your tests. |
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| johnnyx |
I think it's to do with time.
Another experiment is to gate a tone on and off. Vary the duration of the tone with the gate, gradually reducing it.
You get a tone, a short tone, a very short tone, a very very short tone, a click.
At what duration does the tone become a click? |
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| baggystevo82 |
Hello, was done with a
PP KT88 amp (diyhifisupply ella)
B&W 309
Creative labs external sound card (MP3+ I think)
Stereo setup
Good point, i should at least have tried it with headphones, something to do later...
cheers,
Steve |
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| jeff mai |
| quote: | Originally posted by dnsey
It therefore seems likely that the first harmonic of the sq wave is more easily perceived than the fundemental frequency. |
The above is the answer, but no one seems to have understood. There is no need to refer to diodes or transient perception to explain this.
The graph is only showing that the ear is increasingly less sensitive to frequencies below 200Hz. A square wave is a sine wave plus a series of harmonics (a perfect square wave would have an inifinite series.) Below 200Hz the ear perceives the first harmonic present in the square wave as being louder than the fundamental of the square wave. Therefore, where the fundamental of the sine wave of frequency "f" is below 200Hz, the required square wave frequency that is an audible match will be "f/2". Plain and simple. |
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| KBK |
Which is why I said inductively filter the square wave. To remove the harmonics, which give those cues you speak of. To get to a more of a single cause analysis situation. Ringing of the wave at transition, settling, etc. Get it out,and see again what the results are, then you will know if you are paying attention to the ringing or the transition.
Only problem being, is the driver and amplifier will do it too. The diode analysis is solid and well known, regardless. It's pertinence here is the question. |
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| Enzo |
| If you filter the harmonics out of a square wave, does it not cease to be a square wave? And at that point we are no longer doing the assigned experiment. |
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| baggystevo82 |
True, but my amp ought to be capable of making a pretty accurate square wave at only 200Hz.... Maybe at 10k there would be significant rounding
Steve |
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| RHosch |
Oh for heaven's sake, if this is a homework assignment don't go turning in the ramblings of KBK. You do want to stay in the course long enough to finish it, don't you?
The explanation is simple, and has been pointed out here twice. I would suggest redoing the experiment with a single wideband driver or single channel of headphones, and also doing trials at different sound pressure levels. A flat FR transducer is important if you want results reproducible by others, but not if the assignment is only a "neat... look at this" sort of experiment.
Fletcher Munson curves are generalized curves. Specific individuals will have somewhat different curves. Also, by definition the curves show how the human ear (generalized, again) varies in frequency response as a function of SPL. What you will find is that different listeners hear the transition at slightly different frequencies, and also that varying the SPL will result in a given listener hearing the transition at slightly different frequencies.
I suggest the single wideband driver because the presence of crossovers smearing a square wave might have some effect on the perceived transition frequency, and that would be interesting to note because the total energy in each harmonic would not be changed by the crossover. How the phase relationship between harmonic components of the signal affect the transition would be very interesting, and demonstrate an understanding of the phenomenon that your professor probably wouldn't expect. And while wideband drivers do have a limited frequency response, you have already established that the transition effect is high enough in frequency to be within the operating range of good widebands. If you really wanted to do a nice study (not sure how important the assignment is), insert a variable all-pass circuit in line that has an Fc near the transition frequency and try to isolate the role of harmonic phase relationships, or document the absence thereof.
Finally, follow up by examining published F-M curves (and the more recent ones... don't recall the name) and compare the perceived loudness of the fundamental and the second harmonic at the SPL corresponding to the proportion of the signal each contrubutes to a square wave at the SPL you used to test. See if those perceived loudness curves for the two frequency components happen to cross at the transition frequency you observed (in a given trial).... |
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| Carondimonio |
| quote: | Originally posted by dnsey
It therefore seems likely that the first harmonic of the sq wave is more easily perceived than the fundemental frequency. |
| quote: | Originally posted by jeff mai
The above is the answer, but no one seems to have understood. There is no need to refer to diodes or transient perception to explain this.
The graph is only showing that the ear is increasingly less sensitive to frequencies below 200Hz. A square wave is a sine wave plus a series of harmonics (a perfect square wave would have an inifinite series.) Below 200Hz the ear perceives the first harmonic present in the square wave as being louder than the fundamental of the square wave. Therefore, where the fundamental of the sine wave of frequency "f" is below 200Hz, the required square wave frequency that is an audible match will be "f/2". Plain and simple. |
Hi all,
it makes a lot of sense, besides one very small detail:
A perfect square wave has only ODD harmonics.
In other words, if you have a, say, 50Hz square wave, its sinus components are at 50, 150, 250 Hz and so on...
So, where does this "second harmonic", or "double freq. component" come from? Ear' s intermodulation distortion?
Cheers,
Bruno |
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| baggystevo82 |
No, I was thinking the ability to hear the pressure waves of both flanks 'more seperately' at low frequencies. By the way it was mostly a 'neat look at this' question, I was just curious as to exactly why. I've got some more coursework to do now, but when I've got time I will try all these ideas out.
Cheers,
Steve |
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| jeff mai |
| quote: | Originally posted by Carondimonio
A perfect square wave has only ODD harmonics. |
Of course this is correct. Don't I feel silly! Oops! :D
Now what? |
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