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how many samples per second can the ear differentiate? Ribbon Microphones
Old 30th March 2013
  #1
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jnorman's Avatar
how many samples per second can the ear differentiate?

so, visually, the eye sees anything 24fps or faster as basically continuous, so I guess the eye can probably differentiate individual frames up to a rate of maybe 18-20fps.

we sample most digital audio at 44,100 samples per second, or faster, and the ear hears that as no different than analog sound. how many samples per second can the human ear actually differentiate? 20k? more? less? is there any online example of this effect?
Old 30th March 2013
  #2
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And yes i understand the relationship of sampling rate and frequency i am just asking for example if i play a middle c, how may times per sec would i have to play it before it sounds like a continuous tone? and does the answer vary with higher/lower frequencies?

Sent from my SAMSUNG-SGH-I997
Old 30th March 2013
  #3
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king2070lplaya's Avatar
See if you can program a sampler, you could find out manually :-)
Old 30th March 2013
  #4
You need two samples for every wave to achieve a perfect tone at a minimum. Otherwise it just records distortion. 44.1kHz was just a convenient stopping point to reach the limit of human hearing. A sine wave at 40Hz would sound no different sampled at 80Hz than it would at 192kHz. A440 would require a sample rate of 880Hz or higher.
Old 30th March 2013
  #5
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Quote:
Originally Posted by jnorman View Post
And yes i understand the relationship of sampling rate and frequency i am just asking for example if i play a middle c, how may times per sec would i have to play it before it sounds like a continuous tone? and does the answer vary with higher/lower frequencies?
Since the lower boundary of human hearing is around 20 cps (20 Hz), if you play the C more than about 20 times a second with a steady rhythm, you will start to hear a low tone (if your hearing is average). Below around 20 Hz, you will hear individual rhythmic attacks. As you approach the lower threshold of hearing, the attacks will start to resemble a buzz, and you will hear a low tone. In actuality, I think that for many people, there is a "zone of overlap" somewhere above 20 Hz where the rhythmic pulses are somewhat still detectable and the low tone is becoming audible; it is not an instantaneous transition from one mode of perception to the other.

The frequency, envelope, and timbre of your repeated note will affect the timbre of the low note that you hear above the threshold (basically, your repeated note becomes one iteration or cycle of your new, low waveform). Different timbres and frequencies of your original note will definitely yield markedly different timbres for your new low note.

It is reasonably simple to play with this using any sampler with a wide pitch bend range or a frequency modulation control routing input. Use a speaker with excellent bass extension, of course. Sweep a sawtooth, square, or pulse wave (or any waveform with a defined edge) down past the threshold. If you do so, be aware of speaker tap (the inability of the speaker cone to precisely track the changes in a waveform at instantaneous transitions and very low frequencies, as well as its inefficient damping causing resonance and even essentially echoes down there); the individual clicks and timbre you hear down there will really be cone-specific artifacts and not exactly what the waveform should ideally sound like. Or, sample your piano note, turn it into a short loop (say ten cps; a fast stutter-type piano sound as you might find during a drum break in some dance styles), and swoop the pitch bend up several octaves (if your sampler allows). If your loop starts with ten piano attacks per second, one octave up gets you to 20 Hz, and two octaves up gets you to 40 Hz.

20 Hz is just a rough average of the transition point. I have to listen carefully to rhythms at close to that rate while tuning pianos, and with training and careful listening, I think I can probably hear distinct iterations at a faster rate than the average person. I am guessing that some percussionists can pick them out at a higher frequency than I can. I feel fairly sure that by 40 Hz (one octave above 20 Hz) almost everyone will hear a tone and not rhythm. The zone of overlap (the duality of hearing distinct rhythmic iterations and the hearing the low tone) is over well before then, in my experience.
Old 30th March 2013
  #6
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Originally Posted by rumleymusic View Post
A sine wave at 40Hz would sound no different sampled at 80Hz than it would at 192kHz.
This is only true if the 40 Hz sine wave sampled at 80Hz is played back through a DAC with a reconstruction lowpass filter with a cutoff frequency of about 40 Hz.

When you sample a 40 Hz sine wave at a sampling rate of 80 Hz, you turn it into a square wave (exception: see note below), and as such, it will have a theoretically infinite array of odd-number partials at inverse amplitudes to their partial numbers. That's pretty far removed from sounding like a sine wave.

A steep reconstruction lowpass filter in your DAC with a cutoff frequency at a smidgen above 40 Hz will turn that square wave back into a sine wave.

Joe

Note: if your sampling rate is exactly 80 Hz and your sine wave is exactly 40 Hz, depending on the phase relationship between the two, there is a chance that you will repeatedly sample the sine wave at or near the zero crossing point. If you sample it at the zero crossing point, you will get silence; if you catch it near the zero crossing point, you will get an extremely attenuated square wave.
Old 30th March 2013
  #7
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Quote:
we sample most digital audio at 44,100 samples per second, or faster, and the ear hears that as no different than analog sound.
The ear only hears the analog sound reproduced by the playback system, not the digital samples. The d/a converter outputs a smooth waveform, not a series of steps.
Old 30th March 2013
  #8
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I wonder if the OP may have been intending to ask about the maximum frequency of "clicks" can be resolved by the typical human ear, rather than how many instances of a tone. Regardless, that seems to be the direction that the discussion has taken.

DG

Last edited by dgpretzel; 30th March 2013 at 06:50 AM..
Old 30th March 2013
  #9
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Richard Crowley's Avatar
 

Quote:
Originally Posted by dgpretzel View Post
I wonder if the OP may have been intending to ask about the maximum frequency of "clicks" can be resolved by the typical human ear, rather than how many instances of a tone.
Mr. Norman said exactly that in his second post. Without actually trying it (which would be the ultimate test), one would expect that the more "interruptions" to the pure waveform, the more "distortion" one would perceive while still maintaining the sense of "pitch".
Old 30th March 2013
  #10
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huub's Avatar
Did you already see this D/A and A/D | Digital Show and Tell (Monty Montgomery @ xiph.org) - YouTube video?
Very informative!
Old 30th March 2013
  #11
Quote:
If you sample it at the zero crossing point, you will get silence; if you catch it near the zero crossing point, you will get an extremely attenuated square wave.
A sample at a zero crossing is near impossible with the infinite number of possibilities, about as likely as the world exploding after you blow your nose. Near the zero crossing does not matter, the Nyquist theorem will still allow a perfect reconstruction of that wave, amplitude and all.
Old 30th March 2013
  #12
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Yes, can reconstruct 100%, even with arbitrarily near zero samples, provided the sample is acquired with sufficient precision.

DG
Old 30th March 2013
  #13
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Quote:
Originally Posted by Richard Crowley View Post
Mr. Norman said exactly that in his second post. Without actually trying it (which would be the ultimate test), one would expect that the more "interruptions" to the pure waveform, the more "distortion" one would perceive while still maintaining the sense of "pitch".
Sorry.

Note to self: Avoid late night postings.


DG
Old 30th March 2013
  #14
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Quote:
Originally Posted by JoeDeF View Post
20 Hz is just a rough average of the transition point. I have to listen carefully to rhythms at close to that rate while tuning pianos, and with training and careful listening, I think I can probably hear distinct iterations at a faster rate than the average person. I am guessing that some percussionists can pick them out at a higher frequency than I can. I feel fairly sure that by 40 Hz (one octave above 20 Hz) almost everyone will hear a tone and not rhythm. The zone of overlap (the duality of hearing distinct rhythmic iterations and the hearing the low tone) is over well before then, in my experience.
I would also refer to the Haas effect or principle of precedence, which says that any two related acoustic events separated by 50ms or less will be observed as a single event. What the thread appears to address is the notion of articulation - the ability of the perception system to separate any acoustic stream into separate events. I am impressed tha JoeDeF is able to deliver a personal account that aligns with the above principle in such interesting detail.
Old 31st March 2013
  #15
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Roland's Avatar
Quote:
Originally Posted by huub View Post
Did you already see this D/A and A/D | Digital Show and Tell (Monty Montgomery @ xiph.org) - YouTube video?
Very informative!
Brilliant Video! I lost count of how many audio myths he debunced in 24 mins. Should be required viewing for anyone looking to work in audio.
Old 31st March 2013
  #16
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Quote:
Originally Posted by huub View Post
Did you already see this D/A and A/D | Digital Show and Tell (Monty Montgomery @ xiph.org) - YouTube video?
Very informative!
THIS IS FANTASTIC.

A breath of fresh air.

I have grown so weary of conversations with supposedly technical types (usually when I can't resist responding to some allegation about "jaggedy" digital audio), in which I try and try to persuade, cajole, present equations, etc., to make the point that the output of digital audio is not jaggy or stair-steppy. The weariness is because I cannot recall ever succeeding in this. Most folks are simply convinced that the seemingly "obvious" conclusions are necessarily true.

Wunnerful, wunnerful.

DG
Old 31st March 2013
  #17
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The secret lies in the phrase "reconstruction filter" which most people name "anti-alias filter" (which actually belongs in the analog->digital path), or leave out of the signal path between digital and analog.
Old 31st March 2013
  #18
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...

Last edited by dgpretzel; 31st March 2013 at 09:49 AM.. Reason: Deleted to avoid spurious bunny trail.
Old 31st March 2013
  #19
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Quote:
Originally Posted by rumleymusic View Post
A sample at a zero crossing is near impossible with the infinite number of possibilities, about as likely as the world exploding after you blow your nose. Near the zero crossing does not matter, the Nyquist theorem will still allow a perfect reconstruction of that wave, amplitude and all.
Nyquist doesn't apply. To sample a 40Hz signal accurately you need greater than 80Hz sampling rate, at 80Hz exactly you may get an attenuated signal owing to sampling points not necessarily being near the peak.

Old 31st March 2013
  #20
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Richard Crowley's Avatar
 

Quote:
Originally Posted by jnorman View Post
so, visually, the eye sees anything 24fps or faster as basically continuous, so I guess the eye can probably differentiate individual frames up to a rate of maybe 18-20fps.
But note that even that "standard" is being questioned big-time. People are investing $100M's in production and exhibition equipment to present feature movies at 48FPS because the old 24FPS is too "jerky".
Old 31st March 2013
  #21
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Quote:
Originally Posted by Richard Crowley View Post
But note that even that "standard" is being questioned big-time. People are investing $100M's in production and exhibition equipment to present feature movies at 48FPS because the old 24FPS is too "jerky".
the hobbit was 48fps and a lot of people hated it, said it looked like video
Old 31st March 2013
  #22
Coming back to the original question - one thing that people tend to forget is that the ear actually has an integration time. Meaning, the hearing mechanism is digital, and the output is being interpolated in the brain.

I remember knowing the time segments of human hearing as a student, but would have to look them up again. If I will find it I will write again.
Old 31st March 2013
  #23
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Quote:
Originally Posted by Kesh View Post
the hobbit was 48fps and a lot of people hated it, said it looked like video
IIRC, a lot of people hated "high-fidelity" when it first came on the scene. And then a lot of people (perhaps many of the same) hated stereo.

Motion-blur and strobing and other artifacts have come to be "hallmarks" of feature films and when the experience is made more realistic, people resent change.
Old 1st April 2013
  #24
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boojum's Avatar
Quote:
Originally Posted by Richard Crowley View Post
IIRC, a lot of people hated "high-fidelity" when it first came on the scene. And then a lot of people (perhaps many of the same) hated stereo.

Motion-blur and strobing and other artifacts have come to be "hallmarks" of feature films and when the experience is made more realistic, people resent change.
Analog tape? Feh. Bring back 78's, or better yet, wax cylinders. Now they were the real sound.
Old 1st April 2013
  #25
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The FPS needed for pefect recreation of moving objects depends on several factors but studies have showed up to approx. 80FPS being necessary to avoid artefacts in some situations. A 80FPS capable system is compatible with filmic 24FPS but a standard video system (24-25-30FPS) will suffer from visible artefacts and will be crippled compared to the 80FPS system.

The sample rate needed for perfect recreation of a sonic event also depends on several factors but 44.1kS/s or thereabout is the limit. There are no reliable, repeated studies that indicates more is needed. Reducing sample rate to 32kS/s or so will manifest in audible loss of the upper octave on some sources, for some people.

/Peter
Old 1st April 2013
  #26
Quote:
Nyquist doesn't apply. To sample a 40Hz signal accurately you need greater than 80Hz sampling rate, at 80Hz exactly you may get an attenuated signal owing to sampling points not necessarily being near the peak.
81 Hz then. To avoid the critical frequency.
Old 1st April 2013
  #27
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Quote:
Originally Posted by rumleymusic View Post
81 Hz then. To avoid the critical frequency.
at 81Hz the sampling would work if you had a long length of sample and near perfect interpolation. nyquist's sampling theorem assumes infinitely long samples and perfect (sinc function) interpolation.

i believe the choice of 44.1k was to safely reach 20k while coping with the limitations of actual DACs with post filtering
Old 1st April 2013
  #28
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Quote:
Originally Posted by Kesh View Post
the hobbit was 48fps and a lot of people hated it, said it looked like video
The perception of high tech special effects films is changed in an interesting way when the film is is watched in black and white. Somewhat analogous
to using ribbon mics.
Old 1st April 2013
  #29
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Quote:
Originally Posted by Kesh View Post
at 81Hz the sampling would work if you had a long length of sample and near perfect interpolation. nyquist's sampling theorem assumes infinitely long samples and perfect (sinc function) interpolation.

i believe the choice of 44.1k was to safely reach 20k while coping with the limitations of actual DACs with post filtering
Interesting choice 81 = 3x3x3x3. Maybe 83 would be better as it is a prime number.

The "choice" of 44,100 as a sample rate is not so clear cut. Actually broadcast used 32,000 as (then) they needed only to cover frequencies up to 15kHz, and digital bandwidth was very expensive. For LP mastering (the first real application) a bandwidth of 20kHz or more was desired. Videotape was used as the storage mechanism so sampling rates had to fit in with TV standards.

While commercial systems came with rates of 48kHz or even 50.4kHz, when CD was being developed, playing time was an issue and so the lowest possible sampling rate was sought that could still give a 'flat' bandwidth of 20kHz. Philips (who developed the basic concept of the CD - Sony contributed significantly on work on error correction, not to mention marketing!) chose 44,100 as the rate - possibly because it fitted in with the 625/50 TV system, and because that number is 2x2x3x3x5x5x7x7, ie., the product of the squares of the first four prime numbers, which gave some flexibility in generation of clocks and synchronisation. (Note : as videotape would continue as prime storage for some time, there were some embodiments that used 44,050 as the sampling frequency when used in NTSC systems, owing to the different line frequencies - 15,750 versus 15,625.)


As for DAC capability, there is a funny story regarding Philips DACs. The original specification for the CD was 14-bit resolution, and Philips had already completed design work on high quality 14-bit DAC technology. At the last minute, Sony (Marketing) decided that 16-bit was the required standard. Deciding that they would rather avoid the delay of another design cycle to get 16 bit DACs, Philips found that their 14-bit DAC IC design would work very well at much higher sampling frequencies, like 176,400. Considering that the sample/level product of 44100x16 was the same as 176400x14, they then devised their 'oversampling DAC' configuration which came to be known as "BitStream". It also avoided the need for a sharp cutoff reconstruction filter on the output, and was generally judged to be more euphonious than the SONY 16 bit and sharp-cutoff filter of their early CD players.
Old 2nd April 2013
  #30
Quote:
at 81Hz the sampling would work if you had a long length of sample and near perfect interpolation. nyquist's sampling theorem assumes infinitely long samples and perfect (sinc function) interpolation.
You would also need a sampler that as an 81Hz option to even test it out, I'm fresh out of those. So in this case, it is all a big hypothetical. For a general rule of thumb, I think it is safe to say you just need at least two samples per waveform for it to reconstruct properly, within the limitations of the filters.
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