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How many cycles of a certain frequency does the ear need to receive to detect it?

Ron Texas

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#4
Interesting question, but how does it relate to audio gear design?
 
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#5
REW gives us the option to add a frequency dependent window, but my question is how many cycles it takes to understand a certain frequency, assuming this number of cycles is different between frequencies? Or is it the same? If so, how many cycles?
 

PaulD

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#6
It's an interesting question... I do not have an exact answer, but there are a few things we know. The basilar membrane is most easily displaced in the middle (detecting frequency is displacement of the basilar membrane in the cochlea), so I would expect the middle frequencies to more rapidly displace the basilar membrane. At the ends the basilar membrane is much more difficult to displace so perhaps more cycles would be needed to do that (i.e. at the frequency extremes).

The period of 1kHz is 1mS. Human reaction time is usually quoted at around 0.15-0.2S. If we are VERY optimistic and say that the best reaction time to detect a frequency is about half of that (let's go further by rounding it down, best case 0.05S) then we have around 50 cycles at 1KHz.

I have not thought this through or backed it by measurement or research, it's just off the top of my head over breakfast (so may be wildly inaccurate BS). I would expect actual measurements to give a lot of interesting insight.
 

RayDunzl

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#7
REW gives us the option to add a frequency dependent window, but my question is how many cycles it takes to understand a certain frequency, assuming this number of cycles is different between frequencies? Or is it the same? If so, how many cycles?
Audacity allows you to create WAV files of tone types with which to experiment to satisfy your curiosity.
 
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Wombat

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#8
Yep, record and listen to samples of a wide range of frequencies containing, consecutively, increasing multiples of cycles until the question is answered.
 

RayDunzl

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#9
To put a little context...

In 4/4 time, at 120 beats per minute, a 32nd note would occupy a time space of about 15 milliseconds.

Using 1000Hz, that's 15 cycles, and is recognizable for pitch. shorter, for me, it starts sounding like a click with some pitch to it.

https://www.guitarmasterclass.net/ls/32nd-Note-Madness/
 

Kal Rubinson

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#10
It's an interesting question... I do not have an exact answer, but there are a few things we know. The basilar membrane is most easily displaced in the middle (detecting frequency is displacement of the basilar membrane in the cochlea), so I would expect the middle frequencies to more rapidly displace the basilar membrane. At the ends the basilar membrane is much more difficult to displace so perhaps more cycles would be needed to do that (i.e. at the frequency extremes).
Well, the entering energy displaces the basilar membrane directly at the base (where high frequencies are detected) and migrates, as a travelling wave to the apex (where low frequencies are detected). The difficulty/efficiency of displacement is frequency-dependent but I do not know of any data which correlates the difficulty/efficiency of physical displacement with signal sensitivity. If anything, I'd suspect that the vulnerability of HF haircells to intense and/or repetitive high levels, compared to those for lower frequencies, suggests that basal turn is easier to displace.

Not an answer to the original question but I ain't got one. ;)
 

JohnYang1997

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#11
I'll give you a hint. Small cycles of sine can be seen as pulse. Ideal pulse covers all frequencies. Hence the "played frequency" is not real and what matters is the level of the "pulse". If it's a pulse, if it's loud enough, no matter how short it is we will hear it, along with the tail. Or i can say we perceive the impulse response of the whole system from the source (speaker or clap or anything like that) to the environment( reflection reverberation) to our body, ear canal, eardrum etc.
 

Blumlein 88

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#13
Simple minded experiment. Made a 5 second track with high level, but non clipping tone of 100 milliseconds at 1 khz. Sounds like short loud tone. 50 milliseconds sounded like short tone. 25 milliseconds sounded like a slight tick like the dust tick on an LP. Using square instead of sine waves made it much louder and more tone like. But again at 25 milliseconds sounded like a tick.

I created a 25 millisecond tone, 25 milliseconds of silence and another 25 milliseconds of tone, and it sound like a tone again. Extending the in between silence to 100 milliseconds didn't much change the sound as you heard a tone. At 125 milliseconds it varied from trial to trial with sometims a tone, and sometimes a tick followed by a shorter tone sound. This behavior was the same until a gap of 250 milliseconds between the two 25 millisecond tones. I didn't try any larger gaps.

If you try this yourself, mix in some low level (-90 db) noise as some DACs turn off on pure silence and may not turn on fast enough to hear anything. So the answer is less than 100 milliseconds for sure.
 

Blumlein 88

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#14
Continuing the above experiment, at 3 khz a tone was clearly heard at 4 milliseconds and at 2 milliseconds it was still somewhat tone like.

At 300 hz at 25 milliseconds it sound like a low frequency bump, like if you bumped a tone arm on an LP rig. At 100 milliseconds it began to sound tone like. It was only at 150 milliseconds it sounded like a short tone.
 
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#15
I can only share ,my own personal experience with short times of tones. A six cycle burst (limited by a hamming window to minimize out of band energy) is pretty easy to identify up to your limits of hearing. Single cycle burst can be identified most easily in the mid-band. For a single cycle, though, do not use a sine wave due to the high amounts of out of band energy JohnYang1997 mentioned. In this case, use a raised cosine. In the case of a single cycle of raised cosine, I can "hear" 4kHz and 5kHz signals, I can identify that they are high pitched, but I can't tell which is higher.
 
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#16
Blumlein, you were creating the masking effect with 100 Ms separation. Increasing the separation to 500 Ms will have the effect of increasing the alertness for the second sound with some learning trials and will help to determine the actual recognition capacity.
 
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