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What's the frequency resolution of the human ear?

What's the frequency resolution of the human ear?


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I was thinking about audio compression (namely mp3), that "filters" out sound that we would not likely hear.

The MP3 lossy audio data compression algorithm takes advantage of a perceptual limitation of human hearing called auditory masking. from: http://en.wikipedia.org/wiki/MP3

I've also checked the wiki entry for auditory masking, and found this:

If two sounds of two different frequencies are played at the same time, two separate sounds can often be heard rather than a combination tone. The ability to hear frequencies separately is known as frequency resolution or frequency selectivity. When signals are perceived as a combination tone, they are said to reside in the same critical bandwidth.

My question is how much is this critical bandwidth or what's the smallest frequency difference we can perceive as two different tones, if you wish. Let's assume that both tones are equally loud, are coming from the same direction and distance and we are in a quiet room - so basically we eliminate as much noise and affecting phenomenons as possible.

As @ sanchises pointed out (thank you again!) in the comment section the frequency resolution is 3.6Hz between 1 and 2kHz. But since perception threshold is a function of the pitch of the sound I'd assume that the ability to resolve two tones would change with pitch too. Does anybody have any data on that? For example resolution X pitch graph.


The frequency limen, or frequency resolution can be determined in various ways using psychophysical measures. You refer to a simultaneous method, in which two (or more) frequencies are presented at the same time. This has consequences for the test as different frequencies are perceived with different perceived loudness under constant sound pressure levels, meaning that additional cues are present besides pitch cues.

One carefully controlled study Zwicker et al (1957) in this regard defined the critical band basically as "those frequencies where no intensity summation occurs", meaning that adding those frequencies (below or above the center frequency) do not result in differences in loudness perception (as expressed in acoustic threshold of the center frequency). This method nicely prevents loudness summation cues by deploying them in the criterion. This article shows the following picture (after Zwicker et al. (1957)):

The critical band (upper graph) is dependent on frequency, and ranges from 0.1 kHz to >2 kHz.

The markedly lower difference limen of 3.6 Hz as touched upon in the comments may have been obtained using an alternative psychophysical test where the test frequency is modulated by another frequency (bottom graph). This procedure is based on adding a frequency to a certain sinusoidal stimulus, basically resulting in a single stimulus instead of two (or more). This procedure is technically not defined as a critical band and indeed results in a difference limen of ~3.5 hz and up. The other graph plotted in the figure is a masking procedure (middle plot), which basically determines the physiological overlap between frequencies in the cochlea in the intensity domain by determining the amount of masking from one frequency by another.

NB: The authors worked with headphones so no effects of direction.

Reference
Zwicker et al. JASA 1957; 29: 548-57


I think you have already gotten ur question answered. The human auditory system has the resolution of 640 different frequencies, so dividing the hearing frequency range by this you could see the smallest frequency. although the bandwidth is not constant in the whole range (100 for frequencies below 500 Hz and 0.2f for frequencies above 500 Hz). Also, the auditory system of ours has a dynamic resolution of less than 1 dB. hope I got it right :)


Pitch

Sounds may be generally characterized by pitch, loudness, and quality. The perceived pitch of a sound is just the ear's response to frequency, i.e., for most practical purposes the pitch is just the frequency. The pitch perception of the human ear is understood to operate basically by the place theory, with some sharpening mechanism necessary to explain the remarkably high resolution of human pitch perception.

The place theory and its refinements provide plausible models for the perception of the relative pitch of two tones, but do not explain the phenomenon of perfect pitch.

The just noticeable difference in pitch is conveniently expressed in cents, and the standard figure for the human ear is 5 cents.


What happens when the cochlea is damaged?

The cochlea is the main reason that we can hear and the majority of hearing losses in the world are due to damage caused to the cochlea,(sensori-neural). In nearly all cases the patient will struggle with speech discrimination ( “I can hear your voice but you sound like you are muttering”)This is made even worse in the presence of background noise. The fitting of hearing aids will be beneficial, but simply amplifying sounds will not overcome the problems found in the cochlea. We will now look at the various problems within the cochlea.

I am talking here about the various intensities and frequency characteristics of speech. Most people with a cochlea loss will have better hearing in the low frequencies and poor hearing in the high frequencies.So,

VOWELS are low frequency and can be heard,

CONSANANTS are high frequency are less well heard,

Consanants are also quieter than vowels, which increases the difficulties. Background noise is predominately low frequency, which also increases the chances of the quieter, high frequency consonants not being heard by the listener. Nearly all hearing instruments provide greater amplification to high frequency to help the situation. There are also ways of reducing the low frequency performance of a hearing aid ( a vent is a small channel in the earpiece which allows low frequency sound to escape out of the ear)

Loudness Recruitment

People with cochlea damage need a greater level of sound to hear well, but when sounds get louder they become just as intolerant of loud sounds as people with no hearing impairment. As seen in audiometry, this leaves the patient with a reduced dynamic range. This causes problems with speech discrimination, as the dynamic range of speech is about 50dB i.e. a 50dB intensity difference between the loudest and quietest parts of speech. Someone with a reduced dynamic range may not be able to accommodate the whole range of speech, which could become a problem when a hearing aid is fitted.

A hearing instrument with the ability to adjust the amounts of amplification will provide a better option for patients with a reduced dynamic range.Recruitment is found only in patients with cochlea (hair cell) damage. The term “abnormal growth of loudness” is commonly used and relates to patients perception of loudness throughout their dynamic range.

Frequency Resolution

This is the ability of the ear to differentiate between sounds of similar frequencies. Frequency selectivity is very important when dealing with complex sounds, such as speech. A normal hearing ear has the ability to distinguish various frequencies with exceptional accuracy. However when hair cell become damaged this selectivity/resolution becomes less efficient and we then find it difficult to understand what is being said. The active mechanism in this process is the OHC and thus damage to these cells will lead to discrimination problems.

Damage to IHC will reduce the sound getting to the brain and thus increased sound levels are required to overcome the damage. However complete damage of IHC would lead to Dead Regions i.e. a region of hair cells on the basilar membrane no longer working. This is difficult to identify from audiometry as nearby working hair cells will respond to sound of other frequencies. As yet there is no simple clinical procedure for determining the extent of dead regions.

Temporal Resolution

This is the ability of the ear to detect changes over time this involves detecting a short break in a sound, a short sound or a short change in sound. This is imperative for speech discrimination, it stops a voice being one long slur of noise! We also use this to differentiate between speech and background noise. If the intensity and frequency of a sound remains constant, the sound is said to be steady, e.g. a musical note. Noise is also heard as a steady sound even though its waveform is not regular but fluctuates rapidly. However speech is made up of audible gaps and the brain uses this information to hear speech even in the presence of background noise.

A damaged hearing nerve loses its temporal resolution abilities and thus people perceive voices to be slurred or struggle with conversations in background noise. Temporal resolution is not purely a coch.le.a phenomenon the nerve pathway and the brain are involved in the process. Neural or central (brain) disorders can also lead to speech discrimination problems but they are more associated with temporal resolution loss.

Diplacusis

*Patients with unilateral or asymmetrical hearing loss can perceive a single tone differently in each ear. (Diplacusis binauralis)

*Sometimes found in symmetricial hearing losses.

*Can be found in one ear and may be perceived as roughness/impurity to a specific tone or the tone has an additional undertone.(Diplacusic monauralis)

*Causes speech discrimination, which is not easily rectified by the fitting of a hearing aid.

Paracucis

Although not a cochlea disorder, paracusis is a conductive phenomenon, wherby a patient is able to hear well in the presence of background noise. Patients with conductive losses have good cochlea function but reduced hearing threshold. With most speaking voices they hear them quieter in normal listening situations. However in noisy situations the speaker themselves will raise their voices over the background noise.

Hyperacusis

*An intolerance to normal environmental sounds.

*Discomfort from sounds that previously were not comfortable or which other people do not find comfortable.

*Oversensitivity to any sound.

* unlike recruitment, the patient doesn’t have abnormal growth of loudness(even if their dynamic range is reduced, (unless it is due to hair cell damage)


Frequency Weightings - A-Weighted, C-Weighted or Z-Weighted?

The human ear responds more to frequencies between 500 Hz and 8 kHz and is less sensitive to very low-pitch or high-pitch noises. The frequency weightings used in sound level meters are often related to the response of the human ear, to ensure that the meter is measuring pretty much what you actually hear.

It is extremely important that sound level measurements are made using the correct frequency weighting - usually A-weighting. For example, measuring a tonal noise of around 31 Hz could result in a 40 dB error if using C-weighting instead of A-weighting.

A Weighting

The most common weighting that is used in noise measurement is A-Weighting. Like the human ear, this effectively cuts off the lower and higher frequencies that the average person cannot hear.

Defined in the sound level meter standards (IEC 60651, IEC 60804, IEC 61672, ANSI S1.4), a graph of the frequency response can be seen to the right.

A-weighted measurements are expressed as dBA or dB(A).

C Weighting

The response of the human ear varies with the sound level. At higher levels, 100 dB and above, the ear's response is flatter, as shown in the C-Weighted Response to the right.

Although the A-Weighted response is used for most applications, C-Weighting is also available on many sound level meters. C Weighting is usually used for Peak measurements and also in some entertainment noise measurement, where the transmission of bass noise can be a problem.

C-weighted measurements are expressed as dBC or dB(C).

Z Weighting

Z-weighting is a flat frequency response of 10Hz to 20kHz ±1.5dB. This response replaces the older "Linear" or "Unweighted" responses as these did not define the frequency range over which the meter would be linear.

Z-weighted measurements are expressed as dBZ or dB(Z).


What is the precision of the human ear for pitch?

Is the human ear able to disambiguate between 440Hz and 440.01Hz for example?

I found this website a little while back for individual ear training. This test gives you two tones (a base tone followed by one that changes) and you have to determine if the second tone is higher or lower than the first. It's easy at first but the intervals between pitches get smaller and smaller until they sound like almost the same note. Definitely worth giving it a try! (I recommend headphones) http://tonometric.com/adaptivepitch/

When I was in middle school jazz band, the director's ear training exercise consisted of playing two random notes from the chromatic scale on a piano, and then having us write down the interval between them. You can accomplish this either by getting acclimated to each interval's dissonance and consonance and "feeling it out", or by knowing a famous song that opens with that interval, like "Jaws" (minor 2nd) or "The Eyes of Texas are Upon You" (Major 5th).

I got down to 1.5Hz but even at 3Hz they sound nearly identical.

Frequency resolution of the ear is 3.6 Hz within the octave of 1000 – 2000 Hz. That is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting.[5] However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a (low-)frequency difference pitch.

For reference, on a equal temprament A440 scale the frequency for high C (aka soprano C) is 1046.50Hz and C# is 1108.73Hz (62,23Hz difference). 3.6Hz is 1/17 of that difference.


The reality

Classroom exercises on earlobe genetics say that there are two distinct categories, free (F) and attached (A). However, many of the papers on earlobe genetics have pointed out that there are many people with intermediate earlobes (Quelprud 1934, Wiener 1937, Dutta and Ganguly 1965). El Kollali (2009) classified earlobes into three types, based on whether the attachment angle was acute, right, or obtuse. To make the picture above, I searched for pictures of professional bicyclists (because they have short hair), found 12 with their ears showing, and arranged them from free to attached. It doesn't look to me as if there are just two categories instead, there is continuous variation in the height of the attachment point (the "otobasion inferius") relative to the lowest point on the earlobe (the "subaurale"). My own earlobes are exactly halfway in between the two extremes I couldn't tell you whether my earlobes should be considered free or attached.


Building a Novel Regenerative Medicine Platform

We are pioneers of Progenitor Cell Activation (PCA). Similar to stem cells, progenitor cells are pre-programmed to create specific cell types. In the inner ear, for example, they generate the sensory hair cells that enable us to hear.

We believe this approach can be applied to a range of tissues and organs affected by degenerative disease. We’re creating a new class of therapeutics that aims to activate these progenitor cells using small molecules that do not alter genes and which can be delivered with less complexity than current regenerative medicines.


Sharpening of Pitch Perception

The high pitch resolution of the ear suggests that only about a dozen hair cells, or about three tiers from the four banks of cells are associated with each distinguishable pitch. It is hard to conceive of a mechanical resonance of the basilar membrane that sharp. So we look for enhancements of the basic place theory of pitch perception.

There must be some mechanism which sharpens the response curve of the organ of Corti, as suggested schematically in the diagram. Several such mechanisms have been suggested.
Index


Human hearing beats the Fourier uncertainty principle

Each dot represents a subject’s performance on Task 5 (simultaneously measuring the duration and frequency of a sound), with temporal acuity on the x-axis and frequency acuity on the y-axis. All dots within the black rectangle beat the Fourier uncertainty principle. Credit: Oppenheim and Magnasco ©2013 American Physical Society

(Phys.org)—For the first time, physicists have found that humans can discriminate a sound's frequency (related to a note's pitch) and timing (whether a note comes before or after another note) more than 10 times better than the limit imposed by the Fourier uncertainty principle. Not surprisingly, some of the subjects with the best listening precision were musicians, but even non-musicians could exceed the uncertainty limit. The results rule out the majority of auditory processing brain algorithms that have been proposed, since only a few models can match this impressive human performance.

The researchers, Jacob Oppenheim and Marcelo Magnasco at Rockefeller University in New York, have published their study on the first direct test of the Fourier uncertainty principle in human hearing in a recent issue of Physical Review Letters.

The Fourier uncertainty principle states that a time-frequency tradeoff exists for sound signals, so that the shorter the duration of a sound, the larger the spread of different types of frequencies is required to represent the sound. Conversely, sounds with tight clusters of frequencies must have longer durations. The uncertainty principle limits the precision of the simultaneous measurement of the duration and frequency of a sound.

To investigate human hearing in this context, the researchers turned to psychophysics, an area of study that uses various techniques to reveal how physical stimuli affect human sensation. Using physics, these techniques can establish tight bounds on the performance of the senses.

To test how precisely humans can simultaneously measure the duration and frequency of a sound, the researchers asked 12 subjects to perform a series of listening tasks leading up to a final task. In the final task, the subjects were asked to discriminate simultaneously whether a test note was higher or lower in frequency than a leading note that was played before it, and whether the test note appeared before or after a third note, which was discernible due to its much higher frequency.

When a subject correctly discriminated the frequency and timing of a note twice in a row, the difficulty level would increase so that both the difference in frequency between the notes and the time between the notes decreased. When a subject responded incorrectly, the variance would increase to make the task easier.

(a) In task 5, subjects are asked to discriminate simultaneously whether the test note (red) is higher or lower in frequency than the leading note (green), and whether the test note appears before or after the high note (blue). (b) Tasks 1 through 4 lead up to task 5: task 1 is frequency only, task 2 is timing only, task 3 is frequency only but with the high note (blue) as a distractor, and task 4 is timing only, but with the leading (green) note as a distractor. Credit: Oppenheim and Magnasco ©2013 American Physical Society

The researchers tested the subjects with two different types of sounds: Gaussian, characterized by a rise and fall that follows a bell curve shape and note-like, characterized by a rapid rise and a slow exponential decay. According to the uncertainty principle, note-like sounds are more difficult to measure with high precision than Gaussian sounds.

But as it turns out, the subjects could discriminate both types of sounds with equally impressive performance. While some subjects excelled at discriminating frequency, most did much better at discriminating timing. The top score, achieved by a professional musician, violated the uncertainty principle by a factor of about 13, due to equally high precision in frequency acuity and timing acuity. The score with the top timing acuity (3 milliseconds) was achieved by an electronic musician who works in precision sound editing.

The researchers think that this superior human listening ability is partly due to the spiral structure and nonlinearities in the cochlea. Previously, scientists have proven that linear systems cannot exceed the time-frequency uncertainty limit. Although most nonlinear systems do not perform any better, any system that exceeds the uncertainty limit must be nonlinear. For this reason, the nonlinearities in the cochlea are likely integral to the precision of human auditory processing. Since researchers have known for a long time about the cochlea's nonlinearities, the current results are not quite as surprising as they would otherwise be.

"It is and it is not [surprising]," Magnasco told Phys.org. "We were surprised, yet we expected this to happen. The thing is, mathematically the possibility existed all along. There's a theorem that asserts uncertainty is only obeyed by linear operators (like the linear operators of quantum mechanics). Now there's five decades of careful documentation of just how nastily nonlinear the cochlea is, but it is not evident how any of the cochlea's nonlinearities contributes to enhancing time-frequency acuity. We now know our results imply that some of those nonlinearities have the purpose of sharpening acuity beyond the naïve linear limits.

"We were still extremely surprised by how well our subjects did, and particularly surprised by the fact that the biggest gains appear to have been, by and large, in timing. You see, physicists tend to think hearing is spectrum. But spectrum is time-independent, and hearing is about rapid transients. We were just told, by the data, that our brains care a great deal about timing."

The results have implications for how we understand the way that the brain processes sound, a question that has interested scientists for a long time. In the early 1970s, scientists found hints that human hearing could violate the uncertainty principle, but the scientific understanding and technical capabilities were not advanced enough to enable a thorough investigation. As a result, most of today's sound analysis models are based on old theories that may now be revisited in order to capture the precision of human hearing.

"In seminars, I like demonstrating how much information is conveyed in sound by playing the sound from the scene in Casablanca where Ilsa pleads, "Play it once, Sam," Sam feigns ignorance, Ilsa insists," Magnasco said. "You can recognize the text being spoken, but you can also recognize the volume of the utterance, the emotional stance of both speakers, the identity of the speakers including the speaker's accent (Ingrid's faint Swedish, though her character is Norwegian, which I am told Norwegians can distinguish Sam's AAVE [African American Vernacular English]), the distance to the speaker (Ilsa whispers but she's closer, Sam loudly feigns ignorance but he's in the back), the position of the speaker (in your house you know when someone's calling you from another room, in which room they are!), the orientation of the speaker (looking at you or away from you), an impression of the room (large, small, carpeted).

"The issue is that many fields, both basic and commercial, in sound analysis try to reconstruct only one of these, and for that they may use crude models of early hearing that transmit enough information for their purposes. But the problem is that when your analysis is a pipeline, whatever information is lost on a given stage can never be recovered later. So if you try to do very fancy analysis of, let's say, vocal inflections of a lyric soprano, you just cannot do it with cruder models."

By ruling out many of the simpler models of auditory processing, the new results may help guide researchers to identify the true mechanism that underlies human auditory hyperacuity. Understanding this mechanism could have wide-ranging applications in areas such as speech recognition sound analysis and processing and radar, sonar, and radio astronomy.

"You could use fancier methods in radar or sonar to try to analyze details beyond uncertainty, since you control the pinging waveform in fact, bats do," Magnasco said.

Building on the current results, the researchers are now investigating how human hearing is more finely tuned toward natural sounds, and also studying the temporal factor in hearing.

"Such increases in performance cannot occur in general without some assumptions," Magnasco said. "For instance, if you're testing accuracy vs. resolution, you need to assume all signals are well separated. We have indications that the hearing system is highly attuned to the sounds you actually hear in nature, as opposed to abstract time-series this comes under the rubric of 'ecological theories of perception' in which you try to understand the space of natural objects being analyzed in an ecologically relevant setting, and has been hugely successful in vision. Many sounds in nature are produced by an abrupt transfer of energy followed by slow, damped decay, and hence have broken time-reversal symmetry. We just tested that subjects do much better in discriminating timing and frequency in the forward version than in the time-reversed version (manuscript submitted). Therefore the nervous system uses specific information on the physics of sound production to extract information from the sensory stream.

"We are also studying with these same methods the notion of simultaneity of sounds. If we're listening to a flute-piano piece, we will have a distinct perception if the flute 'arrives late' into a phrase and lags the piano, even though flute and piano produce extended sounds, much longer than the accuracy with which we perceive their alignment. In general, for many sounds we have a clear idea of one single 'time' associated to the sound, many times, in our minds, having to do with what action we would take to generate the sound ourselves (strike, blow, etc)."


Brilliance: 6 kHz to 20 kHz

Figure 7 - Brilliance frequency range 6 kHz to 20 kHz

The brilliance range is composed entirely of harmonics and is responsible for sparkle and air of a sound. Boost around 12 kHz makes a recording sound more Hi-Fi.

Be cautious over boosting in this region as it can accentuate hiss and cause ear fatigue.


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