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Thread: why can humans intuitively know when a musical tone frequency is doubled/halved?

  1. #61
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    Quote Originally Posted by Strange View Post
    and then you are into the area of the "reality" thread.)
    Fortunately, that area has been confined!

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    Quote Originally Posted by tashirosgt View Post
    I don't detect that you disagree with my statement. Presumably the cochlea evolved to perform a frequency analysis. Evolution selected that type of mathematical analysis as opposed to different type of mathematical analysis.
    But it is not a maths analysis, it is a neuron excited by a single frequency and transmitted to a brain which interprets it as a pitched note.
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    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
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    Quote Originally Posted by tashirosgt View Post
    I don't detect that you disagree with my statement. Presumably the cochlea evolved to perform a frequency analysis. Evolution selected that type of mathematical analysis as opposed to different type of mathematical analysis.
    I suppose you could say that the cochlea is performing a Fourier analysis. Or you could say that a Fourier analysis is a way of mathematically reproducing the way that physical system works.

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    Quote Originally Posted by tashirosgt View Post
    I don't detect that you disagree with my statement. Presumably the cochlea evolved to perform a frequency analysis. Evolution selected that type of mathematical analysis as opposed to different type of mathematical analysis.
    What other type of mathematical analysis are you thinking of?


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    Quote Originally Posted by profloater View Post
    But it is not a maths analysis, it is a neuron excited by a single frequency and transmitted to a brain which interprets it as a pitched note.
    Are you saying that this is only feasible way to implement a biological hearing system? Remarks to the effect that the architecture of the hearing system archtecture does some sort of frequency analysis are not explanations of why that particular system of analysis evolved. My statement is that it is remarkable that the hearing system evolved to do frequency analysis, which is a mathematical concept. Saying "No, the hearing system does frequency analysis" only contradicts a claim that the hearing system does not do frequency analysis.

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    Quote Originally Posted by Jens View Post
    What other type of mathematical analysis are you thinking of?


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    For the task of recognizing sounds, there are the methods now popular with "big data" - neural networks, support vector machines. If we restrict ourselves to methods that represent a waveform as a sum of other waveforms, there is wavelet analysis. Any family of orthogonal functions could be used to analyze a wave as a sum of other waves.

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    Quote Originally Posted by tashirosgt View Post
    Are you saying that this is only feasible way to implement a biological hearing system? Remarks to the effect that the architecture of the hearing system archtecture does some sort of frequency analysis are not explanations of why that particular system of analysis evolved. My statement is that it is remarkable that the hearing system evolved to do frequency analysis, which is a mathematical concept. Saying "No, the hearing system does frequency analysis" only contradicts a claim that the hearing system does not do frequency analysis.
    The way that our hearing functions is really incredible to think about, but you seem stuck on this idea of something being a "mathematical concept." Speed is a mathematical concept, distance divided by time. And yet we have no problem understanding the speed of an object. Frequency is like that too, it's oscillations per second. And we can feel them. The complicated issue is that the sounds are all superimposed on one another when the oscillations hit our ear drums, so untangling the individual sounds from the single waveform that we can experience is very complex, and you can do it mathematically by using a Fourier transform but our ears actually do the equivalent of a Fourier transform, but mechanically (and then the brain processes it as well, creating things like attention and the "cocktail party effect."
    As above, so below

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    Quote Originally Posted by tashirosgt View Post
    Are you saying that this is only feasible way to implement a biological hearing system? Remarks to the effect that the architecture of the hearing system archtecture does some sort of frequency analysis are not explanations of why that particular system of analysis evolved. My statement is that it is remarkable that the hearing system evolved to do frequency analysis, which is a mathematical concept. Saying "No, the hearing system does frequency analysis" only contradicts a claim that the hearing system does not do frequency analysis.
    No there could be other biological ways, but maths is a higher brain concept, do you think we need maths to identify pain in a toe? Just another neuron map.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by tashirosgt View Post
    For the task of recognizing sounds, there are the methods now popular with "big data" - neural networks, support vector machines. If we restrict ourselves to methods that represent a waveform as a sum of other waveforms, there is wavelet analysis. Any family of orthogonal functions could be used to analyze a wave as a sum of other waves.
    Just to be clear, then, when we say that the brain does a "Fourier transform" it doesn't mean that we are actually doing math. We do something equivalent (get the same result), but not based on a mathematical algorithm like a computer. It begins mechanically. So it would be just as fair to call it "like a wavelet analysis." In the same way, when we run to catch a ball we can predict where it is going to fall, but it's not because we are actually doing differentiation in our brains. Rather, we are doing something approximate that gives a good and similar result, which is why children can sort of do it but imperfectly. If it was just inputting a calculus formula, then we would be able to do it perfectly the first time. A computer can either do or not do an equation. We get better at things, because we are doing approximations based on our experience. And the same goes for sound frequencies. Listen to young children sing.
    As above, so below

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    Quote Originally Posted by Jens View Post
    Just to be clear, then, when we say that the brain does a "Fourier transform" it doesn't mean that we are actually doing math.
    Yes, I agree that the process of hearing does not involve consciously thinking about the mathematics of frequency analysis.

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    Quote Originally Posted by Jens View Post
    Just to be clear, then, when we say that the brain does a "Fourier transform" it doesn't mean that we are actually doing math. We do something equivalent (get the same result), but not based on a mathematical algorithm like a computer. It begins mechanically. So it would be just as fair to call it "like a wavelet analysis." In the same way, when we run to catch a ball we can predict where it is going to fall, but it's not because we are actually doing differentiation in our brains. Rather, we are doing something approximate that gives a good and similar result, which is why children can sort of do it but imperfectly. If it was just inputting a calculus formula, then we would be able to do it perfectly the first time. A computer can either do or not do an equation. We get better at things, because we are doing approximations based on our experience. And the same goes for sound frequencies. Listen to young children sing.
    It may be interesting that catching a ball is a Bayesian prediction in the brain, improved by practice and requiring prediction of the time to get muscles activated as well as the trajectory, While hearing is innate although pitch control to sing in tune is learned in a similar way. We might never learn to catch a ball, if deprived Of practice, but we cannot help hearing . Although even that may be complicated by gateways in the processing.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by plant View Post
    Are there people who don’t perceive this relationship between sound frequency?
    I have this very strange "relationship with music", I love music and listen all the time. I also seem to have perfect pitch when it comes to identifying things that I know, but zero ability to relate such things via musical performance. I can't sing at all. I can usually recognize a song from just one note... even from the middle of the song so long as I have heard it in the past. If I am listening to a radio, I can typically identify the radio station by the "quality" of the broadcast, even if they are transmitting silence. I would call it a "hum" or something, but that isn't right.

    What is truly odd is that I can play a guitar, but not well (it's mechanical, like pressing buttons on a keyboard rather than performing music). What is so odd about this is, I can't tell the difference between a tuned guitar and an untuned guitar. It doesn't sound the same to me, but I can't seem to make the connection between what the tuner tells me and the sound that comes from the instrument or even the relationship between the strings. I have no idea if one is higher or lower than the other. If someone plays a note on one instrument and the same on another, I can't tell if they are the same note. It seems to be a lack of familiarity or expectation that prevents me from making the comparison.
    Solfe

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    Quote Originally Posted by Solfe View Post
    I have this very strange "relationship with music", I love music and listen all the time. I also seem to have perfect pitch when it comes to identifying things that I know, but zero ability to relate such things via musical performance. I can't sing at all. I can usually recognize a song from just one note... even from the middle of the song so long as I have heard it in the past. If I am listening to a radio, I can typically identify the radio station by the "quality" of the broadcast, even if they are transmitting silence. I would call it a "hum" or something, but that isn't right.

    What is truly odd is that I can play a guitar, but not well (it's mechanical, like pressing buttons on a keyboard rather than performing music). What is so odd about this is, I can't tell the difference between a tuned guitar and an untuned guitar. It doesn't sound the same to me, but I can't seem to make the connection between what the tuner tells me and the sound that comes from the instrument or even the relationship between the strings. I have no idea if one is higher or lower than the other. If someone plays a note on one instrument and the same on another, I can't tell if they are the same note. It seems to be a lack of familiarity or expectation that prevents me from making the comparison.
    Your situation is an interesting puzzle. I would need to observe you to see and hear just what you are recognizing and what you are not recognizing. You say you seem to have perfect pitch, but you cannot tell whether or not two different instruments are sounding the same note. It appears to me that you are using "perfect pitch" in a different sense from mine. To me and fellow musicians perfect pitch is short for perfect recognition of absolute pitch. A person with that skill not only is able to tell if two sources are sounding the same note but can accurately identify the note in the standard system of pitch definition. I can do that to some extent with my voice and my horn on certain notes, but I have known musicians who can pick a note out of a cluster of tones and identify it accurately.

    To some extent I can observe from afar. Try listening to the online tone generator here.

    https://www.szynalski.com/tone-generator/

    For starters click on PLAY and then drag the slider back and forth. Let us know if you can hear changes other than just the loudness, which unfortunately varies on this less than perfect generator.

    My hunch is that you can be taught to recognize the attributes you have mentioned, but I cannot be sure because I have know memory of any details of my own learning process. I was exposed to music from infancy and could sing on pitch by age 3 or 4. I don't know what it is like to start learning these skills in adulthood.

    I don't know what you mean by recognizing a song by hearing just one note. If it is a word sung by a singer whose voice you recognize from hearing the song before I can imagine it. If it is a tone sounded on an instrument, with no lyrics, I would not have a chance. It could be from numerous different tunes.

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    Quote Originally Posted by Solfe View Post
    I have this very strange "relationship with music", I love music and listen all the time. I also seem to have perfect pitch when it comes to identifying things that I know, but zero ability to relate such things via musical performance. I can't sing at all. I can usually recognize a song from just one note... even from the middle of the song so long as I have heard it in the past. If I am listening to a radio, I can typically identify the radio station by the "quality" of the broadcast, even if they are transmitting silence. I would call it a "hum" or something, but that isn't right.

    What is truly odd is that I can play a guitar, but not well (it's mechanical, like pressing buttons on a keyboard rather than performing music). What is so odd about this is, I can't tell the difference between a tuned guitar and an untuned guitar. It doesn't sound the same to me, but I can't seem to make the connection between what the tuner tells me and the sound that comes from the instrument or even the relationship between the strings. I have no idea if one is higher or lower than the other. If someone plays a note on one instrument and the same on another, I can't tell if they are the same note. It seems to be a lack of familiarity or expectation that prevents me from making the comparison.
    My daughter organises a community choir and the singing teacher there has achieved remarkable results with people who claim they cannot sing. It seems it’s a combination of good teaching technique and most of all, practice. I am wondering if you are referring to an electronic Guitar tuner which although in pitch will have a completely different harmonic quality than a real guitar string. Guitar players tend to tune by using the fourth or fifth fret of the lower string (depending which string) so that they hear two notes together and when not in tune, as well as sounding discordant , there is a beat frequency. Does that sound Familiar? Recognising a song, in brief snatches, shows you are sensitive to the harmonic patterns but not matching a tuner to a string contradicts that: interesting! When one learns early to sing in tune, we forget how many hours of practice are involved, but once learned it becomes a skill. I used to sing in a choir but cancer of the vocal cords took my voice away for about a year, now I am aware I lost a lot of my skill and must relearn by practice. The brain to muscle link seems to require regular practice.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Hornblower View Post
    Your situation is an interesting puzzle. I would need to observe you to see and hear just what you are recognizing and what you are not recognizing. You say you seem to have perfect pitch, but you cannot tell whether or not two different instruments are sounding the same note. It appears to me that you are using "perfect pitch" in a different sense from mine. To me and fellow musicians perfect pitch is short for perfect recognition of absolute pitch. A person with that skill not only is able to tell if two sources are sounding the same note but can accurately identify the note in the standard system of pitch definition. I can do that to some extent with my voice and my horn on certain notes, but I have known musicians who can pick a note out of a cluster of tones and identify it accurately.

    To some extent I can observe from afar. Try listening to the online tone generator here.

    https://www.szynalski.com/tone-generator/

    For starters click on PLAY and then drag the slider back and forth. Let us know if you can hear changes other than just the loudness, which unfortunately varies on this less than perfect generator.

    My hunch is that you can be taught to recognize the attributes you have mentioned, but I cannot be sure because I have know memory of any details of my own learning process. I was exposed to music from infancy and could sing on pitch by age 3 or 4. I don't know what it is like to start learning these skills in adulthood.

    I don't know what you mean by recognizing a song by hearing just one note. If it is a word sung by a singer whose voice you recognize from hearing the song before I can imagine it. If it is a tone sounded on an instrument, with no lyrics, I would not have a chance. It could be from numerous different tunes.
    I can hear the difference with that webpage. However, I really have no skill or ability to link the words A or C to a particular quality that I hear. If I switch from A to C, I hear a difference, but can't correct identify which is which.

    I am probably using the words "perfect pitch" completely wrong. What I mean by that is if you take a recording, isolate a few notes and play it at me, I am super good at identifying what it is. Sometimes, I can even do it with things that aren't suppose to be in the track, like a cough, a laugh or a background sound. One thing that drives me bonkers is when a recording is supposed to be live, but the sound of the audience is captured elsewhere/when and mixed in. I can hear it immediately. Depeche Mode does this a fair bit, but they seem to be swiping sounds from the same audience and laying them over different sections music. It's super weird hearing the same audience member go "woo!" on three different songs exactly the same way.
    Solfe

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    Quote Originally Posted by profloater View Post
    My daughter organises a community choir and the singing teacher there has achieved remarkable results with people who claim they cannot sing. It seems it’s a combination of good teaching technique and most of all, practice. I am wondering if you are referring to an electronic Guitar tuner which although in pitch will have a completely different harmonic quality than a real guitar string. Guitar players tend to tune by using the fourth or fifth fret of the lower string (depending which string) so that they hear two notes together and when not in tune, as well as sounding discordant , there is a beat frequency. Does that sound Familiar? Recognising a song, in brief snatches, shows you are sensitive to the harmonic patterns but not matching a tuner to a string contradicts that: interesting! When one learns early to sing in tune, we forget how many hours of practice are involved, but once learned it becomes a skill. I used to sing in a choir but cancer of the vocal cords took my voice away for about a year, now I am aware I lost a lot of my skill and must relearn by practice. The brain to muscle link seems to require regular practice.
    I suspect I have some sort of audio processing problem. I work at a school for kids with autism and we have two music teachers. They do this ice breaker thing where they get the kids to clap. I have to fake it, because I cannot clap in time. From my perspective, it seems like they are clapping a rhythm I cannot predict, even though it seems to be completely regular in retrospect.

    I get the same effect from blinking lights and ticking clocks, which is worse because the audio and visual information seems to desync on me. I might see 3 blinks but only hear one tick or the other way around. It seems to be some sort of illusion, as nothing else seems to be affected. It's only when my focus is on the indicator. Out of the corner of my eye, usually the sound and lights are synced. I'm not frozen or in some sort of fugue state, I can move and think and react to other stimuli like trucks.

    Singing goes about as well.
    Solfe

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    Quote Originally Posted by Solfe View Post
    I can hear the difference with that webpage. However, I really have no skill or ability to link the words A or C to a particular quality that I hear. If I switch from A to C, I hear a difference, but can't correct identify which is which. I am probably using the words "perfect pitch" completely wrong.
    Yes, I think you are using it wrong, because your experience (being able to tell the switch from an A to a C but not inherently knowing which is which) is called relative pitch, and it is very common. I am that way, too, and I think the majority of people are. Having perfect pitch means that you can identify a C in isolation, so that if a person plays a C on a piano and you are blindfolded, you can identify the note. Alternatively, there's a joke among musicians that a perfect pitch is when you toss a bagpipe into a dumpster and it lands on a banjo.

    Quote Originally Posted by Solfe View Post
    What I mean by that is if you take a recording, isolate a few notes and play it at me, I am super good at identifying what it is. Sometimes, I can even do it with things that aren't suppose to be in the track, like a cough, a laugh or a background sound. One thing that drives me bonkers is when a recording is supposed to be live, but the sound of the audience is captured elsewhere/when and mixed in. I can hear it immediately. Depeche Mode does this a fair bit, but they seem to be swiping sounds from the same audience and laying them over different sections music. It's super weird hearing the same audience member go "woo!" on three different songs exactly the same way.
    To me that seems to indicate that you have a very good memory (are you also good at remembering the way things look, for example, or the contents of things that people said?).
    As above, so below

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    Quote Originally Posted by Solfe View Post
    I can hear the difference with that webpage. However, I really have no skill or ability to link the words A or C to a particular quality that I hear. If I switch from A to C, I hear a difference, but can't correct identify which is which.

    I am probably using the words "perfect pitch" completely wrong. What I mean by that is if you take a recording, isolate a few notes and play it at me, I am super good at identifying what it is. Sometimes, I can even do it with things that aren't suppose to be in the track, like a cough, a laugh or a background sound. One thing that drives me bonkers is when a recording is supposed to be live, but the sound of the audience is captured elsewhere/when and mixed in. I can hear it immediately. Depeche Mode does this a fair bit, but they seem to be swiping sounds from the same audience and laying them over different sections music. It's super weird hearing the same audience member go "woo!" on three different songs exactly the same way.
    OK, you are hearing the differences. When you move the slider from left to right you are going from what we call a lower note to a higher note. If you click on the field labeled note selector (words appear when you point to it), you will get a table of notes. The ones labeled E2, A2, D3, G3, B3, E4 are the ones sounded by your guitar strings if they are accurately tuned. Expert guitarists will tweak them to get the sweetest sound when sounded in combination.

    It appears that you have good sensitivity, recognition and memory of all sorts of sounds but simply do not have the technical knowledge of the purely musical details. Once again my guess is that can be learned with the help of a suitable instructor. As for the inability to sing, I once heard a voice teacher refer to that as lacking a motor skill needed to adjust the pitch of your voice to match what is coming into your ears. He said that he was usually successful in teaching that skill to diligent pupils who did not already have it.

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    This discussion got me to thinking about something that I personally find a bit mind-blowing. That a plastic disk can have a single groove (in the case of monophonic sound) that drives a needle to move in the vertical plane (for stereo it moves both vertically and horizontally), and that the single groove can encode not only the different harmonics coming from a musical instrument, but the incredibly complex harmonics that come from an orchestra playing together. Granted, we mix them all together and don't clearly hear the individual sounds, but still it's incredible that our brains can tease all those sounds out of that mix.
    As above, so below

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    Quote Originally Posted by Jens View Post
    This discussion got me to thinking about something that I personally find a bit mind-blowing. That a plastic disk can have a single groove (in the case of monophonic sound) that drives a needle to move in the vertical plane (for stereo it moves both vertically and horizontally), and that the single groove can encode not only the different harmonics coming from a musical instrument, but the incredibly complex harmonics that come from an orchestra playing together. Granted, we mix them all together and don't clearly hear the individual sounds, but still it's incredible that our brains can tease all those sounds out of that mix.
    i agree, I remember being amazed that an impact can excite or discover a resonant frequency. In Fourier terms an impact lasting a tiny fraction of a second has all the frequencies in it. Similarly looking at the sea in a harbour, the mix of wavelets contains all the events that have happened but we do not have the right ears to understand those!.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Jens View Post
    This discussion got me to thinking about something that I personally find a bit mind-blowing. That a plastic disk can have a single groove (in the case of monophonic sound) that drives a needle to move in the vertical plane (for stereo it moves both vertically and horizontally), and that the single groove can encode not only the different harmonics coming from a musical instrument, but the incredibly complex harmonics that come from an orchestra playing together. Granted, we mix them all together and don't clearly hear the individual sounds, but still it's incredible that our brains can tease all those sounds out of that mix.
    this is a great video explaining that: https://www.youtube.com/watch?v=umu37m0qUiE
    "It's only a model....?" :-)
    https://www.youtube.com/watch?v=m3dZl3yfGpc

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    Quote Originally Posted by Jens View Post
    This discussion got me to thinking about something that I personally find a bit mind-blowing. That a plastic disk can have a single groove (in the case of monophonic sound) that drives a needle to move in the vertical plane (for stereo it moves both vertically and horizontally), and that the single groove can encode not only the different harmonics coming from a musical instrument, but the incredibly complex harmonics that come from an orchestra playing together. Granted, we mix them all together and don't clearly hear the individual sounds, but still it's incredible that our brains can tease all those sounds out of that mix.
    The groove has a displacement as a function of time which is proportional to that of the electrical signal from the microphone, which in turn is proportional to that of the mixed sound wave that encountered the microphone. When played back through a speaker, the system generates a sound wave that closely matches the original one. Your final remark about the brain teasing the sounds out of the mix is the key point when it comes to miracles. Without that brain capability the mixture might just be an unintelligible dull roar.

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    Just came across this article, which suggests that understanding octaves is cultural (or, at least, an acquired skill rather than innate): https://www.quantamagazine.org/perce...brain-20191030

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    Quote Originally Posted by Strange View Post
    Just came across this article, which suggests that understanding octaves is cultural (or, at least, an acquired skill rather than innate): https://www.quantamagazine.org/perce...brain-20191030
    https://en.wikipedia.org/wiki/Absolu...ch#Linguistics
    Absolute pitch is more common among speakers of tonal languages, such as most dialects of Chinese or Vietnamese, which often depend on pitch variation as the means of distinguishing words that otherwise sound the same...
    ... Among music students of East Asian ethnic heritage, those who speak a tone language very fluently have a much higher prevalence of absolute pitch than those who do not speak a tone language.
    It is possible that African level-tone languages—such as Yoruba,[35] with three pitch levels, and Mambila,[36] with four—may be better suited to study the role of absolute pitch in speech than the pitch and contour tone languages of East Asia.
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