Why does the brain learn to form a strong connection between some pitches and other pitches like having the internal sense that two notes are a fifth apart?

  • Wasn't the original question: Why do humans have perfect pitch? If not I've read it wrong - so we are getting older ... ;) – Albrecht Hügli Oct 4 '19 at 7:56
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    I deny the question, in that some people do not easily (or at all) develop relative pitch to any accuracy. – Carl Witthoft Oct 4 '19 at 13:17
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    @CarlWitthoft - In these sorts of questions, I think we universally disregard the tone-deaf and others who cannot acquire relative pitch. – Dekkadeci Oct 4 '19 at 16:26
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    @StefanH I think there was no evolutionary advantage at all. It's far easier for evolution to create a brain that can develop that sense than a brain that can't. The brain notices a pattern that sinusoidal waves of a certain frequency regularly go with sinousoidal waves of double and triple that frequency. Only sinousoidal waves are registered as exactly one pitch. Any continuous periodic function can be expressed as an infinite sum of sinousoidal waves that are a multiple the frequency of the function. Waves of 5 and 7 times the frequency can be very closely approximated by repeated taking of – Timothy Jun 15 at 23:13
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    fifths and octaves so the bran doesn't put any thought into them. The brain is very adaptable. If we were in a place where we only ever hear a sound wave that is composed of a sinousoidal wave of base frequency and ones that are a fifth, sixth, and seventh root of 2 times higher and it keeps continuously going up and down with time, we might develop another sense of sound while we're there and actually hear a note that's a 210th higher than another note as being gotten from it by repeated multiplication or division of fifth roots, sixth roots, and seventh roots of 2. – Timothy Jun 15 at 23:22

The reason why we are able to learn relative pitch is found in psychoacoustics.

In order to make sense of the jumble of frequencies that reaches our ear we are able to group certain frequencies and assign them to a single sound source. Our brains use a certain physical property of all natural (harmonic) sounds: that they consist of a certain base frequency and a set of frequencies based on that frequency following the harmonic series. In this way our brain has evolved to use the harmonic series as a filter to distinguish sound sources from each other.

The abstract of this paper gives a better description of what happens: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2885481/

Harmonic complex tones are a particularly important class of sounds found in both speech and music. Although these sounds contain multiple frequency components, they are usually perceived as a coherent whole, with a pitch corresponding to the fundamental frequency (F0). However, when two or more harmonic sounds occur concurrently, e.g., at a cocktail party or in a symphony, the auditory system must separate harmonics and assign them to their respective F0s so that a coherent and veridical representation of the different sounds sources is formed.

So, our brain is already wired to compare frequencies and especially the frequencies of the harmonic series.

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  • Well, that appears to explain the ability to separate patterns but it's not clear that it explains the ability to identify (or tune your instrument to) precise harmonic ratios. – Carl Witthoft Oct 4 '19 at 13:18
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    I like that this answer does go into detail on the origins/purpose of relative pitch on a very basic level (speech comprehension, auditory perception). +1 – user45266 Oct 4 '19 at 17:18
  • There was a YouTube video of somebody hearing for the first time at the age of 29 at youtube.com/watch?v=LsOo3jzkhYA. I don't think she would have been able sense fifths right when she first started being able to hear. I think the ability to sense it comes from the brain noticing patterns in the first harmonic, second harmonic, and third harmonic always going together what ever the base frequency is. I don't think we would form it if the only sound we ever heard were sinusoidal either. – Timothy Oct 4 '19 at 17:48
  • I believe that if you never heard anything before, your brain wouldn't have the instinctive ability to sense octaves and fifths. I believe a sinusoidal wave actually registers as exactly one pitch in the ear. I believe the ability to sense fifths and octaves comes from the brain learning by hearing that pitches a fifth apart are heard together when they're the second and third harmonic and ones that are an octave apart are heard together when they're the first and second harmonic. Because of the law of an exponential of a sum, a translation transformation on pitches still preserves properties – Timothy Oct 7 '19 at 4:53
  • such as the property of being a fifth apart. Now the perception of absolute pitch is a totally undescribable detail so in most people, the ability to consciously recall it is lost after enough time goes by. However, I developed absolute pitch to some extent while I was about 30. It just came without any training. Quite frequently, I play a song I heard before at a pitch that's less than a semitone off. Before I developed absolute pitch, I didn't define it as forgetting the pitch. I defined it as not even being consciously aware of which pitch I'm actually hearing in the first place. – Timothy Oct 7 '19 at 4:59

Why do humans have relative pitch?

I think relative pitch comes with the fact that we are able to recognize certain intervals, which then ties to the question of "why do humans need to be able to hear intervals?".

Intervals base the foundation of music with melody and harmony. One idea of why music exists in the first place, in terms of evolution, is so humans can more aptly socialize with each other. And the humans that can't recognize music are rejected from tribes, etc.

Therefore, relative pitch is more of a "side effect" of humans evolving with music. Pitches are also calculated from hairs in the ear which resonate at certain frequencies. The brain then learns about these intervals.

Why does the brain learn to form a strong connection between some pitches

This part is more cultural, European music puts emphasis on the 12 tone intervals. You can recognize these pitches because you've had more practise identifying pitches (E.g. perfect fifth). Enough practice with a more rare interval like natural third will yield similar "connections".

Your idea.

Your idea should be part of your question.

I also noticed from my own senses that what really sounds like an F sharp is a tiny bit higher than what really sounds like a G flat.

This depends on your system of tuning. Also in most tuning systems where the pitch of G-flat isn't the same as the pitch of F-sharp, F-sharp is generally lower (not higher).

... that is log of the frequency, then a B and a C

I'm not sure what you mean here but, yes, the relationship between cents and frequency is logarithmic

The brain adapts and starts noticing a pattern in what's entering the ear.

Are you really trying to ask "How does relative pitch work" vs "Why do humans have relative pitch?". Ask a new question if you meant the former.

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  • I understand the actual answer is here: "relative pitch is more of a "side effect" of humans evolving with music". Do you have any sources to support this? I'm thinking music wouldn't be created if most people didn't already have some relative pitch in the first place. So there must be some other evolutionary advantage of having relative pitch prior to the creation of music. – coconochao Oct 4 '19 at 17:14
  • @coconochao I never really said exactly how relative pitch came around but more of why it turned out to be a useful trait. Mainly because there's too many theories to pick from. Search up "Evolutionary musicology" and you'll find dozens. – Vitulus Oct 4 '19 at 22:39
  • Whether an F sharp is sharper or flatter than a G flat depends on the context. It is typical on a violin that if you play a melodic line where there is an F sharp which works as a leading tone leading to G the violinist will play a very sharp F sharp. But if he plays the third in a sustained D-major chord he will intonate the F sharp so it fits the chord which means a flatter F sharp compared with the leading tone. – Lars Peter Schultz Oct 6 '19 at 21:34
  • @LarsPeterSchultz You're right but I just shortened that explnanation to tuning systems - because generally the F# is lower than the Gb. Also, with stringed instruments I always feel the need to play higher for leading notes - so I agree with you with that. But some say that you should player lower, and for just intonation the major seventh is generally 12 cents lower than the equal temperament. I can't really find any specific infomation online about playing the note higher which is confusing because it is a thing in stringed instruments. – Vitulus Oct 6 '19 at 22:06
  • @Vitulus My point is: relative pitch woudn't have come around if it wasn't useful. It's kind of the same question, because if it wasn't useful when it eventually came around, then it would have faded. I think the evolutionary musicology would be the better way to go in the answer, or maybe include something about it if you want. Anyway, I got your point, I'm upvoting it. – coconochao Oct 7 '19 at 16:46

Because there is a mathematical relationship between frequencies, arising from the harmonic series. This is what causes certain intervals to sound "related".

It works out that (from the harmonic series) a fifth corresponds to multiplying frequency by 3/2 (i.e. the 3rd harmonic lowered by an octave), a major third to 5/4 (5th harmonic lowered by two octaves). (In fact we generally use a slightly compromised version of these numbers to allow us to play chromatically in different keys, but they are very close.)

If you have a guitar you can demonstrate this to yourself by playing up through the harmonics and listening to the pitches produced. It's a useful exercise.

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    this answer doesn't explain why would these mathematical relationships would be relevant at all for our brains. Why would it be useful, to identify these intervals as related? I think this is what the question is about. – coconochao Oct 4 '19 at 17:04

It would be much easier to answer to the question: Why do most people not have perfect pitch?

The question you're asking can be compared with: Why do some people see colours and some not?

Somehow we are all "blind" when we are born - concerning relative pitch and learning to differ sounds in a melody - and we have to learn to "see" (or hear, better listen) like we learn to see in 3 dimensions.

I would pretend: Human don't have relative pitch, a few have perfect pitch - like most of us can see and differentiate colors.

So we have to learn the relative pitch like we learn the mother language. But if our mother and parents don't sing with us baby songs and we are not taught an instrument - also playing autodidactical (self-educated) - most of us don't have relative pitch get laid in the cradle - we have to learn relative pitch like the grammar of a foreign language. And this is a long and hard way to go.

If we have grown up with music and baby songs and other songs it will be much easier to learn the relative pitch as the basic function to this have already been formed.

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I don't actually know the answer to that question so I will just make a guess. Actually the following is a simplifying approximation of my real guess.

I learned that when you go up an octave, the frequency doubles and when the frequency multiplies by three halves, the pitch goes up by what you hear as a fifth.

I also noticed from my own senses that what really sounds like an F sharp is a tiny bit higher than what really sounds like a G flat. The mathematics indeed supports that observation. It can be proven using the math alone without reliance on hearing that an F sharp is a tiny bit higher than a G flat but a lot closer together in pitch, that is log of the frequency, then a B and a C.

A sinusoidal sound wave registers as only one pitch in the ear. When you hear a note with a well defined pitch, it's nearly a repeating sound wave and that can be expressed as an infinite sum of sinusoidal sound waves each of which has a frequency that's a multiple of the frequency of the original sound wave.

The brain adapts and starts noticing a pattern in what's entering the ear. Whenever the first harmonic is a certain pitch, the second and third harmonics will always be a pitch corresponding to double and triple the frequency. It registers two notes as being a fifth apart because those pitches are heard together all the time.

Since the log of 3 to the base 2 is irrational, you can get arbitrarily close to any pitch from a given pitch just by multiply and dividing by 2 or 3. The brain doesn't devote much attention to changes in a factor of 5. Actually, I think a change in frequency by a factor of 5/4 can be misheard as a third but it really isn't. It just differs from one by a factor of 81/80.

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    This should probably be part of your question, not an answer. – Your Uncle Bob Oct 4 '19 at 2:13
  • @YourUncleBob I wasn't sure anybody else was going to be able to answer this question. I also said at the beginning of this answer that it was all just my guess. I thought maybe it was better to write that in an answer than in the question because then I wouldn't have to worry that it can't be answered because I answered it. A lot of what I wrote in my answer to math.stackexchange.com/questions/3102944/…, I originally wrote in the question. After I fixed up the question to be very similar to the way it's – Timothy Oct 7 '19 at 20:53
  • currently written, I voted to reopen it and it got reopened then I answered it and my answer got an upvote. Do you think I should delete this answer because it doesn't add anything to the other answers? Also, can you tell me what you think of this comment before I delete this answer? – Timothy Oct 7 '19 at 20:54

The natural speaking pitch for every speaker is different (and may be different depending on time of day and other variables), inflection is relative to that pitch. Music is processed by the same complex hearing apparatus that has evolved to deal with speech (among other noises with natural pitch relations). Having to employ absolute pitch in order to be understood would be a nightmare for speakers.

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  • I downvoted this answer because it doesn't answer the question. Saying we have relative pitch is not another way of saying we don't have absolute pitch although they're both true for almost everybody. I wasn't asking why we don't have absolute pitch. I was asking why we do have relative pitch which means the ability to sense how far apart different notes are when we hear them close together in time. Maybe part of the answer did answer the questions when you hinted that we evolved relative pitch to hear speech. I think that actually what was selected for was to have relative pitch to some – Timothy Oct 7 '19 at 4:37
  • extent, but the brain is too good and so it can gain abilities there was no evolutionary advantage for, such as the ability to sense fifths. That's probably because those two frequencies actually go together when they're the second harmonic and third harmonic of a sound with a lower frequency so the brain learns that it keeps on over and over hearing pitches that are a fifth apart going together. – Timothy Oct 7 '19 at 4:41

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