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

[plant]

It is not obvious to me why a musical note- lets say “C” sounds ‘the same’ as a frequency double or half.
This doesn’t occur with vision ( except that a ‘color wheel’ seems continuous with violet seeming to nicely shift back into red. )
Presumably this encoding is ‘accidental’ from an evolutionary perspective?
Are there people who don’t perceive this relationship between sound frequency?
Is there any evidence that other mammals e.g. dolphins/whales/ apes perceive intervals differently?
One could imagine an experiment where a ‘reward’ is given when 2 tones are played with multiples of the same frequency etc.

It seems the notion of ‘harmony’ might be a cultural phenomenon rather than a biological one.. but the perception of ‘an octave’ seems biological?

Does anyone have any thoughts about this?

[Jens]

It's a good question, and I don't know the answer. I don't think it's really accidental, I think it's more that music tone is something that is important to us as animals that rely on communication, and so we are sensitive to it. We also, as you noted, perceive a special relationship with thirds and fifths (particularly fifths), which are 3/2 of the base note. So there's a mathematical relationship there that we hear, I guess that the two notes vibrate in a frequency that has them returning together every 3 / 2 cycles. It may be that songbirds, for example, are quite sensitive to the same thing, while animals that don't sing don't perceive a doubling of frequency as an octave (sounding the same).

[DaveC426913]

I would think its because - with the exception of electronic instruments - I think musical instruments pretty much always have harmonic multiples in them.
The octaves are there, to be heard - not interpreted in the mind.

That's not a very informative answer - but maybe someone can riff off it.

[Jens]

I would think its because - with the exception of electronic instruments - I think musical instruments pretty much always have harmonic multiples in them.
The octaves are there, to be heard - not interpreted in the mind.

What you say is true, but the question seems to be, why do we perceive a doubling or halving of the frequency as the same note, just higher or lower? It's not intuitive, as they really are not the same note. It's just (I think) that every two beats, they coordinate, and somehow we perceive that as being the same note.

[plant]

I would think its because - with the exception of electronic instruments - I think musical instruments pretty much always have harmonic multiples in them.
The octaves are there, to be heard - not interpreted in the mind.

That's not a very informative answer - but maybe someone can riff off it.

I don’t think the octaves are there to be heard... why are there no colour octaves?
Clearly some part or parts of the organ of corti, thalamus or auditory cortex map inputs of frequency that are whole number multiples into the ‘same’ output perceived as the qualia of ‘octave’.
I wonder how this processing is accomplished and where it is happening in the brain.
I wonder what sort of ‘neural network’ could analyse every possible audible tone, compare it with another tone occurring either simultaneously (maybe detection of absence of beat frequencies ?) or separated by brief time intervals.... and work out to a very very precise degree (how precise?) whether the two tones are separated by a whole number of mulltiples of the base frequency.
It seems like an unusual task that could have no evolutionary advantage... unless it saves processing power??
I assume that perception of rhythm is required in the human body for locomotion, and speech- and one could imagine that these (cerebellar/ extrapyramidal) structures could lead to the development of rhythmic but atonal ‘music.’
I suppose musical ‘tone’ is really just ‘rhythm’ sped up a few orders of magnitude but i think the systems for dealing with each are different. At some point, rhythm becomes tone.
I’d compare this to how our bodies sense radiant infra-red light as heat via cutaneous receptors vs visible light from our retinas.

https://youtu.be/h3kqBX1j7f8

[profloater]

The why question is hard the how question is easier. The physics of sound vibrations and the way the ear picks them up with a shaped receiver and tiny hairs that vibrate is well known and can be visualised with strings and pendulums. The perception of pitch has a learned part, different cultures have built different scales or pitch intervals. The octave may be common as all those harmonics have physical manifestations. Most animals, even close relatives to us , do not exhibit pitch awareness nor rhythm. All of music seems to have a human speciality, much of it acquired culturally. My guess is that it is a big brain feature linked to social skills and tribal living, bonding, followship and all that stuff which made humans so successful as survivors in changing times. Why the octave or other harmonics sound they way they do to us is much harder, like asking why we see red as red, but we have sensation for all the harmonics as qualites, we hear them in speech too and respond psychologically to voices mixed pitches as alarm, friendly, commanding and so on. This supports the social role of hearing as a group living skill. Singing in pitch is literally group harmony. The octaves link puople with deep and shrill voices.

[Noclevername]

It is not obvious to me why a musical note- lets say “C” sounds ‘the same’ as a frequency double or half.
This doesn’t occur with vision ( except that a ‘color wheel’ seems continuous with violet seeming to nicely shift back into red. )
Presumably this encoding is ‘accidental’ from an evolutionary perspective?
Are there people who don’t perceive this relationship between sound frequency?
Is there any evidence that other mammals e.g. dolphins/whales/ apes perceive intervals differently?
One could imagine an experiment where a ‘reward’ is given when 2 tones are played with multiples of the same frequency etc.

It seems the notion of ‘harmony’ might be a cultural phenomenon rather than a biological one.. but the perception of ‘an octave’ seems biological?

Does anyone have any thoughts about this?

Some people are tone deaf, can they really hear that distinction? Does it require perfect pitch?

[Jens]

It seems the notion of ‘harmony’ might be a cultural phenomenon rather than a biological one.. but the perception of ‘an octave’ seems biological?

I think they are probably similar, in the sense that an octave is a special case of a harmony. I think we perceive them as special because of the way the tones interact, and an octave is probably simply more similar than say a fifth, which is why we (I think most cultures use fifths) perceive a fifth as pleasant yet different, while an octave is perceived as the same. Maybe?

[Jens]

Or adding to my own explanation, suppose that we perceive sound as if we were watching runners go around a track. A runner going twice as fast will cross the finish line at the same time as the skier counterpart, but going faster. While other speeds will not. A person running a fifth faster will create a pattern where they are sometimes in step, and perhaps that causes the sensation of harmony.


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[Hornblower]

I have encountered at least one person who did not recognize the similarity of two notes an octave apart. She was a soprano in our church choir. She could sing along with another soprano or with a piano sounding the same pitch, but when I tried to help her with a tricky passage by singing it an octave lower, she was unable to follow in her range. I don't know whether or not anyone else in the choir had similar difficulty.

[John Mendenhall]

The Wiki article on 'pitch' is here:

https://en.wikipedia.org/wiki/Pitch_(music)

[glappkaeft]

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

When someone ask a why question I always ask myself if the statement is true. I'm far from convinced this is true and is not just a product of growing up in a western culture (and granted many others). Octave equivalence (wiki) (i.e. notes separated by an octave sound alike) is not universal across cultures and have not been true across the ages either. There is a good reason why it is common however, many of the harmonics are identical when comparing two tones separated by an octave if played on actual instruments.

[grant hutchison]

It's all down to the medial geniculate nucleus, which sits in the thalamus on the auditory pathway, and which "collapses" incoming signals separated by octave multiples into similar output. It's not unique to humans - trained rhesus monkeys match pitch chroma in the same way.
The evolutionary Just So story is that complex harmonic sounds, like animal calls and human vowel sounds, easily become ambiguous in pitch, by an octave, if some of the odd-number harmonics are attenuated. So collapsing even-numbered harmonics so that they're perceived as "the same tone" undoes that potential signalling problem.

Grant Hutchison

[Jens]

I have encountered at least one person who did not recognize the similarity of two notes an octave apart. She was a soprano in our church choir. She could sing along with another soprano or with a piano sounding the same pitch, but when I tried to help her with a tricky passage by singing it an octave lower, she was unable to follow in her range. I don't know whether or not anyone else in the choir had similar difficulty.

I can understand, but I’m not sure the analysis is right. I sing in a band, and when the guitar player is playing it’s very easy for me to get the right notes, but sometimes if it’s only the bass playing I have trouble making out the notes. It might be that lower notes are inherently harder to make out.


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[Hornblower]

The Wiki article mentioned octave ambiguity, in which with some tones we can tell if two tones are some multiple of an octave apart but cannot tell for sure how many. I have noticed it with such things as aircraft engines and propellers.I think it depends on the harmonic spectral structure. This video aboard a Super Constellation is an example:
https://www.youtube.com/watch?v=hrdDX5t-KSM
During takeoff the drone sounds like the C an octave below middle C on a piano, but the fundamental frequency of the blades on each propeller is an octave lower. With four engines the synchronization could have something to do with it, but I have noticed the same effect when starting up a large C-130 turboprop, with the first engine run up to close to cruising RPM before starting the next engine. Apparently the props generate a strong octave overtone. Another curious tone can be heard with this Electra, with the same engines and props as an early C-130.
https://www.youtube.com/watch?v=tvFTBXibiLA
Just before going to full power there was an audible whine either three or four octaves above the propeller drone fundamental pitch. I could not tell for sure which it was, even when I whistled the note and compared it with the piano. I may try looking at the waveform with an oscilloscope.

[John Mendenhall]

It's all down to the medial geniculate nucleus, which sits in the thalamus on the auditory pathway, and which "collapses" incoming signals separated by octave multiples into similar output. It's not unique to humans - trained rhesus monkeys match pitch chroma in the same way.
The evolutionary Just So story is that complex harmonic sounds, like animal calls and human vowel sounds, easily become ambiguous in pitch, by an octave, if some of the odd-number harmonics are attenuated. So collapsing even-numbered harmonics so that they're perceived as "the same tone" undoes that potential signalling problem.

Grant Hutchison

Thank, Grant. I get it now. Adaptive! Duh-uh. Of course!

Regards, John M.

[Jens]

This doesn’t occur with vision ( except that a ‘color wheel’ seems continuous with violet seeming to nicely shift back into red. )

I also wanted to respond to this, because people sometimes bring up light. I'll be happy to be corrected, but I think that the phenomena are so different that it's really difficult to make a comparison. First, light is transverse waves, and without a medium, even without mass, so there is no way for us to "feel" light (except for the interaction between photons and electrons), whereas with sound the air is the medium so we can definitely feel the vibrations themselves (if you go to a rock concert you can very distinctly feel the vibrations in the air, especially from bass or bass drums). And also, the difference in the frequency is vastly different, like a trillion times different, so while we can subjectively perceive the frequency of sound (especially with low notes, you can count the hertz), but when it's a trillion vibrations per second there isn't any way that we could possibly feel whether one photon is vibrating faster than another by counting or something like that (even subconsciously, I mean).

[Hornblower]

I also wanted to respond to this, because people sometimes bring up light. I'll be happy to be corrected, but I think that the phenomena are so different that it's really difficult to make a comparison. First, light is transverse waves, and without a medium, even without mass, so there is no way for us to "feel" light (except for the interaction between photons and electrons), whereas with sound the air is the medium so we can definitely feel the vibrations themselves (if you go to a rock concert you can very distinctly feel the vibrations in the air, especially from bass or bass drums). And also, the difference in the frequency is vastly different, like a trillion times different, so while we can subjectively perceive the frequency of sound (especially with low notes, you can count the hertz), but when it's a trillion vibrations per second there isn't any way that we could possibly feel whether one photon is vibrating faster than another by counting or something like that (even subconsciously, I mean).

I don't think the the fact that light waves are transverse and massless is significant. Sound waves and light waves induce equivalent nerve impulses that go from the respective receptors to the brain. They go to different parts of the brain that interpret them in different ways.

[plant]

I also wanted to respond to this, because people sometimes bring up light. I'll be happy to be corrected, but I think that the phenomena are so different that it's really difficult to make a comparison. First, light is transverse waves, and without a medium, even without mass, so there is no way for us to "feel" light (except for the interaction between photons and electrons), whereas with sound the air is the medium so we can definitely feel the vibrations themselves (if you go to a rock concert you can very distinctly feel the vibrations in the air, especially from bass or bass drums). And also, the difference in the frequency is vastly different, like a trillion times different, so while we can subjectively perceive the frequency of sound (especially with low notes, you can count the hertz), but when it's a trillion vibrations per second there isn't any way that we could possibly feel whether one photon is vibrating faster than another by counting or something like that (even subconsciously, I mean).

Certainly you can 'feel' certain percussive sounds, and 'tones' below a certain frequency if loud enough as vibrations in the body but this is not 'hearing'.
Deaf people can drum, and experience rhythm- and low frequency infra-sound.
In any case i doubt that a 3Hz 'feeling' feels somehow 'similar' in an octave-type way to 6Hz.
At 20Hz , rhythm changes into tone.

https://en.wikipedia.org/wiki/Perception_of_infrasound

[plant]

Try this online tone generator.
Set wave to 'square wave'.
If you drop frequency below about 20 (for me)... there is no real discernable drop in pitch.
Below 10 and the individual clicks become definitely rhythmic (to me).
3Hz doesn't feel similar to 6Hz
But 40Hz sounds similar (octavy) to 80Hz
You can open up multiple windows and test it.

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

[grant hutchison]

The Shepard-Risset glissando (YouTube link) is a musical illusion built on the the circularity of pitch, which I find deeply unsettling. The apparent pitch in the linked video "rises" continuously for a minute, and then "falls" for the same time period. It could, of course keep "rising" or "falling" for ever.

Grant Hutchison

[Strange]

I would think its because - with the exception of electronic instruments - I think musical instruments pretty much always have harmonic multiples in them.
The octaves are there, to be heard - not interpreted in the mind.

That's not a very informative answer - but maybe someone can riff off it.

But the instruments are designed that way because people find sounds with simple integer relationships pleasing. It doesn't really explain why people find those mathematical relationships pleasant.

I would guess/hypothesize that it is is because as the signals stimulate processing in the brain they propagate around and, if there are simple mathematical relationships, then they will reinforce one another otherwise, they won't.

I don't think this is unique to humans. I think birdsong, for example, generally uses simple integer relationships between notes.

[Strange]

I don’t think the octaves are there to be heard... why are there no colour octaves?

There are colours that "go" and colours that "clash" in a slightly analogous way. But the difference is probably due to the fact that we perceive them in completely different ways.

[Hornblower]

For most of us we do not have a visual octave because the limits of the visible range are somewhat less than a factor of two. However we can consider a ratio of 3:2 which can be had with red and blue light. Two tones with that exact frequency ratio make a pleasingly "in tune" sensation when sounded together, but if the ratio is off by, say, 1%, it is out of tune and throbbing. With light, however, all the discrepancy does is make an almost imperceptibly different shade of magenta, with neither either more or less pleasant than the other.

[Hornblower]

Try this online tone generator.
Set wave to 'square wave'.
If you drop frequency below about 20 (for me)... there is no real discernable drop in pitch.
Below 10 and the individual clicks become definitely rhythmic (to me).
3Hz doesn't feel similar to 6Hz
But 40Hz sounds similar (octavy) to 80Hz
You can open up multiple windows and test it.

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

Good find! With it I find that my aforementioned whistle is two octaves above middle C.

[grant hutchison]

Thank, Grant. I get it now. Adaptive! Duh-uh. Of course!

I'm not sure I entirely buy the complicated argument about the suppression of odd-numbered harmonics.
But animals from the same species that are of different sizes will naturally vocalize at different frequencies. If a small female can't match the pitch of an alarm call give by a larger male, what's the best way to imitate the call so the message still gets across? Finding a frequency that shares a lot of harmonics with the male call is one solution, I'd guess. And that's what happens when humans of different sizes try to sing together - they match even-numbered harmonics.
It's interesting that matching pitch chroma in this way seems to be so important, at a neurocognitive level, that our brains assign a high priority to it. If that signal wasn't such a strong component of our pitch perception, we'd be immune to the illusion of the Shepard-Risset glissando, because (I presume) we'd keep noticing the fundamental disappearing and being replaced by one an octave lower.

Grant Hutchison

[Squink]

Echolocation may have a part to play here: http://www.sengpielaudio.com/calculator-air.htm
Frequency matters.

[plant]

Echolocation may have a part to play here: http://www.sengpielaudio.com/calculator-air.htm
Frequency matters.

Only if we evolved from bats or dolphins.

[Logix128]

I don’t think the octaves are there to be heard... why are there no colour octaves?
Clearly some part or parts of the organ of corti, thalamus or auditory cortex map inputs of frequency that are whole number multiples into the ‘same’ output perceived as the qualia of ‘octave’.
I wonder how this processing is accomplished and where it is happening in the brain.
I wonder what sort of ‘neural network’ could analyse every possible audible tone, compare it with another tone occurring either simultaneously (maybe detection of absence of beat frequencies ?) or separated by brief time intervals.... and work out to a very very precise degree (how precise?) whether the two tones are separated by a whole number of mulltiples of the base frequency.
It seems like an unusual task that could have no evolutionary advantage... unless it saves processing power??
I assume that perception of rhythm is required in the human body for locomotion, and speech- and one could imagine that these (cerebellar/ extrapyramidal) structures could lead to the development of rhythmic but atonal ‘music.’
I suppose musical ‘tone’ is really just ‘rhythm’ sped up a few orders of magnitude but i think the systems for dealing with each are different. At some point, rhythm becomes tone.
I’d compare this to how our bodies sense radiant infra-red light as heat via cutaneous receptors vs visible light from our retinas.

https://youtu.be/h3kqBX1j7f8

well our brain records sound through vibrations of the parts of the ear, so i'm sure the brain could easily use frequency to categorize different "sounds" into the stuff we hear.

i think a more interesting question is, "why do we hear sounds?"

it's just a vibration that makes its way inside of our ear. correct me if i'm wrong but there's no such thing as "sound" unless there's a brain to interpret the sound waves. machines can't decipher what something sounds like, they can only analyze the patterns of vibrations and output vibrations of specific patterns... "sound" is an absolute phenomenon of life

[Noclevername]

Echolocation may have a part to play here: http://www.sengpielaudio.com/calculator-air.htm
Frequency matters.

There are people who've learned to echolocate, but (anecdotally) they appear to use clicking or finger snapping to generate the sounds.

https://en.wikipedia.org/wiki/Human_echolocation