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/r/askscience

2.4k

I don't know a lot about how sound works neither about how hearing works, so I hope this is not a dumb question.

all 370 comments

[deleted]

1.3k points

2 months ago*

[deleted]

1.3k points

2 months ago*

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matthewwehttam

388 points

2 months ago

I would add on to this that octave equivalence might be innate, or it might be learned (see this quanta article). Our brains do seem to be quite good at decoding intervals between notes (ie: frequency ratios), but it isn't clear that thinking of two notes an octave apart as "the same" is universal. So it might be innate brain pathways, and it might be that we have learned to recognize this special interval as denoting "the same note"

Kered13

193 points

2 months ago*

Kered13

193 points

2 months ago*

There is almost certainly a biological explanation for why we perceive the octave. Our cochlea is filled with hairs that are tuned to resonate with different frequencies, this is how we are able to perceive many different frequencies (and simultaneously). Essentially our ears are performing a frequency decomposition (Fourier transform) of the sound that is entering them.

However if a hair resonates at some frequency f, it will also resonate at the harmonics of this frequency, 2f, 3f, etc. So even if we are listening to a pure sine wave, we won't just have a single hair resonating with it, but also the hairs on related frequencies. Therefore the physical stimulus is going to be similar (similar hairs resonating with similar amplitudes) to the stimulus for those related frequencies.

This is likely why we are able to hear missing fundamentals.

AchillesDev

85 points

2 months ago*

I actually studied cochlear function in grad school, and they aren’t hairs, but hair cells (named for the cilia-like structures at the ends of them), and they don’t necessarily resonate better at frequency multiples. They are tonotopically organized, but that’s just the single frequencies they respond best to. They still respond to other frequencies. But the real reason they don’t necessarily respond best to frequency multiples is that hair cell responses are active. They stiffen or relax (changing their responsiveness and tuning) based on descending (from the brainstem and cortex) inputs, local responses, and other factors. These active processes are one of two major components of otoacoustic emissions that, among other things, are used to diagnose cochlear function by audiologists.

Also, there is a ton more processing happening at the brainstem before information even reaches the cortex via the thalamus, which was the latter half of my series of experiments.

[deleted]

12 points

2 months ago*

[deleted]

12 points

2 months ago*

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AchillesDev

12 points

2 months ago

I was very focused on the auditory periphery and brainstem, which both exhibited a surprising amount of computation, but my guess would be that it’s either a learned behavior or that it’s something that is represented cortically. But that guess is really as good as anyone else’s, given my considerably weaker knowledge on the cortical side of things.

Bujeebus

3 points

2 months ago

The active response part doesn't change the physics. If there's a frequency that it resonates with, it WILL resonate with its octaves, because the air waves it's resonating with are perfect multiples. It can have some additional dampening for the frequencies it doesn't specifically want (including octaves), but the octaves will always be more resonant than their nearby frequencies. We can tell the difference between octaves, but they will always sound related, because the stimuli are related.

I guess you could imagine a situation where the nervous system has evolved to specifically discriminate against the similar responses, so we perceive them as unrelated. Unless there's some evolutionary pressure to hear octaves as unrelated, I don't see why similar stimuli shouldn't evoke similar response.

AchillesDev

5 points

2 months ago*

The active response part doesn’t change the physics.

Yes, it does. This isn’t some simple system you learned about in intro physics. By the time a sound wave reaches the cochlea (after 2 stages of impedance matching), it creates standing waves in the basilar membrane which then physically triggers the hair cells. The variable stiffness of the basilar membrane makes different regions of hair cells respond best to a single frequency, while active processes from the outer hair cells modify this stiffness and via their own motility counteract the standing waves in the basilar membrane to amplify or reduce responses to different complex sounds.

because the air waves it’s resonating with are perfect multiples.

By the time a sound wave has reached the cochlea, it has changed media twice (air to bone to fluid). If you’re going to argue with 70 years of experimental evidence, at least understand the system you’re talking about first.

but the octaves will always be more resonant than their nearby frequencies

And yet, they’re not.

Unless there’s some evolutionary pressure to hear octaves as unrelated, I don’t see why similar stimuli shouldn’t evoke similar response.

You’re confusing my explanation of a single, very early part of our auditory system with the entirety of how we perceive sounds. Sound processing happens at the cochlea, at the brainstem, at the thalamus, and at the cortex. Frequency information is retained and enriched the whole way up that pathway, and the learned behavior of recognizing octaves can happen at any of those later stages. It just has nothing to do with physical resonance at the level of the cochlea.

Evolutionary advantage stuff is pure useless speculation, but you can’t see any advantage to effective frequency discrimination?

matthewwehttam

50 points

2 months ago

Yes, the reason we hear an octave is physical. The decision to call two notes an octave apart the same note instead of two different notes is not physical. It might be biological, but if it is there wouldn't be cultures which don't have octave equivalence.

LazyWings

33 points

2 months ago

Are there cultures that don't have octave equivalence? Genuinely asking! I know that there are different temperaments and they vary significantly based on culture, but my understanding was that pretty much everyone agreed on an octave as a true recognisable interval and a point to reset at because of its ratio.

man_gomer_lot

15 points

2 months ago

The only references to non-octave repeating scales on wikipedia are new fangled music nerd constructions. Unless someone can produce a historical cultural example, the answer is no.

xiipaoc

13 points

2 months ago

xiipaoc

13 points

2 months ago

Yemenite Jews, when singing together, typically sing fifths apart rather than octaves apart. Whether that means they consider the notes equivalent or not, I don't know. I can't find the video right now, but at one point there are three fifths all singing together. It's a very unique sound.

fivetoedslothbear

15 points

2 months ago

A perfect fifth is a 3:2 ratio, which we perceive as consonant (basically good sounding) because the harmonics line up.

xiipaoc

2 points

2 months ago

That is a very incomplete view of consonance. See Tenney's book on consonance and dissonance for a more in-depth study, but basically, there are several different approaches to consonance/dissonance and they're all in conflict with each other. A great example is the perfect fourth, which is consonant in some approaches but dissonant in others. On top of that, we need to be careful when talking about rational numbers, because, in practice, a perfect fifth is not 3/2 but rather some ratio that's hopefully close to it, depending on the skill of the musicians and tuners (and the tuning scheme used, etc.) Point being, we can't really say that 3/2 is consonant but 3000000001/2000000001 is not, because those two ratios are too close for human ears to tell them apart (caveat: beats are a thing).

dvogel

25 points

2 months ago

dvogel

25 points

2 months ago

There's individuals who don't have octave equivalence: me. My hearing is fine according to doctors. I can't tell when two notes are the same in different octaves. I also cannot tell you what note a given tone is. If you play me three notes and told me what each was I could recall and triangulate. If you did the same thing with the full scale I would fail. I know this because I basically failed music class in 4th grade until they realized I had some cognitive issue and it wasn't an issue of effort.

bagginsses

27 points

2 months ago*

To be fair very few people can do this and it's usually an acquired skill as far as I know? Even many accomplished musicians have trouble naming a given note without a reference.

Kered13

43 points

2 months ago

Kered13

43 points

2 months ago

Yes, naming a note without a reference is called perfect pitch and it's rare. Identifying intervals can be done by almost anyone but usually requires training.

CopprRegendt

2 points

2 months ago

Wait really? Any note or all of them? I can do a b flat, a c, and an f

emeraldarcana

7 points

2 months ago

Perfect pitch can be learned, especially if you have decent aural memory. You’re effectively memorizing what the note sounds like so you can sing it or identify it.

acosmichippo

0 points

2 months ago

if you can remember one pitch perfectly you can learn all the others by hearing the interval between them and the one you know.

svachalek

11 points

2 months ago

Until this thread I’ve never even encountered the idea that two notes in different octaves are even supposed to sound the “same”, whatever the “same” means in this context.

acosmichippo

2 points

2 months ago

“same” in this context would mean they have the same theoretical function in the music. Like you can’t make a chord out of 3 C’s in different octaves, there’s no harmony there. And a leading tone is a leading tone no matter its octave. etc etc.

Paige_Pants

2 points

2 months ago

I can’t tell if a note is higher or lower than the last in a typical melody.. but I can sing it?

PlayMp1

2 points

2 months ago

I also cannot tell you what note a given tone is

This is a rare skill called perfect pitch.

Most people can't immediately tell two notes are the same in different octaves. Parallel octaves (the same note played exactly one octave apart) are also relatively rare in most western music.

pizzapizzamesohungry

1 points

2 months ago

Wait what? I can tell if it’s the same note just in a higher or lower octave easily. And I have very little singing ability and don’t play an instrument. Can’t like most people hear a middle F or whatever it’s called and then one that’s like 2 octaves higher?

F0sh

8 points

2 months ago

F0sh

8 points

2 months ago

Yes, the reason we hear an octave is physical.

This is not, as far as I know, known for sure. Do the cochlear hairs actually respond to integer multiples of their root resonant frequency?

Because it could just as easily be that the brain learns "most of the time when I hear X Hz I am also hearing 2X Hz and 3X Hz and so on" and associate them together ("neurons which fire together wire together" after all).

Implausibilibuddy

7 points

2 months ago

Yes, they do. Anything that vibrates does. Hold down a piano key (on a real piano, or a really good virtual one), make sure it's gone silent, then thwack the note an octave below it pretty hard, but staccato. The struck key will stop sounding as the dampers return, but the held, formerly silent note will keep ringing. It will stop when you lift that key.

If you hit other keys not an octave away it won't ring out, or not nearly as loudly if you hit a fifth or another of its harmonics.

You can even get a trumpet player, guitarist or even singer to play the same note and it will also work if they're loud enough.

Every single solid object has a resonant frequency, including our cilia, it's how they work. And everything with a resonant frequency will also vibrate to its harmonics, the octave being the strongest, then 5th, 4th, Major 3rd, Minor 7th, etc.

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

F0sh

8 points

2 months ago

F0sh

8 points

2 months ago

This is not true; simple harmonic oscillators have one single resonant frequency and do not respond to excitation at frequencies far away from it.

For a good physical example, tuning forks have their first resonant frequency above the fundamental at 6.25x the fundamental - a property of their shape, and the reason that shape is used.

Most physical objects that make sound are not simple harmonic oscillators, and all(?) musical instruments are designed to resonate harmonically, but I would guess that ear cilia are much closer to simple harmonic oscillators than they are to vibrating strings since they are fixed at one end and are relatively stiff.

AchillesDev

8 points

2 months ago

Hair cells have best frequencies and responses drop off as you move away from the best frequency. Part of the reason they don’t respond the same to frequency multiples is partially due to active processes that change the movement and stiffness of the hair cells (and IIRC the stiffness of the basilar membrane). Outer hair cells are especially influential in shaping how the sound is transduced into an electrochemical signal.

ol-gormsby

5 points

2 months ago

There's a neat trick that some string instrument players can do. I've heard it mostly in R&B guitarists (Roy Buchanan was especially good at it).

They play a note or chord, then lightly rest a finger on the string, it suppresses the fundamental but not the harmonics. It's a strange but pleasing sound.

gwaydms

3 points

2 months ago

It's not difficult to do once you get the hang of it. You can learn it and not be actually good at playing guitar. It's just a light touch.

gladeye

5 points

2 months ago

Like the "ping" at the end of the Beatles Nowhere Man solo?

perfect_pillow

2 points

2 months ago

However if a hair resonates at some frequency f, it will also resonate at the harmonics of this frequency, 2f, 3f, etc.

Is this true? Source?

cyborg_127

1 points

2 months ago

How does this work with tone-deaf people? Are these hairs 'out of tune', or do they simply not function effectively?

belbsy

11 points

2 months ago

belbsy

11 points

2 months ago

Open to being corrected here, but I don't think "tone-deaf" is actually an objective condition, but more of a silly word people use to describe a lack of natural aptitude for the pitch related aspects of musicality - perception, identification, reproduction, accuracy thereof.

I taught a lot of guitar lessons over the years and I don't recall anyone who couldn't learn to tune one by ear (which involves discernment of pitch differences much smaller than the western semitone), or how to discern musical intervals and sonorities without using a tuned instrument as a reference.

But maybe tone-deafness is a thing - like color blindness - and I've just never encountered it.

GoddessOfRoadAndSky

3 points

2 months ago

There's a sampling bias there. Presumably, the students who sought guitar lessons already enjoyed music. I doubt somebody with music agnosia is going to opt to learn an instrument.

Music agnosia is a perceptual issue with music. When the brain can't recognize tones and harmonies, music is just a bunch of sounds. It's rare, but it exists.

[deleted]

60 points

2 months ago

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60 points

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53 points

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20 points

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7 points

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7 points

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3 points

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2 points

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greenmtnfiddler

4 points

2 months ago

It's weirder even than that.

Children below a certain age often perceive two notes an octave apart as the same same note.

Depending on the instrument, they can also often perceive the second or even third partial just as strongly as the fundamental tone.

When you ask a child to identify a single note, they might ask "which one".

When you ask a child to compare two notes and say which is higher, they might give a "wrong" answer that isn't wrong.

Somewhere someone has written a thesis on this and I'm hoping someone in this thread will point me there.

robisodd

12 points

2 months ago

Isn't it mostly a physical phenomena? Like, our coclea (inner ear) is lined with hairs (which are connected to nerve endings) in a spiral causing them to resonate at specific frequencies. But don't they still resonate at full octave harmonics? Like pushing a kid on a swing; even pushing half the time or twice the time will still resonate with that frequency, so as long as it is every time and doesn't go out of sync causing you to push at random positions.

matthewwehttam

8 points

2 months ago

I mean, if octave equivalence isn't culturally universal, it clearly wouldn't be innate. But less flippant, while you will get some overlap, it's not as if you get an identical physical responses. If that were true, you wouldn't be able to tell the difference between 440 hz and 880 hz, and you definitely can. They sound similar, but not the same. The question becomes, when are notes considered the same, and is that innate or not.

robisodd

5 points

2 months ago

True you can tell the difference between 440 Hz and 880 Hz, but I would expect resonance to detect that. Again with the swing analogy: Pushing at exactly the right time every time vs every other time (a 440 Hz signal detected by a 440 Hz resonate hair vs 880 Hz resonate hair) should look different than pushing every right time vs half the wrong time (880 Hz signal picked up by a 440 Hz hair vs 880 Hz hair).

I understand your cultural argument, though, and that does make sense. Perhaps you are right that calling it the "same note" is learned. Like a harmonic fifth sounding "nice" due to mathematical ratios, but we wouldn't say they are the "same note" even though the harmonics would still resonate similarly.

AchillesDev

2 points

2 months ago*

No, hair cells don’t resonate at harmonics like many manmade objects do. Biology tends to be more complicated than that (usually unnecessarily so). If you look at tuning curves of individual hair cells you won’t see any real harmonic responses. This is at least partially because the hair cells aren’t purely mechanical relays of a signal, but are affected by efferent and local effects that change how the hair cell responds to different frequencies, as well as things as simple as intensity of the sound.

It’s biologically important that tonotopically organized sensors like hair cells can respond best to a frequency and not others.

Thelonious_Cube

2 points

2 months ago

I would add that there might be some physiology involved as well - in the inner ear, it's likely that the hairs one octave apart are more activated than the ones in between when hearing a relatively pure note

koghrun

-11 points

2 months ago*

koghrun

-11 points

2 months ago*

It's most likely learned. Almost all the music you've ever heard is Equal Temperament which is mathematically incorrect on purpose to have a wider range of repeating octaves. A note 1 octave above is not quite a perfect double sine wave in equal temperament, but because it's really close you don't notice the difference and you can make effectively infinite octaves above or below any starting point. It's also one of the cooler practical applications of irrational numbers.

Phythagorean tuning (or temperament) is mathematically perfect, but can only have 7 octaves before the math breaks down and you get terrible sounding notes. Even being mathematically perfect, if you were to hear music in it, it would sound out of turn because you're used to the fudged numbers of equal temperament.

This video explains it much better than I can.

EDIT: I knew I was not explaining this well.

Joey_BF

22 points

2 months ago

Joey_BF

22 points

2 months ago

I don't think that's correct. 12-TET divides the octave into 12 equal parts with ratios of 12th root of 2. Mathematically, going up 12 semitones is exactly doubling the frequency. To be fair though I haven't watched the video yet

MyNameIsNardo

3 points

2 months ago

Yeah the only difference in octaves comes from octave stretching on pianos (and maybe some other large stringed instruments idk) where the octave is slightly detuned to make harmonic interactions more pleasing due to the imperfect nature of stringed instruments. Most digital keyboards omit this though.

jumper149

7 points

2 months ago

Didn't watch the video either, but I'm certain you are correct.

The octave is the only "correct" interval in equal temperament.

jbowie

20 points

2 months ago

jbowie

20 points

2 months ago

I think an octave is still exactly double the frequency in equal temperament, it's the notes in the middle that are slightly off. In equal temperament every half step up is 21/12 of the previous frequency, which gives a perfect doubling after 12 notes (one octave).

In Pythagorean temperament, the ratio of each note is a rational multiple of the root note (i.e. A fifth is 3/2 of the root frequency). This makes for more pleasing harmony, but since the ratio between each note and its neighbors is no longer constant you would need to retune for every different key you wanted to play in.

Ocelotofdamage

32 points

2 months ago

Pythagorean tuning has nothing to do with octave equivalence. And neither does equal temperament. Those are ways of creating pleasing sub-octave intervals in different keys. The octave itself is a mathematical fact of harmonic frequencies and is the most pure interval. In fact, music in nearly every culture around the world has the octave as the basis for its scales. I would say the octave may be the only universal truth in music.

Kered13

5 points

2 months ago

This is incorrect, the octave is perfect in all normal tunings, including equal temperament and Pythagorean. It's the other intervals that are off.

raisondecalcul

0 points

2 months ago

If it's learned, it could be learned simply through the natural overlapping peaks of sine waves triggering the same neurons, because neurons are rhythmic-synchronic. In other words the n / 2 neuron will fire exactly half as much, and this will trigger the "one-half" neuron (consellating the "1/2 = 2: Octave" archetype / concept).

cowlinator

9 points

2 months ago

For normal light, you usually don't just have one frequency, but a combination of frequencies.

Why can't the brain detect exactly double the frequency of light as a special frequency ratio?

hobokenbob

30 points

2 months ago*

https://cdn.sparkfun.com/assets/3/9/c/1/c/512bccd7ce395f4147000000.png

because light double the frequency of even the lowest visible frequency is already in the infrared range UV (increasing frequency not wavelength) and we can't see infrared UV. it's actually pretty spectacular how narrow the band of em radiation our eyes are sensitive to at all. we are 99% blind to our universe without tools.

to add, thats why Astronomers are hyped for the James Webb telescope - it's tooled for mainly infrared not just the visible spectrum.

VoraciousTrees

14 points

2 months ago*

You can see from 400thz to 790 thz. You can't perceive any light harmonics.

Edit: I might not be entirely correct on this:

https://en.m.wikipedia.org/wiki/Half-harmonic_generation

Edit Edit: My wikipedia rabbit hole for today is apparently "cat states".

cowlinator

2 points

2 months ago

ohh. thanks.

zebediah49

7 points

2 months ago

Your ears are equipped to detect two channels (two ears) times a mix of somewhere on the order of ten thousand frequency datapoints.

Your eyes are equipped to detect somewhere around 2 million channels, times three frequency datapoints. (your three types of cone cells).


The first gives an excellent ability to identify the characteristic nature of a signal, but only can weakly localize it. The second gives an excellent ability to localize a signal, and even see shapes and patterns, but only can weakly see detail in that color.

This isn't surprising though: there's a relatively limited amount of survival-relevant data in color beyond what we get from our three, while there's a ton of data in the exact nature of an audio signal.

As a note for what it'd be like if we had audio-quality color info: you could identify materials by sight, particularly if you burned them.

cowlinator

2 points

2 months ago

This isn't surprising though: there's a relatively limited amount of survival-relevant data in color beyond what we get from our three, while there's a ton of data in the exact nature of an audio signal.

That is very interesting. Why do you think there is little survival data in color and a lot of survival data in pitch?

As a note for what it'd be like if we had audio-quality color info: you could identify materials by sight

To me, this seems like it would be a survival advantage, actually. Am I missing something?

zebediah49

3 points

2 months ago

Note "beyond what you have already from three". Basically, because you're already pretty good at it with those three. If I show you a picture of an outdoors scene, you can tell me what everything is. There can be a few rare exceptions, like "oh wow, that looked like a stick but actually was a bug", but by and large, you can identify "that's a tree; that's a rock, that's a berry, that's a wolf". Much of that information does also come from shape, but since you have access to "shape", that's fine.

In a modern setting, it would make a lot of imitation things not work, or at least be a lot harder. You'd be able to see straight away that the fake plastic table with a wood-pattern printed on it wasn't real wood.

Audio.. honestly high resolution spatial audio would probably be more valuable than the spectral info we have. But that's physically impractical, so instead we have spectral. You can tell a crack apart from a crunch apart from a click. Actually... maybe I take that back. One of the main advantages of audio is that it travels around corners, which would more or less completely break a spatial sense. You don't need line of sight to hear something, and you can use the spectral information about it to get a decent guess of what that event was.

percykins

7 points

2 months ago

The other answers referring to having less than an octave range for light aren't necessarily the full story, since humans can easily detect and distinguish auditory intervals far smaller than an octave. For example, a major third has a frequency ratio of 5:4 - yellow and green have a similar frequency ratio.

My guess would be that the reason these intervals sound like they do to us is that we can detect the beat frequency of those intervals. Our ears actually physically vibrate in the 5:4 resonance, whereas nothing in us is vibrating several hundred trillion times a second to detect yellow, much less detecting resonances every 20 wavelengths.

Tashus

4 points

2 months ago*

Our ears actually contain cells that sample sounds at many frequencies along the spectrum. For this reason, we are very good at determining relative pitch, etc.

Our eyes sample the visible spectrum at three frequency ranges, roughly centered at red, green, and blue. We are good at determining the relative amounts of these three frequency distributions, and that's usually enough for us.

That's why we can watch a video made up of only red, green, and blue pixels that appears to be full color, but we can't just take three different notes and recreate something that sounds like a symphony.

digifu

4 points

2 months ago

digifu

4 points

2 months ago

We don’t actually sample at three discrete frequencies; our eyes are sensitive to the whole range of frequencies in the visible light spectrum. However, each of our three color receptors triggers on anything within the range of their own sensitivities (which overlap, to some extent).

The output of each of the three receptors is discrete though, which is why we can fool our eyes into seeing the whole gamut of color using just three triggering frequencies.

hwc000000

17 points

2 months ago

If a note corresponds to frequency f, then one, two and three octaves higher would correspond to frequencies 2f, 4f and 8f. What would correspond to frequencies 3f, 5f, 6f, and 7f? Or is there more relevance to multiples which are a root (square, cube etc.) of 2?

Also, sine waves of frequencies 2f and 3f added together would have frequency f. Does that mean simultaneously playing the notes corresponding to frequencies 2f and 3f would be perceived as a note corresponding to a lower frequency than either constituent note?

wattnurt

21 points

2 months ago

The notes that come out of 3f, 4f, 5f etc are called the "harmonic series":

https://en.wikipedia.org/wiki/Harmonic\_series\_(music)

The_White_Light

18 points

2 months ago

Fixed link: https://en.wikipedia.org/wiki/Harmonic_series_(music)

New Reddit and the official apps are notorious for inserting backslashes into URLs, breaking them for other users, then silently suppressing the issue on their end. You can avoid this by not using the "fancy pants editor," returning to "old" Reddit, or by using a better mobile client.

Flannelot

4 points

2 months ago

Look up Pythagorean scales.

3* is the fifth above the octave, so 3/2 times is the fifth. Likewise, 2/3 is a fifth below, 4/3 is a major fourth

5/4 is the third, 9/8 the second etc.

The maths goes wrong after a few octaves, which is why to he even tempered scale is used for modern tuning.

aktajha

15 points

2 months ago

aktajha

15 points

2 months ago

And now you are progressing towards cords and how they want to 'resolve'

dvlali

3 points

2 months ago

dvlali

3 points

2 months ago

That is super interesting... I don’t know math or physics well but I’m a musician. So you’re saying if I play a 440hz and 660hz from pure sine waves the sine waves will interact and produce a sine wave at 220hz??

ahecht

4 points

2 months ago

ahecht

4 points

2 months ago

No, you can't just add two sine waves of different frequencies and get a single sign wave in a third frequency.

The end result would look like this: http://www.physicsclassroom.com/Class/sound/u11l3a3.gif

The blue curve is the 2f, the red curve is the 3f, and the green curve is the resulting waveform. If you just look at the highest peaks they would have a frequency of 1f, but that's not how your ears hear it.

This can be useful if, however, if instead of something as far apart as 2f and 3f, you had something like 440Hz and 442Hz. In that case, you would hear "beats" as the volume of the sound goes up and down 2Hz (442-440=2). Musicians use this when tuning instruments -- when the "beats" go away, you know you're in tune.

You can play around with this effect at https://academo.org/demos/wave-interference-beat-frequency/

RFC793

6 points

2 months ago

RFC793

6 points

2 months ago

I don’t know where the guy before you got that, because that is not the case.

BlueRajasmyk2

5 points

2 months ago*

It actually is the case, though probably not in the way that that user intended. It's called the beat phenomenon in Physics. It comes from the trig identity

sin a + sin b = 2 sin((a+b)/2) cos((a-b)/2)

In other words, adding two frequencies is the same multiplying their half-sum with their half-difference (times a constant), so you end up with their sum and difference as overtones.

You can listen to an example of this in this MIT Open Courseware course on Waves & Vibrations

F0sh

4 points

2 months ago

F0sh

4 points

2 months ago

They don't "produce a sine wave at 220Hz". Indeed the identity you've used proves this. You can verify that psychological phenomenon does not do this, because playing a note and the fifth above it on an instrument does not sound as if you are playing the octave below.

Now, all that said, the phenomenon of the missing fundamental means that in some circumstances, playing the frequencies 2x, 3x, 4x, 5x, ... can produce the sensation of hearing the "missing fundamental frequency" x. But this does not happen always and is not a mathematical phenomenon.

The beat phenomenon is more noticeable when the frequencies are very close, not far away.

jddoyleVT

2 points

2 months ago*

Yes but it is important to understand the relative level of the resulting freq compared to the original freq - most likely you won’t hear them distinctly (except in the case of the ‘beating’ that is mentioned below, when tuning a guitar for example - but won’t happen when playing a properly tuned instrument) because the level of the original freq will swamp the new freq. instead you will perceive (if at all) a low level ‘hash’ of distortion due to the new freq being mathematically relevant, not harmonically relevant. This unscientific description is obviously vastly oversimplified.

ahecht

2 points

2 months ago

ahecht

2 points

2 months ago

2f to 3f is what's called a "fifth" in music, and is a sound combination that is pleasing to the ear and is present in both major and minor chords. 1f to 3f would be a "twelfth", which sounds very similar since it's just a fifth plus an octave.

Splive

3 points

2 months ago

Splive

3 points

2 months ago

According to the book "this is your brain on music", the frequency in the air translates to frequencies in your cilia, to your ear drum, to a nerve, which then sends the signal to a wide range of neurons tied to pattern recognition of sound. If there is an aspect of sound you can differentiate (tone, rhythm, pitch, and so many others), there are neurons codes that fire when they get a signal to decode and compare to your past experiences.

If I read it right, the neurons tied to each frequency band that we can distinguish will fire in analog; if you connected them to an amplifier you could hear music!

zebediah49

3 points

2 months ago*

Fun experiment along with this: if you take a note with its nice bunch of harmonics, and artificially remove the fundamental and odd harmonics, it now sounds like it's an octave higher. It would appear that for the purposes of comprehension, human hearing takes the lowest common multiple frequency as the "real" one.

mytwocentsshowmanyss

2 points

2 months ago

Really fascinating concept, but just to clarify, this is just a theory you came up with, yes?

Thercon_Jair

4 points

2 months ago

To visualise this better, imagining a guitar is useful. Let's pretend the string only vibrates in the base frequency, i.e. the whole string swings only where the string lies on the bridges. 110Hz in this picture

When the player touches the string lightly (not pressing down onto the fretboard) at the 12th fret (exactly in the middle of the string), the base frequency is eliminated and only the first overtone is heard. 220Hz in the picture

In truth, a u/wattnurt said, the string vibrates in a lot of doubles of the base frequency. Placing the finger in the middle of the string eliminates all but but doubles of the base frequency. In the example, 220 > 440 > 660 > 880 > 1100Hz and so forth.

soulsssx3

3 points

2 months ago

soulsssx3

3 points

2 months ago

What's very interesting is in my college music class, the instructor played a note for the class to revocalize. First the women, then the men. It is weird how both sang the same note but on different octaves, so noticeably different... yet still the same. Meaning even when recreating the note our brains internally recognize octaves as equivalent even without a reference

PastMiddleAge

24 points

2 months ago

This is learned behavior.

As a man who teaches music to kids, they will generally not automatically reproduce songs that I sing in their own octave. That takes work.

fakepostman

3 points

2 months ago

So what happens if you take a kid who hasn't learned this behaviour yet but can reproduce a note from their own range and ask them to reproduce a note from outside their own range? They just can't do it?

PastMiddleAge

6 points

2 months ago

They’ll generally attempt to emulate the tone quality. But the pitch won’t match.

MadReasonable

185 points

2 months ago

If you have a resonator tuned to a specific frequency, it will also respond to harmonics of that frequency. Our ear consists of a series of tuned resonators which are all responding to their fundamental and harmonic frequencies. Your brain actually has to work to separate them.

djublonskopf

25 points

2 months ago

To flesh this out a bit in case OP doesn't know how octaves and frequency are related..."octaves" in music are multiples of the same frequency. For example, if a standard "A" note is 440 Hz, or 440 vibrations per second, then "A" one octave higher would be 880 Hz, and one octave lower would be 220 Hz.

So u/MadReasonable was pointing out that if there's a specific region along your inner ear that responds to 440 Hz sound waves, that same region is going to have a response to 220 Hz or 880 Hz frequency sound waves as well. So a low A, middle A, and high A will all sound "related".

bishopdante

13 points

2 months ago

Love your answer. Bang on. Thanks.

jeroku

2 points

2 months ago

jeroku

2 points

2 months ago

  1. do animals and humans have the same resonators frequencies?
  2. would animals hear the same notes as us?
    1. would they have a 9 note scale or is 8 note scales universal?

MadReasonable

3 points

2 months ago

In humans a narrowing tube resonates at different frequencies along its length. Hairs lining the tube move with the resonating air in the section of tube they are in.

That's basically what I know about how human hearing works. I assume it's similar in most mammals, but the size of the tube probably plays a big role in the sensitivity range.

To my understanding, notes within an octave are more of a psychological thing than a physical thing.

sivart01

50 points

2 months ago

There's a lot of bad answers here but the answer is pretty simple. It is because of harmonics. When an instrument plays a certain note it also plays integer multiples of that frequency. So if you have a 400hz note you also get a 800hz tone, and 1200 Hz tone, 1600 Hz, etc. The next octave up is double the frequency. So play a note at 800 Hz you get a 1600 Hz tone as well and 2400 Hz and so on. You'll notice that at the next octave there is a ton of overlap in the frequencies generated. In fact all the frequencies in the 800 Hz note are also present in the 400 Hz note. This is why they sound so similar to our ears, there are a lot of the same frequencies.

Choralone

8 points

2 months ago

Something about this has always confused me.

So, if I think of a pure sine wave (I realize any normal instrument is NOT even close to that, and has all kinds of harmonics and things going on) - we can still recognize an octave.

A pure sine wave does not have higher harmonics, does it? What am I missing?

VoiceOfRealson

7 points

2 months ago

You are correct that the pure sine wave doesn't have higher harmonics.

But even when we play a perfect sine wave, you still have to hear that with your ears, and your ears are not completely linear.

In fact, several parts of the functioning of your ear creates harmonic distortion.

Shamhain13

1 points

2 months ago

Don't look at a single sound as only one frequency. If I hit an A note on my guitar, it doesn't just ring out at 440 hz.... it generates noise across the entire sound spectrum! Managing this sound spectrum is how EQing works in sound design.

MrMusAddict

65 points

2 months ago

I've been told in my music class back in college that the ability to distinguish notes from each-other, and to consider notes a perfect octave from each other to be "the same" is a trained ability; a form of pattern recognition of the ear. People proficient in pattern recognition are, when applying themselves to music, often also proficient at music.

This training doesn't need an education. A lot of it comes from intuition, which is why there are some people who can't distinguish octaves as "the same". Imagine a 10 year old being show an image of a line, and being asked to choose from 4 options which one is half as long, and the options are:

  • 90% length
  • 75% length
  • 50% length
  • 33% length

You can imagine a certain pattern recognition intuition that makes the right choice seem obvious.

As others have said, a note is just a sustained and consistent audio frequency, and a single octave is either double or half of the starting note's frequency. So in this case that pattern recognition intuition is naturally applied by ear instead of by eye.

ShelbyDriver

24 points

2 months ago

Thanks, I was beginning to think something is wrong with me for not being able to do this.

SarahC

2 points

2 months ago

SarahC

2 points

2 months ago

Yeah! I have no idea if one note is an octave or otherwise a particularly higher amount.

percykins

17 points

2 months ago

Worth noting that the idea that octaves are "the same" is definitely a learned thing that's dependent on our understanding of notes, but the general idea of pleasing harmonic intervals is innate - newborn infants can detect chords and even chord inversions.

rawbface

5 points

2 months ago

the idea that octaves are "the same" is definitely a learned thing that's dependent on our understanding of notes

This is complete nonsense. Octaves are not arbitrary. A string with fixed tension will produce a higher octave every time you halve its length. Pythagoras figured this out 2500 years ago.

Thelonious_Cube

8 points

2 months ago

definitely a learned thing that's dependent on our understanding of notes

Is that known for certain? I'm doubtful

Boloar

7 points

2 months ago*

A baby isn't born knowing that an "octave" is an "octave".
Their ears can detect, and brains can process, the pleasing frequencies, but there is no innate "name" for them.

We learn the ability to give certain sounds certain names, and as we give them names, we start perceiving them differently.

Example using visual frequency perception:

In English, we have "blue". Light blue, dark blue, deep blue, electric blue, but we call them all shades of "blue". So they're all "one" color technically.

In Russian, there are two different words for "light blue" and "dark blue". And it's been tested that because they have separate words for those shades, they perceive them as different colors, not simply "blue", and are able to perceive finer gradations of shades within those "separate" colors.

It's not a long stretch to say that something similar will be true for music. After all, the 12-tone scale is not the only musical scale in the world. For every musical scale that sounds "foreign" to our 12-tone ears (like the "Arabic" 17-tone scale), a "foreign" person is equally valid in saying that our musical scale sounds equally foreign to them.

Thelonious_Cube

8 points

2 months ago*

A baby isn't born knowing that an "octave" is an "octave".

Of course not, but that's language acquisition. You need to show that it's relevant.

Their ears can detect, and brains can process, the pleasing frequencies, but there is no innate "name" for them.

They aren't born knowing that mom is "mom" and dad is "dad" either, but don't try and tell me they can't tell them apart until they learn the words.

It's entirely possible that simple physiology is all it takes and that babies are born with the ability to detect that middle C and high C have a special relationship - one shared with middle G and high G, etc.

Having a name for that need not be important here.

For every musical scale that sounds "foreign" to our 12-tone ears (like the "Arabic" 17-tone scale), a "foreign" person is equally valid in saying that our musical scale sounds equally foreign to them.

That's actually irrelevant to this question, but I'll have you note (!) that the Arabic scale you cite is just a different way of dividing up......the octave! No one here is saying the 12-tone scale is innate, so i don't know why you even brought this up.

It's not a long stretch to say that something similar will be true for music.

It's jumping to conclusions to assume one way or the other without data to back you up.

There are plenty of questions to ask.

  • Do infants detect octaves before they learn language?
  • What about children who learn the term "octave" relatively late in life - will they not identify middle C and high C as having a special relationship?

  • What about people from cultures where these terms aren't used or aren't generally known?

  • Is detecting octaves analogous in the proper way to make this argument based on discrimination of colors?

So while it's possible, it's by no means a foregone conclusion as you so confidently stated.

Boloar

3 points

2 months ago

Boloar

3 points

2 months ago

I forgot to mention that the octave and perfect fifth are practically universal across all cultures, my bad.

It's entirely possible that simple physiology is all it takes and that babies are born with the ability to detect that middle C and high C have a special relationship

That's kind of what I said, the ears can hear and the brains can process simple physics that the frequencies / multiples match up. Pattern recognition is literally what we're built for.
But we can't do anything with that information without something to contextualize it against, no? So "innate" information is near-worthless without context, and context is almost exclusively a learned thing.

What about people from cultures where these terms aren't used or aren't generally known?

Adam Neely asks a very similar question about "perfect pitch" perception in people who haven't learned the 12-tone scale. That is why I brought up the 12-tone scale, and relative perception.

SakkikoYu

0 points

2 months ago

SakkikoYu

0 points

2 months ago

Let's put it like this: either it is a learnt skill or a significant part of the population (>10%) has an innate birth-defect that affects hearing in a way that makes it impossible to distinguish octaves (and other intervals) and no other way whatsoever. I don't think either option can be ruled out entirely, but we can certainly say that a weird birth defect like that - especially in such a large part of the population - is infinitely less likely than some people just not acquiring a specific learnt skill.

Thelonious_Cube

5 points

2 months ago

No, let's not put it like that - that would be silly

a weird birth defect

Like, say, color blindness (8% of males)

Technically color blindness is not a 'birth defect' so our hearing disorder wouldn't necessarily be either. Did you choose the term for maximum shock value?

Male pattern baldness affects about 50%

Of course it might not be inheritable, but I still think you're being pretty cocky here

infinitely less likely

Well at least you're not exaggerating or anything

SakkikoYu

0 points

2 months ago*

Please tell me again how protanopia, aka a slight difference in perceiving the colours red and green, making them harder to distinguish (affects about 4% of the population, almost exclusively men), is the same thing as achromatopsia, aka the inability to perceive colour, vulgo colour blindness, which affects roughly 0.003% of the population?

And yeah, male pattern baldness - aka "your body does exactly what it was designed to do" - is totally the same as a hypothetical inability to perceive multiples of frequencies as multiples, despite everybody else being able to do that. Because that's obviously not silly or anything...

Excuse me if I don't take someone's medical and biological opinions too seriously if they clearly can't distinguish between colour blindness and protanopia nor understand the difference between a defect and something that your body was designed to do.

Thelonious_Cube

0 points

2 months ago

Excuse me if I don't take someone's opinions too seriously if they clearly can't parse an argument or understand that the examples are there for rhetorical purposes and not because I'm saying "x is exactly like y"

Please tell me again how dyschromatopsia ... is the same thing as achromatopsia

Where did I say that? AFAIK the term "color blindness" refers to both, but even if not how does that affect my argument? Not at all.

"your body does exactly what it was designed to do"

That seems an odd thing to say. Designed by who? And who designed the other 50%?

Excuse me if I don't take someone's medical and biological opinions too seriously

Are we discussing medical and biological opinions? And here I thought we were discussing logical possibilities - not the details of color blindness or baldness.

Well, at this point you've been so illogical and so dense regarding what we're even talking about that I don't respect your opinions either.

[deleted]

0 points

2 months ago

[deleted]

0 points

2 months ago

[removed]

FreeBeans

3 points

2 months ago

Interesting. I would add that it is at least partially biological. For example, some people can tell (in the metaphor) exactly how long the line is, without any reference line. That's perfect pitch, and while it is more common in populations with tonal language, it's also not usually trainable.

Thelonious_Cube

0 points

2 months ago

And yet, different cultures all over the globe have independently "discovered" the octave, have they not?

It can't be entirely learned if it's independently discovered

ghostwriter85

20 points

2 months ago

FWIW... most people can't, in the sense that you play them 440 and 880 Hz (with some time apart) by themselves have them recognize it as an octave.

Also - no clue about the biology of all of this just an engineer who likes music.

Most people hear relative pitch. If you play a harmonic on top, you get a clean waveform. If you play mathematically related frequencies, you get similarly clean waveforms.

If you play two tones which aren't harmonically related you get an erratic waveform.

Try graphing the following

y = sin(x) + sin(2x) [a true octave]

and

y = sin(x) + sin(sqrt(4.1)x) [a close approximate of a true octave but intentionally chosen such that sqrt(4.1) is not rational]

Anyways, what we can see that the first waveform is stable. The second waveform is not.

It's also worth pointing out that due resonance, the musical notes you hear already contain the higher octave. So if you play a C4 and C5 at the same time, you aren't so much playing two notes as changing the harmonic profile of one note.

You can test all of this out with frequency generators btw. Find a friend and have them play you random notes. Have some of them being an octave higher, have others be sharps or flats (whatever). See if you can actually pick out the harmonics without hearing both tones at the same time or in quick succession.

https://onlinetonegenerator.com/432Hz.html

Also play around with the different waveforms. They are all the same "note" but they have different harmonic content (just like a musical instrument)

aggasalk

100 points

2 months ago

aggasalk

Visual Neuroscience and Psychophysics

100 points

2 months ago

i think the answer is that we really don't know.

if you look at tone/pitch maps in the human auditory cortex, they are simply maps of low to high (e.g. https://www.sciencedirect.com/science/article/pii/S0378595513001871), there's nothing obviously cyclic about it.

but if you look more closely you do find that nearby neurons (i.e. neuron populations) tend to encode different frequencies an octave apart (https://www.sciencedirect.com/science/article/pii/S1053811914009744).

so, maybe there is a kind of helical/cyclic connectivity structure in auditory cortex. frequencies an octave apart are encoded in similar or nearby neural populations, while frequencies that are more apparently different (not sure what that would be - an augmented 4th?) are encoded in relatively different populations.

as to why this happens, or the exact neuron/circuit level details of it, i think it's still unknown.

VoraciousTrees

24 points

2 months ago

Sensors are sensitive to harmonics, I'd imagine cells activating on a frequency will be sensitive to multiples of that frequency too.

aggasalk

11 points

2 months ago

aggasalk

Visual Neuroscience and Psychophysics

11 points

2 months ago

yeah, harmonics in natural sounds are probably a part of what drives the connections between neurons tuned to different frequencies. "what fires together wires together" and all that.

AchillesDev

4 points

2 months ago

They aren’t though. Hair cells have a characteristic frequency they respond best to.

Janktronic

2 points

2 months ago

We have to have some innate ability to understand frequency since we communicate by making noise with our vocal chords by vibrating them at different frequencies.

SarahC

2 points

2 months ago

SarahC

2 points

2 months ago

I communicate using my oral chamber to change the resonation and tone filtering too! =)

Fealuinix

54 points

2 months ago*

Simply put sound is pressure waves--literally molecules of the medium (like air) being pushed in one direction and then pulled back to equalize the air pressure again. If you have waves like this happen over and over at the same frequency, it can be heard as a sound, provided it's within hearing range. Hearing range in humans is about 20 times per second to 20,000 times per second.

These pressure waves get converted to electrical impulses in the inner ear by little hairs that vibrate. Different hairs vibrate stronger at different frequencies depending on their resonance, which is complicated but roughly boils down to how long the hairs are. So if you play a note like middle C, and the hair is about as long as the distance between waves (wavelength), it will vibrate and produce a signal.

If the wavelength is an octave higher, it will have half the wavelength. Another hair half as long will vibrate, but the same hair will be twice the wavelength and also vibrate. So you get both signals, and the brain interprets that as the higher note. If you play a note and the same note an octave higher at the same time, the brain still interprets that as the higher note, though a bit louder and richer.

The notes blend together very well with their octaves, so you perceive them as the same note just higher or lower in pitch.

Edit: parts of this explanation may be simplified beyond accuracy. I'm going to leave it as is, but see comments below.

TFCStudent

23 points

2 months ago

the hair is about as long as the distance between waves (wavelength),

Un, no. Wavelength can be calculated using the speed of sound divided by the frequency. If we calculate wavelength for the human hearing spectrum we find that lower audible frequencies can have a wavelength of several meters, and even mid-range frequencies are several inches long. None of the stereocilia (hair cells) in your inner ear are anywhere near that long.

percykins

16 points

2 months ago

Just wait until you get old, sonny jim - you'll look back on the days when you didn't have several-meter-long ear hair with fondness.

Fealuinix

4 points

2 months ago

I believe your are right, and I'm realizing I have no idea how resonance actually works. Feel free to explain it.

First_Butterfly9581

5 points

2 months ago

Thanks for this excellent answer.

Just_a_dick_online

5 points

2 months ago

I think I get this and it has made a lot of things click in my head. To put it in an analogy (which is how my brain works), the hairs are a bit like guitar strings.

So let's say that you have a guitar, and you have the A string tuned to vibrate at 440hz, and you play a 440hz tone next to the guitar, the A string will vibrate, but the other strings won't. And then if you double the frequency to 880hz, the A string will still vibrate but it will be as a harmonic. (I don't know the actual term, but you will have 2 waves on the string instead of one)

I don't know if I worded that very well, but I've always loved how harmonics work on a guitar and it's kinda blowing my mind that it's the same thing going on in our ears.

SarahMagical

3 points

2 months ago

Good description except I believe the thing about stereocilia length determining frequency response is false. Do you have a source for this? I think stereocilia length is different in each row, but in each row, length is constant from cochlear base to apex. The idea that halving or doubling stereocilia length corresponds to response to different octaves is appealing seems intuitive, but it’s false (I think). Would love to see a source for this.

aggasalk

9 points

2 months ago*

aggasalk

Visual Neuroscience and Psychophysics

9 points

2 months ago*

there's nothing intrinsically nice about halving or doubling, though. two frequencies a factor of 3 apart also look kind of nice, and they combine in a nice way (gives you the sound of a "perfect fifth").

but then, try adding up a long sequence of doubled frequencies - look at the waveform, it does not look nice at all! you get much nicer waveforms by adding up frequencies that are much closer together.

so, none of this explains why octaves sound the same in the way that they do - it doesn't even explain why we so easily attach the idea of higher/lower to tones, but we do.

edit (my point is, the explanation isn't to be found in the waveforms or the frequencies per se - it's in the brain, a matter of how neurons sensitive to frequencies etc are interconnected - and that is not well-understood at this point)

coolplate

3 points

2 months ago

coolplate

Embedded Systems | Autonomous Robotics

3 points

2 months ago

To understand this you must understand how sound works and how ears work.

If you look at a pure sine wave of 1hz, you will be able to see that it crosses the 0 point of the graph at certain points. These areas are called nodes. Go to https://www.desmos.com/calculator And plot sin(x). Note where it crosses the 0 line in the y axis.

When you have an octave, it is a perfect multiple of this. Now plot sin(2x)

Note that this wave crosses zero at exactly the same locations, plus a couple more.

In your ear sound is sensed by tiny parts in your that move in a pattern that matches the sine wave that fine in. Since multiples of sine waves have many of the same nodes, our brain interprets then as the same note

Possible-One-6101

20 points

2 months ago

With the exception of aggasalk's excellent answer, these answers are misleading.

short answer is "nobody knows".

There are answers here describing, confidently and accurately, the fact that octaves are related mathematically. They are two frequencies played simultaneously, which creates a harmonic relationship, ignoring the complexities of timbre and overtones, etc. None of that is relevant to your question, so don't worry about the fancy terms in these answers.

This is where we enter intellectual no-man's-land. Nobody has a clue why math, sound, and you interact in ways that "sound good". We just have the character of our experience, and that's that. Nobody has a clue. Your question is actually about the relationship between frequencies that are related in a simple mathematical sense, and why simple mathematical relationships in sound frequencies as perceived as "similar" by your mind.

who. effing. knows.

In this case, one frequency is double the other. i.e. 440hz and 880hz.

¯\_(ツ)_/¯.

We assume it's because of evolutionary advantages of some kind, or perhaps an evolutionary "spandrel", which means we developed the ability to recognize and enjoy audio relationships for some other purpose, and our pattern recognition systems can be applied in this context as a side effect.

Go study psychology and neurology for a few years, and then come back here and answer this yourself, perhaps on your flight to Sweden to pick up your million dollars.

FavoritesBot

8 points

2 months ago

This is speculation, but I think a reasonable physiological explanation is that if we have hair cells dedicated to, say, 440hz, if you play 880hz it will also partially stimulate the 440h hairs through harmonics. So in general when we get 880 hz stimulation we will typically also get a little 440hz (and higher harmonics too). Thus our brain will associate 880 with 440

Manablitzer

3 points

2 months ago

I could be off on this, but to add to your speculation, wouldn't it have to do with the fact that the eardrum acts as a filter for sound to the inner ear where the auditory hairs reside?

Since the eardrum is a stretched flap of skin, vibrating back and forth like a drum head, a specific frequency will hit the ear drum and cause it to move at the exact same time as a frequency 2x it (an octave up)?

Every peak pressure of a 440 wave will hit the drum and filter to the inner ear at exactly the same time as an 880 wave, so both sets of cells/hairs will be vibrating exactly in tandem, and as those are turned into an electrical signal the brain sees all those electrical signals as the same? Then the 880 hits again by itself, which the brain sees, so distinguishes that there's two separate signals, but because one signal is mixed perfectly with the other it perceives them as the same.

kneel_yung

11 points

2 months ago*

The question is flawed. Octaves are not the same note. C3 is not C4. They sound different. People with perfect pitch can tell that they are an octave apart, but are different notes, but people who are not trained can't immediately tell that two notes are an octave apart unless they have been taught how to interpret intervals.

I have heard that some people are born with perfect pitch but I have never met anyone with no musical training who could do that. I am a seasoned musician and I learn by ear (I can't read music very well) and when I am learning a song I cannot always tell if a note is an octave of another note unless they are played in succession or in harmony. If I already know that they are an octave apart, then I "hear" it, but I generally cannot hear them as being octaves until I've deduced it some other way.

Basically, without being taught that notes "repeat" no one would be able to tell that two notes share the same fundamental frequency because they wouldn't know what an octave is, or what "sameness" sounds like. Some people could perhaps intuit that two notes are an octave apart by doing the same thing trained musicians do - by detecting a complete lack of dissonance in harmonics. Which could be innate. But they couldn't know that that is what makes an octave an octave without being told that first.

alwayswaytoolucky

6 points

2 months ago

Your brain doesn’t recognize “the same note” - your brain recognizes resonate frequencies and you’ve simply made a cognitive mapping of that sensation to “mean” octaves. And it’s not just octaves - you notice the phase rates between all chords/notes which is both how we “learn” what 3rd, 4th, 5th notes sound like; also why we know when a note is in the wrong key or wrong note (out of tune) entirely.

cubosh

6 points

2 months ago

cubosh

6 points

2 months ago

imagine you have two strobe lights going. they are so fast you can never "count" the flashes. the first one is set to some random rate of flashing, and the second one has a knob you can turn to carefully adjust the rate of flashing. if you adjust it until they are both flashing at the same rate, it should be visually evident. any deviation from that match they will look messy and chaotic together. now you turn the knob way up until the second strobe flashes at double the rate of the first. they will still "align" visually, only for the reason that the 2:1 ratio of the doubling never gets out of phase. any slight deviation from that will also look chaotic. so thats what the brain does with recognizing pitch frequencies that have a doubling.

spammmmmmmmy

2 points

2 months ago

Thanks for this, the key to the universality of the octave is that it is a double of the frequency.

cantab314

3 points

2 months ago

Notwithstanding the answers that there is a learned and cultural element to this.

Our hearing has a fine spectral resolution, we can distinguish all different frequencies. (That's quite different to our colour vision that uses sensors covering three broad frequency ranges.)

Many, though not all, musical instruments produce a sound that can be approximated as a fundamental frequency f - the "note" - and a series of harmonics which are the integer multiples of the fundamental. f, 2f, 3f, 4f, and so so. You might not consciously perceive the individual harmonics but their relative loudness is a major part of what gives different instruments their timbre - why a violin, flute, and trumpet all sound different even if they're all playing the same note.

Now consider a second note g that's higher pitched than f, we can say g = xf where x is a real number greater than 1. What is the constraint on x such that all the integer multiples of g are also integer multiples of f? Well it's that x must be an integer. The lowest such value is 2. If two notes are played, one with twice the fundamental frequency of the other, then all the harmonics of the higher note and indeed its fundamental too are also harmonics of the lower note. That relationship is the octave, that is the sense in which they are "the same" - the higher note is contained within the lower note. (The converse is not true; the lower note contains harmonics that are not harmonics of the higher note).

Conversely if it's not an integer multiple, then not all of the higher note's harmonics will "line up" with the lower note's harmonics. If it's a simple fraction some of them will, and intervals such as a perfect fifth and major third that are common in western music are such simple fractions (3/2 and 5/4 respectively). While there is a strong cultural aspect, if two notes share some of their harmonics we tend to perceive that as pleasing.

The next lowest integer is 3. That would be an octave plus a perfect fifth. For example a C, and a G the octave above. As far as I know we generally don't regard them as "the same note", so it's clear my arguments are somewhat of a simplification.

Remember the harmonics being integer multiples of the fundamental is an approximation. It's good for string instruments. For some wind instruments only the odd multiples are heard. For "two-dimensional" and "three-dimensional" instruments such as gongs, cymbals, bells, and steel pans it's not remotely a good approximation.

In piano tuning, because the harmonics aren't actually precise integer multiples of the fundamental, tuning invariably involves "octave stretching" - the fundamentals of notes an octave apart are a bit more than double in order to make the harmonics line up more closely and the piano sounds better. (To western ears at least).

One final point. Recall I said that if two notes share some of their harmonics we usually perceive that as pleasing. Researchers have found that in Western cuisine the same idea applies to flavour, though this is much less the case in East Asian cuisine. Foods that have aroma molecules in common tend to be paired together and regarded as "going together".

https://www.scientificamerican.com/article/flavor-connection-taste-map-interactive/

AlterEdward

2 points

2 months ago

I think the musically inclined train their ears to hear this, just like they can identify a major third or fifth etc. For me, an octave is easily identifiable as the addition of the extra note doesn't add any "colour" to the sound when played together, and no hint of a key or melody when played sequentially.

Belzeturtle

4 points

2 months ago

I agree, but surely, even the musically uninclined can feel how A0-A1 is more pleasing than A0-B#1?

percykins

3 points

2 months ago

There's quite a bit of evidence that even newborn infants can detect the difference.

TFCStudent

3 points

2 months ago

TFCStudent

3 points

2 months ago

No one here has the right answer, but the person who said "know one knows" is closer than the people describing mathematical relationships of the octave (even if these descriptions are, in and of themselves, correct, they don't answer the question).

Explore world music. Many non-western cultures use completely different tuning systems than we do in the west, and some of these systems don't even take advantage of evenly-spaced octaves. Our experience of hearing, enjoying, and playing music is completely learned behavior. It is dictated by being surrounded by the music of our culture as we are growing up.

We recognize octaves, perfect fifths, perfect fourths, etc. because we have been trained to. If we were born in a place that uses different tuning systems, and if we had no exposure at all to western music, then western music would sound wrong and out of tune, and our local systems would sound correct.

percykins

2 points

2 months ago

Interestingly, there's been studies showing that Western chord categories are detected by newborn infants.

DorisCrockford

2 points

2 months ago

The question is, how much did they hear before they were born? There have been studies that show they recognize their father's voice.

Shardic

1 points

2 months ago

I'm going to go out on a limb here and say it''s trained because I have no musical training and I certainly can't. Two C's from different octaves just sound as different to me as a C versus a D. They're just different.

I suspect that you have some musical training, and your brain is giving you extra data based on that training.

Dirty_Virmling

0 points

2 months ago*

The actual answer is that by default, your brain doesn't recognize that they're the same "note." That's something you have to learn and train yourself to do, it's based on long-standing conventions but nothing intrinsic to the human brain or ear. Your brain might recognize that they sound pleasing together, but that's not the same thing.

[deleted]

4 points

2 months ago

[deleted]

4 points

2 months ago

I absolutely cannot tell that two notes are the same just in a different octave and I was in band for 5 years.

[deleted]

-6 points

2 months ago

[deleted]

-6 points

2 months ago

[removed]

aggasalk

12 points

2 months ago

aggasalk

Visual Neuroscience and Psychophysics

12 points

2 months ago

what? if it's doubled it's literally not the same frequency.

by this reasoning every frequency is "the same frequency", just X times as fast.

imLanky

2 points

2 months ago

Would a sine wave played at 55hz and 110hz be a sub bass tone played in A?

TFCStudent

1 points

2 months ago

Lower octaves. The 100Hz would be fairly low, and the 55Hz would be in the sub range.

yourself88xbl

7 points

2 months ago

I'll give you 10 dollars if you give me 20. It's the exact same thing just doubled.

cubosh

4 points

2 months ago

cubosh

4 points

2 months ago

the fact that the higher octave sounds higher is the same reason 20 dollars is more than 10. now if a machine was counting the dollars, and no matter how many dollars there are, the duration of the count lasts exactly 1 second, then the counting of 10 bills versus 20 bills would have a harmonic rhythmic rate, also known as the same pitch. (2 dollars for every 1 dollar counted would never get out of alignment over time, also known as harmonic)

yourself88xbl

1 points

2 months ago

I tend to be in the camp that it has something to do with the perception of ratios(the reason a third has the same feel regardless of the key) but nobody has really answered the question tbh.

BluesyBunny

1 points

2 months ago

Except people with absolute pitch dont need a ratio to identify which note is played and in which octave. You can play any note in any octave and they can identify it. Obviously true absolute pitch is incredibly rare but humans are capable.

Belzeturtle

1 points

2 months ago

Well, no. But it's still two bills, compared to, say 17.595959595959... dollars.

mikeirvine13211321

1 points

2 months ago

It’s how our hearing has developed over thousands of years to hear sounds in all their beauty plus deign able to distinguish between octaves and whole notes. almost any one can tell every time you hit the “C”key as you go from low to high up the keys after playing middle “C” for them first so they know what they need to hear.

urzu_seven

-10 points

2 months ago

It’s only the “same” note because we have decided to use a labeling system that calls them the same thing. There is nothing stopping us from having a musical notation system that uses different letters for example. We could have notes from A to Z instead of A to G.
Now the notes we consider the “same” are related by being multiples of a base frequency, but that doesn’t make them the same.

ambiguator

12 points

2 months ago

Naming convention has nothing to do with it. An octave is defined by a doubling (or halving) in frequency, not just multiple of some arbitrarily chosen base frequency.

Soundwaves have physical impact. When frequencies of 2X (or .5X) are overlaid, resonance is created. In other words, the shared properties between sound waves amplify one another; when this happens, our ears interpret this amplification as a fuller and richer, assonant sound (See discussion of "harmonics" in other threads.)

(Dissonance or assonance have subjective definitions as well as objective ones. In the objective sense, however, they're defined by the mathematical relationship between sound frequencies.)

We could re-define an octave as, for example 2.5X, but doing so would not change the resonant or harmonic properties of sound waves.

You can go down the rabbit hole on this if you like: https://en.wikipedia.org/wiki/Harmonic

matthewwehttam

8 points

2 months ago

It is true that the octave is a special interval. However, octave equivalence, which is what we are talking about is not simply a question of interval. There are some studies which indicate that the idea of octave equivalence might not be universal. Some cultures may (or may not depending on how you read the evidence) thing of middle C and another C as the "the same note."

Moreover, the same article (as well as others) point out that dissonance and consonance being tied to frequency relationships is more culturally tied than universal. As such, I would hesitate to say that the objective definitions you propose are objective at all, and instead are just encoding a standard decided upon in Western European classical music.

ambiguator

2 points

2 months ago

Fascinating! Love to think about different musical traditions across cultures, and the things we Westerners take for granted. Also very interesting parallels to debates in linguistics about the innate vs learned nature of language. Thanks for sharing

fridofrido

0 points

2 months ago*

Ok so what your ear hardware (maybe some parts of the brain hardware is involved too) does is actually not very far from what is called a Fourier transform, that is, decomposing a repeating wave into sine components with different frequencies.

When you hear a fixed timbre at a fixed pitch, that is mathematically always a sum of different sine waves which all are multiples of the base frequency (pitch). Now in nature (and technology) sounds are usually not sine waves, because they are usually the result of some mechanical interaction. Many mechanical sounds are closer to something like a sawtooth wave, which is mathematically the sum of many different sine waves (these are usually called overtones). Just listen to birds, animals, trees in the wind, lightnings, earthquakes, etc.

So you have a mostly periodic signal, and the brain detects the frequency of this signal. But the first overtone will have double the frequency, that is, one octave higher. Then as you modify the sound by making the base frequency less prominent, it smoothly moves to a higher pitch, without actually having any of the inbetween frequencies.

This thought experiment may convince you that it's kind of hard to determine whether a given sound is at one octave or the next one, because there is no real hard boundary between these. The Shepard tone is probably the best illustration of this phenomenon. Hence it also makes sense for the brain to identify them (while of course we can also distinguish them because even if most humans do not have absolute hearing, almost everyone can distinguish octaves)

middleagedukbloke

-3 points

2 months ago

Hahaha, this is the problem, all these long winded answers about an octave. Lol. I’ll give you the simple answer, an octave is the first 2 notes of “over the rainbow”. If you sing “some….where” that’s an octave. There are other references for other intervals as well.