Evolutionary Advantage to Hearing Octaves as "The Same?"

Factual Questions
1

Humans, and, apparently, other mammals, hear notes spaced apart by octaves as being in a sense “the same note.”

At this site I learn, apparently, that this can be accounted for by features of the structure of our brains. The fact that octaves sound the same is reflected by the fact that the bits of my brain that get activated when hearing the same note in different octaves are all located in columns. Its like I’ve got sort of a layered keyboard in my brain. (Read the site for a bit better of a description.)

Well, why should this be?

It is in fact the case that notes related by an octave have a very simple mathematical relationship with each other: Their frequencies are such that one will be a direct multiple of the other.

But why should it be that my brain, a cat’s brain, and, presumably, the brains of our shrew-like ancestors, should all be structured in a way that responds consistently to this bit of mathematical trivia? What’s in it for us?

Wouldn’t we be just as fit if our brains made us hear fifths as “the same” rather than octaves? Or 11ths? Or 16ths? Or whatever?

To head off a bit of confusion: I’m not arguing against evolution. IMO speciation by evolution through various kinds of natural selection is an established fact. I’m just hoping I can get the skinny on this topic. I want to know what, if anything, scientists or at least smart people have said about this issue.

-FrL-

2

There doesn’t have to be anything in it for us. It could simply be a consequence of a mutation that lead to larger and more complex brains. Maybe music is just part of the package that also makes you better at identifying noises in general. It could, in essence, simply be physics. Maybe being able to tell one bird call from another can get you fed and it could be that music is simply a byproduct of the structures that allow you to tell one bird call from another.

3

My point is, you could have music, distinctions between notes, distinctions between sounds, differential responses to birdcalls, etc, even if you thought of fifths as “the same” instead of octaves. (Or 11ths instead of octaves, or 16ths instead, or whatever.)

So, right, maybe the octave thing is just a coincidence. Except that’s one hell of a coincidence. The notes we hear as “the same” just happen to be the ones in which the frequencies between the notes have, pretty much, the simplest mathematical relationship possible?*

I’m certain there’s a better explanation, that it’s not just a really freaky coincidence. But what the explanation is, I don’t know.

How is it useful to respond instinctively to the fact that C2’s frequency is exactly twice C1’s frequency?

Or alternatively, perhaps its not that this is particularly useful, but rather, that this is for some reason the best (or a particularly good) way to organize an organism’s sound processing for some engineering reason or other. I can’t see why this would be, either, though.

-FrL-

*Measurements of simplicity aren’t that simple of course, but I hope you see my point.

4

Um, I think it’s mathematics, not biology. I don’t think there’s any evolutionary “choice” involved.

5

Harmonics occur everywhere in nature. It’s the most fundamental aspect of resonance and sound reflection. I think you’d need to evolve something special to be able to distinguish octaves well, rather than the opposite. You realize that in the purest sense given two tones an octave apart the higher one has all the same peaks as the lower one (plus extra ones exactly in the middle), so in a way the lower tone is a subset of the higher one.

6

(rolleyes inserted by present author)

Its a biological fact that when I hear one sound, then another sound with double the frequency, I react to them as though they were “the same.” It’s a biological fact that this is the case across several mammalian species.

That’s the biological fact I’m finding somewhat inexplicable.

Things could have gone otherwise just as easily, as far as I can presently tell. We might as well have evolved in the following fashion: When we hear a note, then hear another note with a frequency 3/2 as great as the first note, we react to the notes as though they were “the same.”

You can stick any fraction in there, and it seems to me things could have ended up that way. But they didn’t–they ended up such that the fraction in question is 2/1.

So, it’s gotta be some fraction or other, right? So why am I amazed that it turned out to be this particular fraction?

I’m having a bit of a time explaining why. There’s a mathematical simplicity to this “doubling” operation that there would have not been to a “tripling” operation or a “3/2-ing” operation or a “11/17ths-ing” operation or anything else that might have been used instead. Yet, I can’t think of any reason this particular way of doing it (making “doubled” frequencies sound “the same”) should present an evolutionary advantage over the more seemingly complex ways of doing it. If there were several equally complex ways of doing it, then it would be nothing amazing that evolution had just picked one that worked. But the fact that evolutions seems to have hit on the uniquely simple way of doing things makes me think there’s something to be explained–somehow, what makes this system simple also makes it evolutionarily advantageous. But I can’t figure out why that should be.

What do I mean by simple?

Think of this. Say you have a length of string. You pluck it, it makes a note, call it “A.”

Now divide the string in half, and pluck one of the halfs. It makes another note, one which humans and many if not all mammals hear as “the same” note–in other words, a higher “A.”

Now, go back to the original length of string. Now divide it into two pieces, 1/3 and 2/3. The notes played by the two substrings are no longer A’s. The longer one is going to be the E that comes next after the previous A in the scale, while the shorter one is going to be the next E after that.

Had you divided it into 1/4 // 3/4, the shorter string would play an A, and the longer string a D.

Divide it 1/5 // 4/5 and you get some pair of notes which includes none of the notes listed above.

And it goes on like this.

Anyway, the thing to notice is, with that first division, you have a co-incidence of the two following facts:

  1. You’ve divided the string at its unique point of symmetry
  2. You’ve produced a sound which sounds “the same” as the undivided string.

What I’m expressing amazement at, then, can be put in this way. For any of the possible ways you could divide the string, it could have turned out that we evolved to find that to be the way to divide a string to produce a note that sounds “the same” as the original string. But the way we did actually evolve just happens to be such that we have this feeling about the note produced by dividing the string at its unique point of symmetry. Every other way of dividing the string is asymmetric. This way–this one single way out of the infinity of possible ways–is symmetric.

So we are biologically adapted, crudely speaking, to tend to select the auditory result of symmetrically dividing a string as being of special importance. (That’s of course not what we actually evolved to do, but whatever it is we evolved to do pretty much amounts to this.)

As I said, its the co-incidence, seemingly a suprsing one, of two facts, which I am saying invites explanation. Why should it be that the kind of sounds we identify as “the same” are also the kind of sounds you get when you divide a string at the only point on its whole length which is a point of symmetry?

Well, am I succeeding in communicating the reason for my amazement at all?

-FrL-

7

Maybe so, but can you explain why? The number 200 is a different number than the number 400. I don’t need to do any especially hard thinking to see what the difference between them is. Nothing about them makes me think of them as somehow “the same.” But play me a note with frequency 200 and a note with frequency 400, and I do find them to be “the same.” Why is this the case in the one domain but not the other?

I don’t see what you mean. Sine wave A, if it’s an octave higher than sine wave B, has twice as many peaks as B, over any given interval.

-FrL-

8

Frylock, please don’t add sarcasm to my quote.

Anyway.

Groman is explaining what I was talking about: it’s a function of the mathematical fact of the interim of vibrations, not a biological “choice.” It’s not about evolution, but about physics.

We hear them as the same because, mathematically, their frequencies “fit” together. Math, not biology.

9

Actually, I was expressing sarcasm, not adding it on your behalf. I tried to edit it afterwards to read “<—:rolleyes:”, in other words, to express exasperation with the particular usage of the particle “um” which you were exhibiting.

“Um” used that way is a pet peeve of mine, and I think rightly so.

What do you mean they “fit” together? In the sense I can imagine that 200 and 400 fit together, so do 200 and 600, but I don’t hear notes with frequencies 200 and 600 as “same.” Rather, these two notes would be heard as being a fifth (plus an octave) apart.

Also, even supposing there is some unique way they fit together, I can not think of a good reason I should have evolved to have instincts about sound which reflect this fact. I could have evolved differently. I could have heard fifths as “the same.” But I don’t. Why not?

What you’re saying amounts, I think, to an argument that I actually couldn’t have evolved to hear fifths as “the same.” But why not?

Or if you agree that I could have, then what is compelling about what you’re calling “fit” that makes it something I ought to be able to grasp instinctively as I do?

-FrL-

10

I hear octaves as different notes. One is higher than the other so they seem different to me. On the other hand, in the past when I played in loud bands I sometimes could not distinguish the root from it’s fifth.

It’s all just a function of natural harmonics I think.

11

About the “Its math, not biology” line of argument, I’ll say the following in addition:

In some crazy world, its entirely possible (though highly improbable) that beings might have evolved (or anyway, at least, been designed) to think it perfectly unnatural to see pairs of objects being combined with other pairs of objects to produce sets of four objects. Indeed, they could have been designed to think it perfectly natural to see the pair of pairs combine to form a set of five objects.

Now, this is, strictly speaking, a way that it would be possible to design a creature. But such a creature would be very short lived.

Why would it be short lived? Because there is an evolutionary advantage to thinking it natural that 2 combined with 2 would yield 4. To expect it to yield 5 is going to lead to the making of very few babies, and so, eventually, the extinction of the species.

But now take the sane creature, the one that understands that 2 plus 2 is 4. It is math, not biology, that 2 + 2 = 4. But it is biology, not math, that knowing that 2 + 2 = 4 should be an evolutionary positive.

Similarly, it is math, not biology, that the frequency of the note A2 is twice the frequency of the note A1.

But it is biology, not math, that I hear those two notes, and not some other two notes instead, as “the same.”

It is the biological fact I just named for which I am looking for an explanation.

12

That’s interesting. So you wouldn’t say you hear all the C’s as being in some sense “the same note?”

Like, when I play a song, then play the same song an octave higher, it doesn’t sound at all the same in any way to you except in regards to the intervals between the notes internal to the two playings?

-FrL-

13

So like, does anybody get what I’m asking? I mean, have I made anyone else wonder the same thing I’m wondering?

Please? I hope?

-FrL-

14

Yes, in some sense I do hear them as the same note. They have the same feel, if you will, but I still hear them as different notes. But they are different notes that harmonize with each other perfectly. No harmony can be more harmonious, I would say, yet they are still different notes.

15

In other words, if you were trying to build a machine that differentiates sounds from each other, octaves would be the hardest sounds to tell apart. When you have two sine waves of different frequencies and add them together you are creating another component – the beat frequency. To understand why this happens, consider the example of two tones X - 150Hz and Y - 100Hz. Say the first peak of X lines up with the first peak of Y. The second peak of X does not line up with the second peak of Y, not all peaks of X will line up with peaks of Y. In fact, every third peak of X will line up with a peak of Y – creating a third component, a beat frequency of 50Hz. For octaves, the beat frequency is equal to the lower octave, hence not detectable separately, making the tones more similar mathematically.

Now, your ear is a pressure sensor – it picks up amplitude variations in the air pressure that we perceive as sound. The simplest of all detectors would be “sound” vs. “no sound”. However our hearing is much more complex, and not only can we distinguish how loud sounds are, we are able to distinguish different tones. However it works out neurologically, we still have to extract individual frequency components somehow to be able to perceive any two tones as “different” – converting from time-amplitude domain into the time-frequency domain is not an easy process regardless of how you do it. Mathematically octaves are the most similar sine waves, and tones that are almost but not exactly identical the most different (discordant).

The key point is that your by default argument seems to be “We perceive different tones, then we evolve hearing some of them as the same”. This is simply the wrong approach. As we evolved to perceive different tones as different tones we did not do so completely – some tones that are harder to distinguish sound more similar. Colors and patterns that are harder to distinguish also look more similar. I don’t find this surprising at all.

The question you should be asking is not “Why octaves sound almost the same?” because that one is answered by the math. The question you should be asking is “Why did evolve the ability to tell two tones an octave apart as different?”, because it is certainly harder than just hearing them as the same tone. Could be a fluke or a side effect, or maybe it serves a specific purpose. If you look at electronic chromatic tuners, most of the cheap ones will not even attempt to guess at the octave – it would make the tuner much more complicated. The one right in front of me can be configured with a base reference A as 440 +/- 10Hz in 1Hz increments, and can detect all 12 tones, but it does so regardless of octave.

16

Or, if you can think of notes as colors you might say that A1 and A2 and A3 are all the same hue or the same “shade”, but they each have different* saturation* or different lightness/darkness.

So again—I do not see (hear) them as the same note. A root and its octave are not the same color, but they are the same hue.

17

Although I don’t understand what your idea of “mathematical similarity” is, still, I do think I see what you’re saying here. Play a note together with a note an octave higher, and the sound that results is just like a slightly modified version of the lower note. But play a note together with another one a fifth higher, and the new sound doesn’t look that much like either of the original notes because of the “beats” you mentioned.

I’m starting to see an answer to my question forming. Suppose I had evolved to hear a note and a note an octave above it as different. It would still remain true that I could not distinguish very easily a note from the sound produced by playing that note together with the note an octave above it. This would be anomalous. Why should it be that I can’t distinguish the notes when they are played together, yet they sound completely different when played apart? Well, of course, evolution often doesn’t “care” so to speak about heady abstract questions like this. But I’m starting to see that there might be something literally more efficient or at least computationally simple about doing things the way we actually do them. I can imagine that might lead to an advantage of some kind.

Right, this is confirming my impressions from the above paragraph.

It is not suprising that things that are harder to distinguish seem similar. But I was asking why it should be that we hear notes as the same when their frequencies are, so to speak, “completely different” i.e. not “similar” at all. And I still don’t see how a waveform is “similar” to a waveform with double the frequency, but not “similar” to a waveform with just a slightly different frequency. But I do see how the doubled frequency might be harder to distinguish even though its less similar than the slightly different frequency–on account of the “beat frequencies” involved. And that begins to answer my question. I feel relieved.

In other words, now I’m beginning to see why it should be that two sounds could be hard to distinguish in pitch, even though their frequencies are very dissimilar.

See my previous post on “its math not biology.” I disagree that its answered by the math. There’s the further question why my biology should be such as to give me a kind of awareness that reflects that math so directly.

That is a nice bit of empirical data for me to chew on, so thanks for that as well.

I was hoping for an answer like this. I was hoping someone who knows something about sound engineering would be able to tell me that, somehow, sounds spaced an octave apart from each other are “the same” in some mechanical sense. You’re indicating to my confidence that a sound engineer could indeed give such an account, since it is in fact true about the machines you mention that it takes extra work to be able to get them to make the distinction.

Thanks! This has been driving me nuts.

-FrL-

18

Raises hand.

Unless you spend time listening to signal generators or old VCO synths you are not listening to pure sine waves. Every musical instrument produces harmonics, so that the octave above the note played is always present. So if you play two notes an octave apart you are in a way just changing the relative amplitude of the octave note (and adding more harmonics but let’s keep it simple).

There’s a trick you can do with an electric guitar to make groman’s beat tones very audible. With some distortion, you bend a string to the same note as another, play both notes, drop the pitch of the bent note a tiny bit and you can distinctly hear the sum and difference tones. I’ve heard a Jeff Beck track where he does this maybe someone can name it?

19

Allow me to try. The first thing you need to understand is that this isn’t anything to do with instincts. It is to do with physics. You don’t have any instinct that tells you that it is harder to lift a sheep than a cat. You don’t need one. Physics ensures that a sheep is heavier than a cat, and the heavier an object the harder it is to lift. In the same way two notes that have coinciding peaks will sound the same because physics ensures that the peaks reinforce. You don’t; need any instinct to tell you that. It simply is.

In a nutshell when dealing with frequencies that are multiples of one another the brain has to do some quick calculations to see whether the wavepeaks are identical. If the tone is pure then they will be the same. If there is an interspersed lower tone the reinforcement/interference of the wave peaks will make every second interval different ion intensity. Now you say that you can “can imagine that 200 and 600 fit together”, and they do, being multiples, but not in the same way as 200 and 400. When a 200 and 400 are heard together they perfectly complement each other even if the complementation is destructive. In theory if a 200 and a 400 are sounded at the same intensity and time they will sound like a perfect and doubly intense 200 simply because every second peak will be cancelled. IOW to distinguish a 400 played alone from a 400 played in harmony with a 200 the brain has to contrast peaks simultaneously and look for something that isn’t there. In contrast the brain can always readily distinguish whether a 600 signal contains a 200 because every second peak is out of sync. Being 1/3 of a step out of phase the peaks only align when they reinforce each other. There is simply no way that a 600 can contain a “hidden” 200, and a 600 and a 200 played together will produce interference that does not resulting a perfect tone.

And that in a nutshell is why you can’t hear fifths as the same. It’s because they simply aren’t in sync. While both the 400 and the 600 stimulate all the same nerves as the 200 the 600 can’t be said to harmonise because of destructive interference that the brain can readily detect.

Beyond that you need some understanding of the way the human ear translates sound into nerve impulses. In simplified form the ear contains a long, narrow tube filled with fluid. Incoming sound generates waves in that fluid and the tube is so shaped that a specific wavelength of sound will cause nerves attached to hairs attached to correlating parts of the tube wall to fire, and only nerves attached to those parts of the wall. Your brain then analyses which parts of the tube is producing nerve impulses and uses that to calculate the frequency of the input. Or to put it very simply, the tube in the ear has sections along its length that only generate nerve impulses when the incoming frequency is 200, other sections that only generate impulses when the frequency is 201, others at 202 and so forth for all audible frequencies.

As for why your brain is wired the way it is, it’s actually pretty simple. Consider that an 800 frequency will cause vibrations at 0.025mm along the tube, and at 0.05mm, and at 0.075 and 0.1mm. A 400 frequency will cause vibrations at 0.05mm along the tube, and at 0.1mm. A frequency of 200 will cause vibrations at only 0.1. It should be fairly obvious now why those nerves are arranged in “columns” of an octave in the brain: each octave represents the length of the tube that gets stimulated by the incoming signal plus all the lower tones on the same octave. It’s far easier to compare reinforced signals when the processors are arranged in serial for each octave than to try to shunt the information between parallel processors.

And this is where Groman’s point that two tones an octave apart have the same wave peaks comes in. When you pluck your string at 200Hz it generates a wave within the fluid of the tube at those places that the brain has mapped as 200. But when you cut your string in half and pluck it then it generates a wave at those points that the brain has designated as 400 and at those points the brain has mapped as 200. It can’t do otherwise because as Groman explains the higher tone has all the same peaks as the lower one, and having the same peaks it must produce the same wave peaks within that tube in the ear. As a result the two notes are causing nerve impulses to fire from exactly the same parts of the tube. The only way that the brain can distinguish the two tones is because the higher one also stimulates additional parts of the tube. But 200 and 400 both stimulate the same “200 specific” parts of the tube. If the brain gets signals from the 400 section of the tube it can’t directly tell that there isn’t also a 200 frequency in there as well. That’s because a 400 frequency must be stimulating all the 200 sections of the tube as well.

Once again the point is this has nothing to do with instincts. It has to do with physics. You can’t hear fifths as the same because fifths cause destructive interference that converts a nice simple sine wave into a mess. The brain notices that very easily and it sounds discordant. In contrast notes an octave apart are able to take advantage of either complete destructive interference of complete reinforcement. To process that difference the brain needs to look for some very subtle differences, and the best way to do that is to have all the processors for the same octave arrange din serial.

I hope that made some sense.

20

…Moderating…

Frylock. It’s a pet peeve of ours when you alter a poster’s quote. I know you didn’t mean it to change lissner’s thought, but it’s a rule.

samclem GQ moderator