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A recent episode of the podcast Surprisingly Awesome about music theory featured the line:

So just to be clear, pretty much every human, when they hear a 440 or an 880, it’s going to sound like the same note.

But they don't sound the same to me. One is obviously at a higher pitch than the other. I have no idea why people would hear these two frequencies played separately and think that they're the same sound.

I understand that when both tones are played together at the same time, one will be completely subsumed within the other, because of how the wave forms line up. I also understand that if they weren't perfectly an octave a part, then there would be a slight "wobbly" sound because of the beat frequency. I can hear that, no problem. I think I have a rudimentary understanding of the physics involved too.

I just can't hear or understand why a person would hear 440 Hz and separately hear 880 Hz, and think "Yeah, those are the same". I've been thinking about this for a while and I had previously concluded it must be a cultural thing, until this podcast used the phrase "pretty much every human".

Am I experiencing tone deafness? It goes without saying I lack all musical ability, but I do appreciate music.

syntonicC's brilliant answer has made it clear that the mysterious property I'm asking about is octave equivalence.

Taking a sentence from topo morto's answer:

You may be able to hear that two different A notes, played one after the other, have something 'similar' about them that A and G, or A and F#, don't have.

This "something 'similar'" is what I'm asking about. As far as I'm concerned, A440 and A880 sound as different as A and G. They're all completely different sounds.

Community
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laffoyb
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  • Comments are not for extended discussion; this conversation has been [moved to chat](http://chat.stackexchange.com/rooms/38094/discussion-on-question-by-laffoyb-a-440-hz-and-a-880-hz-are-completely-diffe). – Dom Apr 07 '16 at 16:54
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    If you've ever heard the song "Somewhere over the Rainbow", the first two sung notes ("Some" and "where") are an octave apart. When training to hear intervals, this is often used to remember what an octave sounds like, as humans don't always recognize it. However, when you play them together, you may sometimes not even notice the higher or lower pitched note. – Casey Kuball Apr 07 '16 at 17:24
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    Note the disclaimer "pretty much every human", you may be in the minority of people who don't (easily) identify octaves as equivalent. I haven't been able to find any studies on how rare this is. Since no one else can get inside your head it is hard to tell if this is tone deafness (color analogy: everything is sort of grey) or super-acuity in pitch perception, or something more complicated, and not easily described on a deafness<->acuity scale. – Dave Apr 07 '16 at 19:30
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    Here's a question: Does a C3 and C4 sound as dissimilar as a C3 and B4? Does "Happy Birthday", played one octave higher than normal, sound as dissimilar to the original as if you played it in an entirely different key? If so, you definitely lack the ability to recognize note class. – Dejay Clayton Apr 07 '16 at 20:53
  • Hmmm. I too hear an obvious similarity between 440 and 880, even though I also hear that they are not the same note and are in fact rather far apart. I suspect part of this is training and part is inborn. – Scott Wallace Apr 07 '16 at 15:03
  • It sounds to me like the podcast you listened to used imprecise language. Usually, this is fine because documentaries and their ilk have to cover a lot of technical material for non-technical audiences in a short amount of time, but it looks like it confused you (and understandably so!). To be clear, you're right: An A at 440Hz and an A at 880Hz are different from each other in many important respects. And if you can hear beating (the "wobbly" sound) between two slightly-out-of-tune notes, you probably aren't tone deaf. ;-) – Kevin Apr 08 '16 at 02:04
  • Listen to Hendrix's Purple Haze intro. Octaves consecutively. – Tim Apr 08 '16 at 13:59
  • I can't post an answer, but... another thing to try would be to play three scales - one starting at A4 (440), one starting at A5 (880), and one starting from B.If the one from B sounds more different than the two from A, then you've found the similarity. Note: If the first scale was in C major (ABCDEFGA on white keys), the one from B should be in D major (BC#DEF#GAB). – Random832 Apr 08 '16 at 18:59
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    @Kevin beating is a variation in true volume on a macroscopic timescale - you'd have to be _actually_ deaf to not hear it. – Random832 Apr 08 '16 at 19:01
  • @DejayClayton: well, to me "Happy Birthday" transposed by a small interval sounds more similar than transposed by an octave in terms of my raw ability to identify them heard in isolation, because I have poor absolute pitch. But a one-octave "key change" in the middle of it sounds more similar/natural than a semitone key change. And hearing C3 plus C4 simultaneously is a notably different experience from hearing C3 plus B4 simultaneously, and again from two C3 in unison :-) That's why most of the question is about pinning down what we should ignore in saying they sound "the same" or "different" – Steve Jessop Apr 09 '16 at 13:14
  • "So just to be clear, pretty much every human, when they hear a 440 or an 880, it’s going to sound like the same note." - from the transcript, this was said by "Rachel" who is (acting) as the person that knows nothing, not the expert, and summarising in basic terms. The key is the rest of what she says: "But what they call it — and what they consider a “scale” — those things will vary across cultures.". To extrapolate the sentence in this question, you should read it as: "it's going to sound like the same note: **A**". So they are obviously different pitch, but the same note: A. – freedomn-m Apr 09 '16 at 20:34
  • Let's say I sit and drum with my right and left hands while a light slowly flashed. Each time the light flashed my left hand hit the drum but my right hand hit the drum both when it flashed and half way between when it flashed. If I ask you which hand is hitting the drum when you see the light you'd be correct to say both. That is what is the same. That you're a human, and how your ears work, isn't really the point. This is how waves work. – candied_orange Apr 09 '16 at 20:53
  • The podcast used the term "the same note" loosely. Maybe too loosely. But I suspect you do really recognignise that a tune repeated an octave higher has a closer similarity to the original than one transposed by a different interval? This is what they were talking about. – Laurence Apr 07 '16 at 11:39

12 Answers12

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Note: For the physics and neurophysiology covered in this answer I am going to be oversimplifying for brevity.

They are not the "same" but they have the same pitch class. Notes that sound similar are said to have the same pitch chroma and the collection of all these notes are said to be in a pitch class. The octave, however, does differ in pitch height because 440 Hz and 880 Hz are not the same frequencies. The property you are referring to in your question is called octave equivalence. If you want a color analogy, maroon and red are clearly not the same color (different wavelengths) but they do have the same hue.

Let's first note that the octave has circularity (the new scale is perceived to begin again at the next octave) and that this appears to be a universal feature in all music of all cultures. This highly suggests that it is a matter of neurophysiology and not cultural. Furthermore, this property has been observed in monkeys.

There are a few possibilities for why this occurs:

1) Physics explanation: Note that the two pitches share harmonics in common. A sound at 440 Hz also includes 880 Hz as the next harmonic. If you continue the pattern for 440 Hz and 880 Hz you will see that they share a large overlap in common overtone frequencies. Due to the frequency overlap between the harmonics of the two notes, there is a large similarity in the overall sound of the two notes.

2) Neurophysiological explanation: The brain has representative "maps" that are reconstructed from data given to it about the world. So for the auditory system there is a "map" of the 3-d space in which sounds are represented in different areas by different neurons firing in the brain that preserves their approximate location. Oversimplified: Two sounds that are nearby might activate a cluster of neurons that are near each other, thus preserving proximity within the brain. This happens in the auditory cortex with what is a called a tonotopic map, but it is apparent now that the octave itself is mapped in the brain in an area that feeds into the cortex called the thalamus. Unlike the map in the auditory cortex, which is used for sound localization, the thalamic map appears to identify octaves.

In a subsection of the thalamus, a note at 440 Hz, 880 Hz, and 1760 Hz would activate a layer of neurons that are an equal distance apart, forming a kind of octave map. These inputs are then combined together when they leave the thalamus (rather than being maintained as separate, distinct inputs) to be interpreted by the cortex. Essentially the brain is lowering the complexity of a signal in multiple octaves by condensing it into a single octave. These results were first seen in rabbits. There have been a couple studies showing this in humans, here is one of them. This suggests that the brain thinks they are similar enough and the thalamus is organized to reflect this.

There is still work to be done in this area, but the evidence so far is highly suggestive of the idea that octave equivalence is in determined by our brains.

Conclusion: You're not crazy. They are not the same pitch. But the representation in the brain means that the sounds are pooled so that they are perceived as having a similarity. This is because they share an overlap in harmonics which the brain recognizes and maps as well. So perhaps it is better to say that the two pitches are similar but not the same.

Edit: I have changed the paragraph in the physics explanation to reflect the comments by topo morto.

syntonicC
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  • Wonderful answer. This confirms a lot of what I read, and goes further and ties a lot of it together with actual research. "Octave equivalence" is the term I've been floundering for. I'll try and read the papers you linked. Can you say if there's been any research to indicate if the whole population detects octave equivalence? – laffoyb Apr 07 '16 at 18:01
  • @laffoyb To my knowledge, this information would be found in a mix of studies showing it in different cultures and in infants going as far back as the 1930s. I don't know of any population/cultural-wide data self-contained in a single study. Other than that, there are historical/mathematical records from other cultures that show they believed in octave equivalence. [Here](http://www.ncbi.nlm.nih.gov/pubmed/23007203) is an example of a small group (n = 28) that demonstrated it. Whether this group is a representative sample (college music students) is another question entirely! – syntonicC Apr 07 '16 at 18:31
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    Worth noting that the name of the field dealing with this is *psychophysics*. – user1803551 Apr 08 '16 at 18:04
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    Also, here is [an old paper](http://download.springer.com/static/pdf/103/art%253A10.3758%252FBF03204867.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.3758%2FBF03204867&token2=exp=1460140138~acl=%2Fstatic%2Fpdf%2F103%2Fart%25253A10.3758%25252FBF03204867.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.3758%252FBF03204867*~hmac=f75b8a10b1901f71415cf9b93d61aa72d66cd65112b03c6b2447cf7dc66f12d7) about it. – user1803551 Apr 08 '16 at 18:10
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    @user1803551 or 'psychoacoustics', more specifically..? – Нет войне Apr 08 '16 at 21:33
  • @topomorto Seems so. – user1803551 Apr 09 '16 at 02:48
  • It seems to me that this only applies when two notes are played together, right? When you play one and then stop and play the other, there is no "overlap", unless you hold the old tone in "memory" (which, admittedly, is exactly one of the techniques we used when learning intervals). – Luaan Apr 09 '16 at 07:33
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    “A sound at 440 Hz also includes 880 Hz as the next harmonic.” What? That’s completely false. Most sounds that are used for music are (nearly) harmonic, but we actually *design instruments* that way. Some don’t require much effort (medium sized strings, blown tubes, …), some do (large strings, vibraphone bars, …). – Édouard Apr 09 '16 at 23:00
  • @Édouard You're right of course, but the question is directed at cultures and people who designed musical instruments to sound this way (or as close as they could get). When we talk about these terms musically it is generally in regard to instruments that exhibit these properties. Do you think I should add a clarifying statement? Feel free to edit if you want to make my explanation more specific. – syntonicC Apr 10 '16 at 01:34
  • syntonicC, I'm confused to why you are agreeing. If a string is tuned to exactly 440hz then it will indeed include 880 hz, and it will produce many other frequencies as well. It's not a matter of culture. it is the nature of vibrating strings, is it not? – shaunxer Aug 31 '16 at 20:24
  • @shaunxer The part of my post that Edouard quoted says nothing about a vibrating string specifically. I said "a sound" which is vague. So I was agreeing that a pure tone at 440 Hz (electronically produced) would not have harmonics. However, because in my post I was speaking in the context of human designed musical instruments, it should be implied that when I said "a sound" in my quote I meant "a sound from an instrument designed to produce equal harmonics". – syntonicC Aug 31 '16 at 22:27
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    For colors there is a 1:1 correspondence between hue and frequency; https://en.wikipedia.org/wiki/Hue#Hue_vs._dominant_wavelength – ShadSterling Mar 29 '18 at 23:47
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They're not the same sound, and depending on how specific you're being, they're not the same note (though they're both 'A', 440Hz is A4, 880 is A5).

In most contexts, they'll be the same degree of the scale, which means they'll function similarly (but not the same) as part of chords and harmonies.

You may be able to hear that two different A notes, played one after the other, have something 'similar' about them that A and G, or A and F#, don't have - but it may depend on the amount and type of listening experience you have.

The situation in which most people should be able hear what's special about an octave is when you're playing two pitches simultaneously - try having one sounding a fixed frequency, and the other starting at the frequency of the first, but sweeping slowly upwards. You may at first hear a beat frequency, and then two distinct sounds - but as you reach certain pitches, you'll probably hear how the two sounds suddenly gel together into one. This happens when the frequencies are related by simple ratios, and happens because your ear is constantly trying to work out whether all the sine waves it's picking up are part of the same sound (in which case they are likely to have related frequencies).

You should hear this 'becoming one sound' effect very clearly at the octave, because it's the simplest ratio - 2:1. This is why almost all human musical cultures will find a place for the octave in music. And if we look at slightly a longer quote from your source, they are talking about cultures...

So just to be clear, pretty much every human, when they hear a 440 or an 880, it’s going to sound like the same note. But what they call it — and what they consider a “scale” — those things will vary across cultures.

...so maybe what they were trying to say is that most human cultures recognise the octave as a 'special relationship' between two pitches, rather than necessarily every individual.

Нет войне
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  • The "something 'similar'" seems to be the quality I'm missing. Could you describe that in more detail? I've sat with a cheap tone generator and listened to tones that should have "something similar" and those that don't. I seem to be completely missing out on this quality that seems obvious to a lot of people. – laffoyb Apr 07 '16 at 11:54
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    @laffoyb I find it quite hard to describe how they *subjectively* sound similar - I'll have to have a think. Out of interest, what's your level of musical experience? – Нет войне Apr 07 '16 at 12:26
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    Close to zero. I tried to learn to play violin a few years ago on a whim. Didn't get very far because of this issue. Sat down with a couple of books on the physics/maths of music theory (and subsequently never put in any practise on the violin) and gained an understanding of it from that angle, but I've never been able to hear the "subjective similarity". I've tried asking some musician friends and they either don't understand the question, or find the similarity so obvious that it's like describing colour to a blind person. – laffoyb Apr 07 '16 at 12:30
  • Oh, also when I was a child I took piano lessons but my mother pulled me out of them because it was painful to hear me practise. :-) – laffoyb Apr 07 '16 at 12:39
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    I guess to me subjectively it's (*very* loosely!) analogous to seeing an object from one angle, then looking at it again at another angle - or perhaps seeing two similar objects that are different sizes, like a Mars bar and a king size Mars bar. Of course I don't know how much that perception is skewed by being so familiar with it as a musical interval. – Нет войне Apr 07 '16 at 12:43
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    @laffoyb Pure sine tones are not really notes and don't sound the same or have the same effect in our ears or brains. Better to use a musical instrument than a tone generator when trying to understand notes. – Todd Wilcox Apr 07 '16 at 12:44
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    @ToddWilcox, thanks for the tip. I've mostly done this experiment with sine generators, yeah. I did try it once on the violin, but it's so hard to hit the notes that that obviously wasn't a good idea. I'll try it with a piano as DrMayhem suggests. – laffoyb Apr 07 '16 at 12:53
  • @laffoyb Do you listen to music? It may very well be that you just lack some basic familiarity. Some musical "facts" are shared across cultures, some aren't - it's very much possible that familiarity plays a big role. This doesn't just include e.g. Western music vs. Indian music - it's also stuff like romance music vs. modern pop vs. death metal. Most people not familiar with death metal will have trouble distinguishing the notes, and "understanding" the harmonies and disharmonies. Major vs. minor is also very cultural. Can you learn the interval between two notes? Then you can't be tone deaf. – Luaan Apr 07 '16 at 15:51
  • @Luaan, I'm confident that octaves are a universal aspect of music, not a cultural one. – laffoyb Apr 07 '16 at 19:06
  • @laffoyb Octave equivalence isn't just for humans; http://www.neuroscience-of-music.se/eng7.htm – Dave Apr 07 '16 at 19:17
  • @topomorto Your comment on another answer, to the effect that "universal across cultures" is not the same as "universal across people" is an important point that might be worth incorporating. – Dave Apr 07 '16 at 19:18
  • Another possibility (which might be easier than finding a piano,) would be to download a piano app on your phone. You'll notice that if you play the same a short piece of a song an octave up or down that the melody will sound similar, just at a higher or lower pitch. Whereas, if you were to play each note one note higher (as opposed to one octave higher,) it will sound quite different. If someone plays a song that you know an octave up from its original, you'll immediately recognize the song, for example. – reirab Apr 07 '16 at 20:41
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    @laffoyb Well, wikipedia notes that "octave ... is common to **most** musical systems". The studies section is also interesting - octave equivalence has been demonstrated in infants, but *not* 4-9 olds and non-musicians. In any case, the more I'm listening to octaves, the more I'm sure that I don't actually hear any sameness at all - I just hear the interval, and the interval is an octave. So whether this is a universally human thing or not, it definitely didn't prevent me from learning to play multiple instruments and composing music. Or playing songs like Singin' in the rain by ear! – Luaan Apr 08 '16 at 06:59
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They are both the same note, if note means letter name. They're both A, but 880 is an octave higher than 440. The 440 A has harmonics on most instruments, one of which being the second harmonic exactly an octave higher. In fact, on some instruments, this note is almost as loud as the fundamental, so the two can sound nearly the same. Most of us would hear the two as different notes, but with a certain similarity. If an adult male sung a phrase and a child repeated it, it would probably come out an octave higher, without the child even thinking about that fact.

Tim
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I have been following guitar lessons in a small group for over a year. Recently, we've begun specific training to recognize intervals in scales (such as major third, perfect fifth, and evidently also the octave).

The most basic exercise was that the teacher played the root note of the A myxolidian scale, and a random interval (which we had to guess and name).

All of us have wrongly said "octave", and conversely failed to recognize "octave", on several occasions. Only after some training, some of us began to see how the "octave" was the (slightly!) easier one to recognize.

My point is, the part where they said "pretty much every human [recognizes an octave]", is widely exaggerated and blatantly false, unless they meant to say "pretty much every human who has had at least some ear training". I find octaves almost as hard to recognize as any other interval.

MarioDS
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    I think maybe they've mistaken the fact that all (or most) human *cultures* recognise the octave as special with the idea that "pretty much every human recognizes an octave" – Нет войне Apr 07 '16 at 15:34
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    @topomorto It may very well be that this plays to the olden ages when singing and playing music was a popular past-time. There's a saying, "every Czech is musical", which certainly isn't the truth anymore. All of the people I know who do music also understand (western-style) intervals. Few of the ones who don't do music do. Maybe training is all it takes, and we're simply lacking in that department (even from childhood). But this experience doesn't really distinguish between the two - if it were innate, people who "couldn't" wouldn't do music, would they? :D – Luaan Apr 07 '16 at 15:56
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    I think you recognize it easily when played _at the same time_. Consecutive notes are much harder to identify as an interval. I myself I'm shocked at how much trouble I have sometimes when practising ear training! – UncleZeiv Apr 08 '16 at 11:54
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    @UncleZeiv exactly, played at the same time it's obvious. I also find two other factors make a dramatic difference: 1) the duration with which the notes are played, and 2) the time interval between the playing of two notes. In the situation I've described in my answer, the teacher played both notes only briefly and with a slight delay. I easily recognize the octave when you play both notes, for example during 2 seconds and with a delay less than half a second. Playing them for a quarter of a second and with a 1 second delay is a whole other cup of tea! – MarioDS Apr 08 '16 at 11:59
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Recognizing notes as being "the same" when the sounds are different (two different frequencies produce two different sounds, which may be the same note) is part of cultural training.

You can instantly recognize two bearded men as being both "men" even though one is a dark-skinned baldheaded quadruple amputee and the other is an albino giant, and both are wearing clothes that cover their sexual characteristics. An alien lifeform could not do that, because the differences would be so great as to obscure the very minor similarity of the beards. But you've been trained to do this since birth, so it's easy for you.

In many western instruments, due to the way they are constructed, playing any "A" note will cause harmonics that are other "A" notes - not the same sound, not at all, but the same note in a higher and/or lower octave.

In other cultures the notes have different names and the scale may be constructed differently. Chinese intervals are weird.

You have to be trained to recognize the notes. Use a piano to train yourself.

Charlie
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Simple way to demonstrate this to yourself:

Get a piano or keyboard, and starting from any white note, count up 7 white keys.

These two are an octave apart (so if you started from the 440Hz A, the higher one would be the 880Hz A)

If you play each of those notes, you should be able to tell they get higher by increments (don't worry at this stage about the actual amount, and where the black keys come into it)

When you get to that last note, play the first one again. These are an octave apart, so sound "the same" in terms of the part they play, but you should be able to tell that one is higher than the other.

Do those two notes sound the same to you? If so, your brain is at least recognising they are the same. If you can also spot that the ones in between are not the same, then while you may be a beginner in terms of understanding the structure, you are aware of the way octaves work.

If you play a sequence of notes, moving them up or down en-masse by an octave retains the notes, but changes the octave, so I could sing a baritone note which is the same note as an alto might sing, but we can be octaves apart, providing a nice spread of sound from low bass up to high treble.

Doktor Mayhem
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    Thanks for responding, but your question "Do those two notes sound the same to you?" is the very issue I'm addressing. They do not sound the same to me. Everything I've ever heard or read on the topic takes it as a given that someone can hear a similarity, but I can't hear it. – laffoyb Apr 07 '16 at 12:51
  • We are all trying to understand what you are hearing - as your comments on each answer seem to show that we haven't got it yet – Doktor Mayhem Apr 07 '16 at 12:52
  • So what do you hear as you step up the notes? That would be useful info. – Doktor Mayhem Apr 07 '16 at 12:53
  • I haven't gotten it yet. That's why I asked the question. :-\ I'm trying to understand if this is something other people can do innately, or if it's an ability that musicians have trained. Either way, everyone else is hearing something I amn't hearing. I'm not trying to be awkward, I really do want to learn. – laffoyb Apr 07 '16 at 12:55
  • @laffoyb - I addressed the bit about musicians not needing to be trained when I mentioned children in my answer. – Tim Apr 07 '16 at 13:05
  • @Tim. Sorry, I did not interpret the line about child singers as meaning it doesn't have to be trained. That is a very good point. Thanks for highlighting it for me. – laffoyb Apr 07 '16 at 13:10
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    @laffoyb I think an interesting game to play would be to compare two notes 7 apart on the piano with two notes 6 apart on the keyboard. Are the two notes 7 apart on the keyboard "more similar" *in any way* to your ear than the two notes 6 apart on the keyboard? (make sure your keyboard is in tune!) You can go and play with it yourself, or you can close your eyes and see if you can beat chance with someone else playing either "two notes 7 apart" or "two notes 6 apart". (they play 2 notes, you *guess* if they are an octave apart or not, and see if you can beat chance.) – Yakk Apr 07 '16 at 13:59
  • @Yakk: curiously enough, one might even say that the two notes a tritone apart are _more similar_ than the two notes a fifth apart: in the latter, there's a clear hierarchy that the lower one has root character and the fifth is harmony, whereas the tritone's enharmonic ambiguity thwarts such symmetry breaking. – leftaroundabout Apr 07 '16 at 22:42
  • @left I am no musician; but Piano's don't reliably have perfect fifths? Imperfect could mess up what the OP is trying to learn. So I wouldn't want to bring that in. – Yakk Apr 08 '16 at 02:27
  • @Yakk: I wasn't going for imperfections of 12-edo tuning at all here. (The fifths on a well-tuned piano are only _ever so slightly_ off, they can be considered as perfect in basically any musical context – it's the _thirds_ that you need to worry about.) What I meant was, in a perfect fifth (7 semitones), the tones have a clear harmonic relationship, which means the lower note is clearly the root and the higher note is, well, the fifth. But in a tritone (6 semitones), none of the notes has anything like “root character”, i.e. the two notes are more on an “equal footing” than those in a fifth.. – leftaroundabout Apr 08 '16 at 10:19
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No, you are not tone-deaf.

A4 and A5 are not similar in the sense that, say, a Toyota Corolla is similar to a Nissan Sunny. These are similar in the sense of, you can replace one by the other with little change. (That is sometimes possible in music with notes an octave apart, but not generally without problems.)

Rather, they are compatible in the sense that olive oil and tomatoes are compatible:

  • They go well together in lots of dishes
  • They both tend to evoke a common Mediterranean flair

Yet they serve pretty different purposes. They are not really similar.

However, like in cuisine, it also depends a lot on context. Tomatoes and olive oil fit excellent in pasta dishes, but there are also e.g. Indian dishes with tomatoes, where the typical aroma of olive oil would not blend in so well.

Similarly, A4 and A5 are so commonly paired in Western music that the combination may almost be taken for granted, but the music of other cultures may not share this attitude. Arabic music and Indonesian music, I think, don't make much use of octaves at all.

The reason that octaves are an obvious fit to be paired is that the sound of many instruments (string instruments, brass instruments, vocals...) is a non-sinuoidal periodic signal whose Fourier decomposition already contains the octave as overtones. Not all instruments have this, though, in particular bells or the Idiophones that dominate Gamelan music have quite different overtone scales, making octaves a non-obvious choice.

Even some western instruments don't have octaves in their overtones, in particular clarinets and gedackt organ stops, as well as square synthesizer oscillators. Harps also tend to feature little even harmonics. A musical system that deliberately targets these instruments is the Bohlen-Pierce tuning, in which octaves aren't meaningful at all.

leftaroundabout
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  • Wow. Octaves are the tomatoes and olive oil of musical intervals. Well, tomatoes and olive oil do go spectacularly well together (if we ignore supermarket "tomatoes" in favor of more authentic fruits). I shall not be forgetting the comparison. Now, if I can only hear the relationship with basil.... –  Sep 16 '18 at 00:47
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I suppose comparing two notes in isolation is somewhat subjective, but what about a longer passage of music? A piece of music played one or more octaves above or below the original is likely to sound 'the same' as the original, i.e., in the same key. The same piece of music played at a different dominant frequency, but otherwise in sync with the original, would be said to be transposed or in a different key.

A practical example of this would be where someone sings (or hums or whistles etc) along with a tune. As a male with a tenor voice I would sing along at an octave comfortable for me, but a male friend with a bass/baritone voice might sing an octave below. Similarly, a female with a higher alto or soprano voice (or a child with a treble voice) might sing an octave or two above. The end result is that the person singing along is going to be singing the melody and it will sound 'the same', in a melodic sense. If I chose to sing along in a different key, some parts might sound OK if they were 'in harmony', but if I stuck rigidly to the same note intervals it would almost certainly end up sounding 'wrong'.

What happens if you try to sing along with a song? How does it sound to you and others?

Mark Brown
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  • I wanted to say something similar (a melody transposed by an octave sounds the same); but then I realized that that is probably true for *all* transpositions (is that the word?), even by just a half tone, for most people (unless one has perfect pitch). (To be exact: I suppose that with an equitempered tuning there are minor, occasionally even annoying differences, but that all melodies can be played with a "natural tuning" in any given key and sound the same except for perfect pitch people.) Am I wrong? – Peter - Reinstate Monica Apr 07 '16 at 15:18
  • @PeterA.Schneider I'd say yes if you transpose by multiplying all frequencies by a factor, because to hear the difference between the original and the transposition you'd need perfect pitch. But for equitempered tuning (e.g., on a piano), only a transposition by an octave amounts to uniform scaling of frequencies, and then different scales really do sound slightly different, even for people without perfect pitch – fgp Apr 08 '16 at 13:57
  • @fgp. Exactly. "Multiplying by a factor" was what I thought transposing from one "natural" or "pure" key to another would always achieve (I'm not sure about the terminology, and there are apparently many "temperaments", i.e. ways to tune instruments, in particular pianos). – Peter - Reinstate Monica Apr 08 '16 at 14:18
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[Disclaimer: I'm a total musical layman, but with some physics background.]

What topo morto said was most important: Two tones an octave apart sound similar because they function similarly in chords and harmonics. The reason is in the physics and physiology behind acoustic sensations. Wikipedia has a whole page about that.

The general principle is that sounds with frequencies which are simple fractions of each other sound "consonant", i.e. go well together.

Two tones an octave apart have a frequency ratio of 2; that means that one can, in a melody or chord, substitute one for the other, and all the other tones will still have simple and very similar ratios to it; it will still sound consonant. (You can try that with a piano playing a simple tune or progression, replacing one note with the same note from a different octave.) If you substitute a tone by a tone with an arbitrary other frequency, by contrast, it will change the melody or chord (and usually make it less pleasant). In this sense tones an octave apart are most similar; they are the same "note".

Peter - Reinstate Monica
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  • If I'm reading your answer correctly, you're suggestion is to take a known song and substitute, for example, every occurrence of A4 with A5 (and any A5 with A6, etc.), and note that the tune is still quite recognizable (though a bit odd). Whereas doing the same process but substituting each A4 with G4 (and any G4 with E#5, etc.) would no longer be recognizable as the song at all. – Dan Henderson May 27 '16 at 14:36
  • @DanHenderson I didn't necessarily mean to substitute *every* occurrence of a given note, but yes, that would work, too, I think. Perhaps even better than substituting just *one*. – Peter - Reinstate Monica May 28 '16 at 22:00
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Let me make three comments:

1) I'm not sure the podcast intended to mean that 440 and 880, played separately, would be reported by an average joe to sound the same.

2) Todd Wilcox's observation about performing this experiment with sine waves is apt. Probably better to use an organ stop or something.

3) Try this as an experiment that's sort of halfway between playing the tones separately and together. Play A 440 along with the C (~523) and E (~659) above. This is a minor triad, but that's not important. Now drop A 440, keeping the same C and E, and add A 880. Does this sound essentially the same to you, or different? Most observers would think A/C/E and C/E/A sound similar to each other while, say, C/E/G would sound different. Put another way, in the presence of C and E (or even just one of those two notes) A 440 will sound much more similar to A 880 than it would to G 784 to most observers. But maybe you're not "most observers," which is fine.

bitguru
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Do this: have a seat at a piano or keyboard. With any group of 3 blacks, start at the right most of the 3. Calling that black key "3", play downward: "3 2 1 2 3 3 3" on those 3 blacks. You should recognize this as "Mary had a little lamb".

Then, use the 3 whites surrounding the group of 2 blacks. Play the same pattern, "3 2 1 2 3 3 3". Same song, right?

Now trying both together (or have a friend help). Why doesn't it seem to sound right? You're playing the same song, just with different "notes" (used loosely). Now place your right hand on one set of 3 blacks, and your left on another. Play those together. Much better right? We note have same song and same notes (One octave apart, with one set 2x the frequency of the other). This is the sense in which 2 notes are "the same".

Hope that helps!

Elem-Teach-w-Bach-n-Math-Ed
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To find out, having people describe the experience is not the best way. Instead, find out literally, if your perception differs from most people.

You mentioned using computer-generated tones and playing around. Use that, and make some experiments, e.g. two notes back to back and ask subjects to rate the pair as "related (harmonious)" or "unrelated". Maybe a point scale of how well they go together, or play 2 pairs and ask which pair is better.

See of your answers differ substantially from those of other subjects.

JDługosz
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