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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.

  • 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 Payne Apr 7 '16 at 11:39
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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 7 '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 7 '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 7 '16 at 20:53
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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 8 '16 at 19:01

12 Answers 12

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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.

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    Worth noting that the name of the field dealing with this is psychophysics. – user1803551 Apr 8 '16 at 18:04
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    Also, here is an old paper about it. – user1803551 Apr 8 '16 at 18:10
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    @user1803551 or 'psychoacoustics', more specifically..? – topo Reinstate Monica Apr 8 '16 at 21:33
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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 9 '16 at 23:00
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    For colors there is a 1:1 correspondence between hue and frequency; 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.

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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? – topo Reinstate Monica Apr 7 '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 7 '16 at 12:30
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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. – topo Reinstate Monica Apr 7 '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 7 '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 7 '16 at 12:53
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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.

  • Thanks for your answer. Could you describe further the "certain similarity"? I'm pretty sure that's what I'm not hearing or not understanding. – laffoyb Apr 7 '16 at 12:07
  • It's not easy, although I hope somebody can describe. A bit like asking someone to describe the taste of an orange... – Tim Apr 7 '16 at 13:14
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    @Tim that's easy; it tastes just like the color. – WorseDoughnut Apr 7 '16 at 13:43
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    @WorseDoughnut No, the taste is a lot yellower. – Mr Lister Apr 7 '16 at 13:52
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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.

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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" – topo Reinstate Monica Apr 7 '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 7 '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 8 '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 8 '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.

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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.

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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 7 '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 7 '16 at 12:52
  • So what do you hear as you step up the notes? That would be useful info. – Doktor Mayhem Apr 7 '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 7 '16 at 12:55
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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 7 '16 at 13:59
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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.

  • 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.... – David Bowling Sep 16 '18 at 0:47
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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?

  • 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 7 '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 8 '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 8 '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".

  • 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.

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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!

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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.

protected by Dom Apr 7 '16 at 15:46

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