A (440 Hz) and A (880 Hz) are completely different sounds to me. Does this mean I'm tone deaf?

Question

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.

Answer 1

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.

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

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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.

Answer 9

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?

Answer 10

[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".

Answer 11

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!

Answer 12

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.