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Surely everyone who struggles with relative pitch already has in-built relative pitch, so why is it so hard to actually recognise intervals?

What I mean is from a child I (and most other people I imagine) could sing a tune they had just heard. They might sing it in the wrong key but they would still sing it correctly in a key. To do this you surely need to be able to know the intervals in the tune you have just heard and then replay it back with your voice.

However, ask me explicitly to say whether an interval is a half tone or whole tone and I will struggle. How can this be? How can I easy sing a song whose first two notes are a tone apart yet not be able to recognise a tone in isolation?

Another way of phrasing this question is, why can most people learn to identify intervals easily using reference songs for each interval (took me less than 48 hours to do it within 95% accuracy) but yet actually memorising the intervals in isolation takes months (years in my case).

I realise that this question is not just about music theory but neuroscience and that it may not be wholly understood but I am interested to read your views.

Please note that this question is not about any actual instrument. A good answer will also EITHER explain why I appear to have memorised intervals since I can sing tunes well yet not recognise an interval in isolation OR reveal why my being able to sing tunes does not imply that I have internalised intervals. I write this because there are so many answers on the internet which superficially answer this question without getting to the heart of the query

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    I tried to make the title more specific; feel free to edit or rollback as needed! – Richard Jun 10 at 0:12
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    Interesting, I think this is analogous to an athlete throwing a ball to a teammate. A child can quickly learn to throw accurately to someone 10 m away, 20 m away, 30 m away, etc.; but being able to say how far away that teammate is requires additional knowledge about length units and considerable practice and experience. – Sam Jun 10 at 14:20
  • If someone can jog, why can they not also recognize the muscles used in jogging? – Greg Martin Jun 10 at 17:26
  • I mean, this is partly tongue in cheek but can a tape recorder understand what an interval is? It is entirely possible to reproduce a sound without understanding abstractly how it was designed. – Vality Jun 10 at 19:41
  • Your question immediately made me think of this video which supports your claim. The presenter teaches the audience two notes, which they repeat, but then (at 0:43) jumps to the next note and the audience finds the right note (even better at the end of the video), showing that people do intuitively understand intervals and scales, even if not consciously (since I doubt any significant percentage of the audience would be able to even tell you what an interval precisely is, let alone recognize or measure one). – Flater Jun 11 at 10:50

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I think the answer boils down to what you mean by "knowing" the intervals.

To do this [sing a tune back] you surely need to be able to know the intervals in the tune you have just heard and then replay it back with your voice.

I don't think "knowing" these intervals in order to sing something back means you know if an interval is, e.g., a major or a minor third. When you sing something, you're just mimicking something you already know. There's not necessarily any true "knowledge" here; just ask the countless opera singers that sing for hours in another language without actually knowing how to speak it. They can reproduce the sounds, but they don't fully understand the meaning behind them. The same is true here.

But there's an added wrinkle: intervallic ear training is problematic because it's teaching you intervals within a very specific functional context. People use "Somewhere Over the Rainbow" as an ascending octave, but it's really an ascending octave from scale-degree 1 up to another scale-degree 1. If you're singing scale-degree 3, thinking of "Somewhere Over the Rainbow" won't always be helpful; you may well sing up to scale-degree 1 (a minor sixth), not an octave up to scale-degree 3.

As another example, people can know what a major second is (it begins "Happy Birthday"), but they may only be able to recognize it accurately when it's between scale-degrees 5 and 6 in major (as it is in that tune). They'll likely have some problems hearing—and definitely creating without prior reference—that same major second between scale-degrees 3 and ♯4.

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    So basically, we don't necessarily memorize relative pitch, but tonality, according to this explanation. Does that suggest that internalizing melodies from songs with ambiguous tonality or songs that are deliberately atonal would aid intervallic relative pitch? – awe lotta Jun 9 at 23:39
  • “problems hearing...that same major second between scale-degrees 3 and ♯4” – right. Moreover, they might even feel that the minor second between 3 and ♮4 sounds more similar to the major second between 5 and 6, simply because it fits more natural without that Lydian ♯4! – leftaroundabout Jun 10 at 12:46
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    Mimicking is easy - birds do it all the time. Does that mean birds instinctively have a full understanding of basic music theory? Hardly. – Darrel Hoffman Jun 10 at 13:23
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    @awelotta: I don’t read this answer is saying “we don’t memorise melodies X way, we memorise them Y way instead”. I read this answer as saying “there are many different ways we can memorise a melody, so being able to sing a melody doesn’t imply capability in any one specific approach”. – PLL Jun 10 at 16:57
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I'm going to take this one from the perspective of someone who's long earned a living by being able to sing well, yet has an abysmal pitch recollection without at least some cues to it…
I suppose I also ought to mention that even though I've been doing this nearly 50 years now, I have no formal training to speak of.

Part of singing a tune you already know is that, either consciously or subconsciously, you are also hearing the chord structure that the tune went with. This is a massive 'coat hanger/scaffolding' that holds up the entire structure & gives it recognisable form.
For a song I know well & have performed often I can pretty much hit the right key from the start with no external reference, just because my voice knows where it is even if my brain doesn't, & not drift for the entire song.
Once I nail it, I've got it.

Any tune in isolation, with no chord structure, is going to be harder to remember, especially if it's very chromatic - harder intervals, harder to learn in isolation. Even a song I've heard a lot, but is outside my repertoire, so I'm having to try to pull together this invisible chord sequence without already knowing it well-enough, can be a challenge in this respect.

As a singer with really tight pitch tolerance, but nothing that could even be called good interval recognition [I can find an interval only by singing a scale & counting] I don't know how the guys who can do this… do this.
If I can't hear or at least manufacture in my head a generic chord structure the melody sits on, I will quickly lose it. I'm stumped, not even a clue where the next note should be.

What a muso-psychologist would make of that, I have no idea ;)

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    As someone who's learning Gregorian chant, I don't think that this explanation really holds up; similar for many styles of folk music. It might help as a mnemonic with certain melodies but definitely isn't a necessary skeleton. – chrylis -cautiouslyoptimistic- Jun 10 at 1:18
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    @chrylis-cautiouslyoptimistic- well, different genres, different approaches. I (as an instrumentalist) think very much in relation to harmonic functions too, which works great in a rock/blues/pop setting, pretty useful in a classical setting, but indeed tends to be rather counterproductive when I'm playing folk tunes, especially ones that are not derived from central-, western- or southern-European traditions. – leftaroundabout Jun 10 at 12:55
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Because our brains don't need to consciously be aware of intervals.

Your question is the same as the following question:

If I draw an X on the ground and ask someone to jump from where they're standing to the marked spot, and if they succeed at doing so, why are they not also able to tell me exactly what distance they've jumped?

Or even more succinctly:

If people can perceive the color aquamarine, why can't they tell me its precise RGB values?

For the jumping example, the visual information of gauging a distance and the physical movement required to jump to it is not mentally processed using numbers or any kind of objectively measurable unit.
Cognitively, we could physically measure the distance, derive the required forced to launch our body in a parabolic trajectory from the origin to the destination, work out how to move our muscles to generate this precise amount of force, and then do it. But our brains have been hardwired to deal with sensory information subconsciously.

For the color example, while theoretically your eyes are perceiving individual RGB values using rods and cones, we cannot consciously parse this information separately. Instead, our brain only receives the aggregated RGB output and only sees the big picture. It isn't really capable of independently observing the alpha channels (i.e. the R, G and B information separately).

Similarly, for your question, auditory information doesn't always get mentally processed using music theory. If every human were required to understand the theory behind the music they make, the field of music theory would only be able to focus on exploring new things (that people cannot yet do until the appropriate theory is invented), rather than defining things that people are already doing (but cannot yet theoretically/analytically express).

It's a fairly recurring thing in life where people are first able to do something, and only then figure out the theory behind it (why they are able to do it, how to do it better, ...)
It's very rare for something (especially something sensory) to be discovered purely theoretically before there has been any physical encounter or application.

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My answer is that the solution is: re-formatting our "hard disk". You're correct saying that we have no problem to identify intervals referring to songs, but parallel we need to recognize the intervals by their character of perfect consonance, consonance and dissonance without referring to a song, or integrate both paths to one way of recognition and association.

As long we have to analyze the intervals by references to songs-intervals we are only on the half way. We need more practice and my way is ear training by writing and composing.

So my answer is: Normally we don't have just one approach to identify sounds and chords. The song reference is not every ones approach. And even if we are able to sing a song in tune not everyone is able to play it. But just find out the intervals on an instrument by trial and error is a good practice.

It may be similar to the grammatical analysis of our mother language. We are able to talk and understand others, but to use our words with content of their etymological meaning we have a long way to go of studying and researching.

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There are many things that we learn to do backwards. Personally, I learned to talk as a young child many years before I learned to spell the words I was speaking. Somehow we seem to be able to perform functions such as things we hear and see happening around us without knowing all the details. I can drive my car without knowing the mechanics involved. I can play my guitar without knowing music theory. And like you, I could sing without knowing a thing about intervals. These are abilities that we have. The things like spelling, mechanics, music theory, and intervals, seem to be our attempt to explain the processes that are taking place in an attempt to advance our understanding of what we are doing. This is of value to some of us and completely worthless to others of us depending on our interests. I apologize for not being able to explain the workings of my brain, I've done no studies in that realm.

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I wondered the same thing! I still can't recognise isolated major thirds and minor thirds well, but I can sing them accurately. I don't know the answer for certain, but maybe these anecdotes can help get us closer to the answer.

Singing intervals from song reference is easier because we are singing relative to a tonic. If the song is C major, singing a G -> B major third is easier than hearing it without a tonic because our brains are hearing the C -> G perfect fifth and the C -> B major seventh. Our familiarity with the major scale helps us here. (This was pure anecdote but after a quick Google apparently it's been researched and researchers found that tonal context DID improve interval recognition for musicians. https://www.frontiersin.org/articles/10.3389/fpsyg.2017.01753/full)

Compare this with exercises where an app will play some intervals, ascending or descending, in some order:

  1. The width of an interval varies with pitch, which adds to confusion. The absolute change in frequency of a major third between C and E is narrower than a minor third between the A and C above, for example.
  2. In regards to the neuroscience you mentioned, one "artifact" of interval recognition exercises I noticed myself falling for is an apparent widening/narrowing depending on frequency change between interval pairs. E.G if I heard a major third from, say, C4 to E4, and then another from G2 to B2, I "felt" the second interval narrower than it was, because it had just descended pitch significantly. Similarly, big ascensions tricked me into thinking they were wider.
  3. I found that exercises which used pure tones (no overtones) were far harder than ones which used piano soundbanks. I also find it much easier to match pitch to human voice than piano).
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  • Some of this seems speculative, and #1 doesn't make sense to me. – Ben Crowell Jun 11 at 15:07
  • Hi @Ben, yep I agree it is speculative; I prefaced my answer as such! I'm certainly no expert, just wanted to add my two cents. In regards to point 1 though, that's a mathematical truth. If the width in Hz of a major third from C4 to E4 is X Hz, and the width of a minor third from A4 to C5 is Y Hz, then Y is greater than X. – Alan Jun 11 at 17:15
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I often remember music accurately enough that I can play it back in my head, complete with instrumentation details. This means that, when I sing that song, I pitch-match my singing to the audio clip in my head. I don't necessarily pick up on the intervals I sing.

(This leads to obvious trouble when I'm told to transpose any song that changes keys enough times. In this case, I actually often remember the interval I need to transpose instead of the interval between the note I'm singing and the next or previous note in the song.)

Based on studies of the Levitin Effect, where some people can recognize when music is played in the original or correct key even without musical training, I believe I am far from the only person who remembers music this way. Therefore, I believe that many others, and possibly you, could very well sing songs purely by matching sung notes to memorized audio clips instead of replicating interval chains.

(My experience with interval training with reference tunes, though, is that the tunes actually do lead to quick interval-in-isolation recognition. Ear training for piano exams was particularly cruel like that.)

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Perhaps I'm getting your question wrong but: Think of it like being able to recognizing colors and knowing the names of said colors. You can know what yellow, red, blue feels like, and can discriminate between each other. If someone shows you a yellow sheet and tells you to choose the crayon that has the same color, you can grab the yellow crayon (you can sing the interval you heard). But if you never managed to memorize that the sheet's yellow color is actually called "yellow", i.e. the name given to that color is "yellow" you can't name it (you can't name the interval). So being able to discriminate between pitches, and knowing the name of said intervals are entirely different things.

Of course, most people's visual / color perception is a lot better than their sound perception. So memorizing colors (associating the certain quality of things you see to names) come easier for most (but not all) people. Memorizing intervals are generally harder for that reason.

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    I find the analogy very valid, both are frequencies, even if the tool to perceive them is different, it takes knowledge and learning to be able to tell what is the frequency delta between 2 in both of them – Kaddath Jun 11 at 16:05
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Great question!

Another phenomenon is that for most people (including me) it is more difficult to tell apart intervals in the high registers, and much easier to identify intervals in their own vocal range.

@Richard and many others gave excellent answers. It has much to do with context. Let me note that for my ear training, I use an app called Functional Ear Trainer, that not only plays intervals, but plays them within a harmonic context.

So, my initial remarks and the explanations make one thing clear: intervals are an abstraction! One specific aspect, disregarding everything else. People who sing songs, sing intervals, but not every sequence of intervals makes up a song. There are much more constraints on the intervals to actually make them a (pleasant to hear and memorable) song.

Some analogies: You are much more than merely the chemical components you are built of. The computer in front of you is much more than a bunch of metal, plastic and silicon. This is what Aristotle meant with saying The whole is more than the sum of its parts.

I vaguely remember that psychologists confirmed that people could have good domain specific knowledge that they struggle to transfer to a different task, even though that task might be the same on an abstract level. I am sorry, I cannot cite anything since it is almost teen years ago since I studied psychology. But I can give you some keywords for your own research: domain-specific knowledge, expertise, knowledge transfer, problem-solving, cognitive psychology.

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Another issue not yet mentioned is that some melodies, as popularly performed, may include features like slides, bends, or blue notes that don't fit the normal terminology for intervals. If a singer sings the root, followed briefly by a pitch that's slightly above the major third, but it quickly falls to be closer to a minor third and then its descent slows briefly, before accelerating into a slide back to the root, what interval did the singer perform? One might be able to accurately mimic a popular performance of a piece but be be unable to determine whether an interval is a major third or a minor third because the interval one is performing might not be either of them, but instead some weird hybrid for which no standard terminology exists.

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