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e.g If we played C and D# on the piano in ascending order (Let's call it tune 1) and then D# and F# in ascending order again (Let's call it tune 2), We know both tunes are slightly different but almost sound the same.

What is the reason behind this?

Why does any interval sound almost the same?

Update : What I wanted to ask in the question is why does any minor third on the piano sound almost the same as any other minor third? Why does any perfect fifth sound like any other perfect fifth?

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    I'm not understanding your question here. They sound like the same interval… because it's the same interval. 3 semitones. – Tetsujin Sep 11 '20 at 11:00
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    If the perceived relationship between two tones depended somehow on their absolute position - if, say, C to D# sounded different from D# to F# - then we wouldn't have given names to the gaps between tones! 'Minor third' is only a useful term because it always sounds 'the same' – AakashM Sep 11 '20 at 13:02
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    'We know both tunes are slightly different' - how, in what way do they differ? – Tim Sep 11 '20 at 15:43
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    I don't know if this is close enough to flag as a duplicate, but I believe the question basically reduces to the same question as this one. – Athanasius Sep 11 '20 at 16:11
  • Note, this is only true on modern pianos because we use equal temperament. If you were to tune a piano to have perfect fifths all the way down (as was standard practice on older instruments), it would no longer have perfect octaves, or vice versa. They do not quite line up mathematically, so we have to split the difference to make it sound as close as possible so that things sound good in all keys. On older tunings, the further away you get from the key of C, the more out of tune your instrument would sound. – Darrel Hoffman Sep 11 '20 at 19:24
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Because the ratio of their frequencies is the same.

Humans hear the difference between 110Hz and 220Hz as the "same" as the difference between 220Hz and 440Hz, even though in the first case you're increasing by 110Hz, and in the second it's 220Hz. It's the doubling we hear.

So, in your case, assuming we start on middle C:

  • C has a frequency of 261.626Hz and D♯ has a frequency of 311.127Hz, so we get 311.127/261.626 = 1.1892

  • D♯ has a frequency of 311.127Hz and F♯ has a frequency of 369.994Hz, so we get 369.994/311.127 = 1.1892

We can round that to 1.2, which gives us a ratio of 6/5, which you'll find is the ratio for a minor third interval.

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    In fact most human senses recognize ratios (i.e. they work "logarithmically") rather than absolute distances. One can speculate that this is useful because you can probably distinguish only so many different levels of perception, and a logarithmic mapping lets you represent a wider range. – Kilian Foth Sep 11 '20 at 15:27
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The interval between C and D♯ is an augmented second. The interval between D♯ ad F♯ is a minor third.

Both augmented 2nd and minor third intervals sound the same.

If we called the first notes C and E♭ (enharmonically the same notes, then that would be called a minor third.

If we called the second set of notes D♯ and Ex (E♯♯), that would be an augmented second.

There are several ways to name intervals, depending on what names each note is given. Just listening in isolation, it's virtually impossible to say what the notes are called, thus virtually impossible to give the interval between them a name.

It's hardly any interval sounding the same, but several.

In your case, one interval is an augmented second, the other a minor third - both of which sound the same. Main consideration for intervals is deciding what letter name to call each note. For example, had you called the 1st C, the next E♭ and the last G♭, there would be two minor thirds - C>E♭ and E♭>G♭.

Playing them all, as a chord, would then make C diminished triad.

Edit: now you've pretty well changed the question, my answer, which addressed the original, is pretty well redundant.

There is a straightforward scientific reason, which the other answer provides. But the whole point of having these things musos call 'intervals' is that yes, they will sound the same - they're supposed to.

Let's take P5 - a perfect fifth interval. It could be C>G, D>A, B♭>F, G♯>D♯, and many others. It doesn't matter whether they're low or high notes - as long as the second is 7 semitones above the first. And all the other intervals - and their equivalents - sound the same because that's what they do - physically down to ratios of frequeny - which stays the same for any given interval (and equivalent interval) regardless of which octave the two notes are from (high or low, but they must both be in that same octave). The phenomenon was discovered, and is a useful piece of knowledge

However, you can still take note of my previous answer, as that tries to explain something which you appear to be somewhat vague about - the naming of intervals themselves.

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@seumasmac has given the correct answer. I'll add to it from a different point of view.

  1. People have differently-pitched voices from high to low. When we speak we do not use a monotone, we change pitch to add expression to our voices. If our brains didn't use equivalent intervals but had to use addition of pitch, small children would not be able to understand grown men and vice versa. Note that women tend to have higher voices than men and this helps children understand them better when first learning to speak.

  2. A minority of musicians have perfect-pitch. This means that they can identify each note individually. For them, they can tell the difference between the intervals that you mention. Those intervals have a distinct sound for them. Usually however, they can hear both the similarity of intervals and the difference. Most musicians have only relative pitch and therefore only hear the similarity.

I don't have perfect pitch so I don't know if some people have perfect pitch but not relative pitch. If such people exist, I think music and speaking could be difficult for them. (see Edit)

EDIT

See this question by someone who has perfect pitch and wants to learn/improve relative pitch. How can I develop relative pitch if I have perfect pitch?

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