[remotemass (OP)]

I would like to know what is your theory or explanation and to compare notes with mine.
Here is my participation on the radio with Professor Prosanta Chakrabarty (Louisiana State University):
https://www.youtube.com/watch?v=ZQwXDd6P0Us
The full episode is available on the Global Radio LBC app.

Best regards,
Daniel Alexandre
Creator of 'Cubic Postcode'.

[Bored chemist]

Before you ask
Why did our brains evolve to perceive 12 musical notes?
You should ask
 did our brains evolve to perceive 12 musical notes?
And the evidence shows that they aren't.
https://en.wikipedia.org/wiki/List_of_musical_scales_and_modes

So you went on live radio to explain something that isn't even true.
:-)

[alancalverd]

We can detect much smaller shifts than a semitone - ask anyone who has ever tuned a musical instrument!

Octaves (frequency doubling) occur in most musical systems, and "western" thirds and fifths (integer submultiples) are generally considered assonant, but some Chinese scales recognise up to 40 divisions of the octave.
   
The division of the octave into 12 semitones is convenient for building fretted instruments and keyboards, and for western notation, but has no impact on the construction of  trombones and violins.

What is far more interesting (because it is true and remarkable) is our ability to distinguish the instruments playing in a recording. The loudspeaker can only move forwards and backwards, so we receive a single pressure wave, but we deconstruct it into the original  instruments and voices.  I've always wondered whether someone who had never heard the individual instruments could tell whether even a simple quartet was actually a saxophone, two guitars and ten drums and cymbals, or just one noise. 

Given that humans can deconstruct, and appreciate it, how do other animals perceive our noises?

And our images? I've noticed that my dogs seem less interested in dogs on television than previous generations of dogs and TVs. My suspicion is that their visual persistence  is too short to see a color HD-LED image as anything other than a bunch of flickering dots, whereas the old 25Hz monochrome CRT raster actually produced a near-static image.

[remotemass (OP)]

You can indeed divide the octave into other numbers of notes and still be able to recognize them and identify them but most humans consider the sounds we use in a conventional piano, with 12 keys in an octave, much more pleasant sounds, creating more harmonious and melodic tunes. Just ask anyone that tunes pianos for a living and they will all agree with this. If not, I would like them to write me for me to believe they are real piano tuners, with whom I can have a conversation, doing that for a living. That is the main reason, for using 12 notes. There are other reasons and intrincasities, if you want to go deep into it but not so relevant as the importance of having a scale with notes that don't feel out of tune to most humans with a trained ear or with a perfect pitch one. Lots of material on that on the web, as you can see googling about it.
But as I said on air, on national radio, there is not yet a scientic explanation for it, and the salient features of the first Pythagorean triple, that is the only with consecutive positive integers, may lead to a better scientific understanding of it in terms of our brain evolution and the hidden mathemstical patterns in Nature.
Also note that 5 being the hypotenuse is also curious, since 5 of the notes are less pleasant indeed. And the seven natural notes, quite naturally group into a group of three and four.

[chiralSPO]

I do not think there is sufficient evidence to say that our brains evolved to perceive 12 musical notes (there is room for argument on the bit about evolution to hear music, and the number 12). And plenty of evidence to the contrary.

Many of us may have trained our brains to perceive a 12-note scale. We are also well-trained to think in a 5-note scale, as demonstrated here:

[Bored chemist]

with 12 keys in an octave, much more pleasant sounds,

Do you really not understand that that is a matter of cultural bias?
Try this.

But as I said on air, on national radio, there is not yet a scientic explanation for it,

And, because it is not true, there will never be an explanation of it.

[alancalverd]

but most humans consider the sounds we use in a conventional piano, with 12 keys in an octave, much more pleasant sounds, creating more harmonious and melodic tunes. Just ask anyone that tunes pianos for a living and they will all agree with this.

The majority of humans live in China, the Indian subcontinent, and parts of Africa and South America, where western notation and the even-tempered 12 note scale have little impact. Only Europeans and the descendants of European immigrants think a piano is "conventional", and anyone who plays a guitar, sitar or oud will tell you that it is (a) far more popular than the piano and (b) not a truly even-tempered instrument.

It is entirely true that piano tuners tune pianos. The rest of your post is frankly nonsense.

[evan_au]

Our modern Western instruments are "even-tempered", with the frequency of adjacent notes differing by the 12th root of 2 = ¹²√2.
"Counting up 12 notes" = "Raise ¹²√2 to the 12th power", and you end up with a frequency ratio of 2, or one octave.
- With this tuning, you can play a musical piece written for any (Western) key.

But Pythagoras and friends (who developed the basis of Western harmony) would have objected to this tuning, as it does not produce exact small-integer ratios between the frequencies. They would have described the tuning as "off".
- Before the "even-tempered" tuning was accepted, "Concerto in D Major" had to be played on an instrument tuned for that key.
- Some people prefer "perfect tuned" instruments, and some electronic instruments even let you switch between even-tempered and perfect-tuned (in various keys).

...or you could follow Alan's advice, don't fret about it, and just play a violin.

[Petrochemicals]

But Pythagoras and friends (who developed the basis of Western harmony) would have objected to this tuning, as it does not produce exact small-integer ratios between the frequencies. They would have described the tuning as "off".
- Before the "even-tempered" tuning was accepted, "Concerto in D Major" had to be played on an instrument tuned for that key.

Would that be the big white keys and the little black keys being spread evenly rather than with gaps in?

[evan_au]

Would that be the big white keys and the little black keys being spread evenly rather than with gaps in?

The conventional physical arrangement of black & white keys on the piano allows you to play a C-Major scale on just the white keys*.
-This keyboard arrangement breaks up the scale into intervals of Semitones (S) and Tones (T) as follows, starting at C, and ending at the next higher C: T, T, S, T, T, T, S
- If you played both white and black notes, you would have 11 semitone intervals in an octave.
- This physical arrangement  is most easily seen by looking at a guitar: Each fret is one semitone.

The  physical arrangement gets really complex on an instrument like a saxophone, where different airholes are opened in different arrangements to produce different notes.

So the physical arrangement of keys doesn't necessarily relate to the frequency of the notes (especially on electronic instruments!).
* plus a corresponding minor key - I can't recall what this is called).

[Colin2B]

* plus a corresponding minor key - I can't recall what this is called).

Relative minor. Scale is built on 6th degree of root scale, Am in case of C major scale. The natural Am scale has no sharps or flats, but the harmonic and melodic scales do.

Just read through this thread, OP is talking great deal of rubbish as has been pointed out, will respond if get time.

[Petrochemicals]

Would that be the big white keys and the little black keys being spread evenly rather than with gaps in?

The conventional physical arrangement of black & white keys on the piano allows you to play a C-Major scale on just the white keys*.

That is 7 keys, so would that be each doubling of frequency segmented into 7?