[jng]

The white keys form a sequence of notes (frequencies) that is known as the diatonic scale. It's the foundation underlying all popular western music. It is not random or arbitrary, it has some nice dual mathematical and musical properties: intervals between the notes in the scale have special frequency ratios that sound pleasing to the ear (read Helmholtz's "On the sensations of tone" for a fascinating physically-based take on why it is like that -- he is known as "the father of acoustics", and that book contains the distillation of 8 years of deep, smart research way before we had the means or understanding we hav today). A ton, if not most, of popular music can be played using only the white keys.

There used to be keyboards with other different arrangements, which were actually extremely cumbersome and actually didn't allow very rich and interesting musical excursions like modulations (look up "microtonal keyboards"). Today's standard keyboard and tuning is a compromise between those fundamentally mathematical and perceptual acoustic relations (the tonic, the fourth, the fifth, the sixth, the major and minor third, the "sensible" or subtonic...) and the ability to perform those trans-tonality excursions. A fully regular keyboard like you propose would lend itself more easily to those excursions, at the cost of being less apt at the foundational diatonic model and most popular music.

Interestingly also, the notes used by modern keyboards and all modern instruments, and to which we are all so accustomed that we thing it "just is", is an imperfect compromise that needed a lot of selling back in the day, much of which was done by Bach (the compromise scale is called the "tempered scale", and Bach authored the arch-famous "Well-tempered clavier" pieces to show it off -- impossible to perform on keyboards with other tunings).

And of course, there is a tradition factor. English isn't written like this because it's optimizing for any easily describable or measurable optimization metric, more like it minimized a socio-perceptual function covering many centuries of UX.

Finally, if you want an instrument where all keys are equal, you can always move to a fretboard based one like the guitar. Funnily, it has a one-semitone-short jump between strings 3 and 2 that will throw off the desire of full regularity... again due to diatonic leanings. A bass guitar is fully regular, even when they add a 5th and 6th string, so that may fulfill your wish of a fully regular instrument... and it sounds awesome! Just can't do the same things as a piano or a guitar.

[brudgers]

I agree, the white keys on a piano represent a diatonic scale, but because today’s pianos are rarely tuned to anything other than 12TET, there are few interesting mathematical relationships between notes in practice (and pianos are normally tuned with high notes sharp and low notes flat because that’s how piano strings tend to produce their partials anyway).

Also worth noting the black keys represent a major pentatonic scale and the major pentatonic scale is how many of the earliest bone flutes are tuned.

[ofalkaed]

>Interestingly also, the notes used by modern keyboards and all modern instruments

Vast majority of fretted instruments since the death of the lute are untempered.

Edit: Which is not to suggest that lutes were tempered. Lutes and other tied fret instruments allow for unequal fret spacing so you can temper one string at the cost of more notes being more off from the temperament on other strings, or the frets being at an angle so you could find a bit of a compromise. But often they were EDO or in the ancient tradition of fretted instruments, close enough for rock and roll.

[moefh]

Do you mean equal-tempered?

I never heard someone describe a tuning system as "untempered", but I guess it would mean something like just intonation -- which sounds really great for playing anything in a specific key but falls horribly apart if you try to change the key (which is why it has seen very little use since the renaissance).