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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 r

by jng 1y ago

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.

ofalkaed 1y ago
>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 1y ago
  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).
  - ofalkaed 1y ago
    Equally divided octave (EDO) with no tempering which is distinct from Equal temperament. Tempered scales are generally EDO with tempering. Other methods like just intonation don't really need to be tempered and generally are not in my experience, but it has been years since I was into just intonation and may just not remember. Historically speaking, the advantage of justly tuned scales is there is no need to temper it because it is already just and perfect, things may have changed in 20th century as far as just intonation is concerned and tempering, don't recall. Edit: ET and EDO are essentially the same in the case of most fretted instruments, I am dredging long forgotten stuff from memory here and somewhat off above. Edit2: Refreshing my memory some and seeing how much things have become muddled in my head over the years. Clearly I did not even consider what came out of my memory and just regurgitated it verbatim. ET scales are not tempered but do not mean EDO. Guitar and the like are both ET and EDO. ET and EDO are untempered in the sense that notes are not shifted slightly away from the EDO/ET as they are on the piano and many instruments.

by jng 1y ago

ofalkaed 1y ago

>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 1y ago
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).
- ofalkaed 1y ago
  Equally divided octave (EDO) with no tempering which is distinct from Equal temperament. Tempered scales are generally EDO with tempering. Other methods like just intonation don't really need to be tempered and generally are not in my experience, but it has been years since I was into just intonation and may just not remember. Historically speaking, the advantage of justly tuned scales is there is no need to temper it because it is already just and perfect, things may have changed in 20th century as far as just intonation is concerned and tempering, don't recall. Edit: ET and EDO are essentially the same in the case of most fretted instruments, I am dredging long forgotten stuff from memory here and somewhat off above. Edit2: Refreshing my memory some and seeing how much things have become muddled in my head over the years. Clearly I did not even consider what came out of my memory and just regurgitated it verbatim. ET scales are not tempered but do not mean EDO. Guitar and the like are both ET and EDO. ET and EDO are untempered in the sense that notes are not shifted slightly away from the EDO/ET as they are on the piano and many instruments.