As stated, a lot of practice can help with the fingering and so forth, but I’m completely amazed along with you, if we’re considering the music of someone like Art Tatum. He’d play a mixture of 10th notes, 12th notes, and every other kind all within the same measure with such little effort that you wouldn’t quite know the difficulty until you look at the sheet music score.
When I was younger I played violin and viola, neither of which has frets. The amazing thing is that even though the viola was something like 14% larger than the violin, it didn’t take me long to make the adjustment. Somehow I managed to find the right notes, even though my fingers had to be farther apart. And of course that’s just the left hand; the right hand had its own difficulties.
I recently picked up the violin after several decades of not playing. Surprisingly, my intonation and bowing weren’t as bad as I had expected . . . but I was unable to make my left-hand fingers move fast enough. Probably just an age thing; everything mover more slowly now.
As others have said, it’s all about practice. I play piano, and I’m generally in the 30-60 minutes a day for practicing, not the hours I wish I could spend, but I’m an amateur. But it requires as much practice as any other sort of skill like that. When I was learning to type, I would watch my fingers, and as I stopped looking, I would have to type slowly at first to make sure that I don’t make any mistakes and the speed came with time. Anyone who tries to type 120wpm right away will, of course, be typing nothing but nonsense.
So for me, my practicing will usually involve a few different things. I’ll have a few sort of exercise bits that I work through as sort of a warm up, practice some scales and such for dexterity. I’ll play through most of the newest stuff I’ve been working on to keep it fresh. I’ll also generally pick something kind of old and play through it so I don’t completely forget it. Then I can approach what I’m trying to learn or compose. If I’m actually trying to compose, I’ll have to play close to speed to get the feel down, then I’ll slow it down and go over that part a dozen times or so and work the speed up. Once I’ve got the new part mostly down, I’ll play it in context a few times to help with the segue and consistency and all. Sometimes as I’m practicing a piece I already mostly know, I’ll notice a mistake, and I’ll replay through that part, slower and correctly a few times, to help reinforce the correct way to play it.
And like others have said, it may sound like musicians play perfectly, but they don’t. I remember when I went to see a well known pianist several years ago and he had a question/answer session at the end. One of the questions that was asked was about how he learned to play perfectly, and the first thing he said was that he made a lot of mistakes. I’d picked up on only a couple of them, but I also wasn’t familiar with most of the pieces he was performing, and most of the audience, including my then girlfriend, hadn’t picked up a single one.
Another checking in–I played trombone in concert and marching bands through high school, and occasionally stood in for a guy in a jazz combo in college, but haven’t touched it since. I think I still have the old muscle memory for a few of our standards, but I’d have hell sight-reading anything, and my embouchure is all wrong now. When I play anything these days, it’s usually one of my various flutes, and I don’t practice with any of those enough to be any good. I mostly just noodle around or play a few things by ear.
I need to restring my harp and start practicing with it again
We should start a club! I could be, like, the secretary or something since I can’t play for shit anymore.
One thing I haven’t seen mentioned is “presentation” and “selling it”. One of the biggest mistakes a performing musician can make is to physically react to their own errors. For example, wincing or grimacing when they make a mistake. Basically, doing anything at all that calls attention to the mistake.
I’m primarily a bass guitarist by choice these days, and it’s the instrument I’m best at. But when I sing solo in public I accompany myself on the 6-string acoustic guitar. While I’m a competent guitarist, I don’t consider myself anything more than competent. I know my chords, and know enough technique to add a bit of flair and interest to my playing, but I would never try to be a lead guitarist in a band, because I’m just not good enough for that. Yet, when I play guitar in public, I’m consistently approached by people after the performance, who tell me what an “awesome” guitarist I am. This is even when I know I made numerous mistakes during the performance.
The reason is that, when I make a mistake, I simply don’t acknowledge it. I never break my rhythm, my facial expression doesn’t change, and I don’t give any kind of visual clue that anything is awry. I may be kicking myself mentally for the mistake, but as far as the audience can see, all is well, and they never notice that a mistake was made.
And really, I think that’s what most professional performing musicians do. Unless the song degenerates into a complete train wreck, they just keep going as if nothing is wrong, and in all likelihood, nobody in the audience will notice anything wrong. The only people likely to notice minor mistakes are the musicians in the audience who have played the songs themselves.
Having a solid knowledge of music theory is also a big help. I once performed a song in church, accompanying myself on the piano — an instrument I’m just barely competent on — and since I hadn’t memorized the piano part, I was playing from the sheet music. The piano part was simple enough that I could play it with my level of piano skill, but at one point in the song I completely lost my place in the sheet music. Fortunately, I did have the lyrics memorized, and even though I’d lost my place as far as the correct notes went, I could remember the chord structure of the song. So I shifted from playing the written notes to simply playing the appropriate chords until I found my place again. And nobody noticed that anything had gone wrong.
Oh, yes. Ten years ago, give or take slightly, a bell choir I was involved with played in front of a bunch of school children. We had a pair of narrators telling the Christmas Story, and the bells provided accompaniment.
And there was a spot where we played a very distinctive and familiar riff–I could sing it, but I’m not sure I can type it. At any rate, it ended with a B flat instead of a B natural.
An adult audience would have probably known that was wrong just from hearing it. I’m not sure the kids would have. But, several people laughed.
And during our Q & A session, somebody asked if we’d made a mistake. And said they knew because we laughed.
Just had to chime in on this- it’s true, it’s true! I love that recital. The Mussorgsky is mind blowingly good. That flub at the start just strikes me as charming, as the rest is SO like a boss. I also really enjoy his Schubert- light and fleet footed, but singing lyrically the whole time.
-BB
You took the words right out of my mouth. My mom plays fiddle, and when I used to live with her I would hear her practicing in her room. Her method for mastering a song was to break it down- the particularly difficult/complex parts she would repeat slowly, over and over and OVER to the point where even I could tell if she screwed up the song/skipped a part.
The big pitfall to mastering a musical instrument is a lack of patience. I used to teach beginner piano, and would tell kids that in order to sound really great, you have to be willing to do the boring stuff (scales, particularly) to get your fingers ready. But the upshot is that if you are willing to get through all the boring, tedious repetition, you can amaze yourself. I played Moonlight Sonata to my fellow teachers/students in a recital and everybody congratulated me on the performance. For me, though, it didn’t feel like I did much of anything- I really was just thinking about the song in my head and imagined I was moving my fingers as though my hands were floating in water.
I’m no virtuoso, but I understand music enough to know what you have to put into it. The funny thing is non-musical people tend to veer toward the extremes- they either think its SO EASY or they think its TOO HARD! The ironic thing is that many of these folks are patient enough to keep pulling a slot machine handle for a jackpot, kill boars endlessly for some rare sword in an MMORPG, or rhythmically wiggle their legs to music over and and over. I figure if you can do stuff like that, you can master a musical instrument 
I’m convinced that at the top levels there is a natural ability to just hit the right notes. Cad Jnr. is a musical prodigy. Thats not just me. He plays 4 instruments and his music teachers say he could be a professional but he never practices. Anyways, when he first picked up the violin (his first instrument) his teacher was amazed that he just knew where to put his fingers. He learned to play the oboe while in band simply by watching the fingering of the oboeists while simultaneously playing the clarinet.
Re the chaos of clarinet keys: #23 It might help to know that if on a wood-wind you close all the holes in its length, you get its lowest note. Start at the bottom and open one hole at a time and you are playing the scale. The levers get the notes in between: sharps/flats. Because the configuration of fingers for one note may be quite different from that of the next note in the work, there are 2 or 3 alternate fingerings for many notes. After you learn them, this is an aid to rapid playing, not a distraction. The notes for each octave are fingered basically the same, with an octave key, change in wind, etc. (This ignores the many exceptions to the rules!)
This is something of an oversimplification. The “octave” key throws you up a 12th. It’s usually called a register key. On a saxophone this key does indeed raise the output an octave.
Sorry - small mistake: the octaves are fingered similarly in oboe,flute, sax, recorder; but not on the clarinet.
I actually think one of the best things you can learn as a performing musician is how to hide a mistake. I believe it is a myth that practice makes you perfect. It gets close, but any number of outside factors can make you mess up. Knowing how to handle that is something I think every musician should learn.
And the best way to learn this is to occasionally play things you haven’t practiced. Sight read, or even play by ear. Don’t go into the piece because you want to learn it, but because you want to learn how to handle the inevitable mistakes without them sounding like mistakes.
Sure, the critic with a score will notice, but no one else will.