Sviatoslav Richter’s version of Mussorgsky’s Pictures at an Exhibition, recorded live in Sofia Bulgaria back in 1958 has a noticeable flub, early on. I still consider it one of the supreme recordings of any sort of music ever made.
Still, the answer to the OP: **Practice! **
Yeah, you’re underestimating muscle memory. After a certain amount of practice, it’s actually easier to play the piece right than to play it wrong. I’d go farther than woodstockbirdybird: it’s not just that you don’t *have *to think about it; it’s that thinking about it could actually *make *you stumble. But if you just let your fingers do the work, they’ll get it bang on.
I haven’t lived in a house with a piano in 17 years - I only get a proper go at a piano a few times a year - but I can still sit down and play a handful of pieces* from memory with ridiculous accuracy, because I practised them so hard back in school. My mind has no idea how they go and couldn’t even tell you what key they’re in, but my fingers still know.
*Rondo alla Turca AAAIEEEEEE
I played viola back in junior high and high school, but I was never a genius at it. To start with, it’s just it’s just index, middle, and ring fingers, (1st, 2nd, and 3rd fingers, respectively) and your hand stays in one position. (The pinky would be the same note as the next higher string.) You learn where the whole steps and half steps are. On the C (lowest) string you play 1st finger for D, then a gap with the 2nd finger to E, then 3rd finger close for the F. (G string is the same.) On D string, 1st and 3rd are the same position, but 2nd is played close against the 1st finger. (A string is the same.) Violins have an E string, so you play the first finger back for the E-F half step.
Once you’ve got that down, you start using the 4th finger instead of an open string, so you can get vibrato. Then you start moving your hand up to higher positions; if your 1st finger comes down where your 3rd finger normally would, that’s third position. As you move up the fingerboard, the spaces between the notes get closer, just like the frets on a guitar. And that’s about as far as my string career went. I could get to third position, but when I tried to get back to first position I would pull the instrument out from under my chin.
Now that I write that all out, it does sound kind of complicated. Maybe I am a genius.
I’ve always wondered about brass and wind instruments. You say that you change the ambrochure, but how the hell do you do that? Is it infinitely variable (could you play a glissando with just your mouth) or is there some physical property of the instrument and your mouth that makes only certain notes possible? How do wind players know all the combinations of keys on a clarinet, oboe, etc.? String instruments have patterns; four strings and moving up the fingerboard produces higher notes. A clarinet looks like chaos to me.
I came in here to mention this recording! Such a clunker of a note in the Promenade, but so gorgeous everywhere else.
I’m preparing for a big recital and it’s a combination of:
As all of the other musician Dopers have replied: practice.
I wonder if the OP isn’t trying to get at something a bit more subtle, such as: let’s say you *have *practiced, and *have *the required muscle memory; if you are improvising a solo, how do you decide which notes to play AND successfully execute that choice - while in the flow of the music?
OP, does your question include that dimension of things?
If so - then, to me, there are a few ways this happens:
Practice buys you time: like the X-Men in the Danger Room or an NFL quarterback checking down potential receivers, practice buys you an extra second, the ability to work through options, decide what to play next and have the muscle memory to pull it off.
You fall back on structures: if you know your scales - or on guitar you know the box-shapes of notes that sound good for Blues - then you can buy time by following the structure. That is why some folks playing solo sound like they are playing scales - sometimes they are ;). If used judiciously - i.e., to buy time and figure out the next artistic choices you want to make - it can be helpful. Otherwise, it can sound like you saying “umm” or “like” while figuring out what you really want to say.
You get in the moment: in the zone, inside the music, being in the flow - call it what you will. This is when it all comes together and you feel like you are moving through note choices that come effortlessly and there is minimal application of conscious effort. A good day - heck, a magic day - but no different magic than an athlete getting into the zone in their sport or a scientist getting inside their data to gain new insight.
In another thread currently in CS, there is a discussion of whether “better” means “more technically well-executed.” It leads to a consideration of “slop” in one’s playing and whether that is a bad thing. If you value clean execution above all else, then slop is bad. If you want to get inside the zone and make effortless note choices - well, a lot of great players are willing to have a little slop in their playing in pursuit of that creative spark.
Hope this helps…
Of course, in addition to practice, there’s something else at play.
Non-musicians are often absolutely horrible at picking out mistakes. Even lower level trained musicians have trouble finding flaws in musicians that are significantly better than they are.
For instance: I’m a percussionist, and I used to be fairly decent (was 2nd chair of our schools top symphonic band, out of four such bands in the school). Anyway, when I was a sophomore, I made our top band (which was just called Symphony Band, as opposed to the two Concert Bands). I remember one of the early rehearsals, when we’d been rehearsing a piece (that was by far the hardest concert music I’d played in band), and I was astounded at just HOW GOOD the band sounded as a whole, even with limited practice on this piece.
Then our director stopped the band and basically said “That was awful.” and started pointing out intonation problems in each section, etc. I thought he was nuts. By the time I was a senior, not only could I hear every mistake in early rehearsals, when listening to recordings (our best recordings, which were damn good for a high school group…we always received superior ratings in class AA state competition)…I can hear problems all over the place. The clarinets will be flat, a trumpet fracks a note, the oboe tightens up and goes sharp for a bit.
Meanwhile, my wife (who is now a music teacher and was part of top symphonic and orchestral groups in college), finds errors when listening to recordings from the New York Philharmonic (which, to me, generally sound perfect).
Trust me, there are errors being made, you just can’t hear them if they’ve practiced enough.
Catherine Drinker Bowen, “Fiddlers and Friends”
Jinx, I think the easiest way for you to answer this question is to pick an instrument or a discipline like singing, and give it a go. You’ve got all the evidence you need to prove how hard it is - now, I think it’d be useful for you to prove to yourself how easy it is.
The big thing is - it’s harder for grown-ups than it is for children. (I know, it’s a dangerous assumption to call someone posting here a grown-up. I, myself, am barely 8; don’t tell anyone!) Grown-ups always seem to come at music with a preconceived notion of what they want to sound like, or what they want to be playing. Sure, they understand intellectually that you have to crawl before you can walk, but when push comes to shove, they always have the underlying idea that they aren’t progressing fast enough, and there must be something wrong with them.
Whereas some 6 year old scraping out ‘Twinkle, Twinkle, Little Star’ for a Suzuki class isn’t practicing, in the grown-up sense of the word, she’s just playing. Grown-ups are too impatient for that, and so, little Suki goes naturally from Twinkle to a Mozart sonata in 8 to 10 years (or a piece of equal complexity that catches her interest…). 8 year old Don goes from a melody-only version of ‘Für Elise’ to some Art Tatum-like stuff in 10 years, but his dad, who started out with really basic Grade 6 RCM material is cranky that he’s now working on Grade 8 material instead of that Chopin Ballade or Liszt Hungarian Rhapsody. I see it happen all the time - childish playfulness beats adult over-drive any day of the week.
If you take something up and you can keep it childish, you’ll be amazed how easy it is!
I’m a professional orchestral musician, and have been for over twenty years. I am a music professor a good music school at a major state university, where I teach my instrument (bassoon) and also music theory and composition; I also have been performing professionally in orchestras (meaning, I got paid) since I was 18.
I have never played a completely perfect concert, ever. And neither has anyone else, in fact. Certainly no one I know or have ever heard in concert. Ideally, most people don’t notice the mistakes, or don’t care because everything else is so good. The truth is I notice my own mistakes far, far more than anyone else would (even other professional musicians).
With recordings, errors are usually edited out. When it comes to live performance (which is where it’s at in terms of the real excitement in the musical experience), the risk of errors is part of the drama and fun. If I do my job well, neither the audience nor my fellow musicians care about the inevitable (hopefully very small) mistakes.
The human brain is a marvelous appliance. I often wonder just how we can remember such huge quantities of detailed data, but we can.
To the OP: think of something you do frequently, and well. Driving, ballplaying, walking, flying a plane, reading a book – everyone has something complicated that they do without much thought. The way you remember how to do it is the same way musicians remember where their fingers go.
You don’t consider walking difficult? It requires high coordination between balance sensors and several motor movements of the body, all without continuous use of sight. Pretty amazing, really. Music performance is just more of that.
You move your fingers where they always have gone, then adjust as needed. If someone were to record, in micron-level measurement detail, the position of a trombonist’s hands for position #3 over time, it would be different each time, but not much. Not enough to be called a mistake, and if the player hears the pitch slightly sharp or flat, he adjusts.
In fact, string players (violin, viola, cello, etc.) are all using a fretless fingerboard, but they are trained to provide a vibrato for longer notes. The vibrato, which is a rapidly varying pitch, tends to cover up pitch approximations, especially in a string section. Our ears are pretty accurate, but not that accurate to complain about slight errors.
This is why the ladies love the brass section. 
First of all, it’s embouchure. And, until you have experience, it truly is chaos.
Really good players, brass and woodwind, can produce a barely-credible glissando by mouth action alone.
Most brass and woodwind instruments require considerable skill in hitting a note just right. There is some leeway between a good pitch and one slightly high or low. The skill is in the automatic adjustment. It can be a tightening of the mouth or lips, or a tilt of the instrument to compensate for pure acoustics and practical pitches.
One reason is the harmonic series is not perfect, at least not to our ears. Some pitches are inherently “wrong” and must be adjusted to match what we want to hear.
A musician playing an ascending scale (on woodwinds and brass) is jumping between, say, the 3rd harmonic of one root to the 5th harmonic of another, to the 4th harmonic of another, just to produce adjacent half-step pitches. Each harmonic requires a different pressure, angle or lip shape. Pretty complicated until you get it under your belt, and this is what separates the amateurs from the professionals.
Keyboardists don’t have this problem!
Better to say that the 12-tone Western scale does not adhere to the pure integer-based intervals that Nature provides. Not only doesn’t, but can’t.
The harmonic series is a law of nature. Scales in use in Western music, not so much.
How does anyone speak so well? How does your tongue know how to hit that letter “T” every time you need it? How the throat manage to “guh” just right every time you ask it to?
You practice it until you don’t need to think about it. Your body can just do it; and if you think about it, that’s when you mess up.
Piano is one of the easier ones, IMHO. If you hit the right note with the right ampount of force, you’ll get the right tone every time. If you don’t it’s the piano’s fault.
The hardest instrument I’ve ever seriously tried was the clarinet. You had to soak the reed just right, and then attach it just right, and then twist your fingers into the right ungodly positions, and then fly to the next position with ridiculous speed, and then your diaphragm has to push out with the just the right force while your mouth does whaever it does when the air gets aimed correctly and throughout all this your lips must apply the right pressure . . . Dang it was hard. I gave up after two years. When it worked it was heavenly, but there was just too little return for the effort.
It’s a little incorrect, IMHO, to say “practice makes perfect”. More correct to say “Practice makes permanent” or “Perfect practice makes perfect”.
I used to hear piano students all the time practicing in mistakes. If you’re practicing by starting at the beginning and going to the point where you fuck it up, and you fuck it up every time, and then you stop and you go back to the beginning and etc, etc, etc…
Obviously, practice / experience plays a vital role in achieving a “perfect” performance (if there is such a thing), but one thing that hasn’t been mentioned is the performer’s ability to cover mistakes. I am a guitarist in a steadily gigging rock band, and can really only speak for that instrument, and that genre, but rarely do I have a perfect night, and usually I make some sort of error on most songs. And this still happens even with years of experience and full sobriety :). I would be willing to bet, however, that the casual listener doesn’t notice 95 percent or maybe none of the errors, and a careful listener probably doesn’t notice most of them either. Why? This goes back to knowing how to cover mistakes. When one is made, don’t wince, and for goodness sake, don’t stop and look at your bandmates. Move forward with the groove as if you’ve just gave the performance of a lifetime!! Also, little tricks such as a quick percussive string mute, or a slide into or out of the note can be a convincing cover up. All of these “tricks” can be worked in so seamlessly they literally become part of the musician’s style, and the listener is typically none the wiser.
The other day, a lady with a masters in piano performance asked me how I learned to play harmonica so well.
I was blunt with her: if you know music theory, you can learn blues/folk harmonica in five minutes. Seriously.
Practice, practice practice. I am not a musician but I am a dancer. I practiced at least an hour a day and more than that on the weekends and I still made mistakes.
Not the breath control part you can’t.
Or Bachmaninov. 
My ex wife was a child prodigy. So were her brothers. In the violin / quarter world they are well known.
They practiced incessantly. Every day. For hours. I grew to understand that they were striving for more than note accuracy. They were- every day - striving to create a transformative moment. When the music becomes much more than some notes played accurately.
I get it. And I respect the goal.