Professional Musicians: How long does it take and what approach do you take to memorise a extremely difficult piece of music?

Since I'm a cellist, I'll use an example from the cellist's standard repertoire, the Dvorak concerto. While still in high school, I bought a copy of it. It was crazy-hard, but every once in awhile I'd get it out and try to read through it. When I got to an impossible part, I'd skip it, then play another section that I could wade through. Not the right way to learn a major piece, but I think it's pretty typical for aspiring musicians. It wasn't until my 2nd year of music school that my teacher assigned the Dvorak concerto to me. We went through it measure by measure. (I still have the notebook in which I wrote down many of the things he said about the piece.) At that point, my goal was to be able to play the piece for my jury, or a competition. Typically, my teacher would assign a large section of the piece to be learned by my next lesson. Sometimes a section would be fairly easy to learn (maybe it was one of the famous 'big tunes' that everyone can sing from memory) but sometimes it was incredibly difficult, like a fiercely technical passage that I had to learn the technique for before I could play it. I memorized sections as I learned them, and after several months of intensive study, I could play the whole piece reasonably well. It wasn't concert-ready, it would have needed several months of polishing to get to that point. I'm not a concerto soloist, I'm an orchestral player, so I played part of the Dvorak concerto for several auditions. Each time I'd work on making it more natural and fluent. When the chance came to perform the Dvorak with an orchestra, many intervening years had passed. I didn't have to learn the piece "from scratch", but I had to thoroughly dust it off. I reminded myself what was going on in the orchestral accompaniment so I'd know which instruments to listen for, synchronize with, and what colors to use to blend or contrast with them. I thought about how I'd coordinate with the conductor: give an 'upbeat' in this bar, or wait for the 'downbeat' in the next bar? etc. I recorded myself relentlessly, listening for any lapses of intonation or sloppy rhythm--the kinds of things that audiences pick up on instantly, even if they can't say exactly what it is that's "off" to their ears. The biggest difference between my preparation of the Dvorak concerto and a major soloist's preparation is that the soloist plays the same piece over and over, year after year*. Constant repetition of the piece under performance conditions solidifies the piece both mentally and physically, in a way that practicing and polishing in a practice room can't ever quite match, but it's a luxury that few players have. *(They probably also learned the big pieces when they were younger than I learned them).

I like both of the answers that have already been given. I think that the process varies depending on training and background, on the nature of the music itself, as already pointed out, and on other factors related to timetables, the performance environment and situation, and so forth. You're right: when one hears a musician performing something like the Hammerklavier, it's marvelous to think that a human being has internalized that amount of information and is able to communicate it through essentially athletic means with such clarity, precision, and artfulness. One of the most awe-inspiring experiences I've had in that regard was attending a concert by the great organist and Juilliard professor Paul Jacobs, who performed an enormous, diverse, and virtuosic program from memory--and realizing that for him, that was really nothing special, as he is capable of playing the entire body of organ music by J. S. Bach from memory and has done so before in one extended performance (while in his very early twenties, I believe). As the synthesizer pioneer Bob Moog once put it, "When a pianist sits down and does a virtuoso performance he is in a technical sense transmitting more technical information to a machine than any other human activity involving machinery allows." The same principle applies to other instruments, though the keyboard instruments handle much more complete and complex textures, and often longer works of music, than instruments in other families (this is part of why a large proportion of great conductors have been pianists and organists). For me, music memorization has always been primarily an aural process. One would hope that music is an aural process for everyone, certainly--but what I mean is that the way in which I memorize music, even very complex music, is not much different from the way I feel when I discover to my surprise that I suddenly know the tune and all the words to a song that I've heard on the radio many times. This is probably because as a very young child I learned to play the piano and other instruments by ear, and spent an awful lot of time and energy doing it, so that my formative experiences in what music is and how it works were not tied to notation and were not really generated from contact with any one instrument. Rather, my contact with instruments was caused by a desire to be able to reproduce what I heard, a task I set about with great diligence absent any training. I am certainly not unique in this respect, but it is in my experience contrary to the formative background of a great many professional classical musicians in our time. I could improvise convincingly, if simply, in a variety of styles and could quickly learn music by ear long before I learned to read even the simplest notation. This approach had advantages and disadvantages. Since I played by ear and improvised and composed (to the extent any seven year-old can compose) before studying music according to a more formal curriculum, it was in some ways more difficult for me to learn to read music than it would have been had I started from printed notation. For about a year I was able to fool my childhood teacher into thinking I could read much better than I actually could, simply because I would have her play my pieces for me once in the lesson and then I'd go home and practice them from memory. I also came to my first lessons having acquired some sloppy technical habits at the piano, habits which plagued me for many years and a few of which still do and require great effort to overcome on a daily basis. On the other hand, I developed an uncanny ear and the ability, once I finally did learn to read notation fluently, to easily audiate (hear in my head) even complex orchestral scores just by looking at them, a skill at which many musicians have to work a great deal harder than I ever did. I found that I was also naturally suited for musical dictation, the ability to notate musical ideas accurately on the fly, one of the most invaluable skills for any composer or arranger. Now I make a good part of my living as a pianist by sight-reading (or darned near it) under pressure, but learning to read music was a particularly stressful, arduous process for me as a child ruled by the ears and not the eyes. So, then, my regimen for music memorization consists of spending a lot of time with the music, primarily a process of listening carefully while I practice, and doesn't require any special concerted effort except in relatively rare instances like great extremes of complexity or bizarrely tight timetables. That's not intended to make me sound like some genius--it's just the way I stand in relation to the music as an individual. I combine this with muscle memory, analytical score study, and the varied repetition of particularly tricky passages, facets of music internalization for all musicians. Often much of the finessing work isn't even possible until the passage or piece in question is fairly firmly engrained in my memory. For me, it generally takes a few public performances before I feel truly comfortable performing a large, difficult work from memory, since, unlike some performers, nerves in the solo setting can strongly affect my recall for reasons I don't think are tied to any lack of prior preparation. (Thankfully, my primary activity as a performer is as a chamber and ensemble musician and a collaborative pianist. This field comes with its own thrills and challenges, to be sure...performing large programs alone onstage from memory isn't one of them, though.) I know other musicians for whom the memorization process is much more rigidly structured, and more dependent on the eyes and muscles but less so on the ear, which only really comes to the forefront once they are finessing their understanding and command of the music. That approach seems to work better for their styles of learning and relationships to music. This is not at all to imply that they don't use their ears, it's just that for purposes of memorization they spend more time staring at the score in small chunks than I am prone to do in most cases. For some musicians, including some extremely fine ones, performing from memory is mostly a process of actually visualizing the score in their mind's eye as they play, a concept which seems alien to me but works very well for them.