I disagree. Here's a quote from an interesting site I discovered yesterday:
'In any case, the ability to think musically and, consequently, the ability to complete any kind of musical creation on instrument via internal anticipative [also – creative] hearing, but not via deliberating about notes, keys, names of sounds and/or about hands – is the most basic feature differentiating musical talent from the musically poorly gifted human being.'
https://www.pianoeu.com/indexje.html
I think he's saying you can, and in my experience it does happen magically. It's when you deny the magic it fails to materialize.
He is saying IF there is "musical talent" it will happen magically. So how are we going to relate this to the poster's question? We're going to say she's obviously untalented and should just give up? If the above holds up to any scrutiny, what other answer can possible follow?
More sensibly, we can realise that control over your sound is not about musical talent- but about PHYSICAL talent for being able to make movements in such a way that the resulting sound can be reliably predicted. The poster can then go about finding ways to improve upon the skills that have not come as naturally to her as they do to a small lucky elite. If you use movements where the resulting sound is inherently less predictable and subject to less reliable control, no amount of talent will compensate. The ear only exposes that the sounds are not as intended. Control evolves as a result of using movements that have consistently predictable results in sound. If they don't, you need to change how you move. At the root of it is a physical issue- which allows what is supposedly "musical" talent to evolve. He has it in reverse. When a person moves in a predictable enough way to produce intended sounds reliably, we describe them as being musically talented. When a person has no such talent, we decide that they are not "musical". "Musical talent" for producing the intended sound is the EFFECT of a physical issue that makes it possible, not the cause.
Her post shows that musical talent is exactly what she DOES have. She has enough to observe that her sounds do not correspond to her intentions. Ironically, in many cases it may well be that those who think it's all about the ear and the musical intention are simple deaf to the fine details. Except where ultra-talented, they may actually be relatively deaf to the inconsistencies between what they intend and how they really sound. Those who KNOW that there is a discrepancy may often be more musically talented and better at listening to themselves than those who think that it's only about intentions. If a pianist has never run into a situation where they realise how difficult it is to execute their intentions, either they are a rare genius or too limited as a musician to realise the extent of their failings. Those who are able to observe problems are the GOOD listeners- not the bad ones. Telling them to think more about music (which is why they are already pissed off with the results) is just ridiculous.
Only in piano teaching are we still in the dark ages of believing that magic occurs. What string teacher doesn't bother to deal with bowing issues? What teacher starts with the musical line, if the student can't bow properly? What wind teacher decides that if the student is musical, they'll figure out how to breathe for themself? At the root of piano technique, you need to be able to move the fingers in a mechanically efficient way, if you are to be able to reliably produce the volume of sound you intend. When a student has not mastered this foundation, telling them they are obviously not musical enough is just about the stupidest thing possible.
Here's a recent film of myself playing Liszt:
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While I'm not overwhelmed with the results, the style of music makes it possible to produce something that gives a reasonable reflection of my musical intentions- although there are countless issues where technical issues get in the way of the sound, such as the l.h. arpeggios at 5 minutes in, which I would like to be pppp and I also find the semiquavers at about 5.30 far too "notey" (to mention but two issues).
Anyway, it's not too hard to produce something that sounds relatively musical in Liszt, without having to become furious with yourself time after time. When I play something like a Haydn slow movement or a Bach fugue, just the slightest discrepancy between the intended sound and that which occurs does not blend into the bigger picture. It destroys the musical line. The stronger your musical intentions, the harder it is to produce anything remotely satisfactory. The stronger your desire to produce a specific sound, the more you realise the failings not in your musicianship, but in the CONTROL over what you produce.
Having high standards is exactly why many pianists need to work on the simple issue of moving in a way where every tone can be predictable. If a pool player can't cue straight, they need to start by potting dead straight balls until they can- not by practising elaborate potting angles. Similarly, a pianist needs to work on simple control of tone. If you always make it about elaborate musical shapes, you actually just make it easier to get away with poor control. Control over sound is the foundation of all good piano playing. The easiest way to develop that is to keep it simple- so any failures will be exposed at once. Once you have the means to control a simple even line, you can move on to controlling more elaborate shapes.