@Aaron Ok, if we do know that for sure, 100% and it wasn't some editor, then so? Doesn't change anything. Unless Liszt wrote down why then it is like everything else that will be lost to time. Just facts of life. AND NO MY CAPS WORKS FINE! See? My point was that I wasn't talking about the specific fingering choices as preference but his choice of writing them down as a preference. Bach could have wrote down his preferred fingerings, he didn't, should we ask the same question? What about every other dead composer? When do we get tired of it and just get on with the music?

Our brains work a certain way, it is mathematical, but octaves do not sound the same, they are clearly different, it is just that the mathematical nature of the brain represents sound on a manifold where they are the closest notes. I believe this is probably due to the overtone series, since that is what we are conditioned to by nature and mathematics. So octaves are the closest together due to the OT series which we hear in almost everything and our brains pick up on that connection and treats octaves as the most similar pitches.

well, we have two quick pulses then a space. Our brain will fill in the space with 25bpm to make a periodic sound. Hence 100 + 125 will sound much faster, but do it with 130 and it will sound even faster when you fill in the gaps because the ratio is not as simple(or it might sound slower in triplets). Our brains, for some reason, tries to simplify and align things probably to reduce complexity so it can understand things... so it tries to minimize certain things(I don't think anyone has figured out how it actually works so but we know what it does).

So if you add a metric to R to get "pitch space" then octaves would be the closest notes. It is sorta like p-adics. Ck is closest to Cn. Why? Because Any other note Xn when compared with Ck will produce "intermodulation distortion", e.g, 320hz and 353hz creates all kinds "extra" frequencies". Why? Because our brains can deduce all the combinations when it filters things. Take a metronome at 100bpm, we also can deduces 200, 400, 300, 50, 75, etc but the further the ratio the less likely to be(and it's imaginary anyways). Take another one though, 125bpm, now what?

Um, they DO NOT SOUND THE SAME! Who ever told you that? C5 DOES NOT sound the same as C4, C3, C8, C12, etc. The reason why they sound so similar is because they are so similar, because the vibrations are exactly some power of 2. It is not physical, it is mathematical. There is no way to tell the difference between them. Could you tell the difference between to perfect sinusoidals at the same frequency? Of course not. Well, when you compare a note and it's octave they differ the least.

@Aaron Which I answered "Personal preference". HE CHOSE TO PUT THEM THERE. It is a preference just like some people choose to put ketchup on their pizza. If he didn't do it someone might ask 'Why didn't Lizst write out all the fingerings". Hell, we don't even know if he did it or not. These questions cannot truly be answered unless Lizst, and or the editors were here to answer for what they did. They are not. Unless they wrote down the answers somewhere then they simply cannot be answered in any meaningful way. You can't prove anyone's answers will be correct then.

The only way your answer could be answered in any meaningful way if is someone exactly knew the answer, such as who did it wrote it down somewhere and told someone and so on, but good luck on that. I'm just trying to get you to understand that. The chances of anyone on the internet being able to answer such a question is the same as trying to get an answer for why the sky is blue. Sure you can get in to all the physics of it, of electronic orbitals, quantum mechanics, but that isn't why, that is how. Your question is an infinite regress, it has no real answer.

@KeizerHarm I'm not attacking you. I'm telling you that fingerings are very subjective. That answers your question. If they are subjective then it doesn't matter why they exist. Suppose any of your answers were true, so? What is the point? If they are subjective then it doesn't matter because there is no absolute logic of why. The answer of why they added them is because someone decided they wanted to and you'll never get any answer of why unless you ask that person, no one else and even then it's just their preference to do so. You wanting someone to logically deduce an answer that is illogic

Does it? Or do you just think it does? What are you comparing it against? There are lots of nice resolutions. It's like asking someone why they prefer their steak medium well. Personal preferences are just that. You should learn to recognize that what you perceive as good or bad is not necessarily what is good or bad. Probably why you think it sounds so good is that you like certain songs that happen to use that and that music made you feel good, so you associate those feelings with that progression... that is 99% of how this stuff works.

You do realize that fingering is a personal choice? Everyone has different hands with different capabilities there is absolutely ZERO logic to fingerings across the board. They are a starting point. In general I find fingerings to be pretty useless. A person should be developing their own ability to perform music without having to rely on them, they just get in the way and can be a hindrance to those that do not fit the "norm". In some cases fingerings are flat out wrong for some people and do more harm than good. Only rarely have I run across a fingering that was better than what I chose nat.