Among the world champions, at least Capablanca and Tal have suggested that chessplayers sit closer to musicians than logicians.
Mark Taimanov, WC contender in 1971, was a world-class concert pianist.
More recently (and more mundanely) Nigel Short on guitar accompanied Elizabeth Paehtz's vocals at a Kasparov supporters' rally before the 2014 FIDE elections.
Magnus Carlsen can also sing! https://www.youtube.com/watch?v=cVS-NIkkUrA
The 18th century French player Philidor was a renown opera composer as well as the best chess player of his day.
According to Jewish legend King Solomon, whose father was King David the great psalmist, was the inventor of the game.
Perhaps it's because both music and chess requires patience, disciplined work and tons of efforts.
I was also an amateur but serious musician and chess player, then I quit both of them for computer engineering. Sad. :)
Judging if a move fits the position correctly or goes along well with the flow of the game, is likely similar to judging what note to play in the middle of a song.
Instead of mathematicians I refer to logicians, so that I can imply the scientific mind per se. As for musicians, chessplayers make a difference through composing and performing at the same time, with the possible exception of opening theoreticians.
It was Grandmaster Siegbert Tarrasch who wrote, "Chess like love, like music, has the power to make men happy.
Many, not all, good chess players have a musical bent because of the "analogies" between the two.
For the most part I see logic mainly used in chess theory, it can elaborate why a certain move can be beneficial even when it would be implemented beyond your calculations, such as color affinity, but that's about the only part that takes intense logic.
The rest of the game has aesthetic appeal, I always imagine I am painting a picture, where each major piece is a different element and while certain art styles may incorporate different elements, such as abstract vs realism,the knight is harder to predict while the bishop is sharp and succinct.
I haven't researched, but I feel it's a general consensus among many chess players that the game has an aesthetic appeal. You often hear players call checkmates "beautiful" or certain plays amusing and part of this may be predictability.
In music a strong move is to create something unexpected, like you can create a gentle increasing rhythm, which is anticipated by the opponent and in the song abruptly change with a sharp strike of the violin leading into a face paced "attack" with greater speed and intensity. Of course certain musicians can predict a shift so you work to create a melody that has balance, flow, and unexpected turns to wow the audience.
This beautiful rhythm, that is a game of chess, has personality, flow, direction, even logic, as in chess theory, becomes a mature, beautiful aspect of the piece, where the famed melodies, such as immortal game, are replayed and remembered. And while this may not explain it in the most fundamental way, I feel these are easiest to relate to.
Haven't you ever got a bit excited, humored, or had a spine tingling moment in chess?
Every talent you have/learn develops also your chess skills, as it develops your brain. For example, I am not a musician, but having studied 5 or 6 foreign languages definitely helps a lot with recognising patterns on the board. Fischer said that chess has more in common with good memory rather than logical thought, but this is only true in half. The human brain is like a computer, the faster processor/brain it has, the larger memory it needs.
But that is all too philosophical...