Why is it that notes "start" with C? In key signatures, for example, C Major is the basis and accidentals are added for all other key signatures. I know that the musical alphabet starts with A and goes to G, so why is C the base note of standard notation and keys? Why isn't A the basis?
Notes do not "start" with C; C major is just the easiest major key to notate in modern notation. The concept of a major key came about long after letters were assigned to the notes. Before there were major (and minor) keys, people used modes, usually just using the notes of the modern white keys and starting and ending in different places. The Ionian mode (which became modern major) was a late addition to the modes.
So it's historical accident that C major is treated as "basic."
I feel this question deserves a shorter, more to the point answer:
Because when they decided to name the notes with letters, they took a minor scale and named the notes "naturally": A, B, C, D, E, F, G. This is what we know as the A minor scale.
Therefore the choice of names was accidental - it just happened that they considered a minor scale instead of a major one. Now if we want to use the same "natural" notes in a major scale, then we need to start with C.
If, however, we were to turn back time and influence the early notation to use a major scale as a basis, then they would name "A" the first note in the natural major scale, and then today we would talk about A major as the "standard" scale. But of course this "alternate" A would be the same frequency as "our reality" C.
"... the choice of names was accidental - it just happened that they considered a minor scale instead of a major one. Now if we want to use the same "natural" notes in a major scale, then we need to start with C."
I don't think it was accidental that first mode is A minor. Rather, it represents the music of the people that created music notation: Monks. An 'Aeolian-like' sound was the their preferred mode of music making. The notes of that "Aeoloian-like" sound would have been a minor scale. That is the sound they liked to sing- and the first note of it they named 'A'. Over the course of time there was a shift brought about by the development of the tempered scale, as well the development of craftsmen skilled in tuning instruments, which made it possible for Bach to write his music (dig The Well Tempered Clavier). Bach is really the beginning of modern music and, in a way, modern consciousness. When we ponder the key of C on the piano and wonder why it's not called A, it's because we don't perceive the bias we have for the major scale. It's become part of the foundation of Western consciousness. In my humble opinion...