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It's something that's puzzled me; The key that has no sharps and no flats, in essence the "basic" key, is C Major. Well, fine, but why C? Why not label that key and note A, if it's the foundation of the "basic" key of Western music? A second look, however, shows that A is indeed involved; the minor key with no sharps and flats is A minor.

That then leads to the question; does the pitch named A have that name because it is the start of the minor key, and because the minor key was more prevalent in plain chant as of the creation of written music notation? Or is there another reason?

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possible duplicate of Why is C the base note of standard notation and keys? –  American Luke Sep 14 '12 at 22:21
    
I think this is likely the case, but I can't cite a reference. I believe that around the time that music notation came into being that the interval of the major third was considered dissonant, as were major chords. –  Wheat Williams Sep 14 '12 at 23:40
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Keith, can you comment on whether the quest Luke links addresses this? I'm not totally sure. –  Matthew Read Sep 17 '12 at 15:41
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The succinct answer is that C happened to be the starting note of the latin hymn "Ut queant laxis", which became the "natural" starting note of the hexachordal system used for Gregorian chant. As music theory evolved this remained a standard reference point. –  KeithS Sep 18 '12 at 18:25
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In fact, A was never the starting point of any key in the hexachordal system until the heptachordal system evolved and all seven modes (including Ionian/major and Aeolian/minor) were introduced. –  KeithS Sep 18 '12 at 18:26
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The lowest note in the Greek scale was Proslambanomenos, an octave below the primary note, Mese. The eight notes between Proslambanomenos and Mese (inclusive) in the Greek diatonic genus form the A aeolian minor scale. This is probably why musicians chose to place A, the first letter, on the lowest and most central note.

By the later Middle Ages, it became common to extend this scale downwards by one note to G, which was written with the Greek letter Gamma. Since (after the 10th c.) the first note of a scale was called Ut (now Do everywhere except in French string tuning), this note was called Gamma-Ut. Thus playing the whole scale from lowest to highest involves the whole "gamut" of music.

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A4 is the first note of the first natural complete octave, and A4 is the basic concert note, also is the basic note to which the other notes are constructed for its frecuency in the Equal-Tempered tuning.

A4: 440 Hz, B4: 93.88 Hz, C4: 523.25 Hz ... etc

you can get the frecuency of any other octave by multiplying the A note succesively for two frecuency and using the :

A5: 880 Hz, B5: 923.33 Hz, C5: 987.77 Hz... etc A6: 1760 Hz, B6: 1975.50 Hz, C6: 2093.00 Hz ...etc A7: 3520 Hz, ... etc

So its basically the reason is the physics of the frequency of every note and how they behave. Other than that it's only a convention to name this as the first note.

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This doesn't answer the question. A4 is arbitrary; we could have used middle C (C4 ~= 262), and notes would be a fraction of a Hz higher and we wouldn't know any difference. A=440 is not a universal standard anyway; pianos, other keyboard instruments, and even full orchestras often tune higher, such as A=442 or A=444. The question is, why is the note we know as C not named A, given that it is the basis of the major key with no sharps or flats in the system? –  KeithS Sep 18 '12 at 18:08
    
The specific frecuency for the tuning of the base A note is dependent on the tuning system (thats why I specify the equal-tempered tuning) and the main reason as I specify is that A4 is the first note of the first complete natural octave, so it's more convenient to have that as the first note (at least for mathematicians) –  Lando Sep 18 '12 at 21:06
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