Why can you drop your A string to G, but it sounds nothing like the "g" string (3rd string) on a guitar.

Question

Same with E which is on both the first and last string, but sounds nothing alike?

What makes a "note" a note?

Answer 1

There are more than one of each note, and they're actually called "pitches."

The music alphabet goes A-G (which you probably knew), and each note is separated from the next by steps (the name for the spaces between notes). There are half-steps and whole steps. The notes repeat infinitely both higher and lower, but there is only a certain range in which humans can hear them. The pitches are specifically designated as sounds that vibrate a certain number of times per minute. For example, Middle C (C4, or the key in the very middle of a piano keyboard) resonates at 261.626 Hertz. The next highest C vibrates exactly twice as fast, at 523.251 Hertz. The lower notes of the same name would vibrate half as fast each time you move down an octave. The two E strings, like you asked about, are an octave apart (which means they are eight steps apart).

Have you ever tried to sing along with the radio to a song with a singer of the opposite gender? Chances are you were not singing the exact same pitch as that person, but assuming you were singing in tune, you were singing the right notes in a different range, or octave.

The reason there can be more than one of any given pitch is because there are several, each in different ranges.  

Answer 2

Short answer:

It's one octave lower.

Translation: 1 octave lower means exactly ½ the frequency of the frequency in question.

Q2:  What makes a 'note' is any frequency which is an integral multiple of an already defined note; eg, middle A is 440 Hz-- 1 octave higher is 880 Hz.  1 octave lower is 220 Hz.

The notes normally used in western music (12 '½steps' per octave) are each equal to the note below multiplied by the twelfth root of 2.

Answer 3

The primary frequencies are the same, but the other horminics are different due to the diameter and weight of the string.

A G on a piano sounds different from a G on the guitar, but the primary frequencies are the same.