Earlier it was stated that the frequency of a note is roughly double that of a previous octave. An accomodation is actually made to wire-stringed musical instruments to compensate for the natural inharmonicity of their vibrating elements. This is called, "stretch tuning" and you can see in the chart above how it is done.
Guitar
Standard tuning for a guitar is by fourths. That is to say, from the lowest E string the next one - A - is tuned a fourth above it. This continues on through the rest of the strings with the only exception being the B string, which is tuned a third above G. A bass is tuned exactly like the lowest four strings a a guitar except that the notes are an octave lower.
Violin
Some instruments, such as a violin or mandolin, are tuned in fifths.
Circle of Fifths mapped out
As you recall the circle of fifths ascends by fifths in one direction while the fourths can be seen in the other direction. So it is easy to see that in the case of some instruments, such as guitars and violins you have ready access to the circle of fifths since the instrument itself maps out the intervals. Were you to play a C, for instance, on the third fret of the A string on a guitar you would see that the fourth above it is an F, because it resides in the same position on the adjacent D string. Likewise, you would know that a G is a fifth above it because it resides in the same position on the E string. This pattern is simply reversed on a violin or mandolin. That is why you can take the notes on lowest 4 strings of a guitar chord and play them upside down on a mandolin.
...and if you're curious about the various periods of music you've been seeing in the right column here is a list of people who know a lot more than me: Composers.
