This may or may not tickle your literary fancy, but the number twelve plays a vital role in the Western musical scale.
There are twelve half-steps in an
octave (which gets its name from there being eight notes in the major scale). On a fretted instrument such as the guitar, there are twelve frets to an octave. The length of a vibrating string fretted at the twelfth fret is half as long as the length of the open string. This difference (and similarity) in wavelength and frequency is perceived by the listener as one octave, such as middle C and the C above that, or the opening guitar riff of The Knack's "My Sharona," or the bass guitar riff in Led Zepplin's "Immigrant Song" for you rock and roll fans.
The distance between frets on a guitar is related to the number 12 as well. For a given scale length, such as 25 inches, the first fret is placed at a distance that is the twelfth root of (0.5). (i.e. the number which when multiplied by itself twelve times equals 0.5, which happens to be 0.943874.)
Thus the first fret is placed at 25-25(0.943874) = 1.403142 inches from the nut at the top of the guitar neck, or 23.596857 inches from the bridge.
The second fret is placed at the same relative interval to the remaining length. It is placed 23.596857 * 0.943874 inches, or 22.272467 inches from the bridge.
This iterative process leads to the result that, at the twelfth fret, we have arrived at a point that is 1/2 the distance of the whole string, in this case 12.5 inches.
The musical notes that we experience when we listen to music are our brains' representation of mathematical differences and similarities in wavelength and frequency. Other cultures and musical traditions may divide the scale in other ways, and their music sounds as harmonious to them as Western music sounds to my Western ears.
An online fret calculator used by musical instrument makers is available
HERE, and allows you to enter your scale length and the total number of frets on the neck (not the number of frets in an octave--it's hardwired for a 12-step scale).
