Insight into a Musical Octave

I've been browsing through the online magazine called



Came across it as a link on Prof Artur Ekert's Physics Symposium Profile.

It appears to be Cambridge publication, with many articles being contributed by authors from Cambridge.

Came across an article on the Mathematics of Music which answers many of my musical inquiries.

One exciting insight I gained was the construction of the musical notes in terms of the frequency. I've observed, from messing around with the guitar recently, that the frequency between any note an octave apart is related to each other by a factor of 2, for example the frequency of "Middle C" as i've learnt in the article is 262 Hz, and the frequency of "High C" is 2 times that of "Middle C", 524 Hz. As can be deduced from the fact that length of the guitar string is halved between octaves.

I've also noticed that the tone produced by a string between successive frets sound the same relative to each other. And I've been wondering exactly how this is related with the frequency.

Well, this question was answered in the article. As an octave is divided into 12 equal "tone"s or "semi-tone"s (I'm not sure what is the correct term for it, but there are 12 frets dividing an octave), the way to make each tone sound the same relative to the previous within these 12 frets is to increase the frequency of one to the other by the same factor, which works out to be the Twelveth Root of Two. When this happens, each tone would sound the same relative to the preceeding tone, and after 12 notes, the frequency would have increased by two times!