Monday, September 21, 2009

Equal Temperament: Music Meets Mathematics

Generalized continued fractions and equal temperament
It would be nice if we could divide an octave into equal notes and then be able to have an interval close to a perfect fifth (which raises the frequency by 3/2). That's how equal temperament works: it divides an octave into twelve equal notes and then it turns out that an interval of seven notes is close to a perfect fifth. That's actually why this particular scale was chosen and a reason it has been so successful.


We discuss why there are no negative gravitational sources in General Relativity and show that it is possible to extend the classical theory such that repulsive gravitational interaction occurs.

Interesting, but as the author points out in a previous preprint which provides more details of the theory: A Bi-Metric Theory with Exchange Symmetry "As this example shows, the bi-metric model is not causal ..."