While mathematics and music are inextricably linked, music is often regarded as magical. It transcends emotion and nature in a way that is often hard, if not impossible, to properly explain. For example, many people are deeply affected by the emotional power of Beethoven’s Ninth Symphony, but may not fully understand why. Perhaps great composers simply intuit mathematical connections to music.

But even music has plenty of structures that are clearly identifiable and thus computable. At Wolfram|Alpha, we are working hard to identify these underlying structures and are coming up with exciting ways to bring them to life.

Take a musical scale as an example. While we are used to arpeggios and melodic figures fluttering through familiar musical pieces, it is helpful to see that at its core, a scale has an intrinsic structure. Each pitch relates to the next by a certain measurable difference. Further, each of the pitches, which we perceive generally as high or low in a pitch space, has a specific frequency. More »