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 »

For thousands of years, people have been making music: banging, blowing, bowing, and strumming away as soloists or in groups. With music being an integral part of culture, it is not hard to imagine that the invention and evolution of various musical instruments is a key indicator of human ingenuity. Each instrument is unique, its physical and sonic characteristics often emblematic of the culture from which it emanates.

Wolfram|Alpha now provides a significant amount of information about a myriad of musical instruments. Ask Wolfram|Alpha about any set of instruments to get a side-by-side comparison of parameters and characteristics.

For many instruments, you will notice two pods for range: “Written range” and “Sounding range”. This is because in standard music notation, some instruments are written differently than they sound; these are called transposing instruments. In many ways, it is a terribly confusing notion. A score displays a certain pitch, but the pitch the instrument produces may be higher or lower. Wolfram|Alpha illustrates this difference by displaying the pitch range (along with the corresponding frequencies and keys on a piano keyboard) for how the instrument is written as well as how it sounds. For example, the flute is a non-transposing instrument and is “written as sounds”. However, its close cousin, the alto flute, sounds a perfect fourth lower than written. Still unclear? Click the “play alto flute range notes” in the written range and sounding range pods to hear the difference. Or, you can ask Wolfram|Alpha to give you the interval between the bottom note of the written range and the corresponding sounding note by querying “interval of C4 and G3“.

Today we’re releasing the first three of a planned series of “course assistant” apps, built using Wolfram|Alpha technology.

The long-term goal is to have an assistant app for every major course, from elementary school to graduate school. And the good news is that Wolfram|Alpha has the breadth and depth of capabilities to make this possible—and not only in traditionally “computational” kinds of courses.

The concept of these apps is to make it as quick and easy as possible to access the particular capabilities of Wolfram|Alpha relevant for specific courses. Each app is organized according to the major curriculum units of a course. Then within each section of the app, there are parts that cover each of the particular types of problems relevant to that unit.

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When we launched Wolfram|Alpha in May 2009, it already contained trillions of pieces of information—the result of nearly five years of sustained data-gathering, on top of more than two decades of formula and algorithm development in *Mathematica*. Since then, we’ve successfully released a new build of Wolfram|Alpha’s codebase each week, incorporating not only hundreds of minor behind-the-scenes enhancements and bug fixes, but also a steady stream of major new features and datasets.

We’ve highlighted some of these new additions in this blog, but many more have entered the system with little fanfare. As we near the end of 2009, we wanted to look back at seven months of new Wolfram|Alpha features and functionality.

Pulling an all-nighter? Stay tuned to the Wolfram|Alpha Homework Day website to check out alternative band Common Loon from 12:10–12:30am U.S. CDT.

Is there a subject that’s keeping you up late? Submit your homework questions to be answered by members of the Wolfram|Alpha team.