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The Wolfram|Alpha Team

Comparing Musical Instruments with Wolfram|Alpha

July 8, 2011 —
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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.

Comparing alto sax and clarinet

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“.

Interval of music notes c4 and g3

Even though each instrument is idiomatic, different instruments may still have many commonalities, which Wolfram|Alpha can now help to illustrate and uncover. If you look at the lower part of the output for an instrument, you will see its Hornbostel–Sachs classification, which is something like a Dewey decimal system for instruments. By juxtaposing the results of multiple instruments, it becomes clear how two instruments relate and how they differ. Or try a single instrument to see a list of “related instruments” for each Hornbostel–Sachs classification—often highlighting similarities in instruments from very different cultures.

As we strive to make all knowledge computable, it’s important to remember that along with scientific, socioeconomic, and mathematical data, seemingly unlikely candidates—such as musical instruments—have much that can be computed.


This does not seem to work if one of the instruments is a “guitar;” however, it works if you specify whether you want an acoustic or electric guitar. Strange that such bias should be geared towards the guitar while that same bias is not presented towards the violin/electric violin….

Posted by Ryan July 8, 2011 at 3:31 pm

Ryan – Thank you for the feedback. We’ll make that change ASAP.

Posted by The Wolfram|Alpha Team July 8, 2011 at 3:58 pm

Great feature! FYI, the comparison for the Bass Clarinet and the Contrabass Clarinet are reversed.

Posted by Michael July 8, 2011 at 9:21 pm

Great information on these instruments. This information is very useful while playing these instruments specially saxophone.

Posted by Micheal October 29, 2012 at 1:09 am

I do agree that for thousands of years mankind has been making music and from many cultures and in many different ways. I do really love the sax as well.

Posted by Mark July 18, 2013 at 10:00 am

is there a way to search instruments that have a specific frequency range

Posted by nolopol May 26, 2014 at 7:13 am

You are providing an incredible amount of knowledge and resources to the world of music. Do you have any videos which I could share with others.


Peter Mckechnie

Posted by petermckechnie September 17, 2014 at 7:07 pm