A logarithmic music scale

In an article from the Mercury News Indie rocker mixes math with music [no longer available], we read of a musician who uses a logarithmic music scale.

Schneider [...] has a zeal for math that approaches infinity. He even completed two calculus classes and two physics classes behind his manager's back as he worked on his band's latest CD, "New Magnetic Wonder."

Schneider's two loves, math and music, came together on the new CD. Two short tracks were written using his new scale, which is based on natural logarithms.

The intervals between notes shrink as you go up the scale, and only two of the notes are familiar pitches. The result is a weird, unearthly sound that Schneider compares to "alien classical music."

My own 10-Note Musical Scale

In a previous life when I was heavily into music, I created a 10-note scale. [Western music normally uses 12 notes per octave; 7 white notes and 5 black notes on a piano.]

My 10-note scale was evenly divided, that is, there was an equal "space" between each of the 10 notes. So instead of using 2^n/12 to determine the frequency of the next note in the scale, as is the case with an equal-tempered 12-tone scale, mine used 2^n/10. [To see what I am talking about, go to What are the frequencies of music notes?.]

My scale sounded pretty awful, but mathematically it was kinda neat. I could only "play" it on a computer, since no real instrument could play it (with the exception of stringed instruments like a violin, but it would be very difficult to hit the correct notes, or perhaps a re-tuned piano).

Robert Schneider's logarithmic scale also sounds pretty bad, but it is nonetheless interesting. His scale is only possible on a computer, as well:

Schneider knew the math behind the scale was beautiful, but it took a year before his brother-in-law created a computer program that let him hear it played on a traditional keyboard. The odd sounds from the familiar interface were jarring at first.

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