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A logarithmic music scale

By Murray Bourne, 21 Aug 2007

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 2n/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 2n/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.

See the 8 Comments below.

8 Comments on “A logarithmic music scale”

  1. vlorbik says:

    you know about this guy? mathemusicality.
    i've just *cut* it from my blogroll since it's
    pretty much all about music & i'm from the
    "dancing about architechture" school ...
    but it might just be right up *your* alley.

  2. Murray says:

    Thanks for the suggestion - looks like he and I are on the same piece of manuscript.

  3. carol says:

    I'd like to know about the missing two strings of Davids Harp. It is said that these two strings/ notes were outlawed by Constantine because they were too holy. What were they and how do they sound? Thanks, Carol E.

  4. Murray says:

    Hi Carol

    This is new to me and I couldn't find any more information on it. This resource indicates that David did not actually play what we call "harp" today:

  5. Sabby says:

    I am doing a math project on why a musical scale is logarithmic by nature? could someone give me an equation and an explanation to use?


  6. Murray says:

    Hello Sabby. The frequencies of the 12 notes used in a music (5 "white" notes and 7 "black" notes) increase exponentially. Since exponential and logarithmic functions are inverses of each other, this may be what you are looking for.

    See this page: Frequencies of notes in music

  7. -x- says:

    I'm interested in hearing this scale, could you please provide some sort of sound file or link.

  8. Murray says:

    Hi. I don't have a sound file, and I just tried to find a java or Flash applet that would give something close, but to no avail.

    I'll keep looking...

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