How Low Can You Go?

I heard a great radio interview on NPR this week with Tim Storms, who holds the Guinness Book of Records for the lowest note sung by a human. He sang a few low notes for the interview—so low that my non-bionic ears could barely distinguish a pitch.

In 2008, Storms set a record with a low note of .7973 Hertz (Hz). He subsequently lost the record, but reclaimed it in 2012 with a low of .189 Hz, which according to Wikipedia is eight octaves below the lowest E on the piano. In the interview, Storms describes how the record-checkers determine which low note is actually the lowest. They used a frequency analyzer, which according to Storms, is usually used for testing frequencies of race car engines or “to measure elephants communicating with each other”.

That short little radio bit raised so many questions. I know about 440 A, but what are the frequencies of other notes on the piano and how can I calculate them? Can my ears tell the difference between the 2008 and 2012 low notes? And—what frequencies do elephants use to communicate? So with the help of Wikipedia and Sketchpad, I decided to explore these questions.

Wikipedia gives this handy reference chart for the frequencies of piano notes. (This chart shows the theoretical frequencies; in real-life, piano tuning is adjusted to compensate for string stiffness at the extremes. Wikipedia explains this better than I can.) Starting at A 440 Hz, which is key 49 on the piano, and scanning up and down the chart, I can see that the frequencies double/halve as I go up or down an octave, so the frequencies of the A notes in Hz are nice round numbers like 880, 440, 220, 110, and so forth, on down to the lowest note on the piano at 27.5 Hz.

Wikipedia also tells me that multiplying a frequency by the twelfth root of 2 gives a tone one half step higher. Given that there are twelve half steps in an octave, that seems logical. (I find it’s always good to do a bit of a logic check against any “fact” I find on Wikipedia.)

Now for some help from Sketchpad. First, I explored intervals. I started with that classic and memorable note, 440A. To hear that tone in Sketchpad, I used a Sound Action Button to “play” the function y = sin(440• 2πx). Then I had to do some mathematical thinking about how I would alter that musical function to go up or down a half step. You might want to think through this yourself before watching the video.

Next, I played with some very low tones. After this experimentation, I can see why Tim Storms had to have his notes checked by a machine in a sound-proof room. In my urban office setting, even with headphones on, the tones below about 10 Hz sound like a cat’s purr. Below 6 Hz, I’m no longer sure whether I’m hearing something or just imagining it. And the record-setting tones are completely inaudible. Crazy!

Now think about the math involved. Trigonometry, exponents, modeling. Anything you might want to try with your students? You can find the sketch at Sketch Exchange, along with some other contributions that investigate sound and music. I got too involved with the first few questions to get to the elephant communications. So let me know if you model that in Sketchpad!

7 thoughts on “How Low Can You Go?”

  1. Actually, what you’re hearing anywhere below about 20 Hz is overtones of the real pitch, most likely created by your headphones/speakers/etc. The human ear can only hear from about 20 Hz to 20 kHz (which is the reason a machine had to check Storms’ singing). Overtones are other frequencies layered over the fundamental frequency. They exist everywhere, and you don’t hear them individually, but they are what makes, for example, a piano sound different from a trumpet. Even if they play the same note, they have different overtones at different volumes. The overtones are always higher than the fundamental frequency, so when your slider is on 14.69 Hz, it’s not only playing that frequency, but it’s also playing overtones that are higher (i.e. in the human auditory range). Fun fact for the day! 🙂 The lowest note every sung that’s in the human voice range was a G-0 at about 24.5 Hz, sung by JD Sumner.

    1. Brady,
      That’s a great clarification, thank you! I know a little bit about overtones from playing music, and your explanation makes sense.
      I find it mind boggling––and wonderful––that Storms can sing lower than a human ear can hear.

  2. Hello!
    I found a clip of the De Profundis by Paul Mealor where Tim Storms sings a low e. It is quite astonishing!

  3. Hi my name is Elliot. I watched the u tube about the lowest note . I believe I can sing lower and more notes able please call if interested in hearing or testing . I’m not on u tube my number is07402616888

    1. Hi Elliot,

      Elizabeth’s post is in reference to an NPR interview with Tim Storms, who holds the world record according to the Guinness Book of Records. If you want to challenge that record, you need to contact them, not us. We just discussed the mathematics behind the story.

      Thanks.

  4. Actually it’s not true exactly that you would only experience tones at 20 hz and above, or that anything you detect below that would be harmonics only. With the right headphones you will feel the fundamental and you’ll be able to figure out eventually the difference between the fundamental and harmonics.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.