Now that we’ve generated a .wav file from our sine wave, let’s take a look at some of the limitations of music as it’s written for the human ear[1].

We’ll start with the low end of human perception.

As you may recall, last time, we made a 100Hz sine wave:

This is near the bottom of what most humans can hear (and close to the bottom of what I can sing), but there’s still plenty of room to explore.

One octave down, we have 50Hz:

This is as low as I can comfortably hear (and sing!). Below this, for various reasons, things get much quieter[2] and more difficult to produce.

25Hz:

At normal volumes (halfway up on my laptop) sounds quite soft, but still audible. At louder volumes, it sounds like something you might hear in the 8-bit audio of a game from the early ’90s, perhaps in a dungeon to tell you something is oozing out of the wall.

12.5Hz:

To me, this is inaudible at normal volumes. At high volumes, it feels like what gargling would sound like in an 8-bit world.

6.25Hz:

At normal volumes, still inaudible. At high volumes, almost like water.

3.125Hz:

If the previous one sounded almost like water, this is the real deal. Still inaudible (as you would expect) at normal volumes.

1.0675Hz:

I totally did not expect to go this low in frequency. This sounds perhaps even more like water at high volumes. I wonder why all of these do. Maybe it’s some other effect unrelated to the actual frequency of the sinewave, perhaps waves (and water) do actually make sounds at such low frequencies, or those low frequencies make secondary effects/harmonics at high amplitudes.

Next time, we’ll look at the high end of human hearing. Stay tuned[3]!

[1]I’m leaving out discussion of making music to be felt by other parts of the body, although that is probably a large part of why dance clubs are so popular. We could also talk about different species, using devices, perhaps mediated human listening to music, but that is outside of scope.

[2]I had assumed it had to do with the amount of energy being transmitted being non-linear with the frequency, but apparently it has more to do with human hearing. ‘Equal-loudness contours‘ will show you the way.

[3]Hee.