Comprehending the speed of light

One of the most important mathematical constants in our universe is the speed of light. It clocks in at just under 300,000,000 (three-hundred million) meters per second – a number so large that it’s hard to comprehend.

One way I thought of is to see how it relates to something that we’re all at least somewhat familiar with, that being the size of the earth.

According to Wikipedia, the earth’s circumference is about 40,007,863 meters if you measure it around the poles. From this, we can determine that light could travel this distance in about 0.13 seconds. Finally! A number that’s not ridiculously large!

Now, we just need to figure out a way to think about how long 0.13 seconds is.

Note: all numbers here are computed with high precision, but for the sake of not having large decimals in this blog, I’m truncating them to make them easier to digest.

Sound

Given that I like sound, I thought this would be an effective way to understand this number. Conveniently, there are a lot of things in audio that use units of time.

Hertz

Hertz (Hz) are used to measure events per second. Our ears can hear pressure waves that cycle between 20 times per second and 20,000 times per second, or 20Hz to 20,000Hz. Anything below 20Hz will start sounding like individual events.

Converting our 0.13 seconds into hertz is simple. All we do is divide one second by how frequent the event can happen. In our case, it’s 1/0.13, which rounds to 7.5Hz! Let’s hear what a 7.5Hz saw wave sounds like:

The time between these clicks is the time that it takes light to travel the distance of the earth’s circumference. And it’s just the right speed for clapping!

“Earth-music”

All this culminates in a genre of music that I am calling “earth music.”

The rules are simple:

• Tempo must be an integer divisor of 449.6003 bpm (449.6003/n).
• Tuning must be based around octaves of A = 7.4933Hz, so you can use A = 479.5737Hz.
• Scales must be constructed using 0.1335 somehow. A good scale to start out with is A*2^(0.1335*n), where A is the frequency we defined in the previous bullet. This equal-temperament chromatic scale has 8 notes in an octave.

Rationale

Here is how I came up with these rules.

Tempo

Since 7.5Hz is out of the audible range (below 20Hz), it’s more like a metronome than a tone to us. 7.5Hz converts to 449 bpm, which is quite fast. To make it into a more usable speed, we can divide it by 4, which gets us 112.4 bpm.

Tuning

In western music, we tune our instruments so that A4 is at 440hz. This is not good enough! The laws of nature (as we have discovered here) state that the natural resonant frequency of the earth is 7.5Hz! In order for something to be Earth-music, it must be tuned such that A = 7.5Hz, or more precisely, A = 7.4933Hz. Using multiples of this is allowed, so long as they are octaves (7.5*2^n, where n is an integer number). The closest choice to the current standard of 440Hz is 479.5737Hz, so use that one if you don’t want to destroy your instruments by tuning them down 6 octaves.

Scales (EDO)

Western scales are almost always octaves divided into 12 equal parts. This has nothing to do with the speed of light, so it must go! Instead of the (non earth-based) method of western music for dividing up an octave by multiplying a base frequency by 2^(1/12), earth music equally divides up the octave by multiples of 2^(0.1335).

This choice leads to an eight-note chromatic scale, which is much better than the western scale for many reasons. Most notably is that it has no wasted space. The major and minor scales in western music use only eight notes out of the twelve that the chromatic scale has.

To reiterate, they are WASTING 1/3 of the notes on their instruments at any given time! Instruments designed to play earth-music scales will need significantly less design work and will have less opportunity for mistakes when played.

Scales (Non-EDO)

Of course, we don’t want to limit ourselves to equal divisions of an octave, or even 8 notes. Other divisions of an octave are allowed, so long as they involve the number 0.1336.

For example, a scale that is made up of the harmonics of 7.5Hz would be a valid scale.

Fin

I hope this is inspiring in a sort of crazy kind of way. Go ask wacky what-if questions!