About 1.5 billion years ago, a pair of black holes, each about 30 times the mass of the Sun, collided.

About 4 years ago, the spacetime ripples from this merger caused the length of a set of tunnels to change by about the diameter of a proton. This made a lot of people very excited, and is widely regarded as one of the most important observations in astronomy.

Of course, these kinds of discovery come with a surge of media attention, and this one had an extra advantage (in addition to being about black holes, which are always popular): when treated as a sound wave, the measured distortion in spacetime made a funny sound.

I’ve heard a few different representations of the chirp (as it’s called), and heard chirps from a few different gravitational wave detections, but I’ve never seen anyone try to express it using musical notation.

My self-set challenge then, was to convert this:

into something resembling sheet music.

To determine the correct note pitches, durations, and dynamics, I originally planned to extract the original LIGO data and calculate the frequency spectrum myself. Unsurprisingly, it turns out this is really hard, so I just fit functions for the frequency and amplitude to the spectrogram from the paper. I’d like to say I did something fancy here, but I just eyeballed it (using the same colour scheme helps a lot).

The frequency ranges from 45 Hz initially, and is loudest at 163 Hz, which can be expressed musically as F^{#}_{1} and F_{3}, giving us the range of pitches in the final score.

Next up, I needed to work out the note durations. There was some freedom of choice here, as I could adopt a lower tempo with faster notes. The final scaling is a compromise between having enough resolution to express the note lengths, and resorting to using all quasihemidemisemiquavers (1/128 notes). I decided on using one bar to represent 0.01 seconds of time, which gives a tempo of 24000 crotchets (quarter notes) per minute. Since the spectrogram covers 0.15 seconds, the sheet music will be 15 bars long.

Finally, dynamics – this is arguably the handwaviest conversion. The amplitude of the gravitational waves is expressed as strain – the relative size of the spacetime distortion. For GW150914, this was about 10^{-21} (strain has no units). Plugging the strain into this formula

gives a peak amplitude of -420 dB. Then taking this table and wildly extrapolating, we can determine that at its loudest, the gravitational wave reaches a volume of *ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp*, which I’ll express as *p*^{129}. From there, I can just check my amplitude function to place the other dynamical markings.

Adding a final decoration or two gives the final piece:

By the way, those final few notes are each 0.0003 seconds long – on a piano, the player’s hands would have to move rightward at 64 km/h.