A map of the universe ·

If you like space, you'll love my the 12,000 billion light-year map of clusters, superclusters and voids. Find the biggest nothings in Boötes and Eridanus.The largest map there is shows the location of voids and galaxy superclusters in our visible universe.

There is no sound in space, but there is music (and genomes)

▲ The first 12 seconds of a 1-bit encoding of a 128 mel 3-bit spectrogram of Flunk's Down Here / Moon Above

The Sanctuary discs are 10 cm sapphire wafers. Each disc has about 3 billion 1.4 micron pixels that each store 1-bit of information — the pixel is either on or off. Reading the information off the disc is easy — just look at the pixels. Very closely. In other words, each disc is a very high resolution image.

To send music (or any kind of data), we need to convert it to an image. Enter the spectrogram.

A spectrogram is a 2-dimensional representation of sound. The x-axis is time and the y-axis is frequency. At each `(x,y)` position the strength of frequency `f=y` at time `t=x` is encoded by the brigthness of a pixel. This way to "draw the sound", which can be decoded back.

The National Music Centre has an excellent short tutorial on how to interpret spectrograms. And if you're a birder, then spectograms of bird calls won't be new to you.

And while I realize that aliens (almost certainly) and future humans (quite possibly) might not perceive sound in the same way, I see this as a minor point. I'm sure they'll work it out. You know... science.

I am indebted to Tim Sainburg for providing assistance and code. The analysis uses the librosa music and audio analysis Python library.

This song was written for the Moon. It sounds best there.

Flunk's History of Everything Ever album contains two versions of the song. A final vocal mix as well as an instrumental version, which you get with the purchase of the album.

But there is another. In the intermediate version, when the lyrics weren't quite finalized, Anja sang incomplete phrases and loose vocalizations.

We called this the "gibberish" version and even though the final song was ready before the discs were created, we thought gibberish made for the perfect space language.

Pretend you're an alien or human from the future and give it a listen:

If we had all the pixels on the Moon, we would encode the spectrogram with a large number of frequencies (e.g. `n = 1,024`) with very fine sampling of time (e.g. 5 ms). The song is about 4 minutes, so this would require an image of 48,000 × 1,024 × 8. The last factor of 8 is for the 8-bit encoding of each pixel.

Although this represents only about 13% of the capacity of a disc (about 200 Mb of genome sequence using our encoding) it's more than we had to spare. There weren't enough pixels on 4 discs to write 4 genomes and the proteome and instructions and the song.

It was clear that I needed a reasonably small spectrogram. There are two ways to achieve this: larger time bins and fewer frequencies. It turns out that a 50 ms time window that stepped along every 20 ms was sufficient — the music didn't have a lot of fast notes. To make the most out of the frequencies I used a psychoacoustic scale.

The mel scale is based on psychoacoustics. It is a logarithmic frequency scale and reflects the fact that we can discriminate low frequencies better than high ones. In other words, to faithfully reproduce sound you need to include more of the low frequencies than high frequencies.

The conversion between `f` in Hertz to `m` in mels is `m = k_0 \textrm{log}(1+f/k_1)`. Because mels are very efficient at spacing frequencies based on perception, I can get away with using very few mels! A-mel-zing!

I started with 512 mels and 1, 2, 3, 4 and 8 bits per mel. In this encoding, each pixel, which encodes how much of each mel is present in the sound, can have one of `2^b` values (e.g. in the 3-bit encoding we can have up to 8 values).

▲ 512 mel 3-bit encoding of Down Here / Moon Above by Flunk. The original is 11,688 × 512 pixel, shown here sliced into 10 rows and resized to 600 × 1000.

Optimizing the number of bits is really important because I didn't have that much spare space on the discs. Every pixel of music took away from pixel of genome information. Each bit of each mel requires 11,688 pixels. Thus, going from 3 bits to 4 bits in a 512 mel encoding required an additional 5,984,256 pixels. Two pixels encoded a base, so this corresponded to about 3 Mb of sequence.

Here is what the decoding of the each spectrogram sounds like — this verifies whether the music is reasonably preserved during the encoding-decoding process.

You can hear that the 8-bit and 4-bit encodings are very good. Remember, we're talking about music on the Moon here, so manage your expectations.

The 3-bit encoding is great. This is the bit sweet spot.

The 2-bit encoding isn't awesome but it's not horrible. You can definitely make out the music and lyrics but there's a warble to the sound.

The 1-bit encoding amazingly still sounds like something. It's very ghostly. The 1-bit encoding is binary — it stores whether a frequency exists at a given point in time or not. All frequencies have the same strength. I imagine this is what music in space sounds like.

The 512 mel 3-bit encoding took the 17,852,768 pixels, which was about 9 Mb of sequence. Could we do better?

▲ 128 mel 3-bit encoding of Down Here / Moon Above by Flunk. The original is 11,688 × 128 pixel, shown here sliced into 10 rows and resized to 600 × 250.

It turns out that 128 mels is all we need. Well, maybe not all we need but all we can get! And while the 128 mel 1-bit and 2-bit encodings are sketchy, the 3-bit is amazingly good.

Just think about how little information is being stored here. For each 20 ms of music, we have 128 frequencies, each of which is specified by one of 8 discrete volume levels (because we have only 3 bits).

▲ Instructions of how to decode the spectrogram.

Because the discs are a 1-bit medium, to store each pixel of the 128 mel 3-bit spectrogram, I needed 3 pixels. This was done by taking the 3-bit pixel and representing it as a column of 3 1-bit pixels. Don't worry, everything is explained in the very clear instructions on the discs.

Below is the final spectrogram as it appears on the disc, shown here wrapped into 19 rows of 600 pixels, each of which correspond to 12 seconds of music.

▲ The final 128 mel 3-bit spectrogram encoded in a 1-bit image.