Sunday, April 12, 2015

Getting Real Pt 5. - Entropy

According to Information Theory, Entropy (or Shannon Entropy) is the "average amount of information contained in each message received" or "Entropy is best understood as a measure of uncertainty rather than certainty as entropy is larger for more random sources". Basically, low entropy means predictability which means smaller amounts of information which thus translates into something that's easy to compress. High entropy means lots of unique information, low predictability and thus harder to compress. Remembering in part 3, the last step, and one of the most critical steps, is compression.

Why am I bringing this up? Well, to successfully fit a score into a 4k or 8k production, the composer has to think of the entropy of this music. Think of it this way. Suppose for the 8k we played a single note, A-4, for the entire production. This is easy to compress, all that needs to be recorded is one note playing for the duration.

But suppose we played a different note, using a different instrument, for different lengths, at different volumes, for every possible combination until the demo was finished. There's no way to simplify that, you have to record these combinations somewhere, when they played and all of the other characteristics. There's no way to simplify things.

Another example, now suppose instead of a single note, we played the same note over and over again at a regular interval.

A-4
...
A-4
...
A-4
...
A-4
...

While not as easy to compress as the first example, it's still pretty easy, all that needs to be recorded is that a single note is played every two places for the entire song.

What about this?

A-4
A-4
...
...
...
A-4
...
A-4
A-4
...
...
A-4

Again, this is harder to compress because we don't have a regularly repeating pattern of notes, the entropy is higher.

What does this mean for Second Reality? With 23 parts, about 60 different instruments, and two different composers, the entropy is wildly high.

For fun, I took just the note data from Skaven's introduction, removed all of the effects and compressed the Song.xml file that Renoise produces (inside of the .xrns file) and compressed it with 7zip set to "Ultra". It compressed down to 8,148 bytes. Yikes! This is without the instruments, the player code, the Purple Motion sections and any of the visuals.


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