Piano roll style notation systems can be useful, but they're very hard to use for human playback for basically all the reasons jcranmer states. They're originally intended for automatic playback in mechanical systems, and they work well for that, but for humans they waste lots of space on things that aren't terribly useful. They're about 1 level of sophistication above the "Square Notation" on the chart.

They've become very popular on digital systems were lots of the expressiveness of the notes doesn't really need to be encoded and the playback is automated.

Another popular and very similar system are tracker interfaces [1] which are at a slightly higher level of sophistication than many of the other examples given, but has a similar purpose to piano rolls in terms of automated playback. However, due to robust "effects" columns, can be very expressive in terms of encoding [2]. In this example, all the various pitch bends, volume, vibrato and so on are specifically encoded next to the notes. But it's also almost entirely impossible to read for human playback.

Piano roll systems usually offload this kind of encoding to secondary displays and input systems and this further disassociates lots of the information from the note information. [3]

Compare to a full score [4] which has

- a couple dozen different voices

- phrase encoding (important for performance)

- timing (4/4 4 beats per musical unit with quarter notes being the unit of tempo)

- rests where the instrument isn't being played

- note length, compactly encoded without using visual length to encode, important for human playback (it allows the player to know instantaneously how long a note should last without having to look ahead, which then frees them up to read ahead of where they're playing to "load" the next note into memory)

- chords, without using lots of white space

- absolute and relative volume: mf, f, ff, etc. and crescendo/descrescendo bars

- tempo 144

- various techniques (glissando, spiccato, etc.)

- exceptions (triplets, grace notes)

- instrument specific encodings (see the percussion section here)

- playback notes "hard yarn mallets"

- key (useful for finger placement for playback)

- huge pitch ranges using cleffs, this encoding scheme shows tuba up to piccolo and harp using the same scheme

- large scale patterns are also frequently observable so that you can be informed about how something might be played long before you have to actually play it

One of the beauties is that this scheme is incredibly flexible, the same basic system can encode performance information for everything from a violin to a metal saw submerged in water (I've seen it before). It can be used to encode one voice, two voices, or an entire orchestra, chords, accompaniment, melody, singing, and so on. And if you learn it for one instrument, you can basically "read" the music for any other instrument even if you don't know how to play it and you can look back literally hundreds of years and still basically know how to play something [5]

For people who aren't skilled musicians, many musicians are actually reading ahead and "loading note data into memory" a few moments before they actually have to play it. Very skilled musicians can "sight read" even complex music literally the first time they see it without ever practicing it. [6]

Even better, most 1st year music students can "read" the majority of any music put in front of them.

Music notation of this complexity is actually an incredible technological achievement that seems to have only really been accomplished once in all history.

1 - http://www.charliemccarron.com/wp/wp-content/uploads/2014/09...

2 - https://www.youtube.com/watch?v=u3xHPIuX3s4

3 - https://i.ytimg.com/vi/bTki0n9c3QA/maxresdefault.jpg

4 - https://i.imgur.com/XqUhdiY.jpg

5 - https://www.youtube.com/watch?v=b9IkpUYlOx8

6 - http://oi53.tinypic.com/21cy2ax.jpg