#Minecraft 1.9.0+, 204 162 bytes + 58 36 28 2424 20 blocks = 262 240 232 186 182 blytes
This solution is golfed down, and it can't be seen whole in one, or even two screenshots. Uses two glitches and abuses another two features of the game
This solution uses the same principles as the one below, just a 4 blocks more compact design.
Abuses the fact that Chain command blocks (green blocks) can't be powered by redstone, only by a singal from a impulse command block (orange).
Abuses the fact pistons take 0.30 seconds to extend completely, and redstone needs only 0.10s to register a signal.
Also abuses a twofold glitch to set the timer (TNT) off: the redstone next to the timer (TNT) gets not only powered, but also thinks the TNT is another redstone and powers it.
On top of all these abuses, the signal shortener (thing under the TNT) is one-use, after it gets powered it changes shape, allowing to pass signal through it to the "incrementer" (topmost orange block)
A bit of explanation on the functionality of it's different parts can be seen in older solutions (but best in the one just below)
###Old solution, Minecraft 1.9.0+, 186 blytes:
###Old###Older solution, Minecraft 1.9.0+, 232 blytes:
###Older###Even older solution, Minecraft 1.7.0+, 240 blytes:
Screenshots are of my own, dual licenced under WTFPL and what licence SE decides to use today (currently cc by-sa 3.0 with attribution required
) :-)