As stated in the dictionary, APS = Attacks per second =/= DMG. If you increase the number of attacks per second, then you will obviously increase the DPS.
APS always affects DPS however with high CD, assuming you are ONLY casting that spell over and over again, the effect is non existant as the CD>Animation time. If we take Blinkstrike for example, it has an APS of 1.5s (assuming 0s CD and 0 APS increases) however since CD>0.67s, increasing APS means nothing when it comes to spamming Blinkstrike (you still have to wait for the CD to reuse Blinkstrike) but you can do a different follow up attack faster. IE: Blinkstrike->Quickattack with 0 APS increases will take 0.67s; but if you had 100% APS increase, it would only take 0.33s.
The Dictionary tells you that it is dependent. And please specify that these numbers are for DPS calculations as many people might not understand what you are calculating. The burst damage from +4 Extra and +4 Multi is +600% more DMG (if you are lucky 1/16).
APS and CD are different mechanics. Sadly, the APS you see on the stats page assumes you are spamming the same skill over and over. It also fails to properly calculate Chakramās APS as the weapon is very very special.
All skills have both a default APS and a CD. Discordance, as stated in the Dictionary only affects CD, Cost, DMG, Extra and Multi. APS is not affected. (I am pretty sure the Devās put an internal unreducible 0.5s CD for Discordance Specials but will have to double check)
Example:
Orb has an APS of 1.5 and a 1s CD. Because of this, if you try to spam Orb over and over, you will only cast 1 Orb per second.
Ricochet has an APS of 5 and 0s CD. Therefore, if you try to spam Ricochet, you will cast 5 Ricochet per second.
Discordance as seen in the Dictionary will swap their CD and not affect the APS. So you can cast 1.5 Orb per second and 1 Ricochet per second. With or without this Mythic, casting Orb then Ricochet or vice versa will always take 0.87s with no APS increases.