Epidemiologists use the term 'tipping point' (which is also the title of a fine book about the subject) to describe the moment when a trend goes from being unknown to being ubiquitous. Tipping points are marked by being incredibly fast acting, sometimes occuring in periods of a day or two, unexpected, and precipitated by small changes.

Its a pattern that describes everything from disease spreading to suicide rates, and in most cases, the tipping point is only obvious after it happened. After studying major disease outbreaks, epidemiologists can usually point to one event, or one small group of people that tipped a controlled infection into an epidemic. However, until the epidemic happens, one can't predict which small event is going to cause it to tip.

Societal change isn't always gradual, usually it builds slowly for a while, and then changes all at once, and it seems like the thing you are trying to name is the moment at which things begin to change all at once, the short rise time of the function. I'd go ahead and call that time the 'tipping point', when things were primed and ready (unbeknownst to most), and a small trigger event causes it all to change almost instantaneously.

True singularities probably don't really exist in a social context (and maybe not even in a physical context), since there is always a large amount of mental momentum, and time delay as communication spreads. But changes can be awfully abrupt, seeming instant when compared to years of staticity.