Twitter has become the de facto information sharing and communication platform. Given the factors that influence language on Twitter - size limitation as well as communication and content-sharing mechanisms - there is a continuing debate about the position of Twitter's language in the spectrum of language on various established mediums. These include SMS and chat on the one hand (size limitations) and email (communication), blogs and newspapers (content sharing) on the other. To provide a way of determining this, we propose a computational framework that offers insights into the linguistic style of all these mediums. Our framework consists of two parts. The first part builds upon a set of linguistic features to quantify the language of a given medium. The second part introduces a flexible factorization framework, soclin, which conducts a psycholinguistic analysis of a given medium with the help of an external cognitive and affective knowledge base. Applying this analytical framework to various corpora from several major mediums, we gather statistics in order to compare the linguistics of Twitter with these other mediums via a quantitative comparative study. We present several key insights: (1) Twitter's language is surprisingly more conservative, and less informal than SMS and online chat; (2) Twitter users appear to be developing linguistically unique styles; (3) Twitter's usage of temporal references is similar to SMS and chat; and (4) Twitter has less variation of affect than other more formal mediums. The language of Twitter can thus be seen as a projection of a more formal register into a size-restricted space.