A few Quotations:

Since my goal is to find the relationship between the various movements in Modernism – scientific, intellectual, musical, artistic, social – I thought it would be worthwhile to save the intro to the Wikipedia article on Modernism as well as the one on Postmodernism.

http://en.wikipedia.org/wiki/Modernism:

Modernism describes an array of cultural movements rooted in the changes in Western society in the late nineteenth and early twentieth century. The term covers a series of reforming movements in art, architecture, music, literature and the applied arts which emerged during this period.
It is a trend of thought that affirms the power of human beings to create, improve, and reshape their environment, with the aid of scientific knowledge, technology or practical experimentation.[1] Modernism encouraged the re-examination of every aspect of existence, from commerce to philosophy, with the goal of finding that which was 'holding back' progress, and replacing it with new, progressive and therefore better, ways of reaching the same end. Embracing change and the present, modernism encompasses the works of thinkers who rebelled against nineteenth century academic and historicist traditions, believing the "traditional" forms of art, architecture, literature, religious faith, social organization and daily life were becoming outdated; they directly confronted the new economic, social and political conditions of an emerging fully industrialized world. Some divide the 20th Century into movements designated Modernism and Postmodernism, whereas others see them as two aspects of the same movement.

http://en.wikipedia.org/wiki/Postmodernism:

Postmodernism literally means 'after the modernist movement'. While "modern" itself refers to something "related to the present", the movement of modernism and the following reaction of postmodernism are defined by a set of perspectives. It is used in critical theory to refer to a point of departure for works of literature, drama, architecture, and design, as well as in marketing and business and the interpretation of history, law and culture in the late 20th century. Unfortunately, there is no authoritative definition yet.
Postmodernism is an aesthetic, literary, political or social philosophy, which was the basis of the attempt to describe a condition, or a state of being, or something concerned with changes to institutions and conditions (as in Giddens, 1990) as postmodernity. In other words, postmodernism is the "cultural and intellectual phenomenon", especially since the 1920s' new movements in the arts, while postmodernity focuses on social and political outworkings and innovations globally, especially since the 1960s in the West.
Merriam-Webster attempts to describe the term as either of, relating to, or being an era after a modern one or of, relating to, or being any of various movements in reaction to modernism that are typically characterized by a return to traditional materials and forms (as in architecture) or by ironic self-reference and absurdity (as in literature), or finally of, relating to, or being a theory that involves a radical reappraisal of modern assumptions about culture, identity, history, or language.[1] The American Heritage Dictionary describes the term as Of or relating to art, architecture, or literature that reacts against earlier modernist principles, as by reintroducing traditional or classical elements of style or by carrying modernist styles or practices to extremes: “It [a roadhouse]is so architecturally interesting . . . with its postmodern wooden booths and sculptural clock” (Ruth Reichl, Cook's November 19

I may comment on these later.