While reading more and more of this Krenek Biography, I came across a foot note that spoke a bit about the definitions of serialism and how Krenek used the term:
“Serialism” is often used to designate the twelve-tone technique, in which case the term “total serialism” or “integral serialism” refers to the technique in whichall the elements are treated serially. In his writings on the subject0, however, Krenek never uses “serialism” for the twelve-tone technique; he uses it only where others would use “total serialism” or “integral serialism.” The author has chosen to follow his example. In this account, therefore, “serialism” always refers to the later, more elaborate technique.
Stewart, J. L. (1991). Ernst Krenek: The man and his music. Berkeley: University of California Press. (269)
This is a huge problem with discussions of serialism. Many people tend to use serialism interchangeably with the twelve-tone technique, which is quite silly (and Stewart did it right here!). There are serial works that do not necessarily arrange their pitches through the twelve-tone technique. Not only that, but there are serial pieces that do not necessarily worry about arranging order to the pitches in a progressive fashion! Because of this, one could theoretically write a totally serial work without ever using the twelve-tone technique.
So to be clear. Twelve-Tone Music is a subset of serial music. Integral/Total Serialism is a subset of Serial music. The three overlap quite a bit, but are not the same thing.
Picture above so you don’t have to use your imagination.