It appears that Chang has taken known things and given them new names. It has been pointed out that this is for the purpose of getting at the physical act of playing, otherwise known as technique. However, in any music study, we take the theoretical part of music (what we want to produce) and examine the physical way of executing it. We name the theoretical part by its name, and then discuss the physical way of doing it.
As I understand it, "parallel play" involves the music that you would see lined up vertically in music, where you play a number o f notes at the same time. Two or more notes which are a given set of intervals apart, are played simultaneously. Thus you would play CE at the same time. Or you would play CEG at the same time.
Afaik, this is usually known to be "vertical". The intervals are known as "harmonic intervals". Chang has chosen to call this "parallel play" meaning that all the notes are played at the same time. The term is confusing since "parallel" usually refers to melodic lines that mimic each other.
The notes C E can be played one after the other. If you play C E G C one note after the other, then essentially you have played a chord, but "broken" it, so that it is usually called a broken chord, or arpeggio.
This is known as the "horizontal" flow of music. The intervals from C to E, E to G etc. are known as "melodic intervals". Chang has chosen to call this "parallel sets".
There is a physical way of playing several notes at the same time, and there is a physical way of playing notes one after the other. It seems that this is what Chang is describing.
Would this seem to be correct? Imho, with so many "schools" existing, would it not be advisable for a standard terminology to be used?