This is a possible goldmine.
It is a 2009 Doctoral thesis from Brett G. Clement that discusses the theory underlying Zappa's instrumental works.
He sourced some 150+ songs in his analysis, but I've only started digging into it.
From the abstract:
This dissertation offers the first large-scale analytical study of the instrumental music of Frank Zappa (1940-1993). Following initial commentary in Chapter 1 on the problems of categorization in the repertoire, Chapter 2 offers a preliminary discussion of style and form in Zappa's music. Regarding style, I detail the fallouts of Zappa's unique early musical education as well as the influence of his guitar playing in his compositional style. My investigation of form explores the formal implications of melodic repetition, examining non-repeating forms characteristic of the
hybrid works and repeating forms utilizing variation procedures such as
contour retention and
isomelism.
Chapter 3 is devoted to rhythm and meter in Zappa's music. The primary topics of this chapter are various types of rhythmic/metrical conflict, including polymeter,
metrical dissonance, and
rhythmic dissonance, which are explained in part as an attempted merging of advanced compositional techniques and rock/pop music norms. A theoretical discussion of rhythmic dissonance, which is Zappa's trademark rhythmic device, comprises the bulk of the chapter.
Chapter 4 offers a
Lydian theory for Zappa's diatonic music, loosely adapted from George Russell's seminal jazz theory
The Lydian Chromatic Concept (1953). This theory views the Lydian scale as representing a tonic state in Zappa's music due to its special static attributes. It introduces the concept of a
Lydian system, containing a limited group of diatonic modes related to a common Lydian scale. Within, I demonstrate how the pitch structures of non-Lydian modes are related abstractly to those of the Lydian tonic, and follow by considering
pedal substitutions and
progressions within the Lydian system.
Chapter 5 is devoted to Zappa's non-diatonic music. The first section of this chapter explores Zappa's methods of
chromatic pitch organization, including
pitch-class diversity, chromatic saturation, and
symmetry.
The second section investigates a system of composition based on a Chord Bible of Zappa's own devising. This section includes a preliminary recreation of certain aspects of
Chord Bible and a discussion of the compositional employment of Chord-Bible harmony in the series of orchestral works composed circa 1977-1982.
I immediately jumped to chapter 5 when I saw that Chord Bible part. What in the hell could that be?
Follow the link and download it yourself.
https://etd.ohiolink.edu/pg_10?0::NO:10:P10_ETD_SUBID:82908#abstract-files