How to define and classify "Progressive Rock"?

Your literature review ('Some definition made/used in the past') would benefit from referencing 'definitions' found on the major online prog websites such as PA. BTW, I think you should mention Snider and Couture here rather than later.

Are you concerned with the overall definition of Progressive Rock and/or also definitions of the subgenres of Prog? If I'm not mistaking, the former is what you refer to as a broad definition and the latter as narrow definition(s)? Hence, the sum of the subgenres (narrow definition) constitutes the broadest definition, Prog. 

As ‘narrow’ and ‘broad’ definitions seem essential to your analysis, you should clarify these terms in more detail. It’s not clear to me what you mean by these terms.

What’s your problem statement? What’s wrong with existing ‘definitions’? for instance, what’s wrong with PA’s definition? Why do you bother writing a blog on this subject?! Why should I care to read your blog?

Your approach is not theoretical - I do not see any equations - but phenomenological it appears.

(In the following, I get a bit theoretical - as opposed to your study IMO - sorry, but I hope it can be inspirational to you or others…)

An equation could be a ‘property-ingredient’ relationship where the property could be neo-prog and ingredients (variables) could be instrumentation or musical style (e.g. classical) cf. your statement ‘Some parts of these bands have certain similarities and a part play even very similar kind of music. These similarities can be described’. Obviously the relations would be qualitative rather than quantitative.

Limits can be posed on these relationships either on the properties (e.g. neo-prog is one limitation) or the ingredients (e.g. brass instruments). Another limit could be on a band’s/artist’s song, album or entire album catalogue basis. These limits provide broader or narrower genre ‘definitions’.

I actually did the above ‘scientific approach’ in a PA blog of my own (with affinities to yours) many years ago.

As you can see, the properties of prog depends on its variables which depend on technological and societal changes and therefore varies over time - progressive rock! Hence, obviously, Progressive Rock broadens over time and the ‘definition’/’equation’ should account for this cf. your term ‘broader definition’.

I think you summarize/draw conclusions based on your ‘analysis’ without making it clear to the reader how you end up with your conclusion.

David, your blog is much appreciated, thanks.