Thanks for answering , Luca Sartore. I'm trying to work with non-funcional harmonic relationships found in the works of Fauré, Brahms, Chopin, Mahler and Wagner.

The whole idea of Neo-Riemannian relationships between chords is based on the parsimony of voice-leading. In the case of what you describe as "non-functional" harmonic relationships in Fauré, Brahms, Chopin, etc., parsimonious voice-leading may override local functionality. But, all things considered, the harmony probably remains functional.

What this means is that you may connect chords merely prefering the shortest movements and without minding their local functions. But if the music at large is to make sense, I think that some large scale functionality must be preserved nevertheless. The parsimonious voice leading would then produce local prolongations of chords.

Thanks for answering, Nicolas.  I agree with you that in terms of large scale harmonic structures composers  knew how to expand relationships between chords without abandoning a sense of centricity. But I am searching exactly for those ways of loosening and distancing one's perception from a sense of functionality.

One example of how these ideas were so widely used appears in Michel Legrand's arrangement of one of his songs. A whole-tone melody harmonized with a cycle of minor chords from the octatonic collection as the introduction to his beautiful song

'The Summer Knows': https://www.youtube.com/watch?v=F02jwzSLokc

I like  Cohn`s ((2012, pg 11 and chapter 9, pgs 199-210) arguments for Double Syntax (Code Switching and Double Determination, Cognitive Opacity, The Soft Revolution, On Musical Overdetermination)  in Romantic music against the traditional nineteenth century "commitment to the notion that chromatic triadic progressions are determined by their position with respect to some tonal center." 

"Riemannian functions likewise are catchall categories, such that a student of Riemann's system can analyze virtually any chord into any one of the three functions should the occasion demand"

"Schenkerian approaches allow chromatic triads to degrade into coordinated linear spans, which serve as carpets under which to sweep enharmonic paradoxes"

I am personally very interested in graph theory, abstract algebra and group theory as methods to travel through pitch space, organize melodic contour, and so on.  I have yet to turn this all into an article, but I am in the process and hope to publish (eventually).  There are a lot of good books on this, but I have found A Book on Abstract Algebra by Charles Pinter to be particularly approachable -- very grounded in applications of permutation groups and their associated graphs.

There is a theorem by Cayley that states (I think I have this at least approximately correct!) that every finite group is isomorphic to a permutation group, which is basically to say that if you understand permutation groups you understand a great deal about transformations in general.

As far as music is concerned, I think the first thing I would recommend is David Lewin's Generalized Musical Intervals and Scales and his PLR transformations in particular. Dmitri Tymoczko has a lot on the Tonnetz concept.  Bob Morris has done a lot of work on group theory applications to music, although it requires a fair amount of background.  Also, there's a pretty interesting article by Michele Intermont and Aileen Murphy in College Mathematics Journal 42/3 (2011) called "An Application of Group Theory to Change Ringing" which you might find helpful.  A rather different approach but I think VERY interesting can be found in the Harmony Book of Elliott Carter, regarding how all the possible chords in 12 eq. temp. pitch class space can be broken up into component subsets and recombined into new collections (including a handy analysis of part of his guitar concerto in the preface).

There is a classic article called "Dissonant Prolongation" by Robert P. Morgan if you are interested in Schenkerian approaches; I don't have the article in front of me but I recall him prolonging diminished seventh chords in Wagner.  Really, a lot of his students (notably Salzer) delved into the application of Schenkerian analysis to music other than Mozart, Bach, Beethoven...  Generally speaking, you will find a lot of material like this if you just search for "prolongation" along with other words like "post-tonal", "atonal", etc.

I have a few pieces of music I have written that employ some of the above ideas (such as travelling exhaustively through the power set of a given set using Hamiltonian paths).  If you are interested, I would be happy to send them to you.  I suppose I should also mention that I've been writing a lot of music for classical guitar over the past few months, so if that is of interest, I'd be glad to send that along as well.  Best wishes on your research!

Hi Jason! Thanks for your kindness and generous answer. I've read Tymoczko's and Cohn's books and I like and recommend both. I'm interested in creating referents (in the sense of Jeff Pressing) for improvisation based on harmonic progressions from nineteenth century composers. Cube Dance (for triads in hexatonic and Weitzmann regions) and 4-cube trio (for seventh chords in Boretz and octatonic regions) by Jack Douthett help me a lot in mapping these harmonies. I've read Salzer but I'm not interested in Schenkerian approaches right now.  I know about Hamiltonian paths through some articles by Giovanni Albini. I'd be very happy to hear your music. Would  you mind to send them by e-mail? Best wishes on your future article!