I'm not sure if anybody has made this point already in this thread, but:

Synthesis is NOT useful.

There are many different concepts of mode, for good reason, Which one you want depends on a question nobody here seems to have asked:

What are you going to do with the information?

The nine-mode system of the late Middle Ages had a specific purpose: it was to classify psalm and other liturgical melodies into groups that were easy to sing in the same service or on the same day - you didn't want to force your choir to make rapid changes of range and scale. It was about limiting variety. (A variant of the same idea is used today by the Syriac church - they have a system of modes based on Arabic models where the congregation stays in the same one for each month. Most of them are also associated with one of the Ten Commandments, so you spend a whole month singing in the Thou-Shalt-Not-Commit-Adultery mode). For this system, modes are not just scales - each one has a standard range and a few standardized melodic features.

Boethius's earlier system (which was what the mediaeval theorists adapted) had a totally different purpose - it was a transposition scheme to help you adapt music for the instruments or voices you had available.

Glareanus's post-mediaeval twelve-mode system was developed at a time when polyphonic and harmonic composition was well established, and the people who performed it wouldn't have been bothered by changing range and scale in seconds. It seems to have been intended to catalogue the variety of tonal environments a composer could create - more or less the exact opposite of the mediaeval system. You get a similar purpose for the modal system implicitly used, though not often formalized, by Highland pipers - they exploit changes in tonal centre and harmonic space achieved by shifting from one pentatonic or hexatonic scale to another. The idea of this variety is military expedience: you want to keep the infantry's feet moving by relieving the boredom of a march as far as possible. (Hence, most of the pentatonic march repertoire dates from the 19th century, after the pipes became established in the British Army). With other largely diatonic instruments, gapped scales are an extremely useful resource for expanding the amount of music you can play; they are used implicitly by harpists and moothie players all the time.

Modal systems of Indian music are rather like the mediaeval chant system - you want extreme microtonal accuracy, so ragas have no accidentals or modulations whatever, but to compensate there is an unbelievable variety of them to choose from. Arabic music relaxes the rules a bit and use fewer modes, while Persian and Turkish music have modal systems based on the Arabic model that are designed to allow virtuosic modulatory wriggling. Also like the mediaeval chant system, for all these systems, range is standardized, and there are a great many standard melodic formulas, specific kinds of inflection and reference points that melodies progress through. Here the primary aim of the system is often to organize an improvisation in a way that an audience or a fellow-performer can follow.

Then you have the seven-mode piano-keyboard system that seems to been invented by someone in the middle of the 19th century with too much time on their hands, and really only found a useful application with the academic jazz of the 1960s and its encyclopaedic repertoire of chordal structures. This is the system most folkies think of as THE mode system - it does nothing very useful that I can think of. If all you can think of is "I gotta classify this", don't bother.