Introduction: history and origins
The first prominent "scholar of makam" was undoubtedly al-Farabi, who wrote extensively,
if not in somewhat esoteric terms, about the tuning of Persian music, mentioning a few makams. However, modern makam much more closely resembles the theory of Safi al-Din,
who references al-Farabi, and wrote his large Kitab ve Musiki around the year 1293. He describes a tuning system for the 4-chorus oud, using 17 notes to the octave
(which to this day is still the division of many folk music traditions from the area). He also names many makams, some of which are still in use today (though played differently).
We don't know much about where al-Farabi and Safi al-Din got their information about makam, or more specifically, who invented the tuning systems and makams they describe.
From that time onward, though, we have spotty literature on makam theory, and not a lot of compositional opus. Demetrius Cantemir is a notable exception,
from who we have several dozen notated compositions, and discussions about several makams.
The last 250 years of the Ottoman empire saw the adoption of first the Hampersam and later the western notation system, and thus we have several thousand Ottoman classical works spanning 160 years of compositional output.
We also know about the creation and discovery of many obscure makams; for example, the makam Pesendide is credited to Ottoman Sultan Selim III,
while composers like Dede Efendi are credited with creating other makams. In the literature, some makams "suddenly" appear,
indicating that perhaps one of the Ottoman ethnomusicology outings to one of the distant provinces brought a new village melodic idiom into the classical repertoire.
The naming of some of these makams is indicative; makams Hicaz and Isfahan are named after cities; makams Kurd and Segah (Sikah) are named after ethnicities;
makam Mahur is a cognate to the western term for the "major" mode, a fairly recent addition to the Turkish makam system.
Additionally, when we attempt to define traits that are in common to all makams, we have difficulties, since 1) makams are much more complex than a 1-octave scale and
2) what makes them complex differs greatly. Thus, some makams have specific ornamental playing requirements (such as turkish Huseyni and arabic Saba),
while others have complicated sequences of required modulations (makam Bestenigar must modulate to makam Evic before descending to the tonic),
and others still are most frequent as a point of modulation in the middle of pieces of music in other makams, but few pieces in that makam exist.
Thus, there is no symmetrical logic system by which we can categorize or diagram all makams, though there are principles common to many makams.
There is somewhat of an explanation to the different realms of importance of different makams; they don't have a unilateral origin.
Five makams are automatically charged with associations since they mark the five calls to prayer in a day; these are, in sequence, makam Sabah, makam Rast, makam Huzzam, makam Hicaz,
and makam Ussak (in the arab world, maqam Bayati). Other makams are specific to a region; makam Hüseyni has a lot of associations with Turks as so much
baglama-saz music is written in makam Huseyni. Other makams come from more distant regions, and behave differently; makams Neva, Bestenigar, Beyati Araban,
and others are more structurally like Persian dastagh (Iran's relatively modern modal system) than like many other Turkish makams. And some makams have origins in Byzantine Greek church modes;
makams Nikriz, Neveser, Acemkurdi, and Buselik tend more towards the Byzantine than towards Iran. Finally, a number of makams have been invented in the last 200 years,
including Sed Araban, Ferahfeza, and Muhayyer Kurdi. These have a very "romantic" sentiment, in the sense of matching the Romantic era of central Europe,
and as such pieces in these makams tend to have ornamental multi-octave scalar runs (evocative of Paganini cadenzas) while earlier makams don't feature such a thing.
All this makes the makam system one of the most intricate, but perhaps the least understood, modal systems in the world.