The initial martiria or signature determines the mode of the hymn and the starting note. I don't know whether there is somewhere an English listing of all initial signatures but I think it would be useful to have such a page at analogion.com.
We can see in some Byzantine musical manuscripts that the ηχημα or the invocation was notated before the hymns. Notice that the chanters were obliged to sing these invocations because without the invocation if for example the first not of the hymn was ison the chanter had no way to know which note had to be used for this ison. There are however some manuscripts where we can see that a later hand has simplified the invocations in the following way: if for example the hymn of 2nd mode had to start from Di then the sign for 2nd mode was used (which according to medieval theory started from Zo) and two apostrophi to show that we need to descend from Zo to Di. According to Tilliard this happened because the later scribe founded the long invocations too complicated and wished to imply that a simpler invocation would be enough. There is another possibility - that chanters preferred to sing invocations they had learned orally. Nevertheless, this abbreviation of the invocations created the initial signatures that are used even today (in even more simplified form).
The medial signatures that are used in the modern notation have two parts. One part is one of the letters πβΓΔϰζν; this part points to the notes invented by Chrysanthos (πα, βo∪, etc.). At the time these notes appeared, the trained chanters were used to different system that was based not on the octave but on fifths (the so called trochos) and this system used only four instead of seven different notes. These four notes were the base notes for the four modes. The symbols in second part of the medial signatures point to these four notes. Because of these symbols the trained chanters were not required to learn the new notes (πα, βoυ,...) in order to use the new notation.
The symbol like 9 that is used with πα and the symbol that is used with δι are simply stylized Greek letters alpha and delta. According to Tilliard the two dots (two commas in the medieval scripts) represented the half-circle in the earliest Byzantine manuscripts used over the letters α, β, γ and δ in the earliest Byzantine scripts. If he is correct about this then these dots/commas simply denote that the letters are not actually letters but numbers. I.e. alpha with two dots/commas means "First" and delta with two dots/commas means "Fourth".
The symbol that is used together with βου and high ζο is a λΓ ligature (abbreviation for λεγετος). The symbol that is used together with low ζο is a βρ ligature (abbreviation for βαρυς). I haven't read anything about the origin of the symbols that are used with γα. They are read "nana". According to Werner the syllable "na" in nana, ananeanes, and so on has Semitic origin and I noticed that these two symbols are similar to the Syriac letter for "n" and a dot above or below a letter means "a".
