The development of the medieval modal system was a gradual process, not all the stages of which can be clearly traced. In its complete form, achieved by the 11th century, the system recognized eight modes, differentiated according to the the position of the tones and semitones in a diatonic octave.
All the modes are organized around a dominant or reciting tone, and a final or ending pitch. Four modes (I, III, V and VII) are called Authentic modes. The order of steps and half steps in these modes corresponds to the diatonic octave scales based on D (mode I), E (mode III), F (mode V), and G (mode VII). These modes, however, can be transposed to begin on any pitch. Each authentic mode has a corresponding plagal mode. Each pair of modes (I and II, III and IV, V and VI, and VII and VIII) has the same final. The overriding differences between an authentic mode and its corresponding plagal mode are the range or "ambitus" and their dominants. The authentic mode has a range within the octave of its final. The plagal mode has a range within the octave of the fourth below its final to a fifth above.
Why were there no modes on a, b, and c in medieval theory? The original reason was that if the modes on d, e, and f were sung with the flatted b, they became equivalent to the modes on a, b, and c, and consequently, these three modes were superfluous.
The modes on a and c, which correspond to our minor and major, have been recognized theoretically only since the middle of the sixteenth century. Some later theorists recognize also a "locrian" mode on b, but this is not often used.
The only accidental properly used in notating Gregorian Chants is B-flat. Under certain conditions the B was flatted in modes I and II, and occasionally in modes V and VI; if this was consistently done, these modes became exact facsimiles of the modern "natural" minor and major scales respectively. Accidentals were necessary, of course, when a modal melody was transposed.
A modal "scale" is only a catalogue of the tones which were or could have been used in the melody of a chant or of any other composition. Some chants remain entirely within the range of a fifth above the final and one note below. Others use the entire octave range with perhaps one note beyond in either direction. Still others, like the sequence "Victimae paschali laudes," cover the entire combined range of the authentic mode and its corresponding plagal. Some chants even combine the characteristics of two modes that have different finals; such chants cannot be definitely assigned to either one mode or the other. In short, the correspondence of theory and practice is no more exact for medieval modal melodies than for any other type of actual music in any period.