was, like our dominant, in the middle of the scale. In the plagal modes, on the other hand, the melody wandered freely as low as a fourth below the final, which thus was near the middle of the melodic range; and the dominant was a third below the dominant of the corresponding authentic mode. Whenever the dominant fell on B, C was substituted (indicated by _N.B._ in the table) and in the rejected Locrian G was substituted for F. Each authentic mode had its related plagal. The final of the ecclesiastical Dorian mode was D.[63] The range of a melody written in this mode was limited to notes which may be represented on the pianoforte by the white keys between D and d, including the two D’s and, for the cadence, the C below the lower. The melody would centre about A and come to end on D. The related plagal mode, called the Hypodorian, had the same final, D, but the range of a melody in this mode was from the A below to the A above the final, centering about the dominant, F. The so-called relaxed modes which are frequently met with varied likewise from the authentic modes in range which in such modes might be extended to a third below the final. The dominant remained the same and the slight extension of range hardly altered the _ethos_ or character of the authentic mode from which it thus technically varied. [Illustration: AUTHENTIC MODES.] [Illustration: PLAGAL MODES.] The modes were in as far as possible strictly adhered to, but the occurrence of certain intervals difficult to sing and not wholly pleasant to the ear (notably the augmented fourth, or tritone,[64] from F to B), led to modifications or, as we should say, chromatic alterations. B-flat, for instance, was substituted for B whenever the interval from F to B occurred; and later, in the development of part singing, many other alterations were found necessary. Marks indicating such alterations were seldom written in the score, and singers were specially trained to alter intervals at sight, according to the elaborate rules of the practice called _musica ficta_, or 'false music.’