It will be seen, that, in the Locrian and Hypolocrian Modes, this division is impossible; since in both cases it would substitute, for the perfect intervals, a Diminished Fifth, (Quinta falsa), and an Augmented Fourth, (Tritonus). On this account these Modes are condemned as impure. Some authorities expunge even their names and numbers from the catalogue; calling the Ionian the Eleventh, and the Hypoionian the Twelfth Mode. Others—among whom are the editors of the Ratisbon, Mechlin, and Rheims-Cambrai Office-Books—retain the names and numbers, but, none the less, reject the scales themselves. The true number of the Modes has, indeed, been many times disputed: once, so hotly, that the question was referred to the decision of Charlemagne; who at first said that eight seemed to be sufficient, but afterwards allowed the use of twelve. More than one later theorist, while nominally recognising the existence of eight forms only, has described Modes IX,X,XI, XII, XIII, and XIV,as metamorphosed renderings of I, II, III, IV, V, and VI, respectively. Hence, we constantly find, in the Mechlin Office-Books, such expressions as 'I Modus, antiquitus IX,' or 'X Modus; alii reduxerunt ad II': a distinction sufficiently puzzling to the tyro, from the confusion it creates with regard, both to the nature and the true Final of the disputed scale.
Besides its Final, every Mode is distinguished by three other highly characteristic notes—its Dominant, Mediant, and Participant—the relative importance of which is shewn by the order in which we have mentioned them.
The Dominant of the Authentic Mode lies a Fifth above the Final; unless that note should happen to be B, in which case C is substituted for it. That of the Plagal Modes lies a Third below the Authentic Dominant; unless that third note should happen to be B, in which case C is substituted, as before. In both cases, B is prevented from serving as a Dominant by its dissonant relation with F. The only exception to the general rule is found in the Locrian Mode, the Dominant of which is G, the sixth from the Final. The Hypolocrian Mode follows the strict law. In the Gregorian Psalm Tones, the Dominant is the note upon which the recitation of the greater part of every verse takes place.
The Mediant—so called from its position between the Final and Dominant—is always the third of the scale, in the Authentic Modes; unless that note should happen to be B, in which case C is substituted for it. In the Plagal Modes, its position is less uniform.
The Participant is an auxiliary note, generally in the immediate neighbourhood of the Mediant, in Authentic Modes; and, in the Plagal forms, coincident with the Dominant of the corresponding Authentic scale. Some Modes have a second Participant; and one has a second Mediant, which, however, is not very frequently used.
Each Mode is also influenced by certain notes, called its Modulations, or Cadences, which are of two kinds. The Regular Modulations are, the Final, Dominant, Mediant, and Participant, already mentioned. To these are added two or more subsidiary notes, called Conceded Modulations, (Modulationes concessæ,) among which we often find the inverted Seventh—i.e. the Seventh, taken an Octave lower than its true pitch, and, consequently, one degree below the natural compass of the scale.
Upon one or other of these Modulations, either Regular, or Conceded, every phrase of every melody must begin, and end: subject only to two farther restrictions—(1) The first phrase must begin on one of a somewhat less ample series of notes, called the Absolute Initials; (2) The last phrase can only end on the Final of the Mode.
The following Table shews the Compass, Final. Dominant, Mediant, Participant, Regular and Conceded Modulations, and Absolute Initials, of every Mode in the series, including the Locrian, and Hypolocrian, which, in spite of their manifest imperfection, have sometimes been used in sæcular music.
| Modulations. | ||||||||
| Regular. | Conceded. | |||||||
| Numbers. | Names of the Modes. | Range. | Fin. | Dom. | Med. | Part. | Mod. Con. | Absolute Initials. |
| I. | Dorian. | D–D | D | A | F | G | C1. E | C1. D. F. G. A |
| II.2 | Hypodorian. | A–A | D | F | E | A. A3 | C.G | A. C. D. E4. F |
| III. | Phrygian. | E–E | E | C | G | A. B | D1. F | E. F. G4. C |
| IV.2 | Hypophrygian. | B–B | E | A | G | C. F | D. B3 | C. D. E. F. G4. A4 |
| V. | Lydian. | F–F | F | C | A | G | B. D. E | F. A. C |
| VI.2 | Hypolydian. | C–C | F | A | D | C6 | B1. G. B [♭] | C6. D4. F |
| VII. | Mixolydian. | G–G | G | D | C | A | B. E | G. A4. B. C. D. |
| VIII.2 | Hypomixolydian. | D–D | G | C | F. A | D6 | B. D3 | C1. D. F. G. A. C |
| IX. | Æolian. | A–A | A | E | C | D | G1. B | G1. A. C. D. E |
| X.2 | Hypoæolian. | E–E | A | C | B | E. E3 | G. D | E. G. A. B4. C |
| XI. | Locrian. | B–B | B | G | D | E. F | A1. C | B. C4. D. G |
| XII.2 | Hypolocrian. | F–F | B | E | D | G. C | A. F3 | G. A. B. C. D4. E4 |
| XIII (or XI). | Ionian. | C–C | C | G | E | D | F. A. B | C. D5. E. G |
| XIV (or XII.)2 | Hypoionian. | G–G | C | E | A | G6 | F1. D. F | G6. A. C. D5. |
1 The Inverted 7th.2 Plagal Modes.3 The 5th above the Final.
4 Barely used in an Absolute Initial.
5 Used as an Absolute Initial chiefly in polyphonic music.
6 The lowest note of the Mode.
