Authentic and plagal modes

Here are two short melodies in D Dorian. Both end on D, and both use the notes of the Dorian scale, B natural included.

Hear the passage

Hear the passage

The first rises from its final and moves in the space above it, up to the D an octave higher. The second never gets far from D: it drops below, climbs a little above, and comes back. In medieval theory they are not in the same form of the mode. The first is authentic Dorian; the second, plagal.

The same final, a different range

Every mode has two forms, the authentic and the plagal, and what separates them is range (Lacerda 1966, ch. XXXVI). Lacerda gives the rule in terms of the melody:

• if its range covers roughly the final and the octave above it, the mode is authentic;
• if its range covers roughly the fourth below the final up to the octave of that lower note, and the melody ends on the final, the mode is plagal.

The final does not move. The authentic and plagal forms of a mode share it; only the space the melody occupies around it changes (Lacerda 1966, ch. XXXVI). Blatter says the same in other words: authentic melodies use mainly the notes above the final, while plagal ones keep the final near the middle of the range and use notes below and above it about equally (Blatter 2007, part 2, art. 7).

Laid out as scales, the difference is easy to see. Authentic Dorian runs from D to D; plagal Dorian runs from the A below up to the A above, with D in the middle.

Hear the passage

Hear the passage

Hypo-, below

A plagal mode takes the name of its authentic mode with the prefix hypo-, Greek for "below": Hypodorian, Hypophrygian, Hypolydian, Hypomixolydian (Lacerda 1966, ch. XXXVI). The prefix refers to the melody's reach below the final (Med 1996, ch. XXVI).

In the Middle Ages the eight modes were also numbered, each authentic mode followed by its plagal: Dorian was the first mode, Hypodorian the second, Phrygian the third, and so on up to Hypomixolydian, the eighth (Blatter 2007, part 2, art. 7).

Number	Mode	Final	Range, roughly
1	Dorian	D	D to D
2	Hypodorian	D	A to A
3	Phrygian	E	E to E
4	Hypophrygian	E	B to B
5	Lydian	F	F to F
6	Hypolydian	F	C to C
7	Mixolydian	G	G to G
8	Hypomixolydian	G	D to D

Lacerda, who counts six modes, gives plagal forms to Aeolian and Ionian too: Hypoaeolian and Hypoionian (Lacerda 1966, ch. XXXVI).

The recitation tone

Range and final were not the only things that set the modes apart. Blatter adds a third: the recitation tone, also called the psalm tone, the note sung most often in a modal melody (Blatter 2007, part 2, art. 7).

In an authentic mode, the recitation tone is a perfect fifth above the final. In a plagal mode, it is a third below the recitation tone of the authentic mode. In both cases, if the rule lands on B, which medieval theory considered unstable, C is used instead:

Mode	Final	Recitation tone
Dorian	D	A
Hypodorian	D	F
Phrygian	E	C
Hypophrygian	E	A
Lydian	F	C
Hypolydian	F	A
Mixolydian	G	D
Hypomixolydian	G	C

This is why Phrygian's recitation tone is C and not B, and why Hypomixolydian's is C and not B (Blatter 2007, part 2, art. 7).

Same notes, different modes

The plagal scales make one thing clear: two different modes can use exactly the same notes. Hypomixolydian runs from D to D over the white keys, just like authentic Dorian. Med points out that what tells them apart is not the notes but the rules for using them: where the melody begins and ends, and which note dominates (Med 1996, ch. XXVI).

Hear the passage

The notes are those of D to D, but the melody circles G and ends there. It is Hypomixolydian, not Dorian.

Identifying the mode of a melody

Lacerda turns all this into four steps (Lacerda 1966, ch. XXXVI):

1. Find the final. A purely modal melody always ends on it; if the melody has chords under it, the final is the lowest note of the last chord.
2. Build a one-octave scale on the final, with the accidentals that stay fixed throughout the melody.
3. Look at where the semitones fall in that scale, and name the mode.
4. Look at the range of the melody, and decide between authentic and plagal.

Try it on the second melody at the top of this page. It ends on D. On D, with no fixed accidentals, the scale is D E F G A B C D, semitones between II–III and VI–VII: Dorian. Its range goes from A, a fourth below the final, up to F, and it ends on the final: plagal. The mode is Hypodorian.

Where the books differ

Med describes how to build a plagal mode differently. Take the upper half of the authentic scale, its second tetrachord, write it an octave lower, and complete it with four more notes: Dorian's A B C D, moved down, followed by E F G A, gives Hypodorian. He then says that the tonic of a plagal mode lies a perfect fourth below the tonic of the authentic (Med 1996, ch. XXVI).

Taken literally, that would move the final, and Lacerda is explicit that the final of the plagal mode is the same as that of the authentic (Lacerda 1966, ch. XXXVI). Med's own example points to what he means: his Hypomixolydian melody runs over D to D and ends on G. The note a fourth below is where the plagal scale starts, not where its melodies end. Med also notes that characteristic intervals are not defined for the plagal modes (Med 1996, ch. XXVI).

What comes next

Range, final and the placement of the semitones are enough to name any modal melody. The same questions, with major and minor in place of the modes, are how you find the key of a piece.