Today in music theory class I asked my teacher to explain (Gregorian) modes thoroughly, so I could implement them correctly in the future. I have known them superficially for a long time, but now I'm familiar with their idiosyncrasies. As I didn't take any notes for 3 months my hand writing has degraded from 'rather legible' to 'hybrid between hieroglyphs and cuneiform script' I'll type them up for future personal reference and backing up any claims I will make in my implementation.

An important remark is that a small part of his explanation disagrees with the information found on Wikipedia and The Study of Counterpoint from Johann Fux and edited by Alfred Mann.

## Four, six or seven modes

There are four Gregorian modes, two practical and one theoretical mode. The first were in use from the Greeks onwards, getting their final form in medieval times, the second are the major and minor scale as we know and use today and the last mode is a curiosum. It follows from extending the idea from the previous six modes to the seventh possibility in that scheme, but it has little practical use (unless you're a 20th century composer).

The four Gregorian modes are Dorian, Phrygian, Lydian and Mixolydian. The easiest way to remember musical modes is to take the white keys of a piano and start on a certain note. These four modes correspond to D, E, F and G. These choices give rise to a certain characteristic interval, the interval from the tonic (which is called the finalis) to some note of the scale that is distinct from what you would expect in the normal scenario. These are respectively the raised Dorian sixth, the lowered Phrygian second, the raised Lydian fourth and the lowered Mixolydian seventh.

Aside from the finalis, there is the dominant. This is the fifth note of the scale, unless this is a note that can be used as a leading tone (something Gregorian music tries to avoid at all cost), in which case it is taken to be the sixth note of the scale. Hence we have A, C, C and D. A Gregorian chant will be written in the range of an octave starting from the finalis and will feature the dominant in a prominent role. The range is restricted to an octave, but a changing note that extends the range is allowed.

Another important aspect of these Gregorian modes is their plagal counterpart. The four regular modes can be lowered (not transposed!) by a fourth, resulting in a different range. The name of this mode is the name of the original mode, prefixed with hypo-. So for instance lowering the Dorian mode by a fourth results in the Hypodorian mode. The finalis remains the same, but the dominant is lowered by a third. In case of the Mixolydian mode this would result in a B, which is to be avoided, so the dominant of the Hypomixolydian is C.

The Gregorian modes are numbered from 1 up to 8. Odd numbers correspond to the original modes, the even numbers to the plagal modes. So the 6th mode is the Hypolydian mode.

The two practical modes are the Ionian mode (starting on C) and the Aeolian mode (starting on A). These are the regular major and minor scale and are well-known. The last mode is the Locrian mode, it starts on B and it is immediately obvious why this mode is not so popular: it contains a diminished fifth.

## Writing counterpoint in Gregorian modes

This is where the explanation digresses from statements in Fux. My teacher says: stick to the Gregorian mode, not using a leading tone at the end. Fux says: use any mode you like as long as you use a leading tone at the end. Both approaches have their merits: it's a matter of being (less) consistent and using a (less) common ending cadence. But as I've always learnt to use a leading tone in minor scales, one can say that not using it in Gregorian modes is inconsistent. Anyway, I'll try to make a clear statement about this after the following class.

There is one adagium: let it be clear which mode you're in. That is, don't suggest any other modes when composing and use the characteristic interval. This will influence the ending of a piece as we won't be using a real leading tone. Counterpoint doesn't really focus on functional movement, yet a V-I cadence is preferred when writing in a major (or minor) scale.

But in the Gregorian modes we have

Dorian mode
Use a IV-I cadence, the V-I cadence suggest a (natural) minor scale.
Phrygian mode
As V is diminished which is a strong tonal harmony arising from a seventh chord and we wish to focus on the modal character, but I forgot to write down the preferred cadence. I would guess II-I as it features the characteristic interval and as the structure occurring in the IV-I cadence in the Dorian mode.
Lydian mode
Because V-I would suggest F major, we can use VI-I or II-I.
Mixolydian mode
Now V-I is allowed, but IV-V is to be avoided as this would suggest C major.

These are my notes from today's class. Not much of this subject cannot be found on Wikipedia, but I have put some different accents on the subject as a result of my teacher's view on the matter. When I learn more about this subject, I will try to extend these.