Mediant chords are rooted a third away from the tonic. In chromatic harmony these are sometimes divided into 3 types:

Grade 1 (a.k.a. Diatonic): 2 common tones; mode change (one is major, the other is minor).

Grade 2 (a.k.a. Chromatic): 1 common tone; mode preserved (both major or both minor).

Grade 3 (a.k.a. Disjunct, Doubly-Chromatic): No common tones; mode change (one is major, the other is minor).

One main focus in the previous chapter on neo-Riemannian progressions, is the connection between triads with roots a third apart. For instance, the L-relation connects C-major with E-minor (in either direction, i.e., both from C to E and vice versa). Another way of looking at these third-related chords is in terms of "mediants". Recall from the fundamentals part that the third scale degree (\hat3) is sometimes called the "mediant" and the sixth (\hat6) is the "submediant". And remember that the same goes for chords built on those scale degrees: in C-major, the pitch A is the "submediant" scale degree, and the A-minor triad is the "submediant" triad. Again, the roots are a third away from the tonic.

What does this have to do with chromatic harmony? Well, again as we saw in the neo-Riemannian progressions chapter, third relations do not have to be diatonic. For example, if we're in C-major, then E-minor would count as a diatonic mediant as all the pitches are in C major, but E-major would not: the G\sharp makes it chromatic in C-major. And it doesn't stop there! Still taking C as our reference, the mediant-related triads include those rooted on E and A, but also those on E\flat and A\flat: the roots are still a third away from C.

In some (both English- and German-speaking) traditions the combined collection of possible mediants is divided into three categories as shown in the embedded example score-figure and sections below.

Mediants by FourScoreAndMore

Grade 1 (a.k.a. Diatonic)

Grade 1, (also known as Diatonic) mediants share two common tones with the tonic and involve a change of chord quality type (between major and minor). For example:

The R-relation connects C-major and A-minor

The L-relation connects C-major and E-minor

Please note that these terms ("L" or "Leading-Tone Exchange", and "R" or Relative) are as typically seen in English-language music theory today. Despite that English-language tradition having its roots in German music theory (notably from Hugo Riemann from whom "Neo-Riemannian" theory takes its name), contemporary German music theory would typically discuss these relations with the terms Gegenklang (G) and Parallel (P). This gets confusing, so please see the section on "Function and Transformations" at the end of this chapter. For now, we'll stick with the "LPR" terms used so far (in the previous chapter).

Grade 2 (a.k.a. Chromatic)

Grade 2 (a.k.a. Chromatic) mediants are a step more remote. Here there is one common tone with the tonic and major or minor chord quality is the same in both chords. Some English-language sources give extra labels of Upper Flat, Upper Sharp, Lower Flat, and Lower Sharp to these four mediant types. Upper/lower refers to the root direction, and flat/sharp clarifies whether the interval between the roots is a major or minor third. For instance, C-major connects to:

E\flat-major as the "Upper Flat mediant".

E-major as the "Upper Sharp mediant".

A\flat-major as the "Lower Flat", and

A-major as the "Lower Sharp".

German-speaking theory accounts for these with function-transformational terms like Tonikavariantparallel: i.e., change the mode of the tonic chord (from major to minor or vice versa) and then take the parallel transformation from there.

Grade 3 (a.k.a. Disjunct, Doubly-Chromatic)

In the third and last type, we still have mediant relations (roots a third apart), but no common tones. The major/minor quality also changes. Given these changes (especially the lack of common tones), these are sometime called Disjunct or Doubly-Chromatic mediants.

For instance, C-major connects via Grade 3 mediant relation to:

E\flat-minor

A\flat-minor

In total, these three types or Grades cover all 8 individual mediant relations: all chords rooted a third above or below (from C to A, A\flat, E, and E\flat) and with each in major and minor (i.e., 4 root destinations x 2 qualities = 8). The following table summarises those 8 cases for the example of C major:

From C major to:

-Major

-Minor

E-

'Upper Sharp' mediant (Grade 2)

L-related (Grade 1)

Eb-

'Upper Flat' mediant (Grade 2)

Grade 3

A-

'Lower Sharp' mediant (Grade 2)

R-related (Grade 1)

Ab-

'Lower Flat' mediant (Grade 2)

Grade 3

Function and Transformations

As mentioned above, we need a bit of caution in regards to functions, terms and labels here, as there are some different conventions running in parallel (pun intended!). The main headache is the use of that term "parallel" which in English-speaking traditions connects two modes on the same root (C-major and C-minor, for instance), while the German tradition uses it to for what English-speaking theory calls "Relative" (i.e. C-major and A-minor). I know, right? Watch out, especially if you're reading historical and/or multi-lingual sources. Here's a bold (perhaps foolish) attempt at an overview with both functional labels (in German, taking the example of a tonic starting point) and combined neo-Riemannian transformation as discussed in the previous chapter (English). On the German side "-" indicates that there is no common, functional term.

E.g. from C major to:

Modern German (Funktionstheorie)

(example of tonic function)

Modern English (Transformations)

C-minor

Varianttonart (t)

P. Parallel

A-minor

P. Paral