Chapters in Development
- Grade 1 (a.k.a. Diatonic): 2 common tones; mode change (between major and minor).
- Grade 2 (a.k.a. Chromatic): 1 common tone; mode preserved (e.g., both major).
- Grade 3 (a.k.a. Disjunct, Doubly-Chromatic): No common tones; mode change.
A key focus of 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). Another way of looking at these third-related chords is in terms of “mediants”. Recall from fundamentals that the third and sixth scale degrees are sometimes called the “mediant” and “submediant”. Again, these 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. 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.
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 third is major or minor (and typically corresponds to flat / sharp chords). For instance, C-major connects to
- Eb-major as the Upper Flat mediant.
- E-major as the Upper Sharp mediant.
- Ab-major as the Lower Flat, and
- A-major as the Lower Sharp.
(German-speaking theory accounts for these with function-transformational terms like Tonikavariant-Parallel).
Grade 3 (a.k.a. Disjunct, Doubly-Chromatic), and summary
In the third and last type, we still have median (roots-by-third) relations, 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.
This basically completes the 8-types of mediants with chords on the roots of A, Ab, E, Eb (i.e., x4) with major and minor (i.e., x2) as summarised below:
|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 traditions 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 to clarify matters for our specific case of mediant relations as well as the tricky case of “parallel”, including functional labels (in German, e.g. tP) and combined neo-Riemannian transformation as discussed in the previous chapter (English):
|E.g. from C major to:||Modern German (Funktionstheorie)||Modern English (Transformations)|
|C-minor||Varianttonart (t)||P. Parallel|
|A-minor||P. Paralleltonart (Tp)||R. Relative|
|E-minor||G. Gegenklang (Tg also sometimes Tl)||L. “Leading-note exchange”|
|E-major||Tonikagegenparallel-Variante (-)||LP. Upper Sharp mediant|
|Eb-major||Tonikavariant-Parallele (tP)||PR. Upper Flat mediant|
|A-major||Tonikaparallel-Variante (-)||RP. Lower Sharp mediant|
|Ab-major||Tonikavariant-Gegenparallele (tG)||PL. Lower Flat mediant|
Enough theory! Let’s close with a wonderful example from Augusta Mary Anne Holmès.
- Harmonic analysis: analyse the first 10 measures of the Holmès example above using whichever you prefer of Roman numeral and Functional labels.
- Identify the type (including grade) of mediant that Holmès keeps using.
- Do this step 1 analysis using the other terminological system (Roman numeral or Functional labels, which you disprefer and didn’t use before).