The idea
For Hugo Riemann, every chord of a key is a version of three functions: Tonic (T), Subdominant (S), and Dominant (D). The other chords are "representatives" of these three, linked by third relations. The system, simplified and spread by Wilhelm Maler and Diether de la Motte (Harmonielehre, 1976), is still the standard in conservatories in German-speaking and Scandinavian countries; Berklee uses a similar idea (families of tonic, subdominant, minor subdominant, and dominant).
Main symbols (in C major)
Uppercase letters = major chord, lowercase = minor.
| Symbol | Name | Chord | Degree |
|---|---|---|---|
| T | Tonic | C | I |
| S | Subdominant | F | IV |
| D | Dominant | G | V |
| Tp | Parallel of the tonic (relative) | Am | vi |
| Sp | Parallel of the subdominant | Dm | ii |
| Dp | Parallel of the dominant | Em | iii |
| Tg | Counter-chord of the tonic (Gegenklang/Leittonwechsel) | Em | iii |
| Sg | Counter-chord of the subdominant | Am | vi |
| D7 | Dominant with seventh | G7 | V7 |
| D with a bar (shortened dominant) | leading-tone seventh = D7 without root | B° / B°7 | vii° |
| DD | Double dominant | D / D7 | V/V |
| (D) | Secondary dominant toward the following chord | A7 → Dm | V/ii |
| s | Minor subdominant (in major) | Fm | iv |
| sN or sn | Neapolitan sixth | Db/F | bII6 |
Note: in German "Parallele" means relative (Am with respect to C), while the English "parallel" (Cm) is called Variante. This is the source of much confusion.
In minor (A minor)
| Symbol | Chord | Degree |
|---|---|---|
| t | Am | i |
| s | Dm | iv |
| D | E (with G#) | V |
| tP | C | III |
| sP | F | VI |
| dP | G | VII |
| tG | F | VI |
| sG | Bb | bII (Neapolitan area) |
Why it is useful
- Clear ambiguity: Em in C can be Dp (close to the dominant: it substitutes for G) or Tg (close to the tonic: it substitutes for C). Context decides: G → Em is a deceptive cadence "toward the tonic"; Em → Am sounds like a continuation of the tonic.
- Families by substitution: all T chords (C, Am, Em) can be swapped with one another; all S chords (F, Dm, Fm, Ab, Db) prepare the dominant.
- Quick pop analysis: C Am F G = T Tp S D. The royal road IVmaj7 – V7 – iii7 – vi = S – D – Dp/Tg – Tp: a dominant that avoids the tonic and "slides" to its representatives.
Comparison with Berklee
| Function | Riemann | Berklee (C major) |
|---|---|---|
| Tonic | T, Tp, Tg | Imaj7, iii7, vi7 |
| Subdominant | S, Sp, Sg | IVmaj7, ii7 |
| Minor subdominant | s, sP, sN | iv7, bVImaj7, bVII7, iiø7, bIImaj7 |
| Dominant | D, D7, shortened D | V7, viiø7 |
Complete analysis example
Bach, Prelude in C, BWV 846, first 4 bars: C – Dm7/C – G7/B – C = T – Sp7 – D7 – T over a bass that stays on C and descends to B. In the following bars the music touches the double dominant (D7/C → G/B) and the subdominant: the function guides the arc even though the bass moves slowly.
Exercise
Analyze three of your own progressions with Riemann's symbols. Then replace each chord with another of the same function (C ↔ Am ↔ Em; F ↔ Dm ↔ Fm; G ↔ B°): you'll get reharmonizations that preserve the logic.
Related topics
Diatonic functions T–S–D, diatonic substitution, neo-Riemannian theory, negative harmony (which swaps D and s), Neapolitan sixth.