Harmonic coding systems

The most important systems for coding harmony are:

1. Continuo-notation (mainly in use with music from the baroque era: just a bass-line is provided. The additional harmonies are added by the continuo-player (keyboard, lute). Just a bass-note implies a triad (with notes present in the scale, e.g. without alterations). By adding Arabic numbers, flats, sharps, naturals, scores information is provided concerning the intervallic structure of the harmony and required voice-leading, in the form of "voicings".
   The thinking strategy behind this practice is: constructing harmonies above a bass-note and connecting these harmonies with appropriate voice-leading, including the mentioned "voicings". In the beginning continuo-notation does not include the notion of root-note vs. bass-note, root-position and inversion.
   
   
2. Roman numerals (degrees) (mainly in use with "classical harmony" and harmonic analysis of so called "classical" tonal music. Roman numerals and additions with arabic numerals are used. Using a Roman numeral signifies a link with a key and indicates a triad in root-position on a degree of the scale. In principle chords consist of tones present in the scale. With this approach the notions of root-position and inversion are essential. Arabic numerals indicate an extension of the chord (⁷ and ⁹ for example for a seventh-chord and a ninth-chord), ⁶ for the first inversion of a triad). Sometimes, in order to get desired "voicings" arabic numerals are used in a way similar to continuo-notation: V^4-3 indicates a dominant triad with a suspension (fourth moving to a third above the bass-note).
   Nowadays there is also the custom to incorporate chord colour in the degree number; in major  I ii iii IV V vi vii⁰ ; capitals for major triads on I IV and V; small letters for minor triads on II, III and VI, and the VII diminished triad with small letters and superscript 0 (coming from jazz chord symbols). Does not really add information if you already know in what key you are. 
   
   
3. Chord symbols (mainly in use with jazz, pop and light music): A capital indicates a major triad. Minor chords are indicated with a - or m (A- or Am), sometimes with a small letter in stead of a capital (a for A minor). Arabic numerals are used for extended chords (⁷, ⁹, ¹¹), sharps, flats and naturals are used for alterations. In principle Arabic numerals indicate an absolute interval, and not the interval available in the scale of that moment. So: C⁷, D⁷, F⁷ are all dominant seventh chords. The ⁷ indicates a minor seventh added to the triad. In chord symbol coding we also have the notion of the added note and the suspension. For example F⁶ indicates a major triad with an added major sixth (f-a-c-d). [1]F⁴ or F^sus4 indicates the harmony f-Bb-c. In classical times such a chord would be resolved into f-a-c. The dissonant note Bb resolves to the third of the triad. In jazz (and post-romantic music...) that's not longer necessary. This suspension is not considered to be a dissonant in the traditional sense.
   
   
4. Harmonic function coding: with letters (mainly used in theory education in the German language. The letters T, S, en D indicate the harmonic functions Tonic, Subdominant and Dominant (Tonika, Subdominante and Dominante). T or t is I in resp. major en minor.  Tp (Tonikaparallele) or tP (tonikaParallele) is VI in resp. major en minor. A capital indicates a major triad, a normal letter a minor triad. The third relation between T and Tp depends on the scale of that moment.