Naming of chords
The most common systems of naming chords
Figured bass (approx. 1590 onwards)
The name figured bass chord is based on tonality with the melody and bass line building a harmonic entity. Consonant intervals (3, 5, 6, and 8 above the bass line) were added as necessary. In simple vocal accompaniment, a skilled instrumentalist was expected to play these ornaments and decorations without the help of the numbers; in more subtle compositions, a printed chord-scheme was necessary. The figure 6 is nowadays said to indicate the first inversion of a chord, but Baroque musicians saw it as an interval relation ("sixth instead of fifth"). Chords building on thirds were not introduced until later.
Scale degrees (approx. 1725 onwards)
In this system introduced by J.P Rameau in his book Traité de l’harmonie each degree of the scale gets a harmony built of thirds (two third intervals on a degree build a triad, three third intervals build a four-note chord, and so on). From the viewpoint of music history, it is worth noting that harmonies including the same notes (for example, C, E, and G) are considered one and the same chord. So, for example, a 6 chord is considered merely an inversion in the scale degree system, even though it originally expressed a double suspension (6-5 and 4-3) in a cadence. At least for the present, the scale degree system is the most commonly used in the analysis of classical tonal music.
Functional harmony (approx. 1895 onwards)
The functional harmony theory is based on scale degree markings, which at the end of the 19th century were considered overly mechanical, so the search was on for a system to describe the character of chords. Different chord labelling systems like the one developed by Hugo Riemann, share a common principle of three main functions. The tonic triad is the tonal centre and ending point of a composition. The other functions are the upper fifth (dominant chord, D) and the lower fifth (subdominant chord, S) of the tonic, and all the other harmonies represent (at least in theory) one of these three. The problem in functional thinking is that chords can be interpreted in several ways when one is trying to determine whether they belong to one or another of the functional groups. Diminished four-note chords, which are considered incomplete dominant ninths in functional harmony theory, are difficult to label as well.
Absolute chord symbols (beginning of 20th century)
Used mainly in jazz and popular music and based on chordal thinking, these chords are labelled with a letter denoting the root note. More extensive chords are indicated by numbers according to the interval (9 is a ninth, and so on), and chromatic alterations are denoted by plus or minus signs (though today chromatic signs have become more common). With all the different variants, this is a practical method. On the other hand, it is not possible to indicate tonal (or functional) relationships in a key; that is why jazz musicians indicate them with the help of degrees (for example, Em-A7-D is the same as the progression II-V-I to D).
Set classes (end of 20th century)
As a system of analyzing mainly atonal music, set classes is capable of describing any equal-tempered tone groups (chords, scales, and so on). Notes (or pitch classes) are first written in numeric notation (C = 0, C sharp = D flat = 1, D = 2 and so on) and then arranged in a so-called primary form as a tight cluster.
Each primary form has an equivalent in the code system, which altogether includes no more than 352 different chords. The number is quite small, considering the fact that the number of possible different 12-note rows is 479,001,600 and that an ordinary piano with 88 keys can produce approximately 309 quadrillion (3,0926*1024) different tone combinations.
The first number of the code system (set class or Forte class) indicates the number of notes (see the example below). The major and minor chords both represent set class 3-11, while 3-1 denotes any three consecutive pitch classes in any octave. If the notes are presented in a certain order, set class 5-16 has an equivalent in the system of scale degree or thirds.
In figured bass, numbers indicate interval relations between the harmonies and the bass line, especially if they differ from the "default" intervals 3, 5, and 8 (which, however, are indicated after, for example, suspensions). The numbering of the notes is not done according to their actual order; the numbers keep getting smaller as moves downwards. Chromatic alterations in a chord are indicated with a corresponding chromatic sign.
Below we have the same chordal progression written in systems based on piles of thirds: an absolute chord symbol on the top; a scale degree symbol in the middle; a functional harmony symbol at the bottom.