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The chord is named after this note as well as the chord's harmonic label is grounded on it. The second aspect is, that chord syntax provides norms for altering chords by additional tones. One example is the addition of a fourth tone to a triad, which is the seventh tone of the scale (e.g. in a C-major scale the addition of F to the triad G-B-D ...
For example, the proximity of the C major and e minor chords reflects the fact that the two chords share two common tones, E and G. Moreover, one chord can be transformed into another by moving a single note by just one semitone: to transform a C major chord into an E minor chord, one need only move C to B.
The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle.
Chords are also commonly classed by their root note—so, for instance, the chord C major may be described as a triad of major quality built on the note C. Chords may also be classified by inversion, the order in which the notes are stacked. A series of chords is called a chord progression.
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
Therefore, the combination of notes with their specific intervals—a chord—creates harmony. [22] For example, in a C chord, there are three notes: C, E, and G. The note C is the root. The notes E and G provide harmony, and in a G7 (G dominant 7th) chord, the root G with each subsequent note (in this case B, D and F) provide the harmony. [22]
2 is mostly used as an extra note in a chord (e.g., add2, sus2). 3 is the minor or major quality of the chord and is rarely written as a number. 4 is mostly used as an extra note in a chord (e.g., add4, sus4). 5 is the (perfect) fifth of the chord and is only written as a number when altered (e.g., F7 (♭ 5)).
Determining which additional pitches can be juxtaposed with the chord is achieved by considering the relationship between a particular chord and the scale it implies. An example follows: The chord C 13 ♭ 9 ♯ 11 contains the following notes, from the root upwards: C, E, G, B ♭, D ♭, F ♯, A;