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In harmonic analysis and on lead sheets, a C major chord can be notated as C, CM, CΔ, or Cmaj. A major triad is represented by the integer notation {0, 4, 7}. A major triad can also be described by its intervals: the interval between the bottom and middle notes is a major third, and the interval between the middle and top notes is a minor third.
The above definitions spell out the interval of each note above the root. Since triads are constructed of stacked thirds, they can be alternatively defined as follows: major triads contain a major third with a minor third stacked above it, e.g., in the major triad C–E–G (C major), the interval C–E is major third and E–G is a minor third.
The diatonic harmonization of any major scale results in three major triads, which are based on the first, fourth, and fifth scale degrees.The triads are referred to as the tonic chord (in Roman numeral analysis, symbolized by "I"), the subdominant chord (IV), and the dominant chord, (V), respectively. [3]
It comprises a major triad with the added major sixth above the root, common in popular music. [3] For example, the chord C 6 contains the notes C–E–G–A. The minor sixth chord (min 6 or m 6, e.g., Cm 6) is a minor triad, still with a major 6. For example, the chord Cm 6 contains the notes C–E ♭ –G–A.
This E ♭ major triad is what would be called the upper structure. Considered in relation to the root C, the notes of this E ♭ major triad function, respectively, as the sharpened ninth (the root of the E ♭ major chord), fifth, and seventh in relation to that root.
For instance, the notation C/E bass indicates a C major triad in first inversion i.e. a C major triad with an E in the bass. Likewise the notation C/G bass indicates that a C major chord with a G in the bass (second inversion). See figured bass for alternate method of notating specific notes in the bass.
Major and minor third in a major chord: major third 'M' on bottom, minor third 'm' on top. Major and minor may also refer to scales and chords that contain a major third or a minor third, respectively. A major scale is a scale in which the third scale degree (the mediant) is a major third above the tonic note.
Circle of thirds. The concept of a "circle of thirds" is relatively new in the history of music. Although certainly not the first to use it, a popular American jazz musician named John Coltrane often used a cycle composed of a sequence of major thirds for his unique key changes, hence the namesake for "coltrane changes".