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Major and minor forms: For asymmetrical hours (hours that are formed from two different interval classes), the minor form is the inversion of the triad with the smallest ic on the bottom, while the major form is the inversion with the largest ic on the bottom. So, XIm is equivalent to a standard minor triad (3-4), while XIM is equivalent to a ...
A major triad has a major third (M3) on the bottom, a minor third (m3) on top, and a perfect fifth (P5) between the outer notes. 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}.
An interval is inverted by raising or lowering either of the notes by one or more octaves so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved.
Melodic inversion is not inversion in the usual sense, in which C–E–G becomes E–G–C or G–C–E. Instead, C–E–G is turned upside down to become C–A ♭ –F. A chord's odd limit is the largest of the odd limits of each of the numbers in the chord's extended ratio. For example, the major triad in close position is 4:5:6.
This means that, for example a major triad and a minor triad are considered the same set. Western tonal music for centuries has regarded major and minor, as well as chord inversions, as significantly different. They generate indeed completely different physical objects. Ignoring the physical reality of sound is an obvious limitation of atonal ...
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.
Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...
In some fake books and lead sheets, all triads may be represented by upper case numerals, followed by a symbol to indicate if it is not a major chord (e.g. "m" for minor or "ø" for half-diminished or "7" for a seventh chord). An upper case numeral that is not followed by a symbol is understood as a major chord.