A triad is inverted when a note other than the root is acting as the bass note. Two inversions are possible: the third as the bass note or the fifth as the bass note. When the root is in the bass the triad is said to be in root position. When the third is in the bass the triad is in first inversion and when the fifth is in the bass the triad is in second inversion.
A system of numbers is used along with roman numerals to indicate when triads are inverted. When a triad is in first inversion the number "6" is placed after the roman numeral and when a triad is in second inversion the numbers "6" and "4" are placed after the roman numeral. (No number after the roman numeral means that the triad is in root position.)
Root in the Bass
Third in the Bass
Fifth in the Bass
The numbers after the roman numerals are a representation of intervals found above the bass note. The notes represented by the numberss can be played in any octave above the bass note.
No numbers after the roman numeral in the root position triad actually means that notes a third and a fifth are located above the bass note. The 6 in the first inversion roman numeral symbol means that notes a sixth and a third are located above the bass note. The 6 and 4 in the second inversion roman numeral symbol mean that notes a sixth and a fourth are located above the bass note.
- The following example by Carcassi illustrates a sequence of triads in first inversion. They are moving up the D major scale with the melody in the bass (or bottom) part. This example is for guitar and sounds an octave lower than what is written.
from 25 Melodious and Progressive Studies for Guitar,
op. 60, no. 12 by Carcassi
- Notice that in the following example the number seven occurs with the roman numeral V in the first full measure. The seven with the roman numeral means that a seventh chord in root position is indicated.
from Six Variations on "Nel cor piu non mi sento" by Beethoven
- The following example alternates between the dominant seventh chord and the tonic in second inversion. Notice that the dominant seventh chord contains the root, fifth, and seventh. The third is omitted. Also notice that the dominant seventh and the tonic in first inversion have the same bass note (D).
from Sonatina in G major by Beethoven
- The following example contains the dominant in first inversion. Notice that the dominant in first inversion contains the leading tone as the bass note. The dominant chord in second inversion in the seventh measure serves to connect the tonic in first inversion to tonic in root position.
from Concerto No. 1 for Piano (Strings) by Beethoven