Today in my Music Theory class, we discussed several different types of secondary chords that are available for use in harmonization within a piece of music. Downplaying pop artists often, as well as humorously dismissing anyone who doesn’t take advantage of the secondary analytic methods, Dr. Steven Weigt, my professor of Music Theory, explained the significance of secondary harmony.
Within a specific key, for instance C major, there are a set number of sharp notes and flat notes that make up the 8 tone scale. With each of these different notes, scale degrees 1, 2, 3, 4, 5, 6, and 7 (scale degree 8 being scale degree 1 at a different octave) are the roots of 7 different triads. A triad within a scale is most often made up of 3 different notes within that key that are located a third apart, or essentially every other note. With the C major scale being C, D, E, F, G, A, B and C, scale degree 1 is C. Thus, the I (1) triad or I (1) chord is made up of the notes C, E and G… similarly, a V (5) chord is made up of G, B and D.
Major triads within a key are audibly and analytically different from minor triads, diminished triads, and augmented triads.
- Major triads have 4 half steps between the first two notes, and 3 half steps between the second two notes. 4 half steps are equivalent to a major 3rd interval, while 3 half steps are equivalent to a minor third interval. A half step is represented on the piano by two adjacent keys, inclusive of black and white keys.
- Minor triads are similar to major triads, except their composition is in reverse. They begin with a minor third interval, followed by a major third interval.
- Diminished triads only consist of two minor third intervals. Fully diminished 7th chords include another minor third interval on top of the already diminished triad, whereas half-diminshed seventh chords include a major third interval on top of the already diminished triad.
- Augmented triads consist of a major third interval, followed by another major third interval.
There is much to be said for pieces of music that are written in a specific key and that stay within that specified key throughout the entire piece. However, it can be argued that the music becomes much more interesting and suggestive once a composer introduces new harmonizations based in a different key from the one written in the key signature. For instance, in the key of C major, it is common for composers to modulate into the key of G major. Modulation is a fancy word that musicians use to describe the transition from one key into another.
C major to G major is a simple modulation, because the composer only has to introduce one new note into the piece of music. This note is what distinguishes G major from C major: ♯F, or F sharp. By introducing the ♯F, we understand it as a leading tone into G. (♯F is one half step below G and all leading tones generally want to travel up to the tonic note, or the 1. There are, of course exceptions to this rule.) A common chord containing a leading tone that resolves to the new tonic note is the dominant chord, or the V (5) chord. Altered notes, such as the ♯F, can be explained in many ways, but for the sake of this discussion, we’ll assume that it is some sort of V (5) chord. We determine then that the chord D, ♯F, A is the V (5) chord of G major. Thus, by using a D, ♯F, A chord in a C major piece, the composer has temporarily modulated to the key of G major. It is then up to the composer how long he or she desires to stay in that modulated key until he or she wants to revert back to the original key, in this case, C major.
In the case of C major, as seen above, the D, ♯F, A chord, or the V (5) chord of G major, is considered a V/V (“five of five”) in C major. A composer can decide to use a secondary seventh chord as well. In the case of C major, this V/V chord would consist of the notes D, ♯F, A and C. Seventh chords generally work the same way for the most part as the chord without the third interval on top of the triad. However, they are written differently. For a seventh dominant chord, the root position notation is V7. Thus, a D, ♯F, A, C chord in C major would be written as a V7/V.
I’ve referred to all of the chords above in root position. Root position only means that the root of the triad is in the bass, or is the lowest note within the chord on the staff. For instance, the first I (1) chord above is in root position because the note C is in the bass. But what would happen if the E or the G were in the bass instead? Inversions open up more possibilities when it comes to writing chords in a progression.
First inversion chords begin with the 2nd note in the triad. For instance, a I chord in C major in first inversion would be E, G, C. Second inversion chords begin with the 3rd note in the triad, or G, C, E. In the case of 4-part writing for a choir, the order of notes in the tenor, alto and soprano parts does not matter as far as determining the inversion of the chord. Only the bass note determines the inversion.
For triads, or three note chords, root position, first inversion and second inversion are the only possibilities. Root position is designated by the roman numeral for the chord. Capital roman numerals indicate major triads and lowercase numerals indicate minor triads. Numerals with a 〫following it represent diminished triads, and rarely, the + sign indicates an augmented triad. These roman numerals change from major to minor scales. In a major scale, the chords are written as:
- I, ii, iii, IV, V, vi, and vii〫
Minor scale chords are written as:
- i, ii〫, III, iv, V(with altered leading tone), VI and vii〫
For first inversions in three note triads, whichever chord from above is in inversion is written with a 6, and second inversions are written with a 64 notation. For seventh chords, root position, first, second and third inversions are possibilities because of the 4th note. The notation for these chords changes a little bit. Root position chords are notated with a 7 as in the V7 chord. However, first inversion becomes 65, second inversion 43, and third inversion, 42. Thus, a V chord in third inversion would be written as a V42. Usually, these are superscript and subscript numbers, respectively, but this site doesn’t allow for superscript or subscript numbers easily. Below is an example of triads and secondary harmonies in root position and inversions in various keys. This puts together all of the concepts covered in this post.