Harmony
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Harmony is the use of chords (pitches sounding simultaneously) in music. It can occur as the result of counterpoint (melodic lines played at the same time), or in eastern art music, for example, it occurs incidentally through the combination of improvised vocal or melodic lines combined with a drone. A major misconception among students of western music theory and composition, is that writing counterpoint is a separate skill from writing harmonic progressions, and somehow it is written exclusively according to its own rules. Most theorists today hold this be more or less untrue; counterpoint relies on harmonic principles, and vice versa.
Different schools of harmony
- Tertian harmony
Tertian harmony is a school of harmony that relies on stacked thirds. For instance, to construct a C Major chord, one would start with a C and then add an E (a major third above) and a G (a minor third above the E). Chords can also be embellished with ornaments that typically continue the stack of thirds (for instance a C minor 7th chord contains an added B flat a minor third above the G). For more information on chord construction with Tertian harmony see the page on Chords (music).
- Secundal harmony
Secundal harmony is similar to Tertian harmony except instead of being based upon stacks of thirds, it is based on stacks of seconds. A secundal chord must have at least three pitches. Secundal harmony is usually noted for its sense of motion.
Secundal harmony typically exists outside of traditional Western scales and are consequentially labeled "non-diatonic."
- Quartal and Quintal harmony
Quartal and Quintal harmonies are built by stacking fifths and fourths. These fourths and fifths do not have to be perfect intervals. Diminished and augmented intervals are common in Quartal and Quintal harmony. Jazz soloists usually voice solos with stacked fourths and tritones. Minimalist composers, such as Steve Reich, have utilized Quartal and Quintal harmonies.
- Atonal harmony
A large amount of 20th century music is based on atonal harmony. The word atonal means that a piece has no tonal center. Typically, these pieces use harmony that does not rely on the systematic stacking of like intervals. Consequently, musical set theory has evolved to categorize and label these harmonies.
Harmonic Motion
- Cadences
Most Tertain harmonic progressions are divided into harmonic phrases by cadences. A cadence is a form of harmonic resolution that signals the end of a harmonic phrase. There are countless possible cadences, but there are a few notable ones that are very common
The Perfect Authentic Cadence is a cadence where a V chord resolves to a I or a i chord (see the section on notation of harmony for my explanation of these symbols) where both chords are in root position (see the section on inversion) and the highest voice in the ensemble ends on the first scale degree. When analyzing music this cadence is usually labeled "PAC." This is the most typical cadence to end a piece.
Imperfect Authentic cadences are ones where either a V or a vii0 resolve to a I or a i. Unlike the perfect authentic cadence, inversion, and voicing are inconsequential.
Deceptive cadences are ones where a dominant chord resolves to another chord when it sounds like it should resolve to tonic. The quintessential deceptive cadence is V -> vi. This cadence can be heard in Pachelbel's Canon in D and the Paul McCartney song "Let it Be."
Half Cadences are those that resolve, but to a dominant chord instead of tonic. A good example of what this type of chord progression looks like: I -> vi -> ii -> V. Note that the V chord feels like it is the end of a phrase, but it is not tonic. Pieces rarely end with this cadence, but it is common way to punctuate and exceptionally long musical phrase that needs to be divided into multiple harmonic phrases.
Plagal Cadences resolve from IV to I. They are commonly called the "Amen Cadence" because they are common in Christian hymns and other early written music.
There are many Jazz cadences that are not found in most Western Classical music. These are the product of chord substitutions. A popular substitution results in the following cadence bII -> I. Others allow for more non-diatonic cadences, such as VII -> I.