Harmony, in music, is generally what happens when you put several different pitches together.
It's most common in music to stack notes in intervals of a third (for example, putting do and mi together, or re and fa). If you do this twice (such as do mi so), you get a chord, which is usually defined to be at least three notes that aren't the same or an octave apart. This chord built in thirds is the standard type of chord in Classical Music and most other western music styles. A chord that specifically has three notes (and no more) is called a triad.
The note on which a chord is built is called the "root". The other notes are named based on their interval from the root—the "third" and "fifth" for example.
If you start on notes other than "do", you get different chords—so + ti + re is different from do + mi + so, for example. This "do re mi" holds true in chorus, instrumentals use different notation.
The standard chord that's built on do (do-mi-so) is called the "tonic" chord, also known as the "I" chord (or sometimes notated as "i" if we're in a minor key). Build such a chord on fa (fa-la-do) and you get the "subdominant" or "IV" chord; do so on so (so-ti-re) and you get the "dominant" or "V" chord. These three chords, when combined with the truth, are the foundation of most popular music.
What happens if you don't put the do on the bottom, but rather than the mi or the so? You get an inversion. Inversions of chords have various flavors and uses that differentiate them from non-inverted forms. A chord with the root on the bottom is in "root position", with the third on the bottom is in "first inversion", with the fifth on the bottom is in "second inversion", and so on.
You can also put more notes in a chord. A very common one is to add fourth note that's yet another third away. This gives you the seventh chord. The famous dominant seventh is a chord that contains so-ti-re-fa, in some order.
Common in jazz and some other modern popular styles, you can go one note further and have ninth chords, as well as chords with notes that aren't at thirds away from each other—do-mi-so-la is an example of a "sixth chord", for example (even though it could be alternatively seen as an inversion of a seventh chord starting on la—which one it depends on how the music before and after it uses the chord, and that's not completely clear sometimes). Certain forms of jazz, such as bebop, rely heavily on the use of these overtones, and can use chords as diverse as ninths, elevenths and thirteenths.
The four basic qualities of triads:
- When the basic triad of a chord (the chord stripped down to a triad, no bells and whistles) has a major third interval between the root and the third, and the interval between the third and the fifth is a minor third, it is called a major chord. (So, major below minor = "major". Try playing C + E + G.)
- When that interval between the root and the third is a minor third, and the interval between the third and the fifth is a major third, the chord is called a minor chord. (So, minor below major = "minor", but you should be able to hear the difference anyway. Try playing C + Eb + G.)
- When both of them are minor thirds, it's called an diminished chord. (So, minor below minor = "diminished". Try playing C + Eb + Gb.)
- When both of them are major thirds, it's called an augmented chord. (So, major below major = "augmented". Try playing C + E + G#.)
Common notation for chords is as follows:
- In "jazz chord notation", chords are indicated by what their basic triad is, plus some modifiers. For example, "F" is an F major chord, "Fmin" is an F minor chord, "Fmin7" is an F minor seventh chord (where minor seventh means that the interval between the fifth and seventh notes in the chord is also a minor third), and "Fmin7b5" is an F half-diminished chord (or literally, F minor seventh chord with a flatted fifth, because it's the Fmin7 chord with the fifth taken down one half-step, which results in what's called a half-diminished chord). Inversions or alternate bottom notes are designated by "/[note]", such as "F/A" being an F major chord with A as the bottom note.
- In classical music theory, chords are usually named using Roman numerals based on the scale degree in the key of the music. Do, re, mi, and so on through ti are numbered 1 through 7, respectively, so the chords built using them as roots are I through VII, respectively. Major chords use capitals; minor chords use lowercase. For example, iv is a minor triad built on fa. Seventh chords are indicated by a superscript 7, ninths by a superscript 9, and so on. Diminished is a degree sign (°) and augmented is a superscript plus sign. Inversions are either indicated by lowercase letters a, b, c,... meaning inversions starting on the root, third, fifth, ... (the British system) or by using a set of numbers (or their shorthand versions) that suggest the intervals of the notes above the bottom note (such as superscript 6 over subscript 3 or just superscript 6 for first inversion) (the U.S. system).
- Baroque music usually had figured bass progressions, typically played in the harpsichord part, which were indicated by figures (5 over 3, for example, to indicate a tonic chord) denoting the relevant chords written under each system. The keyboardist was expected to improvise an accompaniment based on these chord symbols.
When you put several chords together, they form a chord progression. Some chord progressions are pretty famous, such as the following (including variants using chords with more stuff):
- any of the progressions consisting of The Four Chords of Pop
- the Circle of Fifths: I IV vii° iii vi ii V I (in major); i iv VII III VI ii° Vnote i. Very famous. Example: George Frederic Handel's harpsichord suite in G minor, HWV 432, sixth movement: Passacaille (Chaconne), which is basically a Theme and Variations on the chord progression. (Listen here.) Parts of the Circle show up in many songs, such as the second half of the Circle in Weezer's "Island in the Sun".
- The "Pachelbel's Canon" Progression: I V vi iii IV I IVnote V (in major) and i v VI III iv i iv V (in minor), usually looping back to I or i. A variant of a very old and popular progression called the Romanesca. Made famous by...well, Pachelbel's Canon. Appears in many other places, such as Vitamin C's "Graduation (Friends Forever)".
- the "Humoresque" Progression: (in minor only) i VI VII III, usually looping back to i through v6 or VII or VII6. Appears occasionally, such as in Mike Oldfield's song "Moonlight Shadow".
- IV V I (or an equivalent in minor) is another very common progression, forming a cadence—a sequence of chords that ends a musical phrase or sentence. So is its variant ii V I (or similar).
- The main cadences include:
- Authentic (V-I), which is characterised by its "final" or "finished" sound and usually ends a phrase. In "stronger" (more "final"-feeling) versiosn of this cadence, the melody generally goes from 2 to 1 or 7 to 1 (re to do or ti to do); if this is the case (and the bass line goes from 5 to 1 (so to do)) then Americans call it "perfect", otherwise "imperfect". Brits call all authentic candences "perfect".
- Plagal (IV-I), the "amen" chord progression, so called because church songs frequently set the finishing "amen" to this cadence.
- Half (?-V), any cadence that ends on the dominant chord, characterised by an "unfinished" or suspended sound. "Half" is the American name; the British name is "imperfect".
- Deceptive (V-?), a cadence going from V to a chord other than I, although it most commonly ends on a VI or vi.
- The main cadences include:
- The Blues progression—common in Blues, obviously, and in Rock & Roll—is usually a twelve-bar progression of the form I, I, I, I, IV, IV, I, I, V, IV, I, I (or an equivalent in minor), usually embellished. There are other variant lengths as well such as the 16-bar blues.
Note that all of the above applies to the twelve-note scale that is almost ubiquitous in Western music. However, this is not the only scale that has ever been used. Seventeen- and twenty-four-note scales originated in the Middle East (notably Persia). Nineteen-, twenty-two- and thirty-one-note scales have also been used, amongst others. These require modifications to many traditional instruments (for instance, guitars would need to be re-fretted for the new scale, and you'd need a piano or keyboard specially constructed for the new scale), and you'd need to learn how to play them in the new scale. Some instruments, such as fretless basses, violins, and trombones, would not need modifications, but you'd still need to learn to disregard the traditional twelve-note scale. Notation is also, necessarily, different in these scales; and, confusing things further, there is not always a single notation standard. For these and other reasons, Western music in other scales is not particularly common, but it does exist.