# Music Theory/Chords

This is a basic introduction to chords. There is also a complete chord reference.
Chords are the vertical arrangement of notes from a scale. The study of chords is called Harmony. Harmony is concerned with how one or more notes interact, and how they follow each other. Many people define chords as several notes played simultaneously. It must be pointed out that it is not possible to play music of a chordal nature on the flute, trumpet, or a lone human voice, all three being monophonic instruments. Since obviously monophonic instruments cannot play a stacked chord where the notes are sounded simultaneously; the chords are implied. A simpler way of viewing this is that when chord tones are played as an arpeggio on a monophonic instrument the human ear interprets that there is a harmonic structure. We therefore define a chord as the basic element of harmony. To start with we will look at examples of the most basic chord, the triad.

## Triads

The triad is a class of chords, specifically three-note chords formed by this formula: 1-3-5 or root, third, fifth. In this example they are constructed of two consecutive thirds.
There are four kinds:
Kinds of Triads :
| | Root | 3rd | 5th |
| Major | 1 | 3 | 5 |
| Minor | 1 | ♭3 | 5 |
| Augmented | 1 | 3 | #5 |
| Diminished | 1 | ♭3 | ♭5 |
| ♭=flat/lowered; #=sharp/raised ||||
The major is very consonant; the minor is a bit less so but still consonant for most purposes. The augmented is very dissonant and the diminished is extremely dissonant as it contains a tritone (augmented fourth or, in this case, diminished fifth).
The major and minor triads may have their third omitted, although this is uncommon. If the third of a major or minor chord is omitted, the result is a fifth chord, which is often called a power chord when played on an overdriven guitar.

## Triads and Inversions

If we look at a C major triad or three-voice chord it is based on combining a root voice (C) with two other voices at slightly different intervals of a third (E, a major third from C and G, a minor third from E). If we compare the key of C major to the C major chord using the names do, re, mi, fa, so, la, ti, to represent the scale degrees 1, 2, 3, 4, 5, 6, 7, the C major chord is constructed from the notes do, mi, and so. This same relationship is true for all major triads in all corresponding major keys.
Building a C Major Triad :
| Note | Degree | Name |
| C | 1 | do |
| D | 2 | re |
| E | 3 | mi |
| F | 4 | fa |
| G | 5 | so |
These three notes (the root, major third and perfect fifth) can be structured or 'voiced', C-E-G, E-G-C or G-C-E. No matter what order the three notes (called voices) are in they still create a C major chord. It does not matter if the voices are the singers in a choir or the instruments of an orchestra, if the notes are all either C, E, or G we simply have a gigantic sounding C chord.
The two consecutive intervals produced by these voicings would be:
* C E G = major third, minor third (root position),
* E G C = minor third, perfect fourth (first inversion),
* G C E = perfect fourth, major third (second inversion).
If the root (C) is on the bottom this voicing is called root position. If the third (E) is on the bottom it is called first inversion. If the fifth (G) is on the bottom this voicing of the triad is called second inversion.
Since there are only three possible voicings of a triad it is relatively easy to hear them in that they are a common feature of the past two centuries of traditional harmonic structures in Western music. The use of the exponentially more complex voicings arising from 4-voice, 5-voice and larger chords is more challenging. Some 4-voice chords are used in traditional, 'classical' and church music but others such as the diminished seventh were strictly forbidden in early sacred music as they contained the tritone interval; the mathematical halfway point in the octave which acquired the name diabolus in musica (the Devil in music) due to its dissonant qualities. Other 4-voice chords were not used in symphonic and 'classical' music until the French Impressionist era and in modern jazz. All triads and 4-voice chords are built within the octave, or eight-note scale which encompasses the do-re-mi-fa-sol-la-ti-do of the major scale, for instance, or the scale steps 1-2-3-4-5-6-7-8; eight being the octave where the pattern starts over again.
All triadic and therefore, common, chords can be constructed the same way : using the 1 3 5 formula. Take the C scale, for instance:
Building Harmonizing Chords in the Scale of C Major :
| Degree 1 2 3 4 5 | Chord Name | 1-3-5 Triad |
| C D E F G | C Major | C E G |
| D E F G A | D Minor | D F A |
| E F G A B | E Minor | E G B |
| F G A B C | F Major | F A C |
| G A B C D | G Major | G B D |
| A B C D E | A Minor | A C E |
| B C D E F | B Diminished | B D F |

## Seventh Chords and More

Seventh chords are triads with another fourth note a seventh from the root; they're characteristic of jazz music and provide more color than a basic triad.
There are several types:
Kinds of Seventh Chords :
| | Root | 3rd | 5th | 7th |
| Major seventh | 1 | 3 | 5 | 7 |
| Minor seventh | 1 | ♭3 | 5 | ♭7 |
| Dominant seventh | 1 | 3 | 5 | ♭7 |
| Minor-major seventh | 1 | ♭3 | 5 | 7 |
| Diminished seventh | 1 | ♭3 | ♭5 | ♭♭7 |
| Half-diminished seventh* | 1 | ♭3 | ♭5 | ♭7 |
*Many people choose not to recognize half-diminished seventh chords, and prefer to call them minor seventh chords with a flat fifth.
These chords have inversions in the same sense that triads do, except seventh chords have three inversions:
* The root position of C major seventh: C, E, G, B
* The first inversion of C major seventh: E, G, B, C
* The second inversion of C major seventh: G, B, C, E
* The third inversion of C major seventh: B, C, E, G

### Sixth Chords

A slightly less dissonant option than a seventh chord would be a sixth chord, with replaces the seventh with a sixth. Only the major sixth is used because a minor sixth would make a dissonant minor second with the fifth; a minor sixth chord would be built with a major sixth despite it not being a minor interval.
| | Root | 3rd | 5th | 6th |
| Major sixth | 1 | 3 | 5 | 6 |
| Minor sixth | 1 | ♭3 | 5 | 6 |

## Chord Notation

People very often abbreviate chords into just a couple letters and symbols and put them on sheet music or jazz lead sheets.
Some chord symbols on chords with the root C (the C can be replaced with any note):
| Full Name | Symbol(s) | Symbol(s) | Symbol(s) |
| C major (triad) | Cmaj | C | C |
| C minor (triad) | Cm | C- | C- |
| C augmented | Caug | C+ | C+ |
| C diminished | Cdim | C° | C° |
| C (major) sixth | CM6 | C6 | C6 |
| C minor sixth | Cm6 | C-6 | C-6 |
| C major seventh | CM7 | CΔ7 | CΔ |
| C dominant seventh | C7 | C7 | C7 |
| C minor seventh | Cm7 | C-7 | C-7 |
| C minor-major seventh | CmM7 | CmM7 | CmM7 |
| C diminished seventh | Cdim7 | C°7 | C°7 |
| C half-dimished seventh | Cø7 | Cø | Cø |
Extensions or alterations are added directly at the end of the chord symbol, often with parentheses: an A dominant seventh flat-nine chord would look like A7♭9 or A7(♭9). For more than one alteration/extension, use a comma between each extension for clarity.
"Slash chords" are chords written with a slash and a note name after it, like E♭Δ7/F. This communicates an E♭ major seventh chord, but with an F played in the bass. While the E♭ is still the root of the chord, there is an F at the bottom for flavor. This is useful if you want to explicitly mark inversions: the first inversion of a C minor triad would look like Cm/E♭.

### Analysis Notation

Theorists very often use Roman numerals in the place of scale degrees when they're talking about chords, so that they can talk about chord patterns that aren't specific to any key. Uppercase numerals indicate major (or augmented) chords and lowercase numerals indicate minor (or diminished) chords, like so:
| Chord Type | Symbol |
| major | I |
| minor | i |
| augmented | I+ |
| diminished | i° |
Thus, all of the triads in any major scale could be listed simply as I ii iii IV V vi vii°, and all of the triads in any minor scale as I ii° III iv v VI VII.
Like any scale degree number, you can put a sharp or flat behind a symbol to specify a chord with a root outside of the scale, so in D major a ♭VI chord would be a B♭ major triad.

## Applying Chords

The easiest way to apply a triad, or indeed any chord, is to pick one on a polyphonic instrument (such as a piano) and play its three notes simultaneously. This is often how chords occur in actual music: an instrument plays all the notes in the chord at the same time. However, there are other possibilities. The simplest is to arpeggiate the chord, that is, to play its notes one at a time in any order, especially in an ascending or descending order. Often melody can be written around the chord, using notes in the chord as well as the diatonic and chromatic passing notes between the chord tones. When this is done, while there is no accompaniment actually playing a chord, the chord is implied.

## Other Chords

Some chords are defined by the relation to the key rather than by any inherent characteristics. The Neapolitan chord, for example, expressed as N in analysis notation, is an ordinary major chord, but its root is the lowered supertonic of the corresponding key, so the Neapolitan of C major is a D♭ major chord. Additionally, the Neapolitan is usually found in first inversion. A borrowed chord is one from the parallel major or minor key. In C major, the parallel key is C minor and borrowed chords include E♭ major, B♭ major, and F minor.