The elements of music :: Chords

22. Triads, and other chords

22.1. A chord is any two or more notes sounded simultaneously (a chord whose notes are sounded in sequence is known as a broken chord).

22.2. The chords used in songwriting are formed from notes stacked up in intervals of a third (begin on a note, move up a third to the next note, and so on). The notes of chords can also be interpreted as sequences of the degrees (or alterations of degrees) of a heptatonic scale, where you use a degree, then skip a degree, and so on.

22.3. A triad is a three-note chord (hence its name) formed from a third followed by a third. So, a triad's notes are spaced a third apart and, since the sum of two thirds is a fifth, the interval between the first and third notes of a triad (in other words, the size of the chord) is a fifth.

22.4. The notes of a triad are known as the root, third, and fifth.

22.5. A major triad is formed from a maj3 (hence the triad's name) followed by a min3. One place it occurs is on 1 3 5 of a major scale, where it is notated as I. For example, the chord C E G, which can be written C major, Cmaj, CM, or C. The major triad's formula is 1 3 5.

22.6. A minor triad is formed from a min3 (hence the triad's name) followed by a maj3. One place it occurs is on 2 4 6 of a major scale, where it is notated as ii (another is 1 b3 5 of a minor scale, where it is notated as i). For example, the chord D F A, which can be written D minor, Dmin, or Dm (after a note name we need the "m"; we don't need it after a roman numeral, because the letter case tells us whether the third is major or minor). The chord's formula is 1 b3 5.

22.7. Because they are both formed from the same building-blocks of a maj3 and a min3 (but not in the same order), major and minor triads are both a perfect fifth in size.

22.8. An augmented triad is formed from a maj3 followed by a maj3. One place it occurs is on b3 5 7 of a harmonic minor scale, where it is notated as bIII#5 (or you can form one by taking 1 3 #5 of a major scale, where it is notated as I#5). For example, the chord E♭ G B, which can be written E♭ augmented, E♭aug, E♭+, or E♭#5. The chord's formula is 1 3 #5.

22.9. A diminished triad is formed from a min3 followed by a min3. One place it occurs is on 7 2 4 of a major scale, where it is notated as viib5 (another is 2 4 b6 of a minor scale, where it is notated as iib5). For example, the chord B D F, which can be written B diminished, Bdim, B-, or Bb5. The chord's formula is 1 b3 b5.

22.10. Augmented and diminished triads are named for their size: an augmented fifth and a diminished fifth, respectively.

23. Memorizing triads by putting them in order

23.1. We can use binary (the base-2 numeral system) to help us remember all of the triads and what kinds of thirds they contain. First, you need to become fluent in counting in binary. The first four binary numbers are 00, 01, 10, and 11. Now, if we replace the binary digit 0 with min3, and the binary digit 1 with maj3, then we get the sequence min3-min3, min3-maj3, maj3-min3, and maj3-maj3. And that gives us all permutations of triads, in other words, dim (b5), min (m), maj (M), and aug (#5).

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24. Triads in the major and minor scale formulas

24.1. The following table shows the triads formed on the degrees of the major scale formula. The triad whose root is the tonic is called the tonic triad, and so on.

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24.2. The following table shows the triads formed on the degrees of the natural minor scale formula.

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24.3. The following table shows the triads formed on the degrees of the harmonic minor scale formula.

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25. Triad inversions

25.1. A triad played with the root in the bass (that is, the lowest-pitched note played by either hand) is in root position.

25.2. Beginning in root position and moving the root up an octave leaves the third as the bass note. This is known as first inversion. An inversion does not alter the identity of the chord, nor its function.

25.3. Beginning in first inversion and moving the third up an octave leaves the fifth as the bass note. This is known as second inversion. Another way to reach second inversion is to begin in root position and move the fifth down an octave.

25.4. Beginning in second inversion and moving the fifth up an octave returns the triad to root position.

26. Seventh chords

26.1. A seventh chord is a four-note chord formed from a triad followed by a third. So, a seventh chord's notes are spaced a third apart and, since the sum of three thirds is a seventh, the interval between the first and fourth notes of a seventh chord (in other words, the size of the chord) is a seventh, hence its name.

26.2. The notes of a seventh chord are known as the root, third, fifth, and seventh.

26.3. A major seventh chord is formed from a major triad followed by a maj3 (that is, a maj3 followed by a min3 followed by a maj3). One place it occurs is on 1 3 5 7 of a major scale, where it is notated as IM7. For example, the chord C E G B, which can be written C major seventh, Cmaj7, or CM7. The chord's formula is 1 3 5 7.

26.4. A minor seventh chord is formed from a minor triad followed by a min3 (that is, a min3 followed by a maj3 followed by a min3). One place it occurs is on 2 4 6 1' of a major scale, where it is notated as ii7 (another is 1 b3 5 b7 of a natural minor scale, where it is notated as i7). For example, the chord D F A C', which can be written D minor seventh, or Dm7 (after a note name we need the "m"; we don't need it after a roman numeral). The chord's formula is 1 b3 5 b7.

26.5. A dominant seventh chord is formed from a major triad followed by a min3 (that is, a maj3 followed by a min3 followed by a min3). One place it occurs is on 5 7 2' 4' of a major scale, where it is notated as V7 (which is the dominant triad plus the subdominant, and that's where this chord gets its name). For example, the chord G B D F, which can be written G dominant seventh, or G7. Note that the last three degrees of a dominant seventh chord form a diminished triad. The chord's formula is 1 3 5 b7.

26.6. A half-diminished seventh chord is formed from a diminished triad followed by a maj3 (that is, a min3 followed by a min3 followed by a maj3). One place it occurs is on 7 2' 4' 6' of a major scale, where it is notated as vii7b5. For example, the chord B D' F' A', which can be written B half-diminished seventh, or Bm7b5 (after a note name we need the "m"; we don't need it after a roman numeral). The chord's formula is 1 b3 b5 b7.

26.7. A minor major seventh chord is formed from a minor triad followed by a maj3 (that is, a min3 followed by a maj3 followed by a maj3). One place it occurs is on 1 b3 5 7 of a harmonic minor scale, where it is notated as iM7. For example, the chord A C E G♯, which can be written A minor major seventh, A minor/major seventh, A minor-major seventh, or AmM7 (after a note name we need the "m"; we don't need it after a roman numeral). The chord's formula is 1 b3 5 7.

26.8. An augmented major seventh chord is formed from an augmented triad followed by a min3 (that is, a maj3 followed by a maj3 followed by a min3). One place it occurs is on b3 5 7 2' of a harmonic minor scale, where it is notated as bIIIM7#5. For example, the chord C E G# B, which can be written A augmented major seventh, or CM7#5. The chord's formula is 1 3 #5 7.

26.9. A diminished seventh chord is formed from a diminished triad followed by a min3 (that is, a min3 followed by a min3 followed by a min3). One place it occurs is on 7 2' 4' b6' of a harmonic minor scale, where it is notated as viidim7. For example, the chord G♯ B D F, which can be written G♯ diminished seventh, or G♯dim7. The chord's formula is 1 b3 b5 bb7.

26.10. By moving the fifth of the dominant seventh chord either up or down a semitone, you can form another two seventh chords. Move the fifth up to form the augmented seventh chord (a maj3 followed by a maj3 followed by a dim3). For example, the chord G B D♯ F, which can be written G augmented seventh, or G7#5. The chord's formula is 1 3 #5 b7. Move the fifth down to form the dominant seventh flat five chord (a maj3 followed by a dim3 followed by a maj3). For example, the chord G B D♭ F, which can be written G dominant seventh flat five, or G7b5 (note that since this notation can only follow an upper-case roman numeral, there's no possible confusion with a half-diminished seventh such as vii7b5). The chord's formula is 1 3 b5 b7.

26.11. The diminished seventh chord is a diminished seventh in size. The half-diminished seventh, minor seventh, dominant seventh, dominant seventh flat five, and augmented seventh chords are all a minor seventh in size. The minor major seventh, major seventh, and augmented major seventh chords are all a major seventh in size.

27. Memorizing seventh chords by putting them in order

27.1. Binary again helps us to remember the seventh chords and what kinds of thirds they contain. The first seven binary numbers are 000, 001, 010, 011, 100, 101, and 110. When we replace 0 with min3, and 1 with maj3, to get chords, we see a pattern emerging. The first two chords take the form of a b5 triad extended by, respectively, a min3 then a maj3. Then the same pattern for m, and M, and finally we end with a #5 triad extended by a min3 (we'll disregard the possible #5-triad-extended-by-maj3 permuation). Those seven chords are, in order: diminished seventh (dim7), half-diminished seventh (m7b5), minor seventh (m7), minor major seventh (mM7), dominant seventh (7), major seventh (M7), and augmented major seventh (M7#5). Then to that list we add on the dominant seventh flat five (7b5), and augmented seventh chords (7#5) (which don't fit the binary pattern, because they contain diminished thirds).

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28. Seventh chords in the major and minor scale formulas

28.1. The following table shows the seventh chords formed on the degrees of the major scale formula. The seventh chord whose root is the tonic is called the tonic seventh, and so on.

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28.2. The following table shows the seventh chords formed on the degrees of the natural minor scale formula.

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28.3. The following table shows the seventh chords formed on the degrees of the harmonic minor scale formula.

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