TRIADS & SEVENTH CHORDS

§1. Triads §8. Voicing §2. Qualities of triads: major, minor, §9. Positions of seventh chords; diminished, augmented inversions; arabic figures §3. Major and minor triads; §10. How to identify triads and consonance and dissonance seventh chords §4. Seventh chords §11. Labeling chords §5. Qualities of seventh chords: §12. Lead-sheet symbols for triads diminished, half-diminished, §13. Alternative symbols minor, dominant, major §14. Lead-sheet symbols for seventh §6. Dominant seventh chords chords §7. Positions of the triads; inversions; §15. Inversion in lead-sheet symbols arabic figures ————————————

Triads

§1. A triad is a kind of chord that has three distinct members, or degrees: ♦ the root, after which the triad is named, ♦ the third, found a third above the root, and ♦ the fifth, found a fifth above the root.

§2. Four qualities of triad are “standard,” and are shown in Example 1:

QUALITY OF: TRIAD MINOR MAJOR DIMINISHED AUGMENTED 5th perfect diminished augmented 3rd minor major minor major

[ ][][][] fifth: E E E b E # third: C C # C C # root: A A A A Example 1. Qualities of triads.

The two most common (and most harmonically stable) triads, major and minor, take their names from the third above the root. ♦ In a minor triad, the third above the root is minor, the fifth perfect. ♦ In a major triad, the third above the root is major, the fifth perfect.

The diminished and augmented triads take their names from the fifth above the root. ♦ In a diminished triad, the third above the root is minor, the fifth diminished. ♦ In an augmented triad, the third above the root is major, the fifth augmented.

These four triads are arranged in Figure 1 according to the size of the intervals above the root, smallest to largest:

diminished • minor • major • augmented (small 3rd, small 5th) (small 3rd, “standard” 5th) (big 3rd, “standard” 5th) (big 3rd, big 5th)

Figure 1. Triads arranged according to size of intervals above the root, smallest to largest.

You might find it easier to think of these triads as stacked thirds, or possibly cookies, shown in Example 2:

minor ] diminished ] minor

] major ] minor minor a)

] minor ] major major

major ] augmented ] major

b)

Example 2. Triads a) as stacked thirds; b) as cookies.

§3. Major and minor triads are the fundamental chords in the huge repertory of music that is in a key, also called tonal music. These triads take their names from their thirds. ♦ Major and minor triads are also the most consonant triads. A consonant triad has more grammatical “weight” than a dissonant triad; it is more stable, more complete in itself. Diminished and augmented triads, which are dissonant, take their names from their dissonant fifths. ♦ A dissonant triad, in turn, is more active; it creates tension in itself that wants to be released (in theory speak, “resolved”) in a consonance.

Triads and Seventh Chords, -2- Seventh chords

§4. A seventh chord is a triad to which has been added another degree that is a seventh above the root. This degree is the seventh of the seventh chord.

§5. Five qualities of seventh chord are “standard,” and are shown in Example 3:

QUALITY OF: SEVENTH CHORD DIM HALF-DIM MINOR DOMINANT MAJOR 7th dim minor minor minor major TRIAD dim diminished minor major major

seventh: G b G G G G# fifth: E b E b E E E third: C C C C # C # root: A A A A A

Example 3. Qualities of seventh chords.

♦ In a diminished seventh chord, the triad is diminished, the seventh above the root diminished. ♦ In a minor seventh chord, the triad is minor, the seventh minor. ♦ In a major seventh chord, the triad is major, the seventh major.

As the italic labels on the example show, the three seventh chords above take their names from both constituent triad and seventh.

♦ In a half-diminished seventh chord, the triad is diminished, the seventh minor. ♦ In a dominant seventh chord (also called a major/minor-seventh chord), the triad is major, the seventh minor.

The five seventh chords are arranged in Figure 2 according to the size of the intervals above the root, smallest to largest:

diminished • half-diminished • minor • dominant • major (dim triad & 7th) (dim triad, min 7th) (min triad & 7th) (maj triad, min 7th) (maj triad & 7th)

Figure 2. Seventh chords arranged according to size of intervals above the root, smallest to largest.

§6. The dominant seventh chord is the principal seventh chord in tonal music.

Triads and Seventh Chords, -3- Position and voicing

§7. Example 4a shows a D minor triad, with the root D on the bottom, the third F in the middle, the fifth A on top.

If we transpose the D up an octave, we get the chord in Example 4b. Like 4a, it has D, F, and A, so it is still a D minor triad, but the F is now the lowest note. By transposing the originally lowest note D up an octave, we’ve inverted the D minor triad, so that the third degree, F, is in the bass.

If we transpose the bottom F of Example 4b up an octave, inverting the D minor triad again, we get the chord in 4c, which has the fifth degree, A, in the bass.

6th 6th 4th 5th 3rd 3rd [ ] [ ] [ ] root first second a) position b) inversion c) inversion or or or 5 6 6 3 3 4

Example 4. D minor triads in three positions.

These three chords are all D minor triads, because they all consist of D, F, and A. They differ with respect to position. A triad has three positions, each named according to which degree is the lowest note: ♦ If the root of a triad is in the bass, as in Example 4a, the triad is in root position; ♦ If the third of a triad is in the bass, as in 4b, the triad is in first inversion; ♦ If the fifth of a triad is in the bass, as in 4c, the triad is in second inversion.

The three positions for triads have also been named according to the intervals above the lowest note. This system comes from a tradition of 17th- and 18th-century performance in which the keyboard player or lutenist in an ensemble was given the bass line annotated with numbers—a figured bass—that indicated the chords over which to improvise. In principle, the practice is similar to that of jazz or pop musicians working off a fake book or lead sheet.

♦ As Example 4a shows, the intervals above the lowest note in a root position triad 5 are a fifth and a third, so it is also called a 3 (five-three) chord. ♦ As Example 4b shows, the intervals above the lowest note in a first inversion 6 triad are a sixth and a third, so it is called a 3 (six-three) chord, or for short, a 6 (six) chord. ♦ Finally, in Example 4c, the intervals above the lowest note in a second inversion 6 triad are a sixth and a fourth, so this is a 4 (six-four) chord.

§8. Example 5a shows D minor triads, all in root position, in different voicings—they all consist of D, F, A (so they’re all D minor triads), and the D is the lowest note (so they’re all in Triads and Seventh Chords, -4- root position), but the various degrees are distributed differently above the bass D. By the same token, Examples 5b and 5c show D minor triads in first and second inversion, respectively, all voiced differently.

5 6 ♦ The Arabic figures 3 , 6 , and 4 apply to all chords in Example 5a, 5b, and 5c, respectively, even though some of the intervals are compounded by one or more octaves. ♦ Root position is the “default ”, so if there is no indication of inversion, the chord is 5 understood to be a 3 chord.

a) b) c)

5 5 5 5 6 6 6 6 6 6 6 6 3 3 3 3 4 4 4 4

Example 5. D minor triads in three positions in various voicings.

§9. Just as triads can be inverted and voiced in many configurations, so too can seventh chords. The idea is the same, as Example 6 shows. ♦ In 6a, the root of the seventh chord is in the bass, so the chord is in root 7 position, or 5 (seven-five-three), or for short, 7 (seven) position. 3 ♦ In 6b, the third of the seventh chord is in the bass, so the chord is in first 6 6 inversion, or 5 (six-five-three), or for short, 5 (six-five) position. 3 ♦ In 6c, the fifth of a seventh chord is in the bass, so the chord is in second 6 inversion, or 4 (six-four-three), or for short, 4 (four-three) position. 3 3 ♦ In 6d, the seventh of the seventh chord is in the bass, so the chord is in third 6 inversion, or 4 (six-four-two), or for short, 4 (four-two), or 2 (two) position. 2 2

a) b) c) d)

7 7 7 6 6 6 4 4 4 4 4 4

5 5 5 3 3 3 2 2 2 Example 6. A minor seventh chords in four positions in various voicings. §10. A chord is a triad if it has three distinct degrees that can be “condensed” or “reduced” to one of the “snowman” or “stoplight” patterns in §2. When it is in that “stoplight” position, the lowest note is the root, and the qualities of the intervals above the root will tell you the quality of the triad.

Triads and Seventh Chords, -5- Likewise, a chord is a seventh chord if it has four distinct degrees that can be “condensed” or “reduced” to one of the “stoplight” patterns in §5. When it is in that “stoplight” position, the lowest note is the root, and the qualities of the intervals above the root will tell you the quality of the seventh chord.

Labeling chords

§11. There are two distinct methods for labeling triads and seventh chords: lead-sheet symbols and roman numerals. ♦ Lead-sheet symbols identify chords absolutely, regardless of their tonal context, i.e. regardless of the key of the music. ♦ Roman numerals identify chords relatively, according to their position (or in theory jargon, their “function”) in a particular key. Roman numerals will be covered in a subsequent handout.

§12. Triads in lead-sheet notation

Lead-sheet symbols are used in much jazz and popular music. They are also called pop chord symbols or simply chord symbols. By convention, lead-sheet symbols are written above the staff when used together with staff notation. Lead-sheet symbols identify the root by letter (G, Eb, etc.) followed by an indication of triad quality. The essential features of the system are clarity and brevity, as it evolved as a format for improvising musicians to read harmonies quickly and on the spot. ♦ Major triads are the most common, so they are the “default”, and the symbol is simply the root’s letter-name. ♦ Minor triads are indicated by the root name followed by min, —, or m. ♦ Diminished triads are indicated by the root name followed by dim or a small superscript circle o. ♦ Augmented triads are indicated by the root name followed by aug or +.

The root name is always written with a capital letter, regardless of triad quality.

E E- or Emin or Em E dim or Eº E aug or E+ B¨ G- G B ˙ #˙ & #w w bw ##w b ˙ ˙ n˙ # ˙ w w w w E 8 E ∆!8 or Emaj 8 E- 8 or Emin 8 or Em8 E dim 8 or Eº 8 Emin8b6 !Example 7. Lead-sheet symbols for standard triads. w #w w bbw bw ♦ &Re#member,w # wlead-sheet symbolsw “ignore” tonal context,w including the keyw signature. For instance, in the key of F you would write “Bb” to indicate a Bb major chord; “B” would indicate a B major chord, even though none of its notes are in the key. E- 8 Edim 8 E+ 8 E+8 or E 8#6 ! ! ! #w Triadsb#w and Seventh Chords# #w, -6- #w & w w # w # w

§13. Alternative symbols (all illustrated using an E root). Major triads are sometimes indicated EMAJ or EMA, but we will discourage this as being unnecessary, and because it reduces the visual distinction between the symbols for major and minor triads. Diminished triads can be indicated with Eminb5 (or Emb5 or E–b5). Augmented triads are sometimes indicated with E(#5). The parentheses are necessary to show that the # symbol does not apply to the root, but is modifying the chord fifth. Note that the sharp or flat before the 5 means the tone is raised or lowered from the perfect fifth, not necessarily that this is a sharp or a flat note. For example, the symbol Eb(#5) means an E-flat augmented triad, Eb-G-Bn.; F#mb5 means an F# diminished triad, F#-A-C.

§14. Seventh chords in lead-sheet notation Seventh chords are distinguished from triads in lead-sheet symbols by the addition of a superscript “7” following the root and quality indicators. (All chords are illustrated below using E as root.) ♦ The dominant seventh (major/minor-seventh) is the most common quality of seventh chord, so its symbol is simply E7. ♦ The major seventh chord is indicated E∆7 or Emaj7. ♦ The minor seventh chord is indicated E–7 , Em7 , or Emin7. ♦ The diminished seventh chord is indicated Edim7 or Eo7. E ♦ EThe- or half Emin-diminished or Em E seventhdim or Eº chordE augis a specialor E+ case. B¨It is traditionallyG- B indicatedG Em7b5 (or Emin7b5 or E–7b5). As with diminished triad˙s, the b˙ here m#ean#˙s a n˙ & #w loweredw (diminished) bfiftwh, which might##w be a naturalb (rather˙ than˙ a flatn) ˙note.n ˙ w w w w E 8 E !∆!8 or Emaj 8 E- 8 or Emin 8 or Em8 E dim 8 or Eº 8 Emin8b6 E wE- or E#minw or Em E dimw or Eº E aug or E+ bwB¨ G- wB G & #w # w w b w bw w w bw #w b ˙ ˙ #n#˙ nn˙ & #w w Example 8. Leadw -sheet symbol# sw for standard seventh chords˙. ˙ E aug or E+ 8 E ∆!8 or Emaj 8 E- 8 or Emin 8 or Em8 E dim 8 or Eº 8 Emin8b6 In jazz andE other popular! music, seventh chords beyond the five “standard” qualities are &fre##quentlyw found.w Their#w symbols are wformed with logical combinationbw s of triad qualitw y indicatorsw& # andw symbols# w for seventh orw fifth quality. b w bw w w w w w

E-!8 Edim !8 E+ !8 E+8 or E 8#6 & #w b#w ###w ##w w w w w Example 9. Lead-sheet symbols for some “modern” seventh chords.

Triads and Seventh Chords, -7- E E- or Emin or Em E dim or Eº E aug or E+ B¨ G- G B ˙ ˙ ˙ ##˙ & #w w bw ##w b ˙ ˙ n˙ ˙ E 8 E !∆!8 or Emaj 8 E- 8 or Emin 8 or Em8 E dim 8 or Eº 8 Emin8b6 w #w w bw w & #w # w w b w bw

§13. Inversion in lead-sheet notation E- 8 Edim 8 E+ 8 E+8 or E 8#6 ! Inversions are indicated !using slash notation:! a chord symbol followed by a forward slash #w and then the bassb# wnote (see Example 10# a# &w b). If there is no such#w notation, the chord is & w understood to be win root position. # w # w

F/A G7/B F-!8/G A¨/D w ˙ ˙ w bw & w ˙ ˙˙ bw bbw ˙ ˙ ? w w (a) (b) (c) (d)

{ Example 10. Slash notation. & ♦ The letter following the slash∑ indicates an individual pitch (the bass), not another chord. ? Slash notation also allows us to indicate more complex harmonies where the bass note is not a member of the chord (see Example 10∑ c & d). {

Triads and Seventh Chords, -8-