Harmony by degree

▶ Open in Aratu to hear the examples, change them and do the exercises

In the last lesson chords had names: Am, F, C, G. Harmony students often think another way: not "A minor" but "the sixth degree of the key". Writing by degree shows what each chord does, and the same progression works in any key.

The degrees of the key

Degrees are written in Roman numerals, from I to VII, counted from the key of the piece, which goes in key:. In C major, I is C, IV is F, V is G:

key: C major
tempo: 90
chords = | I | IV | V | I |

Upper case is a major chord, lower case a minor one. In C major the second, third and sixth degrees are minor: ii is Dm, iii is Em, vi is Am. The most played progression in pop is this one:

key: C major
tempo: 90
chords = | I | vi | IV | V |

Write key: G major in place of key: C major and listen: the same progression, now in G. That is how a song is moved to another key to fit the singer's voice.

Sevenths and other chords

After the degree comes the rest of the chord symbol, as on any lead sheet: V7 is the dominant seventh chord, ii7 the second degree with a seventh, Imaj7 the first degree with a major seventh. viidim (or vii°) is the diminished chord on the seventh degree.

key: C major
tempo: 80
chords = | ii7 | V7 | Imaj7 | viidim |

The ii–V–I is the most important cadence in jazz and bossa nova.

Minor keys

In a minor key the degrees change: in A minor, i is Am, iv is Dm, and V7 is E7, the dominant with the leading note:

key: A minor
tempo: 90
chords = | i | iv | V7 | i |

Chords from outside the key

A flat or sharp before the degree borrows a chord from outside the key: bVII in C major is Bb, the chord that gives that rock flavour. And a slash makes a secondary dominant: V7/V is the dominant of the dominant, D7 in C major, which leads to G.

key: C major
tempo: 90
chords = | I | bVII | IV | I | I | V7/V | V7 | I |

Rolling a chord

With :arp after the chord, its notes sound one after another, from the bottom up, like a harp or a guitar picked slowly. It works on any chord, by name or by degree:

key: C major
tempo: 70
chords = | I:arp | vi:arp | IV:arp | V7:arp |

The arpeggiator

:arp rolls a chord once. An arpeggiator goes through the chord's notes one at a time, in steps, for as long as the chord lasts, the way a synthesizer's arpeggiator does, or a harpist's fingers. Write a line called arp beside the chords, with the way it goes and the length of its steps:

key: A minor
tempo: 110
piano {
  chords = | i | VI | III | VII |
  arp    = up 16ths
}

Each sixteenth plays the next note of the chord that is sounding, from the bottom up, and each chord starts again from its lowest note. The chord itself is not heard as a block: the arpeggiator plays it, the way the strum plays the guitar's chords. Change the chords and it plays the new ones; change one word of the arp and the same chords sound another way.

tempo: 120
piano {
  chords = | Am | F | C | G |
  arp    = updown 8ths 2 octaves
}

In Portuguese the line is arpejo = sobe 16ths, desce, sobe e desce; in Spanish, arpegio = sube, baja, sube y baja.

Melodies by degree

Degrees write melodies too. A number in place of a note is a degree of the key: 1 is the key's first note, 3 the third, 5 the fifth, and 8 is 1 an octave higher. It is how many musicians sing a tune to learn it: "one, three, five, three".

key: C major
tempo: 100
melody = | 1 3 5 3 | 4 6 8 _ | 7 5 2 4 | 3 _ 1 _ |

Change the key to key: E minor and nothing else: the same tune, now in E minor. In a minor key the degrees follow the minor scale, so the third is already minor.

An accidental after the number leaves the scale: 4# is the raised fourth, 7b the flat seventh, the blue note. And a comma goes an octave down: 5, is the fifth below 1, 1,, two octaves down, for the bass.

key: A minor
tempo: 96
melody = | 1 _ [3 4] 5 | 7b _ 5 _ | 4 3 2 5, | 1 _ _ _ |
bass   = | 1,, _ _ _ | 4,, _ _ _ | 5,, _ _ _ | 1,, _ _ _ |

Degrees do everything a note does: brackets ([1 2]), chords (1+3+5), _, staccato, fermatas, x4 and tuplets.

With the guitar strum

Degrees work on the chords line of any instrument, strum and all:

key: D major
tempo: 96
guitar {
  chords = | I | V | vi | IV |
  strum  = D du -u du
}

Exercises

Write I, IV, V, I in C major, one chord per bar.

key: C major
chords = | I | I | I | I |

key: C major
chords = | I | IV | V | I |

The same progression by degree, but now in G major. Change only the key.

key: C major
chords = | I | vi | IV | V |

key: G major
chords = | I | vi | IV | V |

The ii–V–I cadence in C major: ii7, V7 and Imaj7, with the last one lasting two bars.

key: C major
chords = | I | I | I | I |

key: C major
chords = | ii7 | V7 | Imaj7 | % |

In A minor: i, iv, V7, i, with the last chord rolled.

key: A minor
chords = | i | i | i | i |

key: A minor
chords = | i | iv | V7 | i:arp |

Make the arpeggiator go down instead of up, still in eighths.

chords = | Am | F | C | G |
arp    = up 8ths

chords = | Am | F | C | G |
arp    = down 8ths

Write by degree, in C major: 1, 2, 3 and 5, a quarter note each.

key: C major
melody = | 1 _ _ _ |

key: C major
melody = | 1 2 3 5 |