Module 2: Theory ILesson 5beginner⏱ 90 min + two weeks of drills

Harmonising the major scale: diatonic triads and Roman numerals

Build a triad on every degree of the major scale, name the chords with Roman numerals, understand tonic, subdominant and dominant function, and transpose any progression to any key by numerals.

Why numerals instead of chord names

Ask a jazz musician how a tune goes and you will hear "it's a I–vi–ii–V, then it goes to the IV". Not "C, A minor, D minor, G7": those are the chords in one key, and the tune will be called in another key next week. Roman numerals describe a progression by function, independent of key, which is how progressions are remembered, transposed, discussed and recognised by ear. This lesson shows where the numerals come from: harmonising the major scale into triads. Everything you built in the triads lesson and the key lesson comes together here.

Harmonising the scale

Take a major scale and build a triad on each of its seven notes using only notes of the scale (stack the 3rd and 5th from the scale, not from the chromatic scale). The qualities that come out are fixed for every major key, because the pattern of whole and half steps is fixed. In C major:

The pattern is always major, minor, minor, major, major, minor, diminished. Chords built this way are diatonic to the key: they contain nothing outside its key signature. Here it is on the fretboard, as close-position root-position triads on strings 5-4-3 climbing from the open position to the octave. Each shape is the triad lesson's root-position form on this string set; the quality changes by itself because you are only using scale notes.

\tempo 72
.
\ts 4 4
:4 (3.5 2.4 0.3){ch "C"} (5.5 3.4 2.3){ch "Dm"} (7.5 5.4 4.3){ch "Em"} (8.5 7.4 5.3){ch "F"} | (10.5 9.4 7.3){ch "G"} (12.5 10.4 9.3){ch "Am"} (14.5 12.4 10.3){ch "Bdim"} (15.5 14.4 12.3){ch "C"} |

Roman numerals

Each diatonic chord takes the Roman numeral of the scale degree its root sits on. The convention used throughout this course, and in most modern charts and textbooks, is:

• Upper case for major triads: I, IV, V.
• Lower case for minor triads: ii, iii, vi.
• Lower case with ° for the diminished triad: vii°.

So the harmonised major scale reads I ii iii IV V vi vii°, in every major key. Check it against the table: the chord column changes with the key, the degree column never does. Here is the same harmonisation in F and in G; the chord names are all different, the numerals and qualities are identical.

A note on what the numeral does not tell you: it does not say which inversion or voicing to play. A chart marked "IV" in C means any F major triad, played however suits the moment. Numerals are about function, not fingering.

Three functions: tonic, subdominant, dominant

Seven chords, but only three jobs. Every diatonic chord belongs to one of three functions, which describe how it behaves in a progression:

• Tonic (I, with iii and vi as substitutes): home. Stable, finished, where phrases come to rest. The vi shares two notes with I and is the most common stand-in for it; the iii shares two notes as well and is used more rarely.
• Subdominant (IV, with ii as a substitute): away from home. Moves the music somewhere without demanding a return. The ii shares two notes with IV and in jazz is used far more often than IV itself.
• Dominant (V, with vii° as a substitute): tension that wants to go home. The V triad contains the leading tone (the scale's 7th degree), which pulls up a half step to the root, and when a 7th is added, as it almost always is in jazz, the chord also contains a tritone. The vii° triad is the top three notes of that V7 chord, which is why it works as a substitute.

The basic shape of almost all tonal music is tonic → subdominant → dominant → tonic: leave home, build tension, come back. Memorise the functions, because jazz substitution is largely the art of swapping one chord for another of the same function.

The essential progressions in triads

I–IV–V

The progression behind the blues, rock and roll and a thousand songs. Played with the nearest-inversion voice leading from the triads lesson, it needs almost no hand movement.

\tempo 84
.
\ts 4 4
:2 (5.3 5.2 3.1){ch "C"} (5.3 5.2 3.1) | (5.3 6.2 5.1){ch "F"} (5.3 6.2 5.1) | (4.3 3.2 3.1){ch "G"} (4.3 3.2 3.1) | (5.3 5.2 3.1){ch "C"} (5.3 5.2 3.1) |

I–vi–IV–V

Add the vi between I and IV and you get the classic turnaround of 1950s pop and the skeleton of the jazz I–vi–ii–V turnaround (swap the IV for its substitute, ii). The example is in G on strings 4-3-2; find the shared notes between neighbouring chords.

\tempo 92
.
\ts 4 4
:2 (5.4 4.3 3.2){ch "G"} (5.4 4.3 5.2){ch "Em"} | (5.4 5.3 5.2){ch "C"} (4.4 2.3 3.2){ch "D"} | (5.4 4.3 3.2){ch "G"} (5.4 4.3 5.2){ch "Em"} | (5.4 5.3 5.2){ch "C"} (4.4 2.3 3.2){ch "D"} | (5.4 4.3 3.2).1{ch "G"} |

ii–V–I

The single most important progression in jazz, here in its triad form: subdominant (ii), dominant (V), tonic (I). In the next module it becomes ii7–V7–Imaj7, and the whole of jazz harmony can be seen as decorations of it. Play it in F and in Bb and hear that it is the same motion in both keys.

\tempo 92
.
\ts 4 4
:2 (3.3 3.2 3.1){ch "Gm"} (5.3 5.2 3.1){ch "C"} | (5.3 6.2 5.1){ch "F"} r | (5.3 4.2 3.1){ch "Cm"} (5.3 6.2 5.1){ch "F"} | (3.3 3.2 1.1){ch "Bb"} r |

Transposing by numerals

Here is the method you will use for the rest of your playing life. To move a progression to a new key:

1. Convert the chords to numerals in the original key. In C, a chart reading C – Am – Dm – G is I – vi – ii – V.
2. Write out the major scale of the new key (spelling rules from the key lesson).
3. Place each numeral on the corresponding scale degree and apply the fixed quality pattern (I major, ii minor, iii minor, IV major, V major, vi minor, vii° diminished).

In Eb, that turnaround becomes the chords on degrees 1, 6, 2 and 5 of the Eb major scale, with qualities major, minor, minor, major. The progression tables above do this for every key at once, and the reference page lists the harmonised scale for all twelve. Doing it by hand, slowly, is the exercise that makes the tables unnecessary.

Two skills grow from this. First, you can hear in numerals: a bass line that goes down a 3rd then up a 4th is I–vi–ii, whatever the key. Second, you can learn tunes as numerals, so a 32-bar standard becomes a handful of patterns rather than 32 unrelated chord names; the standards module builds on exactly this.

Diatonic bass lines

Comping is only half of what the numerals describe: the root movement is the other half. The most common root motions in jazz are up a 4th (V to I, ii to V), down a 3rd (I to vi) and stepwise (I to ii, IV to V). Playing the roots alone, as a bass player would, fixes the numerals in your ear.

\tempo 100
.
\ts 4 4
:2 8.6{txt "I"} 5.6{txt "vi"} | 5.5{txt "ii"} 3.6{txt "V"} | 8.6.1{txt "I"} |

Try the same roots in F, Bb and G without writing anything down: find the I on string 6 or 5, then move down 3 frets for vi, up a 4th (same fret, next string) for ii, and up a 4th again for V.

Exercises

1. Harmonise aloud. Pick a key, spell its scale, then say the seven diatonic triads with their numerals and spell each one. All twelve keys over the week.
2. Harmonised scale on the neck. Play the harmonised scale (as in the first example) on strings 5-4-3, then 4-3-2, then 3-2-1, in C, F, G and Bb. Say the numeral of each chord.
3. Function drill. Play any diatonic triad; name its numeral and its function (tonic, subdominant or dominant). Then play a substitute of the same function.
4. Three progressions, all keys. I–IV–V–I, I–vi–IV–V and ii–V–I on strings 3-2-1 with nearest inversions, around the cycle of 4ths.
5. Transpose a turnaround. Write I–vi–ii–V in six keys as chord names from memory, then check against the progression table.

Quiz