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Keys, Scales, Chords Part 7

A series of theory tutorials for the theory challenged or curious.

This time:

Figured Bass

First, a recap of some material in the All Things Major tutorial; this will help in understanding some of the discussion further down the page.

Chord function

To distinguish how a chord functions (how it works in the scale it comes from); we identify it using Roman numerals.

Using these rules, we can identify the chords built above the major scale and harmonic minor scale as follows:

Further, when we are discussing individual key centres, we usually use

Why we don't use stacked 3rds to describe chords

Sometimes major chords are said to be a major third plus a minor third stacked above each other.

In the same way, minor chords are said to be a minor third plus a major third stacked above each other.

The same applies to diminished chords: two minor thirds stacked above each other.

In each case, this approach ignores the fifth above the root, leading to difficulties in recognising and understanding later concepts such as altered fifths and chord extensions to the 7th, 9th and 13th.

Figured Bass

Figured bass is the result of identifying which chords should be played over a given bass line. It is a practice that stems from before the time of Bach.

Example from Bach’s music

The figuring is straight forward, identifying what intervals to use above the given bass note. There are several sets of information that these figures tell us:


The last column shows the usual figuring used when working with individual lines.

Altered tones

The first assumption made in figuring is that everything references the home key scale, whether it be major or minor. If a chord is altered for whatever reason, then the alterations are shown based on which note(s) of the scale are changed to arrive at the required chord.

It is important to realise that any altered tone does not last beyond the chord it is indicated for; each new chord that contains the same altered tone needs the altered tone to be correctly indicated in the figuring.

Added tones

The second assumption made in figuring is that we are dealing with triads consisting of a 3rd and a5th above a given root not. Any chord can have added tones. Added tones are indicated by the number that shows its position (its interval distance and quality), above the given bass note, as the smallest possible interval; e.g a 9th would be reduced to 2.

Seventh chords

For seventh chords and other higher extensions our inversions are

Figuring applied to several tunes

When figuring a bass line it is a common mistake to attempt to treat each note of the bass line as if it were the start of a new chord. This is not always the intent of the composer nor should it be viewed as the best place to start. The following examples show gradually how each chord can be built from several notes within the bass moving towards individual notes for a more complex harmonic rendering of the same material

Example 1

Here is a typical bass line and two ways of figuring it:

In the audio for the following two examples, each example is first demonstrated at speed and then at 1/4 of the speed so that the changes can be heard more clearly in an IDM context.


This is a straightforward harmonisation/figuring in C major using some (unacknowledged) deviation into A minor before returning to C major.

The progression is

IDM version

IDM variation


This is a chromatic harmonisation/figuring, borrowing chords from distant keys.

The progression is:

The Bm/A is probably an unnecessary annotation, but is included to show the level which a figuring can go down to.

IDM version

Example 2

This example looks at the bass line and treats it as if it were moving through two key centres

Firstly, in the key of c minor

then the next section continues as if it were in Eb major (the relative major of c minor)

The whole progression is:

This audio example demonstrates this progression in an IDM context.

Extending the idea

Example 3

Something darker

An alternate version of the bass line

Harmonised it becomes:

In the key of Gminor

then the next section continues in Db minor

The whole progression is:

This audio example demonstrates this progression in an Ambient context.

Next time:

Going in Circles: The Cycle of Fifths