# Chord Inversion Calculator

Created by Rijk de Wet
Reviewed by Steven Wooding
Last updated: Feb 20, 2023

Welcome to the chord inversion calculator, where we explore the world of chords and their inversions. With this calculator, chord inversions will be a breeze — read on to learn more about:

• What a chord inversion is;
• What the inversions for 7th chords are like;
• The different chord inversion notations; and
• The crazy number of inversions that Bach's most famous prelude has.

## How to use the chord inversion calculator

The chord inversion calculator is simple to use but powerful in its capabilities. Follow these easy steps:

1. Select the key of your chord. We've included the common keys that you'd encounter in classical and modern music.
2. Select the type of your chord. Pick between triads, sevenths, and ninths of many flavors, and more.
3. Select which inversion you'd like your chord to have — root position, first inversion, second inversion, etc. Remember that chords with fewer notes have fewer inversions.
4. The chord inversion calculator will tell you your chord's notes and in which order they appear.

If our chord calculator with inversions doesn't quite quench your thirst for knowledge, read on!

🔎 Struggling to identify a chord in your sheet music or aurally? Our chord finder will help you determine what chord it is based on the constituent notes.

## What is a chord inversion?

A chord inversion describes which note of a chord is written as the lowest (a.k.a. the bass note). For simpler chords like triads and sevenths, an inversion can accurately describe the intervals between the bass note and the remaining notes.

🔎 You can consult our music interval calculator for more information on these fundamental building blocks of chords.

## How do chord inversions work? First inversion, second inversion, etc.

Easy — take a chord, pick one of its notes, and move it to the bass. Ta-dah! You've made an inversion.

For a given chord, there are as many inversions as there are notes — because each note can be written as the bass note, and thus can represent an inversion. Let's use C major (C, E, and G) as an example to discuss some inversions:

• First, there is the "root position", i.e. the root note stays in the lowest position. For C major, that's C-E-G.

• In the "first inversion" of a chord, the first note above the root is made the bass: E-G-C.

• "Second inversion" means taking the second note above the root and making it the bass: G-C-E.

This pattern continues for chords with more notes:

• The "third inversion" of G7 (normally G-B-D-F) is D-F-G-B.

• The "fourth inversion" of Dmin9 (normally D-F-A-C-E) is E-F-A-C-D.

The notes above the bass can be rearranged into any order (and even moved into higher octaves) without changing what we consider to be the inversion — we'd instead talk about the voicing of the chord, which is a whole separate matter.

## How do I write a chord inversion?

There are two common ways to denote a chord's inversion:

• Figured bass denotes the intervals from the bass note with numbers. Instead of using note names, it typically uses Roman numerals to denote the chord's root relative to the current key.
• Modern notation writes inversions as slash chords: the chord's name and the bass note is denoted, separated by a slash.

🔎 Want to learn more about the Roman numerals used in figured bass notation? Check out our Roman numerals calculator!

## Chord inversion notation: figured bass vs slash chords

#### Figured bass

Figured bass writes chords as degrees of the key's scale using Roman numerals. To indicate inversions, figured bass also denotes numbers that correspond to the intervals from the bass note to each other note.

For example: In the key of G major, C is the fourth degree of the scale, and the corresponding Roman numeral is $\rm IV$. C major in the root position is C-E-G: the intervals are a major third (C to E) and a fifth (C to G). Therefore, with figured bass, we can write all of it — the key, the chord's degree relative to the key, and the constituent intervals — together as ${\rm G: IV}^5_3$. It's conventional to throw away the $^5_3$ and just write ${\rm G:IV}$.

If the chord was in first inversion (E-G-C) instead, the intervals have changed: it's a third (E to G) and a sixth (E to C). So we can write it as ${\rm G: IV}^6_3$. It's common to discard the $_3$ and just write ${\rm G:IV}^6$this is not the same as a sixth chord like C6 (C-E-G-A) or F6 (F-A-C-D)!

In the second inversion (G-C-E), the intervals have changed again: The chord contains a fourth (G to C) and a sixth (G to E). So, we get ${\rm G: IV}^6_4$.

The rules are similar for the inversions of seventh chords, except there are now three intervals to denote. Below, you'll find a handy table for the inversions of triads and sevenths.

Inversion

Intervals

Symbol

Root

$^5_3$

$\rm I$

First

$^6_3$

$\rm I^6$

Second

$^6_4$

$\rm I^6_4$

Inversion

Intervals

Symbol

Root

$\scriptsize 7 \\[-6pt] 5 \\[-6pt] 3$

$\rm I^7$

First

$\scriptsize 6 \\[-6pt] 5 \\[-6pt] 3$

$\rm I^6_5$

Second

$\scriptsize 6 \\[-6pt] 4 \\[-6pt] 3$

$\rm I^4_3$

Third

$\scriptsize 6 \\[-6pt] 4 \\[-6pt] 2$

$\rm I^4_2$

Figured bass is simple for inversions of seventh chords and triads, but it falls apart when the chord gets more complex due to additional notes like ninths, suspensions, and more. This is partly because there'd be too many intervals to keep track of on the fly and partly because the interval notation would conflict with that of the additional notes. Figured bass is best for chorale music, where the number of voices remains constant.

💡 In the style of basso continuo, an organist or pianist would only be given a root note and chords in figured bass notation, with no explicit sheet music — they had to improvise the other notes!

#### Slash chords

Slash chords are simpler: they consist of a chord's name (e.g. Cmaj, G7, or Emin) and the bass note of the chord's inversion, separated by a slash. For example:

• C major in the first inversion (E-G-C) is denoted as C/E, because we have the notes of the C major chord with the E in the bass.

• G dominant seventh in the fourth inversion (F-G-B-D) is denoted as G7/F (note that G/F might sound the same, but is technically incorrect).

Slash chords are much more direct about which chord you're actually playing, at the cost of the context given by the current key and each chord's degree on that key's scale. The system can be extended to non-inverted chords — there might not be a G in the chord of D minor seventh, but there's no denying the power of Dmin7/G (G-D-F-A-C).

## A side-by-side comparison

Below, we've annotated the first few chords from Bach's Prelude in C (BWV 846) using the two different chord notation systems.

We can see that the figured bass indicates the starting key ("C" for C major) as well as the new key when the piece modulates ("G" for G major) and that the chords are denoted in relation to those keys.

See if you can annotate the whole prelude with both notation systems! Test your theories with our chord inversion calculator.

## FAQ

### What are the notes of G dominant seventh in first inversion?

B-D-F-G. The bass note is B, and the remaining notes (D, F, and G) can be rearranged for better voicing.

### What are the notes of D minor seventh in third inversion?

C-D-F-A. The bass note is C, and the remaining notes (D, F, and A) can be rearranged for better voicing.

### What 7th chord inversions are there?

Seventh chords can be inverted four ways:

1. Root position leaves the chord as-is, with the chord's root in the bass.

2. First inversion places the third of the chord's scale in the bass.

3. Second inversion places the fifth of the chord's scale in the bass.

4. Third inversion places the seventh of the chord's scale in the bass.

Rijk de Wet
Chord key
C
Chord type
Major (maj)
The chord C major (Cmaj) has notes C, E, and G.
Inversion
Root
The root inversion of C major (Cmaj) has notes C, E, and G.
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