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5/3 – Root Position Chords

5/3 means “root position chord”, or “a” chord. We must add a 5th and a 3rd above the bass note to make a complete chord. The bass note is the root of the triad.

If the bass note is C, we add G and E.   The other notes can be written in any octave, as long as they are higher than the given bass note. (The best octave for each upper note will depend on other factors such as voice leading).

5/3 figure

In fact, because root position chords are so common, the figure 5/3 is normally not printed, and is just taken for granted. A bass note with no figure on it at all requires a 5/3 chord. When the figure is blank, the 5th may be omitted, but if the 5/3 figure is written in full, you should not omit the 5th.  

5/3 figure omitted

Occasionally, root position chords are figured as just “5”. This also means you must include the 5th. The 3rd must always be included.

6/3 – First Inversion Chords

The next most common chord is the 6/3 chord, the first inversion chord, or “b” chord.

The bass note is the 3rd of the triad.   Above the bass note, we need a note which is a 6th higher (the root of the triad), and a 3rd higher (5th of the triad).  

Bass note E: the 6th higher is C, and the 3rd higher is G:  

6/3 figure first inversion

6/3 chords are normally abbreviated to just “6”, and including the 5th is optional. But if the “3” is written, then you must include the 5th of the triad.  

6/3 with 3 omitted

6/4 – Second Inversion Chords

6/4 is the least common inversion. It is a second inversion or “c” chord. The bass note is the 5th of the triad.

We need to add the notes which are a 6th and a 4th higher than the bass note:

Bass note G: the 6th higher is E, and the 4th higher is C.

6/4 figure second inversion

6/4 chords are never abbreviated, and the triad must include all three notes.

Don’t forget there are rules about where second inversion chords may be used.

The most common 6/4 chord is found in the cadential 6/4. The 6/4 figure is always followed by a 5/3 figure (rather than a blank). This helps to identify that it is a cadential 6/4, and also indicates the correct voice-leading to use.

  • The part with 6 should move to 5, and the part with 4 should move to 3.

In example A below, the 6 (E) is in the tenor part, so this needs to move to 5 (D) also in the tenor part. The 4-3 voice-leading (C-B) is found in the soprano part.

cadential 6/4 voice leading

Example B shows an alternative correct way to write the cadential 6/4.

Example C is incorrect. Although the chords have the right notes in them, the notes are in the wrong parts (the voice leading is incorrect).