This chord inversion numbering system is considered 'Classical'. It is a numbering system of describing intervals based on the bass note. I haven't used this type of system since music school. This is a reference page.
Like many things musical, inversions use a numbering system to symbolize sound. Be sure not to confuse this numbering system with other types numbering systems (e.g. chord symbols). When we use this interval numbering system, we typically place these numbers next to Roman Numerals to describe relationships in a harmonic rhythm.
This system utilizes numbers to indicate a type of interval (relationship between two tones) from the bass note (the lowest note) of a chord.
When we 'count' intervals, we 'count' the bottom tone as the one. Then, we 'count' each next line or space, up to the next tone. We always start counting from the bottom tone (bottom tone to middle tone, then bottom tone to top tone for triads). This gives us 2 numbers, which we stack on top of each other.
This first set starts with a root position chord. Root position means that the chord is not yet inverted. It means that the root of the chord (the tone from which the chord is built) is in the bass of the chord. Root position doesn't need an intervallic number to indicate it, yet can have a 3 (we drop the 5).
To create the first inversion, we take the root from the bottom of the chord at place it at the top. This creates intervals of a 3rd and a 6th from the bass note (now the 3rd of the chord). We can shorten this inversion to just a 6.
To create the second inversion, we take the 3rd of the chord and place it above the root. This creates intervals of a 4th and a 6th (what we call a 6-4 chord which has the 5th of the chord in the bass).
This is a basic triadic chord first given in root position. We then take the bottom note and move it to the top to create a 1st inversion chord. Then we repeat that process to create a 2nd inversion chord. Then we finish it out by returning to a root position chord, yet we've had to move to a new physical guitar position (3rd) because we ran out of guitar neck in 1st position.
In the first example, we have a basic I-IV-V-I progression. The chords are kept in a closed position (as close to each other as possible).
In the second example, we hear a very common classical sounding progression, where the I chord appears in 2nd inversion, giving a suspended type of sound, moving to the V chord, before returning home to a root position chord.
Like scales, chord inversions can arrange themselves on the fretboard in fixed position (a position area, e.g. between frets 1 through 4), or in a linear manner (up the neck).
Practice inverting chords in as many ways as you can consider. Have fun and keep your fretted chord library growing.
Above are 7th chords in Root position and then 1st, 2nd, and 3rd inversions. The symbols use the same intervallic counting scheme as triads, plus adding the 7th, and we end up with a new set of descriptors.
Again, be sure not to confuse this numbering system with other types chord numbering systems (e.g. chord symbols).
Quick review: this system utilizes numbers to demonstrate a type of interval from the bass note of a chord. When we 'count' intervals, we 'count' the bottom tone as one. Then, we 'count' up to each next line or space, to the next tone. We always start counting from the bottom tone (bottom tone to middle tone, then bottom tone to next, then bottom to top for 7ths).
For 7ths, we get 4 sets of numbers (7 - 6/5 - 4/3 - 2).
We begin with a root position chord. Root position = not inverted (the root of the chord) is in the bass. For root position, we get intervals 3, 5 , & 7 (how chords are built - in 3rds, every other tone). We shorten this to just a 7 (doesn't tell us what kind of 7 this - depends on the type of chord being built - Major 7, Dominant 7, or minor7, etc.).
First inversion means the 3rd is in the bass. When we move the root to the top, we create an intervallic scheme of 3, 5, 6 and shorten this to 6/5.
Second inversion means the 5th is in the bass. We move the 3rd to the top which creates the intervals 6, 4, 3, and shorten this to 4/3.
Third inversion means the 7th is in the bass. We move the 5th to the top, and we have intervals of 6, 4, 2, and shorten this to just 2 (or 4/2).
To finish off this process, we move the 7th to the top of the chord and this puts the chord back in root position an octave higher than where we started.
This shows an easy way to remember the chord inversion symbols. We can see the descending intervallic scheme.