Diminished 7th chord Formula: 1-♭3-♭5-𝄫7
A diminished seventh chord is built by stacking three consecutive minor 3ʳᵈs. Since every interval is the same size, the chord is symmetrical.
Example:
Cdim7 = C-E♭-G♭-B𝄫 (A)
♭♭7 is enharmonic to 6, but is spelled ♭♭7 because the chord is constructed entirely from stacked 3ʳᵈs.
Inversions
Because every note is a minor 3ʳᵈ apart, each inversion becomes the root position of another diminished seventh chord.
Root Position: C-E♭-G♭-A
First Inversion: E♭-G♭-A-C
Each of these notes are a minor third apart. This chord is also a Cdim7 in first inversion (third in the bass) and E♭dim7 in root position.
Second Inversion: G♭-A-C-E♭
If we invert it once more, we get Cdim7 in second inversion, which is the same as E♭dim7 in first inversion and G♭dim7 in root position.
Third Inversion: A-C-E♭-G♭
Repeating the process one more time, we get Cdim7 in third inversion, which is the same as E♭dim7 in second inversion, G♭ dim7 in first inversion, and Adim7 in root position.
Finally, we get back to Cdim7 in root position, which is the same as E♭dim7 in third inversion, G♭dim7 in second inversion, and Adim7 in first inversion.
Equivalent Chords
These four chord names contain the same notes:
Cdim7 = E♭dim7 = G♭dim7 = Adim7
Only the bass note changes.
Cdim7 Root = Adim7 1st = G♭ dim7 2nd = E♭ dim7 3rd
E♭ dim7 Root = Cdim7 1st = G♭ dim7 3rd = Adim7 2nd
G♭ dim7 Root = Cdim7 2nd = E♭ dim7 1st = Adim7 3rd
Adim7 Root = Cdim7 3rd = E♭ dim7 2nd = G♭ dim7 1st
Consequently, there are only three unique diminished seventh chords in the chromatic scale. All remaining diminished seventh chords are inversions of one of these three.
Interval Pattern
Each inversion contains:
Minor 3ʳᵈs: 1-♭3 • ♭3-♭5 • ♭5-6 • 6-1
Tritones: 1-♭5 • ♭3-6 • ♭5-1 • 6-♭3
As the roots move upward in minor 3ʳᵈs (C-E♭-G♭-A), each voice moves downward by a minor 3ʳᵈ, creating smooth voice leading.
Fretboard Pattern
The diminished seventh shape repeats every three frets across the fretboard, regardless of inversion.
Tritones: 1-♭5, ♭3-6, ♭5-1, 6-♭3
Minor thirds: 1-♭3, ♭3-♭5, ♭5-6, 6-1
Below are C dim7 chord inversions across the entire fretboard.
Observe how the chord repeats itself every three frets with the exact same shape, regardless of the inversion.