(3.11)  Diminished Chords

The diminished triad produces a series of additional chord types, two of which have common alternative names.

The m7♭5 chord is often known as half diminished because only the fifth degree is diminished compared to the minor seventh chord.

The dim7 chord is also called fully diminished because both the fifth and the flat seventh are diminished compared to the minor seventh chord.

The degree notation for the dim7 chord is a little unusual, as it includes a ♭♭7 (flat flat seventh).  This is the same as a 6 degree, but the naming here is important to the nature of the chord.

The dim7 chord also has the interesting property of being symmetric, being formed by a minor third interval between all of its adjacent notes (1-♭3, ♭3-♭5, ♭5-♭♭7, ♭♭7-1).

This means that dim7 chords whose root notes are a minor third apart contain the same notes, just in a different order (and enharmonically named).

Most ChordWizard products contain the Chord Synonyms tool.  This identifies and allows you to explore symmetric chord types, and also the other chord types which are inversions of each other, producing identical sets of notes.