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What’s the terminology for changing a major triad into a diminished chord?
C major – C°7 – Gmin7 – C7 etc.

I can’t remember the term!

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It's called a common-tone diminished chord. For more on common-tone diminished chords, see Understanding function of diminished chord in Paganini's 4th caprice.

However, in the specific case presented, the chord labeled as Co7 would actually be F#o7, because it's leading to the G chord. That is, the diminished chord is the leading-tone diminished chord for G minor.

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    Thanks ! F# °7 and then specify the inversion if I want the root to be C on both chords . C - C#°7 becomes C - f# °4/2
    – Boaz
    Sep 27 at 21:16

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