A diminished seventh chord is a four note chord that comprises a diminished triad plus the interval of a diminished seventh (alternatively regarded enharmonically as a major sixth) above the root. Thus it is (1, ♭3, ♭5, 7), or enharmonically (1, ♭3, ♭5, 6), of any minor scale; for example, C diminished-seventh would be (C, E♭, G♭, B), or enharmonically (C, E♭, G♭, A). It occurs as a leading-tone seventh chord in harmonic minor and can be represented by the integer notation {0, 3, 6, 9}.
Because of this it can also be viewed as four notes all stacked in intervals of a minor third. The diminished seventh contains two diminished fifths, which often resolve inwards.
In most sheet music books, Cdim or C° denotes a diminished seventh chord with root C; but it may also happen, mostly in modern jazz books and some music theory literature, that Cdim or C° denotes a diminished triad chord, while Cdim7 or C°7 denotes a diminished seventh chord.
Read more about Diminished Seventh Chord: Uses, Diminished Seventh Root, Inversions, Diminished Seventh Chord Table
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