diminished seventh chords, the other nine being enharmonically equivalent to those three. Using Piston's incomplete-ninth analysis discussed above, a single diminished seventh chord, without enharmonic change, is capable of the following analyses: V, V/ii, V/III (in minor), V/iii (in major), V/iv, V/V, V/VI (in minor), V/vi (in major), V/VII (in minor). Since the chord may be enharmonically written in four different ways without changing the sound, we may multiply the above by four, making a total of forty-eight possible interpretations. More conservatively, each assumed root may be used as a dominant, tonic, or supertonic, giving twelve possibilities. The octatonic scale (or diminished scale), a symmetric scale, may be conceived of as two interlocking diminished seventh chords, which may be rearranged into the alpha chord. Diminished seventh chord table {| class="wikitable" !Chord !Root !Minor third !Dim. fifth !Dim. seventh |- !C7 |C |E |G |B (A) |- !C7 |C |E |G |B |- !D7 |D |F (E) |A (G) |C (B) |- !D7 |D |F |A |C (B) |- !D7 |D |F |A |C |- !E7 |E |G |B (A) |D (C) |- !E7 |E |G |B |D |- !E7 |E |G |B |D |- !F7 |F |A |C(B) |E(D) |- !F7 |F |A |C |E |- !G7 |G |B (A) |D (C) |F (E) |- !G7 |G |B |D |F (E) |- !G7 |G |B |D |F |- !A7 |A |C (B) |E (D) |G (F) |- !A7 |A |C |E |G |- !A7 |A |C |E |G |- !B7 |B |D |F (E) |A (G) |- !B7 |B |D |F |A |- !B7 |B |D |F |A |} See also Enharmonic scale Diminished seventh interval Leading tone seventh chord Irregular resolution Half diminished chord Subtonic References Seventh chords Musical symmetry