When you want neither a major or a minor sound you can use a suspended chord. In a suspended chord, the 3-note in the chord becomes either a 2 or a 4.
A few other tidbits picked up during Wednesday's session:
In a major key, the 1, 4 and 5 are major chords.....HOWEVER.... in a minor key the 4 and the 5 are not necessarily minor chords (the 1 will be a minor, by definition).
Also, in the major and minor keys, in the first 5 notes of the scales, only the 3 is different. This can be easily remembered via a certain hand gesture involving the third finger that is universally recognized for an entirely different meaning, but is nonetheless useful for recalling this important musical fact.