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The m7b5, or 'half dimished' chord is a minor 7th chord with a flattened 5: 1-b3-b5-b7

It is used as the chord that most naturally leads to a dominant 7 resolving to a minor chord, e.g. Dm7b5 >> G7 >> Cm

Standard scale choice

For this chord you would most usually use the locrian mode, which is the 7th mode of the major scale (so B locrian has the same notes as C major): 1 b2 b3 4 b5 b6 b7

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A very common alternative scale choice is to un-flatten the 2nd degree of the locrian mode, giving: 1 2 b3 4 b5 b6 b7 This is often called the 'locrian #2', for obvious reasons. It avoids the clash between the b2 and the root note of the chord.

Another way of thinking of the same thing is to imagine the m7b5 chord as a 'minor sixth chord with the sixth in the bass', as Dizzy Gillespie did. This means that you read a m7b5 as the m6 chord a minor third above. If you see Em7b5, think Gm6, and so on for the other keys. Now play Gm(Maj7) -- that's exactly the same notes as E locrian #2, but a lot easier to think of.

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C C# Db D D# Eb E F F# Gb G G# Ab A A# Bb B