Let's look at the diminished scale using the linear concept so we can incorporate the arpeggio and scale into our melodic lines.

The make up of the diminished chord allows us to use the same chord shape for 4 different chord names. A diminished chord is made up of: Root, b3, b5 and 6th (otherwise known as diminished 7th). That means that each interval is exactly a minor 3rd away from each other. If we took the root as A, the chord tones would be: A,C,Eb,Gb. If C was the root note our chord tones would be: C,Eb,Gb,A. If Eb was the root, our chord tones would be: Eb, Gb, A, C. Finally if Gb was the root note our chord tones would be: Gb, A, C, Eb. The minor 3rd intervals keep going up until the end of the 4 note sequence and start over again.

This means that the diminished scale is quite difficult to really hear as there seems to be no final note to feel comfortable about when you get to it. There are 4 final notes! However, this also means that there are only 3 scales to learn as opposed to 12.

The diminished scale can be thought of as quite simply, the notes of the diminished chord with a leading note placed before each chord tone. The scale then looks like this:

Every dominanth 7th b9 chord has a diminished chord within it. This allows us to utilize the diminished scale when playing over chord 5. It also gives us nice stepwise resolutions when we finally get to the 1 chord. Look at the following 2, 5, 1 progressions and study the diminished lines when they appear over chord 5. Have fun!