When you play music at the highest level, the tune should takes on a life of it’s own and become a sincere form of self expression ever time you play that tune. The more knowledge you have, the more doors of creativity you can open. Symmetrical scales are built by using repeated interval patterns and will add more options to your arsenal of lines to play.
Chromatic Scale
Intervals – R b2 2 b3 3 4 #4(#11) 5 #5(b13) 6 b7 7 R
Key of C – C C#(Db) D D#(Eb) E F F#(Gb) G G#(Ab) A A#(Bb) B C
This scale is made up of all 12 notes within the octave and intervals are therefore semitones apart.

Whole Tone Scale
Intervals – R 2 3 #4(#11) #5 b7 R
Key of C – C D E F# G# A#(Bb) C
The whole tone scale is made up of 6 notes, and is built by using a tone between each note. There are only 2 possible whole note scale combinations: C, D, E, F♯/Gb, G♯/Ab, A♯/Bb. and C♯/Db, D♯/Eb, F, G, A, B. To build any whole tone scale, you simply start on the root and go up in tones until you reach the octave. Works well over 7#5 chord, which will also have a #11 in it as you can see above.

Half Whole Diminished Scale
Intervals – R b2(b9) b3(#9) 3 #4(#11) 5 6 b7 R
Key of C – C Db Eb E F# G A Bb C
This scale is built by alternating half steps and whole steps. 1/2, T, 1/2, T, etc. until you reach the octave. A symmetrical diminished scale consists of eight notes, thus making it an octatonic scale. This scale is used to improvise over a 13b9 chord, which will also bring the #9 and #11 colors to the table as you can see below. Here is how the half whole diminished scale looks from an intervallic standpoint as well as in the key of C.

Whole Half Diminished Scale
Intervals – R 2 b3 4 #4 #5 6 7 R
Key of C – C D Eb F F# G# A B C
Another octatonic scale This scale is built by alternating whole steps and half steps as you build the scale up from the root. T, 1/2, T, 1/2, etc. This scale works well over a Dim or Dim7 chord.

Tritone Scale
Intervals – R b2(b9) 3 b5(#11) 5 b7 R
Key of C – C Db E Gb G Bb C
This scale is built by combing the notes from the root triad and the triad a tritone away from the root. Works well with 7b9#11 chords

Augmented Scale
Intervals – R b3(#9) 3 5 #5 7 R
Key of C – C Eb E G G# B C
The augmented scale is built by combining two augmented triads a minor 3rd apart. The scale has all the notes of a maj#5 arpeggio, it can therfore be used to create tension in your solos over a maj7 or Maj7#5 chord as you bring this scale into your playing.
