Diminished scales have eight notes. They consist of a symmetrical series of alternating tones and semitones. This scale may have originated in Persian music. Passages of music implying a scale of this type occur in classical music in the 18th century. The scale was set down in the late 19th century and later termed the octatonic scale. In standard theory the diminished scale starting with a tone followed by a semitone is the fundamental version. Starting from the note C, the scale is written out with four flats with the seventh degree treated as a double flat. This is sometimes referred to as the whole half scale and abbreviated as WH.
C D Eb F Gb Ab Bbb Cb C
This can be simplified:
C D Eb F Gb Ab A B C
The flats be written down enharmonically as sharps:
C D D# F F# G# A B C
Starting from the note C there is also one other diminished scale. This starts with a semitone, and is sometimes called the half whole scale and abbreviated as HW. It is also referred to as the auxiliary diminished scale:
C Db Eb E Gb G A Bb C
There are three diminished scales, and each one can be treated as a self contained system which has separate linear and harmonic applications from the others. The third scale does not contain the note C and can be written ascending from a Db:
Db D E F G Ab Bb B Db
Any one of the twelve chromatic tones can be used to build two different diminished scales, either the one starting with a tone (whole note) or a semitone (half note). In other words there are potentially 24 scales, if diminished scales are treated as having a starting point. As diminished scale patterns repeat symmetrically in minor thirds, there are in effect only three discrete scales. Diminished scales are not approached theoretically as having a tonic.
On the guitar, I particularly like using diminished scales with one note as a starting point, or central note. The obvious one is open E at the bottom of the instrument. This is not a tonic, but instead can be treated as a pedal tone and as a root for a series of chords. This is a more advanced and interesting way of looking at these synthetic scales consisting of alternating tones and semitones with a symmetrical form.
Initially I’ve chosen the scale starting with a semitone or half step HW. It’s inspiring to focus on this scale and listen to the notes and their resonance and colour. Playing ascending and descending scales from all the other E notes on the guitar and treating this as a central note makes it much easier to build sophisticated frameworks. This scale can function as a powerful chromatic language which is often superimposed over a dominant chord such as E7, E7#9, E7b9 and E7#11, E13, E13b9 and a number of other combinations of chord tone extensions. These can then be resolved to a tonic minor such as A minor. This is why it is sometimes called the dominant diminished scale.
This is the ascending scale starting with a semitone, written with sharps with enharmonic equivalents (which are important) running from E. It contains the same notes as the third scale above , the HW ascending from Db.
E F G G#(Ab) A#(Bb) B C#(Db) D E
These notes can be written out as chord tones for an E dominant type chord with alterations.
E (root) F (b9) G (#9) G# (third) A#/Bb (sharp eleventh/ flat fifth) B (fifth) C#(sixth/thirteenth) D (seventh)
In contrast, here is the other diminished scale ascending from E, which starts with a tone followed by a semitone. This scale is normally the version which is used running from the root of a diminished chord. It contains the same notes as the second scale above , the HW ascending from C.
E F#(Gb) G A A#(Bb) C C#(Db) D#(Eb) E