15. DIMINISHED SCALES AND THEIR ASSOCIATED CHORDS
A diminished scale is composed by eight notes in alternating intervals of half and whole steps (HW). Thus, for example, if we begin with note B, the following diminished scale is obtained:
B diminished scale (HW)
Due to the existing symmetry in this scale, 4 from its 8 notes can be considered the tonic: B, D, F and G. Its representation on the Harmonic Wheel is very simple, for it corresponds to 2 consecutive radii (Fig. 22). And the 4 possible tonics are the notes contained in the left radius. (Remember that the notes located at the ends of each radius are repeated).
Figure 22. Diminished scale representation.
A diminished scale can also be defined as an 8 note scale in alternating intervals of whole and half steps (WH). Using this definition and beginning with note C yields
C diminished scale (WH)
Due to the existing symmetry in this scale, again 4 from its 8 notes can be considered the tonic. In this case: C, E, F and A. And, because the C diminished scale (WH) has the same notes as the B diminished scale (HW), its graphic representation is newly that in Fig. 22, but its 4 possible tonics correspond now to the right radius. It is easy to prove that there are only 3 different diminished scales.
Every diminished scale contains 8 consonant chords and includes, for each of them, its corresponding relative chord (Major or minor) and its parallel chord (that is, the one obtained by changing the mode). Furthermore, it contains every diminished chord formed by considering any note of the scale as the root.
The diminished scales are widely used in modern music and jazz. And, particularly, in improvisation techniques.