A Diminished Scale Swap
The polytonal is a scale inversion of the diminished scale which is inverted by a major third down.
As with the diminished scale students don’t really learn about polytonal scales unless they study the former and even then they might not truly understand why this scale is different.
Because we have taken the time to discover the diminished scale in detail the inversion of this scale should go very smoothly.
The same characteristics apply for this scale as did for the former one. There is simply one difference that you must start with.
This scale is defined as: starting the scale on the root of a dominate 7 chord which is the major 3rd below the diminished scale.
Not exactly straight forward but the practical application is to use the same notes but start a major 3rd below the diminished scale.
The New Pattern
The significance of this inversion is that the pattern now becomes a half – whole repeating pattern rather than the whole – half pattern.
The staff below shows the relationship between the diminished scale and the polytonal scale. The polytonal starts on the note a 3rd below and uses the same notes.
You can work this out in your head as you consider the steps from note to note.
Constructing Polytonal Scales
These scales are developed mathematically using half and whole steps. To make sure we understand the difference in notes we will build the ‘C’ polytonal scale.
1 – m2 – m3 – d4 – d5 – 5 – 6 – 7 – 8
C – Db – Eb – Fb – Gb – G – A – Bb – C
S + H + W + H + W + H + W + H + W
Here is that pattern shown on the keyboard.
Notice that a diminished chord ‘D – F – Ab – B’ are the notes not played for the C polytonal.
You can create the other two polytonal scales using these formulas. Start on C# and D to accomplish the full scale notes.
Scales of Diminished and Polytonal Relationships
There are lots of similarities between these two types of scales as would be expected by the simple application of an inversion of notes.
Once again there will be three diminished chords that are not played. The pattern similarities are just inversions of previously explored diminished scales.
The thing you will quick discover in relating the scales is that the notes remain the same but the starting point is different.