Slonimsky-Schillinger Symmetric System
Slonimsky scales are introduced in what Schillinger calls Symmetric Scales. They are scales built on multiple Tonics that we obtained by splitting the Octave into equal parts. See the chart:
To construct scales of multiple tonics we must use the same intervals for each Tonic.
Slonimsky’s Scales 1-4 uses 1,2, 4 and 5 intervals from the Tonics. So Scale 1 is one interval so starting on C(Tonic 1) C# (one interval) F# (Tonic 2) G (one interval).
Scale 2,3 and 4 use the intervals 2,4 and 5 respectively.
Using this as an example you can see the possible scales that can be created once you start adding scale notes between the tonics.
See the chart:
As you can see the number of scales that are possible are great. The number of permutations of scales is actually 3,68,800. Slonimsky pares that number down by his approach techniques.