Another way to organize scales are tetrachords. They consist of four notes within the range of a fourth.
There are six tetrachords that span a perfect fourth and seven tetrachords that span an augmented fourth. Additionally there is one diminished fourth tetrachord.
The numbers represent the number of half tone steps between the notes. For example, with C as a starting note, 221 would mean C – two half tone steps – D – two half tone steps – E – one half tone step – F.
Scales can be constructed by putting two tetrachords on top of each other. This way every mode of the ionian, melodic minor, harmonic minor and harmonic major systems, some scales which can be described as octatonic scales missing one note and a few special scales like neapolitan minor and some of the modes of the double harmonic scale can be constructed. Additionally there are some scales no name can be put on.
We can organize these scales into groups defined by the lower tetrachord. This kind of organization can help you to become more flexible in your thinking.