> Is there a 1212122 scale (end every other possible combination)?
The steps have to add up to 12 to end up on the same octave. I'm not sure about every possible combination but there are other scales called "modes" which are rotations of that pattern (which can be derived from the white keys on the piano, just starting one of the 7 different notes; whether something is a 2 or a 1 depends on whether there is a black key between the white keys). The different scales derived from that are:
2 2 1 2 2 2 1
2 1 2 2 2 1 2
1 2 2 2 1 2 2
2 2 2 1 2 2 1
2 2 1 2 2 1 2
2 1 2 2 1 2 2
1 2 2 1 2 2 2
The first pattern is a typical Major (associated with happy songs) scale. The sixth one is a standard Minor scale (associated with less happy songs). The third one is called Phrygian and has a dark/exotic feel that works well in metal ( https://www.youtube.com/watch?v=-DzGlzdbkDI )
The steps have to add up to 12 to end up on the same octave. I'm not sure about every possible combination but there are other scales called "modes" which are rotations of that pattern (which can be derived from the white keys on the piano, just starting one of the 7 different notes; whether something is a 2 or a 1 depends on whether there is a black key between the white keys). The different scales derived from that are:
2 2 1 2 2 2 1
2 1 2 2 2 1 2
1 2 2 2 1 2 2
2 2 2 1 2 2 1
2 2 1 2 2 1 2
2 1 2 2 1 2 2
1 2 2 1 2 2 2
The first pattern is a typical Major (associated with happy songs) scale. The sixth one is a standard Minor scale (associated with less happy songs). The third one is called Phrygian and has a dark/exotic feel that works well in metal ( https://www.youtube.com/watch?v=-DzGlzdbkDI )
(My comment based on referring to https://learningmusic.ableton.com/advanced-topics/modes.html )
You could have other scales such as:
1 1 1 1 1 1 1 1 1 1 1 1 (chromatic scale, i.e. every white and black key in order https://www.youtube.com/watch?v=xUpKPaKhsEc )