| > The chromatic scale is a special case of a symmetric scale which cannot be transposed. I would not agree here. I think you can transpose a chromatic scale, but you end up with the same "set" of pitches. (So you _can_ transpose, but if you only consider the _set of pitches_ you end up with a invariant. But scales are not just a set of pitches, but also have a root note. You can establish the key of C and play a chromatic scale from c' up to c'' and there would be the feeling to accept C as the root of the scale. So the chromatic scale is kind of a _total_ (all 12 pitch names) and _trivial_ example, as you pointed out, very symmetric and usually not so interesting for analysis if you want to detect and describe structure. In general it depends on the music. If the music is based on diatonics, then a major scale or it's modes will be a fitting primitive for analysis, considering chromatic notes something like side notes. On the other hand 12-tone music uses a chromatic scale as a basis, negating the structure and hierarchy of diatonic scales. So I don't see a problem with transposing a chromatic scale, it's useful and necessary for mathematical sound systems (helpful for computation) to define operations, even if there is no direct gain (functionally speaking - identity / mempty etc.) : 1 + 0 = 1 |