As far as I understand Scales are defined on intervals. So, for example, the major scale is defined by the following intervals from the root:
C - Root D - Major Second E - Major Third F - Perfect Fourth G - Perfect Fifth A - Major Sixth B - Major Seventh
This is perfectly clear to me, and it makes sense, because we have 7 note names, so every note must be included on the scale, but then when trying to figure out the proper name notes for an octatonic scale it becomes blurry to me. I mean when building an octatonic scale you only stack Tone-Semitone-Tone-Semitone...
But how do I properly define the Note names??
For the semitone spacing the interval could either be a augmented prime, a minor second, or even a doubly diminished third.
For the tone spacing the interval could be a doubly augmented prime, a major second or a diminished third.
How do I find the proper note names for non heptatonic scales? Does the same rules apply for the chromatic scale?