Carl's 1st Law of Notation

I would like to distinguish between two types of notation:

  1. isomorphic notations - systems in which a given interval always sits the same on the staff, covering the same 'distance' in terms of lines, spaces, and accidentals.
  2. diatonic notations - systems in which a given generic interval (2nds, 3rds, etc.) always sits the same on the staff.
For non-diatonic music, the former type is preferable, and the number of nominals is more or less irrelevant. For (generalized) diatonic music, the latter type of notation is preferable, and the ideal number of nominals is equal to the number of tones in a period of the scale being notated.