I have a few questions regarding the correct naming of pitch and interval collections.
We call an ordered collection of adjacent pitches a scale. For example, (C D E F G A B) is called C major (or Ionian) scale.
But an ordered collection of intervals, without reference to any pitch, is also called a scale. For example, (1 1 1/2 1 1 1 1/2) is called major (or Ionian) scale. Are there more specific terms to distinguish the two?
What about a collection of adjacent pitches without one of them being considered special, like the white keys on the piano? That is, is there a generic name that encompasses all of C Ionian, D Dorian, E Phrygian etc.?
Finally, is there a word for an unordered collection of intervals? That is, is there a word that encompasses all modes of major contrasted with all modes of melodic minor?