Do the naming conventions and their implied function still apply to modes outside the major and minor scale?

Is the minor second of the Phrygian mode called the supertonic?
Is the augmented fourth of the Lydian mode called the subdominant?
Is the diminished fifth of the Locrian mode called the dominant?


Yes: in my experience, these scale-degree names can still be used to indicate members of various modes. In practice, however, I would say that references to the dominant and tonic of any of these modes are far more common than references to other scale degrees.

I can only think of two caveats with my answer:

  1. Like in major and minor, the use of "leading tone" and "subtonic" will depend on whether scale-degree 7 is a half step or a whole step below tonic.
  2. And in scales of more or less than 7 notes (that is, scales that are not heptatonic), we have to be really careful with what we mean. In a C-major pentatonic collection, for example, people use the term "dominant" not to mean the fifth scale degree (which is in one sense actually an A here), but rather the interval of a fifth above tonic (and thus G).

For a closely related question (and one with some different viewpoints), see What are the degrees of a pentatonic scale called?

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