Post History

"Properly" naming rotations of unusual scales?

Consider the following musical scale, with a root of A:

>A — B — C — D — E — F — G# — A

This is, quite clearly, _A Harmonic Minor_.

Let me rewrite the above scale in terms of tone (step) differences:

>W — H — W — W — H — A — H

where _A_ refers to an _augmented second_, or three half-tones.

Consider the following rotation by a fourth:

>W — H — A — H — W — H — W

and correspondingly the original scale beginning on D:

>D — E — F — G# — A — B — C — D

**What would this scale be called?**

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Consider the regular _seven church modes_ — Aeolian, Locrian, Ionian, Dorian, Phrygian, Lydian, Myxolydian — where _A minor_ would properly be called _A Aeolian_ and is a rotation of _C major_ — rather, _C Ionian_ — and, relevant to the above example, _D Dorian_.

Just like adding a sharp seventh converts an Aeolian scale to a Harmonic Minor, is there musical nomenclature that a sharp fourth converts a Dorian scale to a Harmonic Dorian, and likewise for the other five rotations?