"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?
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?
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It seems that a Ukrainian Dorian scale exists which matches the scale you wrote out.
In music, the Romanian Minor scale or Ukrainian Dorian scale or altered Dorian scale is a musical scale or the fourth mode of the harmonic minor scale. It is "similar to the dorian mode, but with a tritone and variable sixth and seventh degrees"
Apparently also known as the Romanian minor scale, and used prominently in Jewish and Roman music. So it seems a lot of cultures lay claim to it...
I couldn't find some sort of standard for naming these scales, but it seems many of them do exist. For example, if you rotate the A minor harmonic scale to start on F, you seem to get what is called a Phrygian Dominant Scale.
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A while ago I came across this amazing video, which answers your question thoroughly:
https://www.youtube.com/watch?v=Vq2xt2D3e3E
According to that video the specific scale pattern you gave is called Dorian #4 (the # here denotes a sharp sign, not a number sign). This basically means that it is like Dorian, but the with the fourth tone raised by a halftone.
The specific scale starting at D therefore is D Dorian #4.
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