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I sort of stumbled upon an unusual scale in a black metal song.
It goes: E-F-G-A-A#-C-C#-D#-E
or
HWWHWHWH
It is not a scale I recognize, though it resembles a mixture of familiar scales. Would anyone happen to know what scale this is?

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This is an interesting scale. Out of curiosity, are all eight of these pitches a relatively equal part of the tune, or could some be seen as minor notes occasionally found in a chord, or as brief melodic ornamentations? –  Pat Muchmore Jul 2 at 13:10
    
In response to Pat Muchmore, I kind of deduced the scale from a number of sequences throughout the song, but it is possible that it was based on a more traditional scale with some dissonant "ornaments" of sorts. –  user3574546 Jul 2 at 22:22
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Can you share what song it's from, please? –  rishimaharaj Jul 3 at 3:56
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Its from "Freezing Moon" by Mayhem. –  user3574546 Jul 8 at 22:28

2 Answers 2

Per Wikipedia, there are three classic octatonic scales which are made up of 2 interlocking diminished seventh chords. The scale that you mention can be described as a diminished seventh chord interlocked with a dominant seventh chord (with note renaming):

E - F - G - A - B♭ - C - D♭ - E♭ - E

which is created with an Edim7 chord E - G - B♭ - D♭ and an F7 chord F - A - C - E♭.

I have not yet found a name for this structure, but it is indeed an octatonic scale. Again, per the same wikipedia article (emphasis is mine):

In classical theory, in contradistinction to jazz theory, this scale is commonly simply called the octatonic scale, although there are forty-two other non-enharmonically equivalent, non-transpositionally equivalent eight-tone sets possible.


FYI: Why did I rename A♯ to B♭, C♯ to D♭, and D♯ to E♭? For a few reasons:

  • Traditionally, each step in the scale is the next note up (in C major, D is followed by E, not Fb). This means we should try to include some variation of B in the scale.
  • The the other examples of the octatonics from the wikipedia page, there were only one set of repeating letters, not two. (Example: E♭, F, F♯, G♯, A, B, C, D, E♭ contains a single pair of F's and D, E, F, G, A♭, B♭, B, C♯, D contains a single pair of B's).

I first changed A♯ to B♭ and then questioned whether the following ones should either stay the same or be changed as well. In reading through the wikipedia page, I found that the scales were formed by seventh chords, so ended up changing them to try to figure out what chords they were (and the above portion is what I found).

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This is only "octatonic" in the sense that it has eight tones. I wouldn't call it an octatonic scale though, because that specifically refers to the alternating H–W or W–H scales. It's like if I were to call the this—E–F–F#–G–Ab–E—a "pentatonic" scale. Technically true, but misleading. –  Pat Muchmore Jul 2 at 13:04

Have to say I agree with one of @Pat Muchmore's comments here. Although this is an eight-note scale, it is certainly not what I understand to be an octatonic scale (also called a diminished scale), which usually follows a repeated pattern of alternating tones and semitones.

Usually, my first port of call when trying to describe a collection of pitches I haven't seen before (and a scale is an ordered set of pitches, after all…), I use pitch class set theory. Using a PC set calculator, such as this one, we find that this set of pitches is PC Set 8-27. However, I usually then go to this PC set list to see if a collection has a particular description; for 8-27 it doesn't.

I tried finding some other PC Set lists, to see if any others had a name for 8-27, but didn't manage to find one.

Next, I tried a "brute-force" approach, and put "E F G A Bb C C# D#" into Google. Well, I arrived at this site, which claims to list all named scales. Despite it's undoubted breadth and ambition, and it having quite a number of scales I'd never heard of (Chromatic Hypophrygian Inverse, anyone?), it didn't in fact seem to have a name for the OP's scale (or indeed list it on the page, even after looking for enharmonic spellings…)

But, in the end, a colleague pointed out to me that there are plenty of ways this could be described. For instance, one effective way to describe this scale would be to look for commonplace subsets within the scale. This colleague suggested seeing this as F Major notes (alright, starting on the leading note), with the top four notes being a Bb Dorian Tetrachord (with the Bb and C being an overlap between the two subsets).

Hmmm, I think we can do a lot better…

Essentially, this is likely to easily fit the description of a number of seven-note scales, with an extra pitch added. This scale has one three-note semitone cluster (D#-E-F), which is relatively unusual; so to treat one of these as the "added" pitch seems like a good approach. So, how about:

  • the fifth mode of Bb Melodic Minor (asc.) F G A Bb C Db Eb with an added E. Not bad, but it's a bit weird that we're adding the note that is (presumably) our root note…

  • seventh mode of G Locrian #2 (also known as the half-diminished scale). Well, we still have to add the E in; not surprising, locrian #2 and melodic minor asc. are modes of each other…

Well, how about going back to octatonics? Any root pitch is part of two octatonic scales (of which there are only three anyway, as @rishimaharaj points out). It is part of an octatonic that has its second note a semitone above the root, and one that has its second note a tone above the root. Well, if we take the second of these we get E F# G A Bb C C# D# (yes, this could have other enharmonic spellings…) All we need to do is lower the second pitch and we get the OP's scale. As all octatonic scales are modes of limited transposition (which is why there are only three of them), we can get the same set of pitches (and indeed a mode of this scale) by flattening any of the notes of an octatonic scale which usually has a note a semitone above.

TL;DR

I did quite a bit of research, but couldn't find a name for this scale. But, it is produced by flattening the second note of any octatonic scale which starts with a whole-tone, so that instead it starts with a semitone; all other notes remain unchanged.

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Thank you for your extremely detailed answer! I doubt that there was that much theory put into the song's writing, but it is always interesting to analyse the theory! –  user3574546 Jul 2 at 22:34
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Yeah, this is nice work. Almost like a "Phrygianized" W–H octatonic scale. –  Pat Muchmore Jul 3 at 12:35
    
@PatMuchmore Funny, that’s exactly what I was thinking! I don’t know the song mentioned in the question, but I wonder whether it has a Phrygian feel. –  Bradd Szonye Jul 3 at 21:41

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