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My understanding of the various modes is that, relative to the base note’s natural major key:

  • Ionian is the same as natural major;
  • Dorian flats the third and seventh;
  • Phrygian flats the second, third, sixth, and seventh;
  • Lydian sharps the fourth;
  • Mixolydian flats the seventh;
  • Aeolian flats the third, sixth, and seventh (natural minor);
  • Locrian flats all but the prime and fourth.

I also understand that there’s a concept of a Harmonic minor, in which the minor seventh is sharped (or, in other words, only the third and sixth are flatted). I further understand that there’s a concept of a Harmonic major, in which the sixth - and only the sixth - is flatted.

Can these be applied to other modes, besides Aeolian and Ionian, respectively?

Regarding Harmonic minor: Since this obviously would only apply to keys in which the seventh is already flatted, this means that, in addition to Aeolian, only a Harmonic Dorian (flat third), Phrygian (second, third, and sixth), and Locrian (flat second, third, fifth, and sixth) would be possible. I don’t count Harmonic Mixolydian here, since that’s just the same as Ionian.

However, when you consider that the purpose of a Harmonic minor is to enable the dominant chord to be a major chord, rather than minor, then this picture changes a bit, since a major dominant requires that the fifth, seventh, and second all be not flatted. Therefore: the Phrygian mode requires sharping its second as well, making it into normal Harmonic minor. If Harmonic Locrian requires its fifth being sharpened, then it will devolve into normal Harmonic minor as well, and if not, then its fifth is already major. So either way, no new modes there.

That leaves Harmonic Dorian. This would entail flatting the third and nothing else. Is this actually a mode used? If not, is there a reason why not?

Regarding Harmonic major: Following the same logic as above, only modes with a sixth not flatted can have it flatted; excluding Ionian, this leaves Dorian, Lydian, and Mixolydian. Dorian wouldn’t work, since flatting the sixth just gives a normal Aeolian scale. Lydian could technically work, but having a sharp fourth and flat sixth not only feels weird but also sounds horrendous. And then there’s Mixolydian, which would have a flat sixth and seventh.

Narrowing it down further based on a normal Harmonic major yielding a minor fourth chord, Lydian would be impossible without flatting the sharped fourth, but a theoretical Harmonic Mixolydian would work just fine. As with the Harmonic Dorian above, is this a mode actually used, and if not, why?

  • I understand the math behind why these modes are the way they are, but I find it fascinating that the theoretical Harmonic Dorian and Harmonic Mixolydian, when overlaid on each other, actually yield a normal Aeolian scale. So I guess another way to put it would be that Harmonic Dorian starts out Aeolian and ends Ionian, while Harmonic Mixolydian does the opposite. – DonielF Nov 21 '18 at 22:26
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    What you are referring to as "Harmonic Dorian" (ie D E F G A B C# D) is actually just the melodic minor scale, so yes, it is used — very frequently as a matter of fact! – wskerpan Nov 21 '18 at 22:45
  • @wskerpan Partial answer? – DonielF Nov 21 '18 at 22:48
  • Just like the melodic minor (ascending) starts off minor and ends with major. – Tim Nov 22 '18 at 8:40
  • "Harmonic Aeolian" - ?? – Maika Sakuranomiya Apr 2 at 9:03
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Your approach to this investigation is really interesting, but it ultimately doesn’t yield any new scales. The “harmonic Dorian” you posit is ultimately just an ascending melodic minor scale. However, there are several new scales generated if you approach mode in terms of the intervals between successive notes.

Your description of the seven church modes is accurate, but, in some ways, it’s more useful to define mode in terms of rotations. Ionian is a whole step (W) followed by another W, then a half step (H), followed by W–W–W and then the final step is H. So, we could define Ionian as the interval succession WWHWWWH. Now, let’s rotate this list of intervals one click to the left. In other words we’ll make the second interval into the first, the third interval into the second, etc. and move what used to be the first interval so that it’s at the end. Like this WHWWWHW. If you check, you’ll see that this is the interval sequence of Dorian. Do it again and you get HWWWHWW, which is Phrygian. All of the church modes are created this way; the last rotation is HWWHWWW, which is Locrian. After that you just start over with Ionian again, that’s why there are seven church modes (actually, in the Mediæval period, Locrian didn’t exist, that’s a modern invention, but whatever.

Ok, now let’s changed Aeolian (Natural Minor) into harmonic minor. Aeolian is WHWWHWW, but when we raise the seventh note, that changes both of the last two intervals. Think of the Aeolian scale that starts on A: instead of moving HWW at the end, E–F–G–A, we have E–F–G#–A. The final interval is now a half step, and, more importantly, we created an entirely new step size between F and G# that is a half step larger than a whole step. The technical name for that is “augmented second,” which I’ll abbreviate as A. The harmonic minor succession of intervals, therefore, is WHWWHAH.

You’re right about the original reason for using harmonic minor—it creates a leading tone that allows the dominant chords to resolve more strongly to tonic chords—but another way of looking at it is a scale with a unique interval in it. And, just like we did with the diatonic intervals above, we can rotate the intervals to generate new modes, which are usually called the “harmonic minor” modes. For instance, rotate it once and you have the second mode of the harmonic minor: HWWHAHW. Starting on B that would be : B–C–D–E–F–G#–A–B. Perhaps the most famous of these is the fifth mode of the harmonic minor (sometimes called Phrygian dominant) with the interval series HAHWHWW. For example, E–F–G#–A–B–C–D–E. These scales are fairly common in Industrial and Metal music. In other words, another way to answer your question is to create a series of modes that preserve the augmented second of harmonic minor instead of preserving the “raised seventh scale degree” of harmonic minor. Ultimately, it’s far more fruitful in this form.

If you’re curious, one can also create seven modes of the ascending melodic minor by the same method. In this universe, you don’t usually use a different version of the scale for descending. The interval succession for normal melodic minor is WHWWWWH, and this can be rotated to get a somewhat less common set of seven modes.

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First, some background:

Actually, your approach is my favorite analysis technique for scales. I find it much more convenient than the concept of modes, i.e. shifting (rotating) the tonal center of a particular scale to a different degree. Because I feel altering one note of a scale yields a scale that is somewhat similar to it but rotating it takes you to completely new territory. "Families" of scales are more readily understood in terms of alterations.

For heptatonic scales (scales that contain seven notes), we can do a much more complete analysis:

You have six degrees (other than the root): the second, the third, the fourth, the fifth, the sixth, and the seventh.

At first, let's stick with perfect fourth and perfect fifth. If we keep those constant, the second, the third, the sixth, and the seventh can be either minor or major. It gives us 16 scales (4 degrees to the power of 2 options):

These four have a Phrygian flavor, they work well on Neapolitan chords,
that's why two of them ara named after that chord:

m2 m3 p4 p5 m6 m7 => Phrygian
m2 m3 p4 p5 m6 M7 => Neapolitan minor
m2 m3 p4 p5 M6 m7 => Dorian b2 / Phrygian #6
m2 m3 p4 p5 M6 M7 => Neapolitan major

These four have an eastern flavor because they sound like the popular
Middle Eastern Hijaz family of maqams:

m2 M3 p4 p5 m6 m7 => Phrygian dominant
m2 M3 p4 p5 m6 M7 => Double harmonic
m2 M3 p4 p5 M6 m7 => Mixolydian b2
m2 M3 p4 p5 M6 M7 => Ionian b2

These four form the minor scale family. Western music likes to alternate
between them almost freely:

M2 m3 p4 p5 m6 m7 => Natural minor / Aeolian
M2 m3 p4 p5 m6 M7 => Harmonic minor
M2 m3 p4 p5 M6 m7 => Dorian
M2 m3 p4 p5 M6 M7 => Melodic minor

And finally, these four form the major scale family:

M2 M3 p4 p5 m6 m7 => Mixolydian b6
M2 M3 p4 p5 m6 M7 => Harmonic major
M2 M3 p4 p5 M6 m7 => Mixolydian
M2 M3 p4 p5 M6 M7 => Major (Ionian)

You obtain 16 more scales by sharpening the fourth. They're not all very usable but the Lydian (Ionian #4), the Dorian #4 and the Hungarian Gypsy (Aeolian #4) are nice and popular.

Flattening the fifth yields 16 more. They're harmonically quite unstable but some of them are melodically usable and somewhat popular: Locrian (Phyrigian b5) and Aeolian b5 for instance.

Although less usable, you have some more options like flattening the fourth (and optionally the fifth) of Phrygian flavored scales (example: super Locrian = Locrian b4), or augmenting the fifths of scales that end with a M6 and M7 for some quasi-whole tone scale flavor.

Back to the question:

As you can see, a few of these scales have the word "harmonic" in their names. The common point is that they all have a minor sixth and a major seventh in their structure. Neapolitan minor is not named that way but it certainly has some of the others' character.

One can also observe that augmented second gives such a character to a scale even if it's not between the sixth and the seventh. The Phrygian dominant (5th mode of harmonic minor), Mixolydian b2, Ionian b2, and the aptly named Double harmonic all have a similar character. So do the Dorian #4 (4th mode of harmonic minor) and Hungarian Gypsy scales.

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