How can I explain/understand a flattened 2nd in a minor melody

Question

My 10yo daughter (~grade 4 piano level) likes composing her own tunes, and then we'll discuss them and expand on them. Recently she composed a melody that appears to be in c# minor, except that every so often she uses d-natural instead of d#. I have played around an I have to admit it sounds "right" where she has used it, so I don't think it can be unusual. What sort of musical theory explanation is there for this note sounding correct? Should we think of this as momentarily modulating to F# minor for a phrase and then back again - and is there any justification for why that sounds "good"?

Edit: Here's an example

In this case the same phrase is dropping down one place in the scale of c#-minor, which means the first note drops a tone each time (c#, b, a), and the quaver on beat 3 seems to mirror this (f#, e, d)? But doing so takes it out of scale - and plenty of other notes do not drop down a tone (so the melody is exactly transposed on each repetition), e.g the last note (a, g#, f#)

Answer 1

Those flattened 2nd scale degrees could point to tonicization of or temporary modulation to the subdominant (e.g. if ^1-^♭2-^1-^4 is harmonized as i-VI/iv-V/iv-iv).

But those flattened 2nd scale degrees could also be signs of - and harmonized as - the ♭II a.k.a. Neapolitan chord!

In classical music, the ♭II chord is treated as a subdominant-function chord, and it is indeed sometimes substituted for iv (so, for example, ^1-^4-^5-^1 can be harmonized as i-♭II6-V-i). Occasionally, minor-key music even modulates to the Neapolitan chord's key (e.g. near the end of Franz Schubert's Moment Musical in F Minor, D. 780 (Op. 94), No. 5, there is a striking modulation from F minor to G flat major (the key of ♭II of F minor) and back):

While already occasionally to more than occasionally appearing in classical music if you know where to look (e.g. Ludwig van Beethoven's "Moonlight", "Appassionata", and "Tempest" piano sonatas), the ♭II chord may as well be a first-class citizen in heavy metal and (shockingly often therefore) edgy enough video game music. In those types of music, dominant chords are often omitted entirely, so you often hear chord progressions like i-♭II-i and i-♭II-VII-i.

Answer 2

♭2 is a common chromatic alteration in minor keys. It might imply the ‘Neapolitan’ ♭II chord. It might be just a melodic decoration. If it’s used consistently in place of the major 2nd, we might be in Phrygian mode!

Answer 3

EDIT: My original answer starts in the second paragraph. This was based on not having a musical example. Based on the musical example that was added after I posted my answer I would say the use of D natural is not Phrygian but rather part of a circle of 5ths sequence that ends on the implication of a Neopolitan bII chord. The melody seems to imply C#m, F#m, B, E, A, D, G#m, C#m. She came up with a very interesting line.

Without hearing or seeing the music for the piece your daughter wrote I would just say: Welcome to the Phrygian mode!

The Phrygian mode is identical to the natural minor scale except for the 2nd degree, which is M2 in minor but m2 in Phrygian. This gives the Phrygian mode a darker and some might say a slightly Spanish or Middle Eastern flavor.

It’s possible she doesn’t use it exclusively in the piece. That’s ok, the great thing about composing is that there are no rules that say a piece must only contain certain notes, unless you are writing something as part of some kind of assignment with rules to follow.

In case you’re not familiar with where it comes from, it is one of the 7 modes built from the 7 degrees of the major scale. Information on modes is universally available so I won’t go into a detailed explanation but here is a link to get you started : https://en.wikipedia.org/wiki/Mode_(music)

The Phrygian mode is built on the 3rd degree of the major scale so in essence if she is in C# minor that is the 3rd degree of A. The key of A is the relative major of F# minor which is the key you mentioned in your question so you weren’t far off with what you heard. However in this case if the piece sounds like the tonal center is C# then it is better to think of it as either C# minor with some borrowing from the Phrygian mode or if there are no D#’s or a lot of other chromaticism you can think of it as being in C# Phrygian.

Answer 4

Scale degrees are regularly altered (modified), and it sounds like what it sounds like. Now you've heard what this particular modification sounds like, and you'll be able to use that sound in the future, when you want that sound.

An essential element in sheet music notation is accidentals which are used to show alterations to scale degrees. By notational convention, the alterations are temporary and are automatically cancelled at the next barline. This convention is because that's how pieces are usually built. Alterations are temporary, and when they are returned back to normal, that's a kind of a tension/release element.

I wrote a chord accompaniment harmonization for this melody.

To add further scale degree alterations, I made a change in the last bar, making a proper dominant-seventh (G#7 instead of G#m) accompaniment chord fit better with the melody.

Try making further modifications and listen to the new sounds. How about this one, do you like the sound?

Many of the scales and/or chords obtained via alterations have specific names, but I'm not sure if learning a lot of fancy names does more harm than good. The names don't matter, only the sound matters and that you know how the sound was made.

What "understanding" means for different people varies. For me, it is enough if I can relate the change to something I consider familiar or conventional. Another thing that helps to gain a feeling of understanding is if I have encountered example pieces where this particular thing is used. What comes to the flattened 2nd in minor, unfortunately I can't name any specific tune from the top of my head, but it is very commonly used.

You can also do the same trick in the backing chords, without the alteration being reflected by the melody at all. How about this:

Now there are many more chromatic alterations of scale degrees. During the D7 chord, even the tonal center C# is altered! I don't claim to particularly like this chord progression, it feels slightly weird at places, but you can do that and it sounds like what it sounds like.

Answer 5

All the Neapolitan comments seem off the mark, because it isn't really functioning like a subdominant N6 that would normally move to a dominant chord of some kind. In other words, it isn't followed by a G#7, so it isn't a convincing subdominant to dominant in a minor key movement.

But, there is a very obvious melodic sequence happening, and the pattern of that sequence is a decoration of a third, an implied root position triad, that leaps up a perfect fourth. Not just any old fourth, but specifically a perfect fourth.

Two important points should now be mentioned:

• melodic/harmonic sequences are frequently used to modulate to new keys
• the perfect fourth above a tonic is an important tonal degree and chromatic alterations that form that tone are important in modulation

The second point I think is less in effect for this passage, but at the very least when we get to the third measure, the D4♮ really stands out as a perfect fourth above the outlined A C#, and it has a strong A major feel. The D4♮ rather than sounding like solfege RE lowered in C# minor, sounds like FA in A major, even if that event is just a temporary shift. The sequence continues, so at this point we wouldn't want to settle on A major as a new tonality.

The first point is probably the more important one. When you see sequential passages with accidentals, it should signal you to look for a modulation or temporary shift of tonality. When such changes aren't modulations, then it's most likely about altered chords, and altered chord usually stand out for their particular "sounds" and they often have conventional resolutions. If we want to consider the possibility of an altered chord - such as the Neapolitan N6 chord - we really want to see conventional handling to make the case.

One way or the other, harmonic analysis is usually clearest when it reveals the most conventional harmonic identities.

Let's continue with the premise it is modulating and see if it fits a common convention.

The passage stops on C#4.

The natural on D4 has the temporary effect of a key signature of three sharps, which would be F# minor.

C#4 is the dominant of F# minor.

The decorated third of G#3 B3 in the fourth measure outlines a iio chord in F# minor.

iio V makes a nice half cadence in F# minor. From a common practice tonal perspective that conventional harmonic progression makes much more sense than a supposed N6 chord moving to an implied minor dominant to tonic move, which would not be conventional common practice harmony.

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EDIT

The D4♮ sounds like a Neapolitan, lowered ^2 is being introduced, but the fourth bar doesn't continue along those lines and play a proper dominant, like this...

To leave the line as written, I tried a modulation to F#m that made functional sense...

I'm not really satisfied with that ending in F# minor, but that does leave the line unaltered.

If I wanted to go the way of a Neapolitan chord, and wanted it to sound like common practice, I would change the last bar accordingly.

The basic cadential formula for a Neapolitan chord is...

...the tonic enclosed by the lowered ^2 degree and the raised ^7 degree in a minor key.

The Schubert example in the accepted answer is an example of modulating to the key of the lowered ^2, but it doesn't demonstrate the cadential use of N6. It's interesting, but doesn't provide the same kind of continuation/ending that is presented in the original question.

Answer 6

I see that an answer has already been accepted, but I think this is worth pointing out. I don't know why I didn't see/hear it the first time. The composer has written a brief sequence. Since beat 3 is metrically strong, I wonder if at some level she felt D# was a "wrong note" and corrected it down to D natural. All the other iterations of the sequence outline a perfect fourth between beats 1 and 3. D# would form an augmented fourth, and interval that takes some getting used to - and one that often sounds "wrong."

I wouldn't hesitate to explain the N6 to her, as it could be a perfectly valid way to harmonize this melody! But I think the effort to maintain a consistent motive in a sequence explains where it came from.