What really constitutes a modulation?

Posted by: MathGuy

What really constitutes a modulation? - 02/24/13 03:27 AM

The other current thread titled "Bach" reminded me of something that's puzzled me for a long time: what exactly qualifies as a modulation as opposed to just a harmonic progression?

I'll use Bach's two-part invention number 1, in C, as an example. ( Here's a score from IMSLP, with numbered measures.)

Measures 4 through 8 of this invention seem to be solidly in the key of G, and there's even a perfect cadence in G, concluding on the first note of measure 7. I think everyone would agree that the piece modulates to G.

Now consider measure 15 and the first half of measure 16. They appear to be in D minor: all the notes are from what we used to call the D melodic minor scale, there's a C# in the left hand that explicitly isn't part of the tonic (C major) scale, and the implied harmony seems to be a resolution from A major to D minor. But does this qualify as a modulation to D minor, or is it just a harmonic progression that happens to wander outside the tonic for a bit?

Finally, if the first example is a modulation and the second one isn't, what exactly makes the difference? Is it duration? Presence or absence of a perfect cadence? The expectation that there will be an early modulation to the dominant key?

I actually doubt that these questions have truly cut-and-dried answers, but if there are some relevant rules or principles - or even just opinions - I'd appreciate hearing about them. Thanks in advance.
Posted by: wouter79

Re: What really constitutes a modulation? - 02/24/13 04:03 AM

This may be useful

http://en.wikipedia.org/wiki/Modulation_%28music%29

I think generally if you have to explain a chord using a different tonality than the one you were in, we have a modulation. I suppose it can even be for just one chord, eg with the progression (V)->V I

(if you don't know this notation: it refers to for example the chordsequence Dmaj Gmaj Cmaj where we are in Cmajor. In that case, the f# in the Dmaj can not be explained in the Cmajor tonality and we assume we are temporarily in Gmajor.)
Posted by: sleepy

Re: What really constitutes a modulation? - 02/24/13 09:48 AM

I feel that the cadences are the most important landmarks. So, for me, I would not think to myself that I am solidly in the key of G during measures 4-8; I would think that the piece begins in C and arrives at a cadence in the key of G in measure 7. Then I would say that it arrives at a cadence in the key of A minor in measure 15, and then it wends its way back to conclude in C major. The meanderings in between cadences have a lot of different harmonic colorings, which is what you want to bring out in your playing. So, lots of color and 3 definite points of arrival.
Posted by: Mark_C

Re: What really constitutes a modulation? - 02/24/13 01:42 PM

Originally Posted By: MathGuy
....if the first example is a modulation and the second one isn't, what exactly makes the difference? Is it duration? ....

Basically yes.

But besides that, there can be differing views on whether something is or isn't a modulation; there's a large gray area, and therefore room for lively argument on whether something is or isn't. If anybody ever led you to believe it's always clear and inarguable, they were fooling themselves. smile

Sometimes we might even argue with ourselves over it, and it can affect the way we play phrases, whether we view something as a modulation or not, and we might change our minds back and forth.
Posted by: BruceD

Re: What really constitutes a modulation? - 02/24/13 03:31 PM

I've often pondered this same question - but only pondered since I've had little formal training in harmony, and, hence, have lost little sleep over the pondering - as it would apply to the Chopin Prelude, Op 45. Chopin goes through almost every key in the book in this hauntingly beautiful Prelude, but which of these keys have been modulated to, and which of them would be considered only passing harmonies to a new - if temporary - tonic?

I would be intrigued to see how a theorist would carry out a harmonic analysis of this Prelude.

Regards,
Posted by: Mark_C

Re: What really constitutes a modulation? - 02/24/13 05:00 PM

Originally Posted By: BruceD
....Chopin Prelude, Op 45....
I would be intrigued to see how a theorist would carry out a harmonic analysis of this Prelude.

You mean the infinitely varying ways that different theorists would carry it out, with no two being the same. smile
Posted by: ando

Re: What really constitutes a modulation? - 02/24/13 06:42 PM

I consider it a modulation if there is a new tonal center and I'm not thinking about the original or previous tonal centers anymore.
Posted by: MathGuy

Re: What really constitutes a modulation? - 02/25/13 01:30 AM

Thanks to all who have replied for your time and thought.

I like what ando said:
Originally Posted By: ando
I consider it a modulation if there is a new tonal center and I'm not thinking about the original or previous tonal centers anymore.
which seems like a quite practical (and very personalized) criterion.

Like BruceD, I think an expert harmonic analysis of Chopin's Opus 45 would be really interesting. And Mark_C, it would be delightful if you're right about no two theorists agreeing on that analysis, as there'd be so many interesting viewpoints to examine. (Not that I'd expect to fully understand them.)

Thanks again, folks.
Posted by: Dave Horne

Re: What really constitutes a modulation? - 02/25/13 05:45 AM

Originally Posted By: ando
I consider it a modulation if there is a new tonal center and I'm not thinking about the original or previous tonal centers anymore.


That sounds pretty good.
Posted by: wouter79

Re: What really constitutes a modulation? - 02/25/13 05:58 AM

Originally Posted By: ando
I consider it a modulation if there is a new tonal center and I'm not thinking about the original or previous tonal centers anymore.


I would vote for a more objective definition to make the concept and discussions clearer.
Posted by: theJourney

Re: What really constitutes a modulation? - 02/25/13 06:46 AM

Unfortunately, analysis of music is not subjective to democratic voting nor is it a cut and dried, objective science with one answer but rather a subjective craft or art.
Posted by: wr

Re: What really constitutes a modulation? - 02/25/13 08:25 AM

Originally Posted By: theJourney
Unfortunately, analysis of music is not subjective to democratic voting nor is it a cut and dried, objective science with one answer but rather a subjective craft or art.


It's not as subjective as all that, at least when it comes to music from the common practice era. After all, there's nothing particularly subjective about what a key signature is, for example.

Sure, since the music itself is an artistic product, there are all kinds of ambiguities that arise, but the harmonic analysis of any given music doesn't necessarily have to be as mystical as reading tea leaves. Quite a number of the principles are pretty well established, even if they are not exact enough to say that here is precisely where a modulation takes place, every time.
Posted by: theJourney

Re: What really constitutes a modulation? - 02/25/13 08:39 AM

Originally Posted By: wr
It's not as subjective as all that, at least when it comes to music from the common practice era.


The Vienna Classical Period can be pretty straightforward. However, even if you agree on a modulation, you might still disagree about the point it was established, for example.
Posted by: wouter79

Re: What really constitutes a modulation? - 02/25/13 10:57 AM

I agree that it may be unclear WHERE it happened. But I think we can agree that it MUST HAVE happened at some point, specifically if there appear signatures at that point that don't fit the previous signature?
Posted by: Mark_C

Re: What really constitutes a modulation? - 02/25/13 05:02 PM

Originally Posted By: wouter79
....I think we can agree that it MUST HAVE happened at some point, specifically if there appear signatures at that point that don't fit the previous signature?

Those are obvious and clear modulations. This is mostly about ones that aren't so clear and which might be debatable.


I like Ando's reply too. But the thing is, it's often debatable whether there's a "new tonal center." One person's new tonal center is another person's parenthesis. smile
Posted by: MathGuy

Re: What really constitutes a modulation? - 02/25/13 05:35 PM

Regarding about theJourney and wouter79 said about where the modulation happens, I agree that it's pretty hard to pin down, and there's bound to be disagreement.

Even deciding where a modulation starts depends on hindsight, because you can't tell where things are headed when listening to a piece for the first time. In Bach's first two-part invention in C, the first F# in measure 4 might be the start of a modulation to G, or one of Bach's little dashes of chromaticism, or maybe even the start of a modulation to some other key (suppose the F# were followed by a G#).

Later on, when things are clearly perking along in G, you can look back and say the whole thing started with that first F#. But it's kind of like identifying when you first started catching a cold; later on you may remember the first sniffle and realize that was the onset, but you couldn't have known that for sure at the time.

Of course, listening to music is a constant process of wondering "where is this headed?" and then finding out (and I guess monitoring your health is too smile ). Recognizing modulations is just one little aspect of it. You know, maybe that's why we appreciate repetition in music so much: it could be that it symbolizes the repeatability and knowledge of what's coming that we long for in life itself! Naaah...
Posted by: Pogorelich.

Re: What really constitutes a modulation? - 02/25/13 11:54 PM

Originally Posted By: BruceD
I've often pondered this same question - but only pondered since I've had little formal training in harmony, and, hence, have lost little sleep over the pondering - as it would apply to the Chopin Prelude, Op 45. Chopin goes through almost every key in the book in this hauntingly beautiful Prelude, but which of these keys have been modulated to, and which of them would be considered only passing harmonies to a new - if temporary - tonic?

I would be intrigued to see how a theorist would carry out a harmonic analysis of this Prelude.

Regards,


You just need to look at the big picture more with that piece... A lot of passing chords. if I remember correctly. God, I played that and I can only remember how it starts.....
Posted by: jeffreyjones

Re: What really constitutes a modulation? - 02/26/13 12:17 AM

There are different kinds of modulation. In classical music, the shift is typically temporary (to some degree or another) and is done with some respect or connection to the home key. In many cases, you are prepared for it with a kind of chromatic foreshadowing, especially in Beethoven. He introduces non-harmonic notes that hint where he might be going next. This kind of modulation should be considered as distinct from "tonicization," which is a temporary re-centering in mid-phrase in order to reach a cadence on a different tonic, and which doesn't reset the key center.

In pop music, modulation is often used as an artificial and cheap way to add excitement and make it feel like the music has changed somehow, even if it's exactly the same material recycled over and over. It's always a pleasant surprise when I find a pop piece that legitimately transitions into a contrasting key; it's such a rarity to find actual composing in this kind of music.
Posted by: MathGuy

Re: What really constitutes a modulation? - 02/26/13 12:51 AM

Thanks, Jeffrey - particularly for mentioning tonicization, which is a word I'd never heard before for a concept that comes up all the time. It's nice to have a term for it!

Speaking of pop music, do you have an example in mind of a pop song that does a "real" modulation? I was just trying, without much success, to think of one that does something more sophisticated than just temporarily switching to the relative minor (like in the Beatles' "We Can Work It Out", in the section with the lyrics "Life is very short"), or worse yet just popping up by a half-step. Perhaps the latter technique could be named manilowization, especially when loud reverberating drumbeats are introduced at the same time. (On those occasions when hearing a Manilow ballad was unavoidable, my wife and I used to call those drumbeats "the whaps", as in "uh-oh, last chorus, here come the whaps.")

Oh, Jeffrey, this it OT, but I just noticed from your sig that you gave what must have been heck of recital a couple days ago. Congratulations! And how did it go, if you don't mind my asking?
Posted by: Verbum mirabilis

Re: What really constitutes a modulation? - 02/26/13 02:49 AM

Originally Posted By: wouter79
This may be useful

http://en.wikipedia.org/wiki/Modulation_%28music%29

I think generally if you have to explain a chord using a different tonality than the one you were in, we have a modulation. I suppose it can even be for just one chord, eg with the progression (V)->V I

(if you don't know this notation: it refers to for example the chordsequence Dmaj Gmaj Cmaj where we are in Cmajor. In that case, the f# in the Dmaj can not be explained in the Cmajor tonality and we assume we are temporarily in Gmajor.)


A D major chord in C major is quite easy to explain using C major.

I think most people would analyze a "(V)->V I" progression (also notated as V/V V I) as a secondary dominant (had to search for the term on wikipedia since I wasn't sure of the english name for it). In the case of D G C the D major chord is quite clearly just a "flash" of G major, and after this flash the G major chord resolves on the real tonic (C major). This flash being merely a flash is even more clear if the D major chord resolves on a G7 chord that has a F in it.

Sometimes it may be quite unclear if a composer is using a lot of secondary dominants or if it is a modulation. A cadence on a new tonic is usually a pretty good sign of a modulation.

Also, some chords that may seem irrelevant to the current tonality can be explained using the current tonality. For example the Neapolitan chord, modal chords (most commonly minor IV chord in major), augmented sixth chords (for example the Italian chord) and the Picardy third (the last tonic in a minor key chord progression is the parallel major chord).
Posted by: izaldu

Re: What really constitutes a modulation? - 02/26/13 07:48 AM

I think Ando┬┤s definition is what it really is. You need to introduce the new tonality and make it obvious, and remove the previous one from the listener's perception of tonal center. The new one needs to be stablished and take relevance ... otherwize a secondary dominant would maybe constitute a modualtion, and it's definitely not ...