Modulation - Music-Web Forums

crimson · #1 05-05-2007, 08:13 AM

I was not sure whether to post this in the Music Theory section or here, but anyways... I've been studying various things, including modulation to other keys within a piece. However, one thing that puzzles me is the exact modulation procedure. Based on my reading of a book, it was not clear whether a modulation can occur in other places than just at the ends of sections (through a cadence). To me it sounds like the most natural way to modulate is to end a section with a cadence whose final chord is shared by the new key (common key modulation).

For example, if I'm currently using C Mixolydian and I'd like to modulate to G Minor, I'd use a cadence ending on V (Gm) which is the tonic of G Minor, thus a common chord. From there I'd just start a new section in G Minor. Is this correct? I read from Wikipedia, that it is common to complete a modulation by a cadence in the new key, which I don't quite understand as opposed to my method if it's not the same thing.

Chromatic modulation and enharmonic modulation are beyond my understanding, so if anyone would like to clarify them also, I'd be grateful.

reith · #2 05-05-2007, 02:47 PM

I don't think there is an exact modulation procedure - not to cover every case. The process/progression to choose depends on things like:

i) how remote is the new key?
ii) how obtrusive/smooth should it be?

which govern the amount of preparation needed. A traditional modulation is best confirmed through a cadence in the new key.

The simplest is to modulate via the dominant of the new key (as long as the new key isn't too remote) simply by getting onto the dominant of the new key.

Say the current key is C maj, modulation to the dominant (G, chord V of C) is easy. A regular harmonic progression (without modulation) would be I - ii - V. So you need to conver the ii into a major chord by sharpening the third, making it I - II - V (C...Dmaj...G - if you like, add the 7th to the Dmaj chord to enhance the cadence).

Same with modulating to the subdominant (F in Cmaj). - Cmaj7 is the dominant of F (so you need the 7th this time (B-flat) or it won't modulate. And this is where you start thinking about progression. It might be better to approach the Cmaj7 by way of a B-flat chord (the flattened VII#3) depending on the effect you want. Cmaj...B-flat maj...Cmaj7...F (or substitute Gmin for the Bflat maj).

You can modulate to chord ii (Dmin in C) via the dominant of D-min (Amaj7 - chord VI7(#3) ). Same, getting to iii (E minor) or III, (E major) via its dominant (Bmaj7 - that's VII7 with the 3rd and 5th sharpened) but be careful with the part-writing here if you're in conventional harmony.

You can cascade modulations together like this. Cmaj-Amaj7-Dmaj7-G7-C.

Modulating from minor to major (except the tonic major), or minor to minor keys can be a bit tricky if you want to avoid weird or obtrusive-sounding intervals. Best to modulate to keys that are closely related like, in the minor, the relative major, submediant or subdominant. (In Cmin, that would be to E-flat maj, Fmin or A-flat maj).

You can sometimes use diminished-7th chords as pivot chords - i.e the chord common to both keys on which the modulation therefore pivots. In keyboard terms, only three diminished 7th chords exist (along with their inversions). This means they each appear in 4 major and 4 minor keys. So if you're in a given key, there are 7 other keys you can modulate to with minimal effort and, depending on the layout of your harmony, you can usually get onto the other diminished chords, thus can get into almost every key. That doesn't mean they'll all sound smooth and nice but the possibilities are there. The effectiveness, smoothness and "permanence" of the modulation depends on progression and cadence.

Some effective modulations are "sudden". Just start a new passage in a new key where some commonality exists between the end of the first passage and the start of the new one - usually the treble note in the harmony. Modulating to the flattened submediant is an effective one. Eg. (E major to C major) The first passage is in Emaj and cadences with E in the treble. The new passage is in Cmaj with the E (3rd of chord I, C maj) in the treble. Then you can get back to the home key or go elsewhere.

My humble view about modulation is that it happens. We need it to raise and lower the tension so one just has to practice it. I used to look through piano pieces to see how people like Mozart and Beethoven worked their tricks. It's just a matter of time, practice and musical taste.

Modulation can be temporary like in a cascade of modulations that can add interest to otherwise plain harmony.
Like this
- a phrase from twinkle twinkle harmonised different ways
- the first two bars are "plain" harmony, the next two are the same tune with some passing modulations, the first using Amaj-7 to get to D min, the second using the "domninant of the dominant" to get to the imperfect cadence. Some members here call this a V/V or V9/V progression - I prefer it as II9b / Va (just my view on chromatic harmony) but either are ok!

reith · #3 05-05-2007, 05:50 PM

As an afterthought...I've posted the above with specific key examples and Roman nomenclature but I don't know if you're familiar with the Roman.

crimson · #4 05-05-2007, 05:57 PM

Arr, sounds complicated... But I think I'm starting to get a better idea of the whole thing. So the 7th in the modulation chord is not necessary unless it's part of it in the new key?

Thanks for the thorough explanation! I'll try to check on my books again and see if I can now make better sense of them.

Edit: Yes, I think I understand the Roman notation... Or at least so far as "in the key of C Major, the chord C is the tonic or 'I', and Em is 'III' and so on".

stevel · #5 05-05-2007, 07:09 PM

However, one thing that puzzles me is the exact modulation procedure. Based on my reading of a book, it was not clear whether a modulation can occur in other places than just at the ends of sections (through a cadence). To me it sounds like the most natural way to modulate is to end a section with a cadence whose final chord is shared by the new key (common key modulation).

Ok, there are two things: Tonicizations and Modulations. A Tonicization is a "hint" at some key other than the home key (and by the way, C Major to C minor is considered a change of mode, not a modulation), and Modulation is an "establishment" of a new key.

The way you tonicize a chord other than the tonic is to introduce its dominant chords, or a few chords that are unique to some other key. The way you modulate is to "confirm" the new key by way of a cadence (and that also implies a continuation in the new key).

There are a couple of types of modulation:
1. Common chord modulation.
2. Common tone modulation.
3. Direct modulation (also called abrupt, or phrase modulation).
4. Enharmonic modulation (which is actually a type of common chord modulation, but hte common chord is reinterpreted as an enharmonic equivalent)
5. Seqeuntial modulation (which is often a type of direct mod, though can also be common - the sequential pattern is the key here).
6. "monophonic" modulation - that is a mod that's made by a single, unaccompanied melody line that implies harmonies. Really it would probably be a common chord mod but we don't have the chords to be sure!

In a common chord mod, you find a chord common to both keys and use it as a "pivot". For instance, if you want to mod from C to G, there are a couple of chords that are common to both keys - C, em, G and am. I and V are usually not the best pivot chords, so usually something like am would be used in this mod:
C F G7 C | C am/C D7 G |G-----

The am in m.2 would be heard as vi6 in CM, but when we hear the D7, we're forced to re-evaluate that thinking and we hear am also as ii6 in the key of G. Now, this could be a Tonicization of G if we went right back into C major. But if we continue in G major it's more obviously a mod. The difference between the two can be really grey sometimes.

The important chord here is the D7 which is the V in G. Since F# is the only note different in G from C, it's important to "neutralize" the F natural (and likewise if we were to mod back to C, we'd need to neutralize the F#). The reason V7or viio are frequently used is because they are unique to a key. D7 doesn't exist in C, so we go back one chord and find that am could exist in both keys, and that's the pivot chord.

A Common tone mod is usually used between to more remote keys such as C major and E Major. There are no chords common between these two keys but there are notes. Often, a composer singles out the note (unaccompanied) so you get a C chord with an E melody then the harmony drops out leaving the E note, and then a new harmony E comes in and pow, you're in the new key. This was a favorite of Beethoven's.

A Direct mod is like - pow, you're in the new key. This is common in pop songs where you hear the chorus, and when it reaches the end of a pass, it jumps up to a new key. Classical cats call these Phrase mods because they usually happen between phrases. They don't have to though. In a direct mod, usually the last chord of your home key is not in the new key, so you must be in a new key - again, usually this happens at a structurally significant point (like the repeat of a chorus) so it's pretty obvious.

Enhnarmonic mods take a chord like B dim7 (B D F Ab), which is viio7 in C, and reinterpret it as viio7 in some other key. For instance, E# G# B D, which is viio7 in F#.

Again, sequential mods are like so:

C F C C | D G D D | E A E E, etc. It's really a direct modulation to the new key, but that fact that it's in a sequential pattern is usually noted.

For example, if I'm currently using C Mixolydian and I'd like to modulate to G Minor, I'd use a cadence ending on V (Gm) which is the tonic of G Minor, thus a common chord.

Well, the problem is, you're using modes. The chords in C mix are:

C dm eo F gm am Bb

the chords in Gm are:

gm ao Bb cm D Eb f#o

Thus the common chords are gm and Bb. To make a common chord modulation, it would be better to use the Bb:

C gm C Bb | Eb D gm D | gm------

If you simply "cadence on v", it might be a little too abrupt (though you may want that). If you want a smooth modulation, it's best to start sneaking in "anonymous" chords sometime before the cadence. In other words, you make the person think - hey, were definitely in C mix........ wait, what just happened? now it sounds like were in G minor? - wow, there must have been some period of time back there when the chords were neither C mix or Gm, but could have been either and I didn't notice.

Otherwise your mod is like, hey we're definitely in C mix, haye there's a cadence in Gm, oh, now we're in Gm. It depends on how "sneaky" you want to be about it.

From there I'd just start a new section in G Minor. Is this correct? I read from Wikipedia, that it is common to complete a modulation by a cadence in the new key, which I don't quite understand as opposed to my method if it's not the same thing.

You're method of cadence on gm, which you called "V" is correct. But really, by using gm's V chord, (D7), you are "tonicizing" (making it the tonic) the gm chord. The cadence on gm *AS* i of your new key will be confirmed by the music in gm which follows.

Chromatic modulation and enharmonic modulation are beyond my understanding, so if anyone would like to clarify them also, I'd be grateful.

See above for a VERY brief overview.

But Crimson, I want to caution you about something. Common chord modulation is really something that is part and parcel of the Tonal system. You are not writing tonal music if you're using C Mix. Common chord modulations are really not part of the style of contemporary music. Since composers have extended tonal resources to include modes, synthestic scales, quartal harmony, and everything else under the sun, the idea of a "common chord" as a pivot point doesn't fit. Therefore usually, modulations, if used at all are generally Direct (again, like pop songs that go "up a step" at the end).

In the early days of modality, modes didn't modulate, but they "mutated" into other modes. Dorian (D) would become Mixolydian (G) through a focus on different reciting tones and final - but the notes were the same (like trying to mod from CM to am rather than CM to dm). Trying to make modes modulate to keys (or to another mode) opens up a whole new can of worms!

So I'm not saying Common chord modulations shouldn't be used, but they're even trickier in a non-tonal system. The unfortunate thing is most people have absolutely no understanding of how a tonal common chord mod works so they have no idea of how to apply those principles to a non-tonal system effectively. This might be part of the reason they've fallen out of use (the other is that they are just stylistically "old-fashioned" to some).

HTH, Steve

stevel · #6 05-05-2007, 07:36 PM

So the 7th in the modulation chord is not necessary unless it's part of it in the new key?

What you need Crimson is a chord or chord progression that is "unique" to the new key.

For instance, in C major there are 3 major chords and 3 minor chords. If I play an am to C progression you don't know if it's am, CM, FM, GM, em, or possibly dm using non-dominant v and VII. You can't tell what the key is from just those two chords.

But there's only *1* diminished chord in the key! If you hear Bdim, it MUST be the key of C (CM or cm).

Note: Actually, we can kind of guess that am to C is *most likely* am. Bdim is also the iio chord in Am so it *could* be am, but we understand a dim chord to more often be viio, and not iio.

If you make 7th chords, there are TWO unique chords - V7 and viio7. When you hear G7, you KNOW it must be C Major.

Disclaimer: Although in modern pop music and Jazz, 7th chords are used all of time outside of the key sou it could be the Tonic for all we know. Likewise, it *could* be VII7 in am, but we'd assume it's a V7 before a VII7.

There are not only unique chords, but unique progressions. For instance, if you hear a Bb chord followed by a C chord, chances are *extremely good* that you are in the key of F. If it's Bb to C7, then it's 99% positive it's F.

One of the most unique pair of chords is ii-V. If we use ii-V, or iio-V in minor, it MUST be the key. There is no key that has dm-G other than C Major. Am is unlike to go iv to VII - it would go iv to viio instead (dm to g#o) to establish Am as the key center. This is still why even in Jazz II-V-I is such an important progression.

An aside here Crimson - I mentioned in my other response about you're using a non-tonal sytem. That's a problem. You see how this stuff falls apart? dm to G is unique to C Major as ii-V in a TONAL system. But the progression dm to G in a MODAL system suddenly can be:
i to IV in D Dorian
ii - V in C Ionian
iii - VI in B Locrian
iv - VII in A Aeolian
v - I in G Mix
vi - II in F Lydian
vii - III in E friggin.

We *might* assume that it's most likely Dorian or Mix because that makes one of the two chords the "tonic" without any other reference. But if you're already palying music that is modal to begin with, there's no guarantee that this progression we would recognize as99% ii-V in Mozart would have a 1 in 7 chance of being recognized as indicating the "Key of C" (or even C Ionian).

But back to the original question: Usually the addition of the 7th on either the V or viio chord of the new key CONFIRMS that it's from a new key. It doesn't have to be present but it makes it MORE UNIQUE. For instance, moving from C to F, you could treat C (I) as V in the key of F. But where's the clue that you did so? C is in both keys, and you've done nothing to highlight its new function as V rather than I - you can't just wish it so. So if you add the 7th to the C chord making it a Dominant 7th (Major-minor 7th chord) it becomese unique to the key of F, not C. On the other hand, using a D Major chord without its 7th in C is unique enough that we can surmise it's leading to G.

Again, here's where there's a problem with modern "what people often call tonal" music: In classical music, there is no I7 (C E G Bb). There is IM7 (C E G B ) in major, and i7 (C Eb G Bb) in minor, but there's no Dominant 7th construction on I. But in Jazz and Blues, I7 is common. So C E G Bb is no longer unique to F major. It could be I7 in C, IV7 in Bb, or V7 in F (or VI7 in E, a tritone sub in B, etc.).

So modern people have had to fall back to, not unique chords, but unique progressions, or no common chord mod at all. If you think about a song like Satin Doll, it really is a sequential mod - it goes ii-V in one key, ii-V in another key, then ii V in yet another key. So in this case it's the stylistically common ii-V progression (with approriate melodic material) that distinguishes the key, not the fact the V7 of X key has appeared (though this is closer to that principle then when more obscure progressions are used).

Edit: Yes, I think I understand the Roman notation... Or at least so far as "in the key of C Major, the chord C is the tonic or 'I', and Em is 'III' and so on".

Actually, I ii iii IV V vi and viio are used - uppercase for Major and +, and lowercase for minor and dim. Unfortunately, many people use the "generic" system that doesn't identify chord quality.

Best,
Steve

stevel · #7 05-05-2007, 07:49 PM

Some members here call this a V/V or V9/V progression - I prefer it as II9b / Va (just my view on chromatic harmony) but either are ok!

V/V in C, D.
V9/V in C, D9.

What is II9b?

Is "b" the inversion?

II9 in first inversion is:
F A C D E in C major,
F Ab C D Eb in C minor.

If you are using specific upper and lower case RN,

ii9 in FI is F A C D E in C Major
ii9m7b5 is (fig bass inversion sybols are stacked) F Ab C D Eb

And "II9" in FI would be:
F# A C D E in C major and minor.

If it's IIb9 ("two flat nine") then it's
D F# A C Eb

But again, this doesn't show the chord's function if it is in fact acting like the dominant of the dominant. If it's doing so, it should be Vb9/V. If it's a standalone chord, I have no problem with it being IIb9 in contmeporary popular music.

Steve

reith · #8 05-05-2007, 08:13 PM

I think this is one of those times when too much theory may be a bad thing at first. Once you learn to modulate to, say, the dominant of a key; and maybe the subdominant, (or relative major/subdominant and dominant in the minors) you can get more adventurous.

The main thing is that modulation is just shifting the tonal centre of a piece. The easiest way to do that is to get to the dominant of the new key/tonal centre and form a cadence. It may not be easy to get to that dominant with remote keys but you can usually get to one with closely related keys...the dominant, subdominant, submediant, supertonic.

You mentioned chromatic harmony.

Basically a chromatic chord is a chord that contains notes not found in the basic scale of a key.

Chromatic harmony is harmony that uses a preponderance of such chords.

Thus when you modulate you inevitably use notes not in the scale of the original key. The chord on which the modulation depends is therefore chromatic.

Here's an example: the framework for modulating to the dominant in C major. The dominant is G. So you need to find the dominant of G which is D major.

So you basically go from C to D(major) to G. Since the F# in the D major chord does not occur in C, the chord is chromatic.

This example gives the basic scheme of things - tonic to dominant....then back again (which is effectively a modulation in G to it's subdominant, C)
then a simple example of a tune modulating to the dominant and back again - not good music...I'd never write something like this for a composition! But it'll give an idea...

reith · #9 05-05-2007, 08:27 PM

Huhhhhh....I guessed this would happen. Differences in terminology, academy etc.

Originally Posted by stevel

V/V in C, D.
V9/V in C, D9.

What is II9b?

Is "b" the inversion?

Yes, in the UK and to the ABRSM syllabus, a = root position, b = 1st inversion etc.

II9 in first inversion is:
F A C D E in C major,
F Ab C D Eb in C minor.

As II is written in caps rather than ii, it's regarded as a major chord. Properly, I should have written it with #3 beneath to indicate the raised 3rd making it major (Supertonic Chromatic) but it's difficult because of the typography.

So II9b
would be F#-A-C-D-E

But again, this doesn't show the chord's function if it is in fact acting like the dominant of the dominant. If it's doing so, it should be Vb9/V. If it's a standalone chord, I have no problem with it being IIb9 in contmeporary popular music.

Steve

Quite so, and I did say I used it because of how I regard harmony - usually fairly chromatic so all chords are seen from the previous tonality. As it's a pivot chord it could be written as V(whatever) in the new key or II(#3 underneath)(whatever) in the current key. But V/V is anticipating a new key - chord V of degree V. To me it's plain II until the V degree has been affirmed (if at all) as I. Has nothing to do with contemporary pop. I learned it as the "Supertonic Chromatic" triad so... II, because it by no means forces a modulation - it can go straight on to V7 or Ic (6/4) or elsewhere.

Still, I don't want to confuse crimson who is trying to work out a method of modulating, so perhaps I should edit my original response. See what others think.

ttw · #10 05-05-2007, 09:04 PM

I've never seen this described explicitly, but I like to think of a "key" as a (key-)note and a bunch of harmonic (and melodic) relations. Relations are things like ii-V7-I or for that matter, just the existence of a certain set of chords with some musical "meaning" (not just isolated chords.)

Modulation is the process (or result?) of shifting the key-note so that other relations hold. For example, the relation ii-V7-I in C is Dm-G7-C but in E it is F#m-B7-E. If, using melodic and harmonic means, it sounds like ii-V7-I (and thus an extended cadence), the key is established. Modulation just establishes a key after another has been established.