question for music theory experts.

[Derek]

What are these so called "smooth" modulatory transitions I keep reading about?  The only ones I am familiar with in repertoire and in my own playing are very simple ones to the dominant, subdominant, etc.,  and some sudden changes, and so forth.

But could someone show me how one would "smoothly" transition between say C major and A flat?  I'm under the impression that the circle of fifths is often employed for smooth transitions, so that to get to A flat from C, you would play (chords) C, F, Bflat, Eflatseventh...and then prepare some sort of cadence into A flat major.  Is that considered "smooth?"  If so, are there others, and are there any experts here who could give me more examples?

I'm not sure any of this will actually end up being useful in my own creations, but it doesn't hurt to try.

[Bob]

The circle of fifths is smoothly and will get you there... eventually.

Smooth means it's not abrupt, more that you realize the modulation after it occurred. 

Abrupt from C to Ab would be,    C Eb7 Ab     


I know there is more than one way to modulate smoothly.

One way is with common chords, the chords that the two keys share.  C and Ab are distant on the circle of fifths -- common chords are easier with near-related keys, ones next to each other on the circle.

You can do modal borrowing -- substitute c minor for a C Major chord...   This might make it less "smooth" but the only difference is a half-step between those two chords.

     c  f Eb Ab
C:  i  iv
Ab:iii vi V I


Common chord modulation works well with predominant chords or the level before that.  The c and f chords in this example make it a little ambigious about exactly when the modulation takes place -- is it the c minor, the f minor, or maybe there isn't a modulation and it's a secondary dominant tonicizing bVI in C Major?  ooooo

An easier way of saying this -- take a ii, iv, or vi chord and see what other keys those function as a ii, iv, or vi chord.  That makes near-related modulation easy.

And this is all for smoothness.  If you're composing something, you may not want that effect. 

There are other ways, like using o7's....
       C  bo  Eb Ab
C:    I   viio III
Ab:       viio/V  V I



Anyone have more?

[Derek]

what are o7's?  I know what the rest of your symbols are but not that.

Its kinda funny, I'm not much of a composer, I mostly improvise. I'm seeking to learn and have as part of my vocabulary a large amount of conventional harmonic things to do. Cause I mean. they DO sound good.

"Abrupt from C to Ab would be,    C Eb7 Ab     "


Ha, I'd be even more abrupt than that....I'll just jump straight from C to Ab.  switching keys by major and minor thirds suddenly sounds really awesome actually.

[Bob]

diminished seventh chords   viio7's

I think that's right, the abbreviation    o7

Yeah, the numbers are just for the function, the o means diminished.

If you put a slash on the o, it means half-diminished.

[Derek]

Here's another question: What about chord voicings and connections and so forth? Is there a simple principle behind this?

I'm under the impression the idea is to keep all your voices moving as stepwise as possible (especially with the middle and higher ranges) instead  of just having root position chords all over the place.

[Derek]

Hmmm....I just tried out some of those and I still think I prefer the sudden change directly from C to A flat!

you know, I think prepared modulations lend themselves better to composition than to improvisation. When one is improvising one is inclined to consider more immediate effects, since improvisation is all about immediacy, anyway. That doesn't mean improvisation can't include deeper structures and composition like elements, of course!

[BoliverAllmon]

What are these so called "smooth" modulatory transitions I keep reading about?  The only ones I am familiar with in repertoire and in my own playing are very simple ones to the dominant, subdominant, etc.,  and some sudden changes, and so forth.

But could someone show me how one would "smoothly" transition between say C major and A flat?  I'm under the impression that the circle of fifths is often employed for smooth transitions, so that to get to A flat from C, you would play (chords) C, F, Bflat, Eflatseventh...and then prepare some sort of cadence into A flat major.  Is that considered "smooth?"  If so, are there others, and are there any experts here who could give me more examples?

I'm not sure any of this will actually end up being useful in my own creations, but it doesn't hurt to try.

this one is real easy. play this I, ii6, V7, bVI 6 (which is A-flat) when you get to this chord notice you are 2 half-steps from having a I chord. A typical romantic cadence would then resolve itself into the I chord, but instead of doing that just continue on in a-flat. Tell me what you think about that one.

boliver

[ted]

The first task my teacher assigned to me was to devise effective cyclic progressions and sequences of chords. The best ones exhibit as many nice changes as possible without bouncing around too much or running out of  keyboard space. I remember one good example:

Right hand on an A minor chord (for example) A,C,E  Left hand on an E somewhere below.

Move the left hand down a semitone each time.

In the right hand, move each of the three notes upwards one step cyclically in threes, thus:

A,C,E             
A,C,F
A,C,F#
A,C#,F#
A,D,F#
A,D#,F#
A#,D#,F#
B,D#,F#
C,D#,F#

etc

accompanied by E,D#,D,C#,C,B,A#,A,G# etc in the left hand

I don't know why Derek's post brought this to mind. My teacher used to remember hundreds of these things and stuff them into his improvisation in different ways. He made me devise a few new ones each lesson. Much of his improvisation tended to be a fearsome display of rapid mental arithmetic using an encyclopaedic memory of patterns. I don't care for improvisation of that type now but it is certainly a first rate learning tool.
 

[Daevren]

You can only modulate smoothly to a new key that is not too distant. The difference between C major and Ab major are four notes. Important thing for a modulation is chords that are diatonic or native to both keys.

Ab major has these chords.

Ab Bbm Cm Db Eb Fm Gdim

There is not even one common chord. The more common chords the smoother the modulation. Also, if you take alot of time/chords/measures for a modulation it will sound smoother. So smooth modulations from C and Ab are impossible. This means that either a modulation from C to Ab will take alot of time. Eg C to Gm first, then after the music repeats a theme or something in Gm and the music moves on to modulate to Ab. These are still kind of big leaps. Looks at the circle of fifths. Exotic music requires less 'smoothness' or from another point of view, smoothness is relative to the harmonic spice of the music. So there are many different rules and guidelines for this, many tricks and techniques.

Lets say we modulate from C major to F major. These two keys lie next to each other, F Major has one flat. If you want to have a modulation to F major you need it to end unambigiously in F major. That means a cadence on the F major chord. So V-I, C-I. So lets say after we moved to the new key we will have the following chords Dm - Am - C - Fm (vi - iii - V - I). This will be our ending. We start out from C major. We could add a section in C major ending with a cadence on C, but lets ignore that part and just start with C.

So we have: C [modulatory section] Dm - Am - C - Fm. 

How do we go from C major to F major smoothly? The difference is the B in C major and Bb in F major. So we avoid all chords with a B or Bb, because either one will point to either C or F. If we have a chord with a B in our modulatory section then it cannot modulate because it defines the music as C major. When we use a chord with a Bb in that section we move to F major too fast, we wanted to do it smoothly. So we have the chords: C Dm F and Am. So we could do it really fast, have only the F chord in the whole modulatory section.

C - F - Dm - Am - C - F, (V - I - vi - iii - V - I), why not?

Now you may notice none of these chords have B or Bb. So is this in F major or C major? Because of the V-I cadence on the F chord it is clearly in F major. Also the B note is a very important note in the key of C, while the Bb is not very relevant. the E note has the same role in F major as the B in C major. Both lead to the tonic chord. This example has another problem, not enough variation, we repeat C to F two times. 

Lets do another example. We go from G major to D minor. We can do this two ways(well alot more of course). We can clearly go to C major or A minor first. Or go to D minor immediately. Lets do the last one. Lets borrow all but the modulatory section from the previous example: G [Mod. Section] Bb F A Dm 

Bb F A Dm is a copy of the vi - iii - V - I we had before. But now the sixth chord is major. Also, Am is diationic to Dm, but A makes a stronger cadence.

G major and D minor have two uncommon notes. G major has F# and B while Dm has F and Bb. So no chords with either of these notes. So that leaves Am and C.  For variation reasons we will now deploy a deceptive cadence in Dm, so A to Bb ( V-vi). Personally I would prefer a minor version this time, so Am. We could also have used a IV-I. So Am - Bb and that Bb chord will be the first Dm chord. We will put the other shared chord in front of it: C - Am - Bb and we could put an Em chord before the C chord.

If we do that we will have two Bb chords next to each other, one of the deceptive cadence and one of the phrase we loaned from the first example. We replace the VI chord from the loaded chords into a vi chord.


Then we have G - Em - Am - Bb - Gm - F - A - Dm (in Dm: IV - ii - v - VII - IV - III - V - I)

You can also alter the triads to seventh chords if you want.

There are many more possibilities. If you get the general idea you can figure out some yourself. You can jump to the V or V7 of the new key and resolve it and there you are. You can use Dim7 chords to go everywhere.
 
Connecting chords? This is even more complex and there are many different theories and styles, baroque, hard rock, jazz, romantic classical, modern, pop etc.

A very basic principle would be to have each voice move with the smallest steps possible. If you want some more detail I will put up some examples.

[Bob]

Voice leading should be as smooth as possible.  There are certain ways the notes "want" to move.  You really need a theory book for all this.  There are lots of little rules of things you need to avoid to keep the lines independent (parallel 5th, parallel 8ves, etc.)

This is all traditional.  I think "rough" modulation sounds good sometimes too depending on the style.  Of course, there are those pieces that make you wonder if the composer just hit the transpose button on software and created another section.

[Derek]

Would any of you care to analyze these little baroque compositions I wrote? I'd be interested to learn what I used in them unwittingly:

https://www.personal.psu.edu/dga112/sonatadminor.mid

https://www.personal.psu.edu/dga112/sonatainaminor.mid

https://www.personal.psu.edu/dga112/fugueinc.mid

[Derek]

Tell me, do any of these pieces use smooth modulation::

Fantasy Impromptu by Chopin
Nocturne opus 9 no 2 in E flat by Chopin
Pathetique sonata by Beethoven
Invention no 7 in e minor by Bach.
Reverie by Debussy

As far as I can tell, all of these pieces just move around, change modes, land on V7's (or dominant 9ths in the case of Debussy heh) and change. 

However, I think there is a possibility that my understanding and feeling for the harmonic practice of these composers is somewhat more intuitive and simpler than the textbook approach. I hope that is the case, for if I had to consider thousands of examples from repertoire and their pros and cons every time I improvised, I wouldn't be able to play a single note!

[Daevren]

Thats alot of questions. It would be alot easier if you could provide the sheet music of those pieces directly. Importing a midi file makes everything messed up.

The fugue was rather small. It starts with a theme that is clearly in C. When the second voice comes in and plays the same theme in the dominant it is a real answer. This means that to exactly answer the first voice we will need a F# instead of F. You use a F# and so its a real answer. This also means a modulation to G major. Because this is voice and melody based you cannot look at it in terms of chords. Firstly, before a third voice enter its hard to talk about chords. Secondly, you have to repeat and retain the theme as accurately as possible. You do not want to sacrifice the subject for some chord progression. Usually after all voiced played the subject, either in the dominant with a F# or in the tonic key with a F you will get a small free part and then a cadence, usually a incomplete or deceptive one on the I chord, or one on the V. So the first section might even end in G major. Yours does in measure 14, the G chord. Then you could have a second exposition/reexposition. Then a development and end in C major. I am not sure what happens then, seems like an half inverted subject or something.  So I guess that part is a development section. 

Your last 6 measures are in C major again and it ends on C with a V-I cadence.

I am not sure what the third voice is doing. It should start with the subject too. Also you can have countersubjects. Have voice A play something after voice B starts with the subject and have voice B play that too when voice C starts. You can be alot more flexible with the countersubject. It also gives some more thematic material for the development.

I opened the Dm sonata, it looks like a mess I see C#s or Dbs. What are they doing there Maybe D harmonic minor? In measure 9 you get a chromatic sound because of the Edim to Cbdim7 chords. These are strange. It sounds cool. And the next measure you throw in the A chord and then to an E major chord(huh! ). So Dm Edim C F Edim Bdim7 A E. Or i-iidim-VII-III-ii-bvii-V-II In terms of smooth modulations that isn't very smooth. It creates a very distinct sound. You mix all three minor scales and more. I never have the guts to do something like that

You might not know what you are doing, but you are sure doing alot of stuff! I am no expert on genres, but I don't think this is typical baroque harmony. If it wasn't for the melodic and ritmic elements it wouldn't be baroque, I think.

Romantic music generally doesn't have any smooth modulations like the really basic textbook example I explained above. Bach does some crazy stuff on occasion. Beethoven is generally kind of a conservative romantic harmonic wise. Like he was a romantic in melody, style and shape/strucute, but not in harmony. And now I am talking about his latter works.

Do the modulations sound smooth to you?   

So original sheet music will help alot. But why do you need help? You can write down the chord names yourself, assign roman numbers etc, right?

You just need to devolop your own harmonic style. Seems you are already on your way with that. Thats it.

You don't really consider textbook examples. And you don't even consider anything the moment you improvise. That is kind of based on reflexes, muscle memory. Like Ted pointed out in his post, you just practise things the his example and have it ready as a reflex in your hands. Then just play it.

[Derek]

Hi, I wrote it as a 2 voice fugue, there isn't any third voice in it....did I accidentally introduce one and not know that I was? hahahaha.  oh well.

[Derek]

So like, what sort of music DOES use smooth modulations? I don't think I know of any.

[Derek]

I'd like to add, as an experienced-intermediate improviser, that it is possible to improvise outside of simply memorized patterns and so forth. I do practice patterns sometimes, but when I truly IMPROVISE,  my hands come up with all sorts of things I never heard, saw, thought of, or considered ever before. THAT is improvisation. Stravinsky said: "What fascinated me most of all in the work [of composing Petrouchka] was that the different rhythmic episodes were dictated by fingers themselves......Fingers are not to be despised; they are great inspirers and in contact with a musical instrument, often give birth to unconscious ideas which might otherwise never come to life.

[ted]

Agreed, Derek. Patterns such as I described above are used more for vocabulary building and getting the geography and sounds of the keyboard into the unconscious. It's the old question of getting the right balance between conscious and unconscious processes. Really interesting music starts at the magical point where a chaotic (in the mathematical sense) loop starts up between the two states. Too much conscious structure produces accomplished but uninteresting stability and too little leads to randomness and incoherence, which are just as uninteresting.

[BoliverAllmon]

You can only modulate smoothly to a new key that is not too distant. The difference between C major and Ab major are four notes. Important thing for a modulation is chords that are diatonic or native to both keys.

not necessarily, distant keys can be quite smooth.

FI does modulate smoothly. It modulates to B maj in measure 10 by use of C# chord.

Bach always modulates smoothly. I don't have the Pathetique in front of me, but what Beethoven I do know it is always smooth.

boliver

[Bob]

An anthology collection for analysis would have examples.

[Daevren]

not necessarily, distant keys can be quite smooth.

FI does modulate smoothly. It modulates to B maj in measure 10 by use of C# chord.

Those are next to each other.  Actually it moves a little through G#m first, which employs a G# harmonic minor.

These are the chords: C# [...] C# - D#m7b5 - G#7 - C# - A#m7b5 - G#m D#7 - G#m

In C#m its i -  ii - V - i - #vii - v II64 - v
In G#mits  iv - v - i - iv - ii - i64 V - i 

Notice the ii V i's in both keys. For some reason he put a G#m inbetween the ii and the V. Its a second inversion and it kind of functions as a preperation for V7. So because the D# is the most dominant note in this chord it does not sound like a tonic chord in root position. Its not an ending. It actually increases momentum.

Also note this is a romantic piece in the minor scale, and its fast. In romantic music spicy harmony is already common. Minor already sounds a bit exotic and strange, especially with harmonic minor scale used, like in this piece. Since something like the term 'smooth' modulation is relative to its surroundings you can do alot of harmonic changes and modulation in a piece like this.

I most also note this isn't a very good piece, both to my and Chopins taste. Chopin didn't order it to be burned for nothing

[BoliverAllmon]

Those are next to each other.  Actually it moves a little through G#m first, which employs a G# harmonic minor.

These are the chords: C# [...] C# - D#m7b5 - G#7 - C# - A#m7b5 - G#m D#7 - G#m

In C#m its i -  ii - V - i - #vii - v II64 - v
In G#mits  iv - v - i - iv - ii - i64 V - i 

Notice the ii V i's in both keys. For some reason he put a G#m inbetween the ii and the V. Its a second inversion and it kind of functions as a preperation for V7. So because the D# is the most dominant note in this chord it does not sound like a tonic chord in root position. Its not an ending. It actually increases momentum.

Also note this is a romantic piece in the minor scale, and its fast. In romantic music spicy harmony is already common. Minor already sounds a bit exotic and strange, especially with harmonic minor scale used, like in this piece. Since something like the term 'smooth' modulation is relative to its surroundings you can do alot of harmonic changes and modulation in a piece like this.

I most also note this isn't a very good piece, both to my and Chopins taste. Chopin didn't order it to be burned for nothing

yes next to each other is smooth. C# min. has 4 sharps. B maj has 5 sharps. Smooth transition.

The reason why you like going from C to Ab is because you are just imploying modal borrowing. You are temporarily using the VI chord in C min then just using it as a transition into Ab.

another thing you can do is play a C chord with split thirds. that is with both an E and Eb. resolve the third and keep it at Eb then use it as a iii chord in Ab.

here is another one. use a Db as  a N6 chord but instead of resolving like normal use it as  a IV chord in Ab.

use a Ger +6 chord in C (F#AbCEb) which normally goes to G maj, instead make it G dim. or a Eb Maj. chord and go on in Ab.

I can think of more transitions if you like. play around with them. tell me what you think. Have you tried my first suggestion from above?

boliver

[BoliverAllmon]

I forgot this one.

play B dim. move the B to Bb. Now, you have a bVII.

from bVII go to bIII, bVI (which is Aflat but don't stay there), N6 (use this as the pivot chord into Ab) then just use a cadential formula and establish the key. Notice how we created a circle of fifths progression? cool huh?

[Derek]

I've tried some of those changes you listed. So the idea is to go through shared chords and at some point introduce a cadence for the new key, correct?

I think I already do some of these, for example to get from C major to A minor I'd play C, F, then E major dominant seventh, then resolve into A. And the F, E major, A is a VI V I cadence. right?....

There are lots of other ways of doing things like "going through" the dominant seventh of the new key more than once and so forth right?


I'm not really sure I should bother learning too many of these....I change key so often and so abruptly I'm not sure my style is even suited for smooth modulation.


oh yeah, another one I know is say I want to get from D flat to E flat minor. I'd play an F minor chord, then a B flat minor chord, then I'd modify the B flat minor chord into a dominant seventh and then resolve into E flat minor.  That would be like a ii V i type thing I think.   Those aren't very complex modulations though are they.   oh well

Ted: I tried the ascending chromatic cyclic chord thing you listed above. That sounds really wicked! I think I'll try my hand at coming up with some cyclic chord changes like that.

[Azazel]

So how would one go about learning this kind of stuff? There a book y'all recomend for music theory?

[Derek]

The piano itself is a music theory book, I think. Pretty much everything I know about music theory I discovered first by improvising. Its much easier to build intuition for music theory in this way I think.....incredibly verbose discussion of harmonic practice of the Masters in textbooks is very intimidating and can deceive one into thinking that music is an unsurmountable edifice of complexity when in fact most everything, even traditional harmony, is based on a handful of simple, intuitive principles which can only be gained through a lot of experience with playing music.

I own Arnold Schoenburg's Theory of Harmony, Piston's Harmony, Schoenburg's Fundamentals of Musical composition, The Craft of Tonal Counterpoint by Thomas Benjamin, and a couple of other things.

The only use any of them have been to me is to provide labels for what I already found by ear.  I find it impossible to motivate myself to do any of the dry sheet music exercises that these books ask of you.

Speaking of the Fundamentals of Composition book, there's one part where he shows the first few bars of Fantasy Impromptu and saysomething to the effect of: "This technique of making the piano 'roar' was much abused in the 19th century."   As well it should have, in my opinion! I LIVE for making my piano roar!

[BoliverAllmon]

So how would one go about learning this kind of stuff? There a book y'all recomend for music theory?

I recommend college

[ryno200sx]

Not everybody has the circumstances to go to college for music. I really wish there were some arrangement by which I could go to college to study piano. Starting with the piano at 27 and engrossed in a career in IT, it simply cannot happen unless I hit the lottery or something. (ugh-thanks for reminding me).

Seriously though-I think what Azazel is asking for is recommended resources from people that know.

Thanks,
Ryan