Let's Analyze a Theme and Variations

Analyses of individual works for Classical Guitar and general discussions on analysis. Normal forum copyright rules apply.
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Let's Analyze a Theme and Variations

Post by stevel » Mon Oct 12, 2015 4:26 pm

My previous analyses can be found here:





For this analysis, I've chose a piece with a LOT of non-chord tones - some of which have been discussed at length in the analyses above, but some of which are new to us, common, and necessary to understand.

The piece is Fernando Sor's Le Folies D'Espagne Variees, et un Menuet Opus 15, found in Delcamp 07, page 58.

The title says "in mi" which is "In E" - but is it E Major or E Minor? Well, had we not had that information we would have, as always, looked at the key signature (knowing of course this is a CPP work) and seen 1 sharp, which means either G Major or E Minor. It's pretty clear it both begins and ends the "Variations" part (i.e. before the Minuet) with an Em chord. Pretty safe to say it's in Em.

The initial measure should be easy - the only thing that might be different from some of our earlier analyses is the "harmonic rhythm" - the rate at which the harmonies change. Previously I picked pieces that changed once per measure, maybe twice. Here we're going to encounter some measures with one chord per beat (3 per measure) or modifications of a chord (like changing inversion of voicing) at the same rate.

So let's start from the top:

m. 1: i - i6 - iv

This should be pretty clear. They are only 3 note chords, but they are complete, meaning there's one instance at least of each chord member, the root, 3rd, and 5th. The chord on beat 2 is E-G-B, but the G is in the bass, making it first inversion, or i6. Clear? Good.

Now, m.2. What the heck?

B-F#-E (from bottom to top).

Well, that's, er, I dunno.

We could try to stack up 3rds:


a-ha! It's a B 11 missing the 3rd, 7th, and 9th. No, wait, if a 9th chord or larger is missing the 7th, it's called an "add X", so this is a Badd11.

Or, if I want to be specific, it's a Badd11(no 3rd, no 9).

Ok, moving on.

"Wait wait wait wait Steve, why are you over complicating things, it's clearly a Bsus4".

Oh, so you know about "sus" chords. Good. Ok, you're right, it's a Bsus4.

Moving on.

"Wait...all you've done is given this chord a name, and not told us anything about where that name comes from or what it means".

That's right. And that's the problem with "naming chords". Simply slapping a label on a set of simultaneously-sounding notes doesn't tell us anything about it. It tells us nothing about how it's used in the style, it's evolutionary origins, and so on. That's only good if the name itself carries some particular connotation (which is why I pointed out in one of the previous analyses why authors like Kostka and Payne give "name" names to certain chords).

This unfortunately is the way many people are taught to "analyze" music. And while it may be a perfectly valid method of analysis for some styles, it's not for this style. The composers of this era didn't think that way. They were at a crossroads. Music before the CPP was primarily HORIZONTAL - melody-driven. Harmonies at first were merely results of melodies being combined. As time went on, a shift in the style occurred where composers became more and more concerned with the VERTICAL aspect of music (harmony). We now, maybe unfortunately, live in an age where music is being harmonically-driven. In fact, you'll find posts on the internet every day like "how do I write a melody to this chord progression". I blame Jazz :-) But seriously, that kind of thinking is totally different from the way CPP music was constructed.

While it varied within the style, some forms (such as a fugue) being more melodically driven, and some forms being more harmonically driven (a chorale - though it's still wrong in most cases to conceptualize that as being *purely* harmonically driven as most people are taught), much music of the CPP is written rather evenly - with as much emphasis on the horizontal as the vertical.

In fact, I hope I maybe pointed that out in some of the previous analyses: remember that first Prelude that is basically an arpeggio study? What about the Sor Study in Bm? Those are essentially "chord after chord after chord" type pieces. But it should be clearer in the Sor that there is a melodic component, even if it's just one of the notes of the harmony.

Still, while on the surface, these pieces appear to be largely "chord progressions with an arpeggio pattern", they are much, much more. They are steeped in a tradition of melodic motion - voice-leading. And harmony itself evolved from voice-leading - the horizontal created the vertical.

And even when a piece appears to be largely vertically-based (in the CPP), it may still contain MANY horizontal elements.

And analysts felt it was important to point out (and understand) these horizontal elements. These elements do not always or typically play as big a part in styles like Jazz or modern pop, so it's less necessary to discuss them (if at all). Likewise, the harmonic elements do not always or typically play as big a role in pre-CPP styles like Renaissance Polyphony, or earlier modal music (or Gregorian Chant, for which there is no harmony at all!).

So what makes CPP music interesting is that it represents a transition from melodic-based thinking to harmonic-based thinking. For some, that duality represents the pinnacle of musical achievement, but it's also interesting to see it as a "stop along the way" as part of a larger evolutionary process moving from horizontal to vertical emphasis...and what's next?

So we just don't look at a collection of notes and call it a chord all the time. In fact, coming up with names just to fit the collection of notes is counter to what we're doing. If a collection of notes doesn't fit a "standard" CPP harmonic unit (Triad or 7th chord basically), then something else is going on. And we want to find out what that is...

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Re: Let's Analyze a Theme and Variations

Post by stevel » Mon Oct 12, 2015 5:20 pm

So what is this thing?

We've already discussed Non-Chord Tones.

And the point of that long diatribe in the previous post is, I want you to understand that CPP music a roughly 50/50 vertical and horizontal. Very few works are primarily chordal, or primarily melodic. Sure, some may lean more greatly to one end of that spectrum than the other, but we're talking 25/75, not 5/95 (with rare exceptions which by that point are no longer part of the style really).

If you can't name a chord as a Triad or Seventh Chord (M, m, +, o, Maj7, 7, m7, %7, or o7) then it's got non-chord tones (NCT hereafter). Don't go giving it some "add/sus/omit/9/11/13" name. They simply didn't think of music that way. We might say, they might have been starting to, but they weren't quite there yet (and maybe thankfully...).

m. 2. B-F#-E

Is this any common Triad or 7th chord?

No. We can't make it fit.

That means one (or more possibly) of those notes is not a chord tone.

But one?

It could be B-F#, with the E being a NCT.

It could be E-B, with the F# being a NCT.

Or on a limb, it could be F#-E (F#7) with a B NCT.

Well, gee, that wasn't very helpful was it? Which one is it?

B is in the bass - that *might* be the root. Is it though? What if it's inverted? How do we know?

You could, god forbid, PLAY it, and see (hear) what it sounds like, and that might (and really should!) help you determine the sound and function of the chord. But that may still not tell you about what the NCT is doing there.

So it's really helpful when dealing with NCTs to understand the various types and their origins, because that will in turn help you identify if a note is a NCT or not - because if it behaves like one, it probably is, but if it doesn't, it might be a chord tone!

And one good thing for us is, NCTs generally follow a pretty strict formula - just like how the 7th resolves downward in a 7th chord, each NCT operates in a predictable manner.

So here we go:

There are two "families" of NCTs: Accented and Unaccented.

Simply put, Accented NCTs fall on the beat, or on the strong part of a beat, and Unaccented NCTs fall on the "upbeat" or the weak part of a beat.

Often, analysts don't make a distinction - you may find a Passing Tone that is accented, or not, and many people will only mention that it's a Passing Tone and nothing more.

But, there is a special family of Accented NCTs that get special attention, because they either don't appear unaccented, or, if they do, they don't have anywhere near the "oomph" of their Accented counterpart - and for this reason some theorists use the word "Essential" for those types of dissonances (versus "unessential" for the other ones). Essential doesn't mean "it has to be there" but it means that, since it's there, it becomes a more important aspect of the tension/resolution paradigm than other tones that just kind of "pass by" (unessentially as it were).

Here, play this:

E - D - C (in 8ths)
C - - - C (in quarters, holding the first C)

Assuming you start on beat 1, the D (within an implied C Harmony) will fall on the weak beat - the upbeat or after beat if you like. This is a common, unaccented Passing Tone. It's a NCT that "passes" from one note of the harmony (E) to another note of the chord (C).

Now do this:

E - D - E

Now you have a Neighbor Tone, more specifically, a Lower Neighbor (or Lower Auxiliary). Like the PT above, it falls on the weak beat again.

Both of these are Unaccented, or "unessential dissonances". They don't really affect the harmony too much, nor do they provide much need for internal resolution (especially since the chord doesn't change).

Now play this. Start the E on the up-beat - the pick-up to beat 1:

E - D - C - E

This puts the D, the NCT, on the *accented* part of the beat (downbeat or beat 1).

This gives it a different character. It's "essential" (these as you might have guessed are not really the best choice of terms for this but it's what they used).

But hopefully you hear, it adds - er, - something. It's sort of an indescribably quality, and for us, with 200 jaded years of conditioning to "vertical" music, it may not be as strong, but for them, it provided forward motion. A sense of a need for resolution.

And some types of NCTs provided more of a sense of a need for resolution, basically giving composers an entire spectrum of "intensities" from which to choose.

Now, if you reverse the pattern above, and play C-D-E, you may feel the D even more strongly "leaning into" the E note. If you ever play blues, and play a D# (Eb) into an E over a I7 chord, you'll hear a very common (and still valid today!) sound - this "leaning into" the note. And blues is actually a good example because there are ones that go down too that sound like "sighing" or "moaning" or "wailing" so associated with field hollers and slave songs that led to the blues.

We call these "leaning" notes Appoggiatura (plural is Appoggiture, but I'll be inconsistent in my use because the singular is used in most cases).

Appogiatura are a type of NCT that "leans into" a chord tone (the Italian root word is "to lean"). They are an essential dissonance that create a need for resolution. As a result, they must be accented.

So in our examples above, we have a Passing Tone, and an Accented Passing Tone.

But, the Accented Passing Tone belongs to this whole family of Appoggiatura.

Some authors use the term Appoggiaura (App. henceforth) for ANY accented dissonance that's not one specific type (the Suspension, or Syncope Dissonance). That agrees with the historical use, but, that basically means it means the same thing as Essential...

So some authors have given specific names to certain types of App. One of these historically has always been separate - the Suspension. Others may have come along later, such as the Retardation.

Kostka and Payne reserve the term App. basically for any accented NCT that is not one of the other named types. That's basically the broader historical use - they just gave (or use) more specific names for the other App. that might not be specified as such by earlier authors or people not needed to make a distinction.

I'm going to follow their lead though.

Unaccented (unessential) NCT dissonances include the Passing Tone, Neighbor Tone, Anticipation, etc. These happen on the weak beat or weak part of the beat (unaccented).

Accented (essential) NCT dissonances are all basically Appoggiatura, but types such as the Suspension, Retardation, etc. have specific names, while others, Accented Passing Tone, etc. may just be called App. These happen on the strong beat or strong part of the beat (accented metrical position).

So let's look at some specific types, analytically:

Taking the example above, you can have an accented NCT resolve either by step down, or step up. This was all that was allowed. Additionally, it could be prepared by the following: The same note, a note a step up or down, or a leap.

Simply put, here are the criteria:

If an Accented NCT is approached by the SAME note, then resolves DOWN by step, it is a Suspension.

If an Accented NCT is approached by a step or leap, then resolves down by step, it is an App.

If an Accented NCT is approached by the SAME note, then resolves UP by step, it is a Retardation.

If an Accented NCT is approached by a step or leap, then resolves up by step, it is again, an App.

So you can see, both Suspensions and Retardations are approached by the same note - the difference is in which direction they resolve.

App. are approached by step or leap, and resolve in either direction.

This means, if the following melodic lines are played over a C Bass note, with the first of the 3 notes being on the upbeat and the 2nd of the three notes (*) being an Accented NCT on the down beat, you would have:

F - F* - E = Suspension (resolves down)

D - D* - E = Retardation (resolves up)

G - F* - E = App. (also called an Accented Passing Tone when distinction is important).
A - F* - E = App. (note: A leaps down to F).

E - F* - E = App. (also called an Accented Neighbor Tone etc.).
D - F* - E = App. (note: D leaps up to F).

Any other combination of "preparation" note that's a farther leap (B, or C from above, or C or B from below, etc.) is still just considered an App with no other specific name. However, I have run into some authors who specifically call only those things that are Leapt to, or more specifically, only Leapt to from below App. (thus they call the Acc. PT and Acc. NT. specifically those things).

One further issue with the Suspension and to lesser degree, the Retardation:

A Suspension consists of 3 parts: The Preparation, the Suspension itself, and the Resolution.

The Preparation is a Chord Tone in the current harmony.

The Suspension is a NCT in a *new* harmony.

The Resolution is to a CT either in the same new harmony, or a new harmony altogether. But it resolves to a consonance.

So, armed with this knowledge, let's look at m. 2 of this piece again.
Last edited by stevel on Mon Oct 12, 2015 10:18 pm, edited 1 time in total.

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Re: Let's Analyze a Theme and Variations

Post by stevel » Mon Oct 12, 2015 5:56 pm

OK, we're not quite sure what m. 2 in this piece is.

If it's once of the 9 types of Triads or 7th chords, one of the notes is wrong, meaning it's a NCT.

But now, you should know that, since this chord happens on the beat (and beat 1 no less!) it's in a very strong - accented - metric position.

That means, if there is a NCT (and there probably is), it's one of the Accented/Essential types, which means it could be an App. in general, or more specifically, one of the specific types of named App. ideas, such as the Suspension, Retardation (or if we want to make the distinction, Acc. PT or Acc. NT).

Let's use some logic here.

Some of the App. family, such as Suspensions (and Retardation) have very speficic requirements with their Preparation, dissonance (the Sus or Ret) and their Resolution.

In the case of the Suspension, it has to be prepared by the same note that at first is a CT, then becomes NCT in the new chord, then resolves down.

Since this one is so specific (and I'm going to go ahead and tell you, EXTREMELY common), it's a good idea to see first if that's what it might be, then you can use process of elimination.

So, if this were a Suspension, we'd expect to see a note that is the Suspension (the NCT itself) resolve DOWN BY STEP to a note that is a CT in the same (commonly) or next harmony (not uncommon).

Is there anything happening here like that?

Look at the top note E. It's different isn't it? It's quarter note.

It does what? That's right, it moves DOWN BY STEP to a D#.

If, this were a Suspension, and the E was in fact the Suspended note, it would have to be preceded by an E, it would have to be a NCT and resolve down to some form of D that was a CT.

So, we know it resolves down to a D (D# here).

If the E is a NCT, and the D# is a CT, we're like 66% there. But we haven't been able to figure out which of the notes is or isn't a CT or NCT on beat 1 at this point.

So look at Beat 2. What's going on?

There's a D#. But, more importantly, the B and F# are *still sounding*. They're half notes.

So on Beat 2, the notes sounding are B, F#, and D#.

What is that? Is that anything in our home key of E Minor?

You Betcha! It's the V chord. The holy grail!!!!

So what if this thing on Beat 1 is a V chord, but has a "wrong" note in it - this NCT that moves down into something we now know is a CT making a V chord on Beat 2?

Well, if that E that we think is a Suspension is preceded by an E in the previous harmony, we have all the ingredients for a Susepension:

Preparation: CT E in the old chord
Suspension: NCT E in the new chord
Resolution: CT D# in the same chord (or could be a new chord, as long as it's a CT).

Do we have that? Yes we do - E-E-D# over an Am to ? to B chord (or iv-?-V if you like).

But what do we call that thing on Beat 1 of measure 2?

We call it what it would be if the NCT weren't there. We've done this before with other types of NCTs (simple PT and NT for example).

And this is the major difference between "naming a chord", especially in the Jazz sense of just taking the collective vertical construct and giving it a "chord symbol" versus seeing this - E in this case - not as part of the chord, but as part of a *melodic* or *linear* event that covers horizontal space/time (you didn't know there'd be Physics, did you ;-).

And that's why analysts want to point this out.

Now PLAY these first 5 beats. Doesn't beat 1 of m. 2 *sound like* a "V chord with a wrong note"? A "V chord with a note that needs to resolve"? And when it resolves, doesn't it "sound just right"?

That's your classic Suspension.

But what if it hadn't been a Suspension? What if the NCT E on beat 1 of m. 2 had been preceded by an F#, or a G, or a C from below? Well then it would just be an App. (or if we wanted to make the distinction in the case of the Acc. PT for example, we could do that).

Now, we're not done. Suspensions are actually one of the most common accented NCT ideas. That's why it got its own name instead of just being lumped in with general App. So they also have some more details:

We name a Suspension based on the distance of the suspended note (the NCT) from the BASS, and the interval it resolves to.

So in this case, the E is a 4th above the B (we reduce them all except 9 to less than an octave) and it resolves to a 3rd above the Bass.

So we call this a "four-three suspension". 4-3 Sus.

The common suspensions (over the same bass note) are:




There's one that happens in the bass voice called a 2-3 (notice the numbers get larger in that one). And there's one that's called the "Consonant Suspension" or sometimes just a "Suspension Figure" becuase it looks and acts like a Suspension, but the "suspended note" is actually not a dissonance (though it is a NCT) called the 6-5. An A note suspend into a C chord would be a 6-5.

So we would analyze this as:

i - i6 - iv - V4-3 - V....

Usually with the 4-3 superscript. Some analysts will also put a 4 on the first V and draw a horizontal line connecting it to the 3 at the point of resolution on the paper, with the second V repeated or not:




Something like that. Still others will just put the "V" below, and put 4-3 or 4-3 Sus up in the melody where they would also put in other NCTs.

The important part is that the V chord is called what it would have been without the NCT, and the NCT is identified as a Suspension and which type.

So let's move on to beat 3 of m. 2

It's just an A and a B.

What could that be? At this point you should start using your powers of deduction. What's it LIKELY to be?

Could it be just the Root and 7th of a V7 chord?

Well, given that we've had a Dominant harmony (even with the Sus on beat 1) thus far this measure, and these two notes could certainly "add the 7th" to that Dominant Harmony, that's pretty good evidence.

What would make it pretty solid is if the V4-3 - V7 idea moved on to the Tonic, as every good Dominant typically does.

Does it?

Yes it does.

So it's an incomplete V7 in third inversion (V4/2). We just heard the F# and D# (and the D# has been emphasized as the resolution of the Suspension!) so our aural memory has a hold on those notes and we won't miss them.

"Hey, but wait Steve, you told us the 7th resolves down, but the bass jumps from A way down to E instead of G".

Well, yes, in a perfect world that's true. But this is guitar. We have logistics. Aurally-speaking, the A does resolve down to the G - it's in the middle voice in the next chord (beat 1 of m. 3). See it?

Sor may have chosen to leave out the "bass voice" at this point simply because it may have been too heavy or too plodding and he wanted to lighten the texture, or treat this more as a typically single note pickup, but imply the 7th.

The important thing is, we still *understand* that the 7th is resolving down to the G (our ears kind of assume the shorter distance) rather than the "correct inversions" in this context.

m. 1: i - i6 - iv
m. 2: V - V - V4/2

To be continued...

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Re: Let's Analyze a Theme and Variations

Post by stevel » Mon Oct 12, 2015 8:25 pm

Let's continue:

m. 1: i - i6 - iv
m. 2: V - V - V4/2

(note, many analysts would just put a V at the beginning of measure 2, and nothing on beat 2 (or maybe a dash) and then just put 4/2 under the last chord without repeating the "V" numeral on each beat, of course including the 4-3 either over the melody on or the numerals - just shorthand notation when the chord doesn't change - only inversions (or Suspensions) are marked).

m. 3: i - i6 - iv again.

Now, measure 4.

It kind of looks real similar to m. 2 doesn't it.

Assuming similar things, it could be a D chord (bVII in this key, or V/III) with a 4-3 Suspension - which would be a G note as the NCT (4th above the bass) resolving to the F# (a CT a 3rd above the bass).

But there's a difference here. Do you see it?

The G note is *not prepared*. It doesn't have a consonant G as part of the previous chord.

So this is simply an Appoggiatura. You'd mark the G as "App." and leave it at that (there's no interval nomenclature for anything besides Suspensions).

Note, there are some rare outliers who call things like this "unprepared Suspension" or will use "Suspension Figure" to describe these as well, but IMHO the Preparation is an integral part of the entire Suspension idea (that evolved from the Syncope Dissonance which operates similarly) such that without it, it really needs to be termed something else other than saying it's "like" or "similar to" a Suspension. So I'm happy with calling this an Appoggiatura - and this is the "classic" form - leap up, resolve down.

Now, what about the chord? Is it bVII, or V/III?

Notice, the pattern is similar to m. 2 in that m. 4 has this "similar suspension idea" and then moves to a 4/2 inversion before resolving - as it should, to a III chord.

Is this a Modulation to G? Well, not really. But it's one of the more lengthy forays into a different key area we've encountered.

However, the full 8 bar phrase ends on a Half Cadence and the full Theme ends with a Perfect Authentic Cadence in Em.

This is more a "touching upon" G rather than a full-fledged modulation.

But, if you wanted to show more strongly the "touching upon" aspect, it would be good to use V/III for the D chords. However, if you felt it unnecessary or was "fleeting" at best, the use of bVII would be fine as well. Most people understand that bVII-III in minor is *like* V-I in the relative Major key, so just using those numerals carries enough baggage. But again if you wanted to reinforce it, the "V of" concept helps to point out that the Tonic chord of the relative major (III - G in this case) is getting some added attention here.

And you can always show both interpretations.

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: V/III - - -V4/2 of III

of course including the Sus details in m. 2 and the App. in m. 4.

Now, if you're calling it "something of III" it typically should be going to III. Does it? Yes, it does:

m. 5: III - i - ?

last one may be a bit tricky.

It's A-C#-E, which is an A Major triad. But the normal "4" in a minor key is a minor chord.

We actually have two options, and this is something I've not yet discussed in detail, but "4" in minor has two states, just like "7" does. In minor keys, you can have a Major IV chord. It's purpose is to move up to V (the raised 6th scale degree that turns the normally minor iv chord into a major moves up to the raised 7th scale degree that makes the V chord V and not "v").

Nope. This goes back to a D chord, not on to a B chord.

So Major IV that goes to V is out, and of course it's not the other state (normal minor iv), so it's something else.

Remember again, that a chromatic like this (besides raised 7 in a minor key) is often an indication of a Secondary Dominant.

It is a Major Triad, so it could be a "V" chord from some key. What key is an A Major Triad the Dominant chord in?

That's right, D Major. Which is bVII in this key.

So this is V6/bVII.

That's a good reason to call the D chord in m. 4 a "bVII" instead of a V/III though. But let's come back to that.

"Hold your horses there Steve, you keep saying it goes to a D chord and you just said D-F#-A, but there's no F# - it's D-G-A".

Well, that's certainly not a V is it?

So what else would a "Major IV" typically go to - as V/bVII it should go to bVII. Does it? "Well, you said it did Steve, but there's a wrong note".

A-ha! You should have just caught yourself.

This is the same darn thing again!

Do you see it? Do you see how the G resolves down to the F#. Do you see how the G is a NCT and the F# is?

So it's another Suspension. Or, another App. Right?


Which one?

Or is it?

Well, let's look at where it comes from. The note that precedes the G is an A. So this is not a Suspension because it's not the same note.

"It's an Appoggiatura". Right you are.

Though it's not the "classic" form, with the leap up and step down. No matter, it's still that.

But, if you wanted to be more specific, you could call it what it is - A - G - F#. A CT, F# CT, G NCT. G passes between A and F# and falls on the accented part of the beat.

Accented Passing Tone.

Or simply "App."

Depends on what you're trying to point out, who you studied with, what academic journals you read, and so on.

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: V/III - - -V4/2 of III
m. 5: III - i - V6/bVII
m. 6 V/III - V7/III - oops, wait. V/III should go to III right? But this goes to V6/5 instead (B-D#-F#-A with some NCTs and in first inversion on beat 3 of m. 6).

So wait, maybe it's better to call all of these D chords just plain old bVII, right?

Sure. Sometimes, the context of something earlier doesn't become clear until later on.

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: bVII - bVII4/2
m. 5: III - i - V6/bVII
m. 6 bVII - 7* - V6/5

That's nice and tidy.

*that bVII turns into a root position 7th chord on beat 2 when the C note enters so you could just add the 7 there. I think it's functional enough to call it a 7th but otherwise it would be a non-functional 7th as a PT - harder case to make IMHO.

One other option exists:

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: bVII - V4/2 of III
m. 5: III - i - V6/bVII
m. 6: bVII - 7* - V6/5

See what I did there? I called the "D7" on beat 3 of m. 4 a "V/III" because it does go to III - and we sort of interpret it that way after the fact on hearing it. Otherwise, these D chords are toying with us - playing a dual role of "is it bVII or is it III" - and that's a question we can't answer until it resolves. In one case it does, in the other it doesn't. So by using this different symbology it could help to point out to a reader that you're trying to make that more obvious. That's one of the beauties of this music - we're conditioned to expect things, but that means composers can trick us. And they frequently do. For fun. They love it. Listen to Mozart. He was a real trickster that one.

Also, you could include written text pointing such dualities out. Kind of like an excerpt of prose that can be (and probably was intended to) be taken multiple ways.

m. 7 is nothing exciting:

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: bVII - V4/2 of III
m. 5: III - i - V6/bVII
m. 6: bVII - 7* - V6/5
m. 7: i - VI - iio6

A few things to note about m. 7:

1. The E is missing its 5th. We discussed this previously. No big deal.
2. Notice that the A that is the 7th of the B7 chord on beat 3 of measure 6 does resolve down to the G in this tonic chord. Additionally, notice the Leading Tone (D#) in the Bass moves up to the Tonic note for the root of the i chord. That's a super common thing.
3. Watch out on this chord on beat 3 - a lot of people see the A in the bass and assume "iv" especially coupled with the C note. The Jazzers will go "Oh that's Am6" - not first inversion but A-C-E-F# missing the E (and the 5th is a common omission in classical music, but especially so in Jazz).

But they didn't have these type of 6 chords. This is a TRIAD - F#-A-C in first inversion (A in the bass. It's iio in this key.

And ii6-V7-I in major and iio6-V7-i in minor are the two most common cadences in CPP music.

It's tricky because the root of a II6 chord is scale degree 4 and again our modern conditioned ears tend to accept the thing that seems like an "added 6th" as an added 6th, but really it's the Root of the chord!

So a lot of people think "IV-V-I" because piano lessons and such teach them that. But it's II-V-I (which amazingly, is the understood Jazz progression, so they got that one right ;-)

So iio6 should lead to V.

Does it?

Yes, it do.

But again, with a suspensiony-type-like idea.

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: bVII - V4/2 of III
m. 5: III - i - V6/bVII
m. 6: bVII - 7* - V6/5
m. 7: i - VI - iio6
m. 8: V - -

Is it a Suspension this time? Nope. It's an Accented Passing Tone again (or just "App.").

m. 9 and 10 are just a repeat of earlier material. You can figure that out.

What's this new chord on beat 3 of m. 11?

Well, where does it go? That can help you figure it out.

It goes to a D again (with a suspensiony-type-like figure again).

Could it be a V/bVII. Well we already know that's an A right? But this has a Bb. Is the Bb a NCT?

It is leapt up to and resolves down by step - hey - that's an App. In it's classic form, right?

No. Not right.

What is an App.? It's in a family of ACCENTED dissonances. This Bb is on a weak beat (3) and resolves into the Strong beat (1). That's OPPOSITE of what an App. is.

Well, that makes it just one of those regular unaccented ones, right? Well, sure - is it a PT, NT, Ant.? Not really. Because it's jumped to. And those aren't jumped to.

So if you're going through this much trouble to "prove" it's a NCT, it's probably not! What if it's a CT instead?

C#-E-(G)-Bb does make a chord. C#o7.

That's a "leading tone 7th chord". That comes from the key of D (and Dm - we assume the G is natural because of the prevailing key).

Does it go to a D? Darn tootin.

This is a viio7/VbIII.

\It really works the same as the measure directly above, were A = V/bVII goes to bVII in the next measure, here we have C#o7 = viio7/bVII going to bVII in the next measure.

A is V in the key of D, C#o7 is viio7 in the key of D. Both chords have a Dominant Function (as discussed previously). We call the A a "secondary dominant" chord, and the C#o7 a "secondary leading-tone chord".

That's all.

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: bVII - V4/2 of III
m. 5: III - i - V6/bVII
m. 6: bVII - 7* - V6/5
m. 7: i - VI - iio6
m. 8: V
m. 9: you got it
m. 10: you got it
m. 11: i - i - viio7/bVII
m. 12: bVII - V6/5 of III

notice I'm doing the same thing here as I did in the bold thing in m.4 because it's a similar idea - the bVII "turning into" the V7/III because it goes to III again (notice the resolution of the leading tone of the key of G and the 7th of the D7 chord).

m. 1: i - i6 - iv
m. 2: V - - - 4/2
m. 3: i - i6 - iv
m. 4: bVII - V4/2 of III
m. 5: III - i - V6/bVII
m. 6: bVII - 7* - V6/5
m. 7: i - VI - iio6
m. 8: V (half cadence BTW)
m. 9: you got it
m. 10: you got it
m. 11: i - i - viio7/bVII
m. 12: bVII - V6/5 of III
m. 13: III - you've got the rest - it's a repeat.
m. 14: repeat
m. 15: similar - just notice beat 2 and 3 - full-fledged iio6 to V7. Classic.
m. 16: i (Perfect Authentic Cadence BTW).

Note the resolution of the 7th and the Leading Tone in the B7 chord on beat 3 of measure 15.

I'm going to do one more post to talk about the form of the Theme and the overall form, but one last thing I wanted to point out:

In m. 6 and 14 on beat 3 (the measures are identical) there is another accented PT - the G on top.

Be careful with this. A lot of people are taught that the Augmented Triad "exists" or is used because it appears on scale degree III in minor keys when using the Melodic Minor version of the scale, so they'll often show "III+" as a typical triad.

This is a gross very gross oversimplification. Actually, it's just plain wrong. Composers wrote in KEYS, not scales. They used the KEY of Em and adjusted the IV, V, VI, and VII chords with scale degrees 6 and 7 being raised or lowered. But they did not do the same for I and III (i.e. no EmM7 or G+).

Textbook authors will frequently use III+ in minor as an example of an Augmented Triad - BECAUSE IT'S THE ONLY ONE THEY CAN MAKE in any given key!

But that's led people to believe it's used in this way, and it simply is not.

The job of III in minor is to act like the Tonic of the relative Major temporarily, or to move on to VI functionally speaking.

An Augmented chord can not be a Tonic chord (there's no such thing as "the Key of G Augmented) and this one certainly doesn't move on to VI. It goes to i instead.

And I know I've said "one" can go anywhere, but play this and see what it *sounds* like. It should sound like a chord of DOMINANT function, leading to one of TONIC function.

That G note is merely a passing tone. Sure, a little more attention is drawn to it because of the metric position, but just like the other Suspensions (Which have much more weight!) don't change the underlying harmony, neither does this passing tone - accented or not.

So it's simply an App. (or acc. PT) and the chord is V6/5.

If you see something you think is a "III+", it's probably a V with a NCT instead.

Meaning of course that it's not III+ with the F# and A on the weak beat being the PTs, but the reverse!

The only commonly used Augmented Triads are on the two biggies in the key - the Dominant, and the Tonic. V+ goes to I (Major Tonic only) and I+ goes to IV (and a case could be made that all of those are actually V+/IV).

Next post, on to the form.

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Re: Let's Analyze a Theme and Variations

Post by stevel » Mon Oct 12, 2015 8:51 pm

So let's talk about the Form of this Theme and Variations, excluding the Minuet for now, which is really a separate piece kind of "tagged on".

This is a classic CPP T&V.

It's kind of a "nested" form.

The "Theme" itself is typically a complete little piece. This makes it what is called "Sectional" (or closed) Variations.

You could easily just play the first 16 bars of this piece as a little piece, complete on its own.

Typically, there are a set of variations on the Theme. Each Variation usually follows the form of the Theme, as well as the general Harmonic scheme (with *variations* of course!).

Often, one of the Variations will be in a Parallel Key - normally in E Major we'd expect one variation to be in Em, often a much slower and somber variation - a real mood changer (in this particular piece, the role of the Major key variation in an otherwise minor set if filled by the Minuet tagged on at the end).

The Theme is usually a simple, closed, binary, rounded binary, or ternary type form. A quick glance through most of the T&V from the CPP will show Guitar Composers used a lot of Opera Melodies. These were the "hits" of the day. Usually these were "cacthy" tunes. Songs everyone of that time period were very familiar with.

It was also self-serving - it was a way to sell sheet music! People still do it today (how many Jazz albums of Beatles songs have I seen, and why am I picking on the Jazzers so much today???). So Sor might pick something popular, like, oh, I don't know, the Magic Flute, pull out a very well-known and "hummable" melody, then under the guise of an "homage" and composing their own bits claiming "inspiration", would write a set of variations sure to sell.

Sort of like bands recording covers today.

Anyhoo, all that aside, in terms of form, you wanted your audience to be familiar with the tune.

A quick Google search of this theme shows it to be one of the oldest and most familiar in European music. So Sor (and many others) was banking on that both for the compositional aspect, and the potential income (well, probably).

So obviously, no analysis of this piece would be complete (or any T&V for that matter) without some research into the original theme - sometimes they were folk tunes, sometimes they were opera arias of recent popularity, and sometimes they were original compositions. A great example is Mozart's Variations on "Ah vous dirai-je Maman" known to most of us a Twinkle Twinkle Little Star (or the ABC song).

I always get a chuckle when people chuckle not knowing this piece when it's performed. Mozart takes this simple little tune and just knocks it out of the ball park. Genius. Check it out.

But you see the point - familiar tune - so you can hold on to the tune throughout the variations - though sometimes composers intentional obscure it, or only follow the harmonic scheme, etc. - kind of like jazz improv on a standard. Interestingly, the harmonic progression on this one is kind of a "standard" in CPP terms (based on Ground Bass ideas from centuries before) so it's as much about the "theme" as it is about the Chord Progression in this one!

So this Theme is a Paraellel Period. It's an Antecedent Phrase (ending on a HC in m.8) followed by a Consequent Phrase (ending at m. 16 on a PAC).

Here's your assignment:

1. See if you can analyze as much as you can from each Variation.
2. Pay attention to the way the material is embellished - do aspects of the melody re-appear? What about the harmonic aspects - do they remain consistent? How are they similar, how do they differ?
3. Does one section concentrate on a particular type of NCT? We already saw a lot of App. in the Theme. What about the 1st Variation?
4. There are some NCT types we've not discussed but do as many as you can.
5. Play as much as you can. Even if only slowly. Get the *sound* of these things.


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Re: Let's Analyze a Theme and Variations

Post by tom2977 » Tue Oct 13, 2015 12:07 pm

Steve.......an early thanks for writing this. I am not through it all yet i just wanted you to know that this is being appreciated. These essays of yours are real treasures. :)

Posts: 578
Joined: Thu Jan 06, 2011 2:15 pm

Re: Let's Analyze a Theme and Variations

Post by stevel » Tue Oct 13, 2015 8:52 pm

tom2977 wrote:Steve.......an early thanks for writing this. I am not through it all yet i just wanted you to know that this is being appreciated. These essays of yours are real treasures. :)
Thanks Tom!

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