Let's Learn Functional Harmony (with Analysis)!

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stevel
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Joined: Thu Jan 06, 2011 2:15 pm

Let's Learn Functional Harmony (with Analysis)!

Post by stevel » Mon Aug 10, 2015 1:30 am

In our previous analyses, we looked at a Carulli Prelude, and a von Call Adagio.

Both were Common Practice Period (CPP hereafter) works and both were analyzed using the terminology and concepts designed for analysis of music from that time and within that style.

Both consisted of a harmonic analysis, and the von Call also introduced a bit of analysis of Form.

While many concepts were introduced, and will be revisited in the future, I wanted to take a little time in this Analysis to expand on something introduced in the previous Analysis: Functional Harmony.

If you look at a piece by Palestrina, or a piece by Syd Barrett (original member of Pink Floyd), you'll find that, just like a piece by Mozart or Carcassi (both CPP composers), they contain Notes and Chords.

But what makes Tonal Music, or "Tonality" in the CPP different from other music that has notes and chords in it, is the WAY in which those notes, and especially the chords, were used.

It uses what we call "Functional Harmony". This is something that did not exist prior to the CPP (though of course, being an evolutionary system, aspects of it appeared gradually over time) and ceased to exist in "forward-thinking" music after the CPP (some composers today still compose in a CPP style though).

Functional Harmony basically is a system where there is a hierarchy of chords. Each chord plays a role or "function" in establishing and maintaining the tonality (and chords may actually play multiple roles). The "goal" of this system is to establish a "Key". This is done by using "Key Defining chords" or "Key Defining Progressions" (Key Defining notes can be used in the absence of harmony as well).

Best to show this with an example.

Let's say I wrote a piece that had only one chord, F Major.

You'd probably say it was "in F Major". You might not be wrong, but a single chord does little to establish "Functional Harmony". The F chord is established as the "Key Center" not by any harmonic progression, but byt virtue of the fact that it's the ONLY chord there!

But let's say I have an F chord and C chord, in alternation.

What's the Key? It could be F, and F is the I chord and C is the V chord. Or it could be C and C is the I chord and F is the IV chord.

And it's probably not Am, even though both of those chords are found in that Key?

The problem is, some chords, and some chord progressions do little to tell us what Key a piece is in. A single chord, maybe, but a piece (in the CPP) with a single harmony throughout is exceptionally rare and not, shall we say, "typical" of Tonality (and of course, hard to teach functional harmony from!!!).

So what composers did was, reserve chords or progressions that did little to reinforce the Key for coloristic purposes, and concentrate on chords or progressions the strongly reinforce the Key for most purposes. Mind you, that doesn't mean that all sections of all CPP music uses Functional Harmony - there are plenty of "non-functional" passages. But these are for times when a composer wants the music to "drift" or be "aimless". But otherwise, they want to smack you over the head with the Key and they choose chord progressions that do that.

Now, think about this: Each Major Key has THREE Major chords, I, IV, and V. That means, any Major chord by itself doesn't really imply the Key well. Even 2 of them, all things being equal, can be inconclusive as the F and C example above.

So what we need are UNIQUE chords, or chord progressions - things that DEFINITIVELY tell us the key (or at least provide enough circumstantial evidence).

V7. That's the Dominant 7 chord. There's only one of those in a Key.
I and IV are Major 7, ii, iii, and vi are minor 7.

So the V7 structure is unique.

A G7 by itself is a really strong indication that it's a V7 chord, so the Key must be C Major or C Minor (becuase it happens in both).

viio7 is also a unique chord - it only happens as "seven" in a Minor Key, and can be used in Major. A Bo7 by itself strongly implies the key music be C or Cm.

But, these are not necessarily conclusive, and of course music has usually more than just a single chord (if it doesn't have a single major or minor chord to be the Tonic, it's not really "Tonal" anyway!).

Suppose you have an F chord followed by a G chord. That HAS to be C Major, becuase C Major is the only Key that has those two chords in order (it could be C minor as well, but still C).

If it's Dm followed by G, again, there's no other Key that progression exists in.

So composers tended to bang you over the head with the Tonic chord, and then use other chords (V7 and viio7) in combination with it, as well as progressions (IV to V, ii to V, etc.) that DEFINE the Key, both aurally and theoretically.

Those chords that do not define the Key by themselves were avoided (when a composer strongly wants to define the Key) or they would be placed into progressions that gave them a little help in defining the Key.

As such, a hierarchy arose. Here it is:

Tonic Function: I in Major, i in minor.

Dominant Function: V or V7, viio or viio7 in Major or Minor, and vii%7 in Major.

Subdominant Function: ii or IV in Major, iio and iv (and IV) in minor.

Mediant Function: iii and vi in Major, III and VI in minor.

If you add a 7th chord to any chord, you merely heighten its function, except for the Tonic chord, which by addition of the 7th becomes a dissonant structure and can no longer be a tonic.

The more "in key" notes you use in your chords, or the more chords from the key you use, the stronger the implication of Key. But, composers didn't always feel the need to "load up" the music with in Key notes. In fact, only a few chords (sometimes just V7 and I) are enough to solidify the Key in many cases. This allows us to use CHROMATIC notes - notes out of the Key in both melodies and chords. These "out of key" notes do not destroy the Tonality unless they "overpower" the "in key" notes and chords. So composers were careful which they used depending on the effect they wanted (and this goes back to the whole bit about using the Leading Tone and V chord in minor to keep it from drifting towards Major).

The general flow of Functional Harmony is like this:

Dominant to Tonic

Subdominant to Dominant to Tonic (Subdominant is also called "Dominant Prep" or "Pre-Dominant" because it "prepares the Dominant").

Mediant to Subdominant to Dominant to Tonic

Now, the chord progression that was considered the "strongest" for progressions in general, but also for Functional progressions, is what we call "Root Movement Up a Fourth". Meaning a chord with a Root of G, would most strongly move to a chord with a Root of C.

G7-C. Play it. You should recognize it. I mentioned before that this is one of the "defining" aspects of Tonal music. This is why.

Within a key, one can find a lot of Root movement up a 4th, but not all of them are equally as strong.

Another movement is "Up a 2nd" such as F to G. This is "strong" but it's also "abrupt" in that all the notes of the chords change. So while useful, it's not the most utilized move.

Finally movement "Down a 3rd" is used, like Em to C. It's not as strong. That doesn't mean it's not used, it's just not as strong. And think about it - Em to C - are we in the key of Em, or C major? Either is possible. G7 to C on the other hand points way more strongly to C. F to G points way more strongly to C.

So they basically used progressions that more strongly implied the Key when that's what they wanted to do.

In this move from Mediant to Subdominant to Dominant to Tonic, chords fall into those classes, but can move within classes, and some other directions too. Here's how it works:

I (or i) the Tonic, can go anywhere. It's like the Queen in chess. It can appear anywhere at any time in any progression. It's the Tonic, you want to hear it a lot!.

V and viio are Dominant class chords. V can move to viio and vice versa, but both of them ultimately lead to I (or i).

IV (iv) and ii (iio) are Pre-Dominant chords. IV can move to V or viio, and ii can move to V or viio. IV also may move to ii, the reverse less common.

iii (III) and vi (VI) are Mediant chords. iii moves to vi or IV. vi moves to IV or ii.

So we have this kind of movement:

iii - vi - ii - V - I - notice that's root movement of a 4th up for each pair. (in C, this would be Em, Am, Dm, G, C - play your lowest 4 strings and you have the roots of these chords in order).

You also have:

iii - vi - IV - viio - I

vi to IV is Down a 3rd, and viio-I is up a 2nd, but that's OK.

So you sort of get this:

iii - vi - ii - V -- I
-----\-IV-viio-/

Where vi can go on to ii or move to IV, and viio moves to I.

But IV can also move to ii, V, or viio, and ii can move to V or viio, and viio can move to V or vice versa.

So the most important "Key Defining" chords aside from the Tonic are the Dominant chords (V and viio) and the most important Key Defining progressions are movement from Pre-Dominant to Dominant (and on to Tonic of course).

iii and vi are not as good at defining the key. That doesn't mean they're not used, it just means they're not used as frequently, or when they are, they're used in combination with the other chords.

By the way, I stopped continually spelling out the minor key versions, but they work the same way.

There a couple of exceptions that we'll discuss in the analysis to follow, but it's important here to understand that most Tonal music uses primarily Functional Harmony, and Functional Harmony is a progressions of chords that strongly imply or define the Key, usually without question when that's what the composer wants. In order to accomplish this, chords and progressions are used in a hierarchical manner moving from Mediant to Subdominant to Dominant to Tonic function chords, with the Mediant being less able to define the key and the other classes increasingly able to define the key as you move through the classes. Chords "progress towards the Tonic goal" by moving from one class to the next (a Mediant Chord moving to a Pre-dominant chord for example) but movement within a class happens as well. The Tonic, can do anything it wants!

So let's move on to a piece that demonstrates these principles. Next post please.
Last edited by stevel on Mon Aug 10, 2015 4:43 am, edited 2 times in total.

stevel
Posts: 558
Joined: Thu Jan 06, 2011 2:15 pm

Re: Let's Learn Functional Harmony (with Analysis)!

Post by stevel » Mon Aug 10, 2015 3:51 am

For this analysis, I'm going to do a perennial favorite, Sor's Exercise 22 from Opus 35 (Segovia #5). This can be found once again in Delcamp D04 on pages 54 and 55.

Key Signature. 2 Sharps. Could be B Minor or D Major.

Begins and ends with a B Minor chord, probably B minor (note, final chord missing 5th).

B minor it is.

Here are the chords:

Bm - Bm - F#7 - Bm/F# (note, I assumed the A# in the F#7 chord as that's what would typically be used).
F# - Bm/F# - Em/G - F#.

So Roman Numerals are:

i - i - V7 - i6/4 - V - i6/4 - iv6 - V

Do you see how it concentrates on i to establish the Bm Tonality?
Do you see how it couples i with V and V7 to establish the Bm tonality? (remember, V7 is a unique Key identifier).
Do you see how, after establishing the Bm tonality through the use of i and V, it then moves from Tonic to Subdominant (the iv6) to Dominant?

While all the V to i moves are functional, the real functional progression is at the end of the line, with the iv to V move. That leaves little doubt as to the Key.

Let's look at the next set of measures, starting at m. 9:

Bm - Bm - F#7 - G - C#o/E - Bm/F# - F# - Bm.

i - i - V7 - VI - iio6 - i6/4 - V - i

Do you see, how, after establishing the tonality of Bm again, we have a Functional Progression in VI - iio - - V - i?

(remember, i can go anywhere).

VI = Mediant, iio = Subdominant, V = Dominant, and i = Tonic.

And the only thing that might look a little strange to you is V to VI. This is actually a common exception. VI (or vi in Major) shares two notes with the Tonic chord so V moving to it seems quite logical, but it's a "surprise" in a way. We call this the "Deceptive Progression", or more properly, when it appears at a cadence, we call it a "Deceptive Cadence", because usually at a cadence, we expect V to move to I, but sometimes the composer "deceives" us and goes to VI instead, but it sounds OK because of the notes VI shares with I (I'm being major/minor neutral with those numerals there).

This is all textbook Functional Harmony. And it SOUNDS like Bm, doesn't it?

The next section is simply i and V or V7 in alternation but notice this is a "focus on the Dominant" in the middle of the piece (hmmm...) with the F# always in the Bass.

Quick Aside: In case you're wondering, even though the lowest note doesn't happen until a beat into each measure a lot of times (or sometimes at the end), we still analyze it as if it were a "block" chord stacked up in arpeggiated textures like this, unless there's some overwhelming reason not to.

Now it gets interesting:

Measure 25:

B7 - Em - A7 - D - C/E - C/E - E#o7 - F#

B7 is not "i". It's a Dominant 7 Structure Chord. When you get one of these that's not on V, and you don't think you've modulated, it's most likely a Secondary Dominant. The V7 of some other key. What is B7 the V7 of? E. So check to see if it goes to some type of E chord. If it does, you're probably right. Since Em is "iv" in the key of Bm, we call the B7 "five seven of four" or, V7/iv.

Is A7 in Bm? Well, it could be, but remember our G7 to C in the Carulli? I analyzed that as V7/III to III.

Look here - D is III. A7 is the V7 of the key of D.

A7 is V7/III.

So our first four chords are:

V7/iv - iv - V7/III - III

Do you see a pattern there? It's basically a V-I in the key of Em, then D, or it's the same progression twice in a row, one step lower. This can sometimes be hard to see with the notes or the letter names for chords, but with Roman Numerals, it becomes more apparent. Let's try a "pop" analysis:

I7 - iv - VII7 - III

It's not even as apparent there, though you may notice I and VII are a step down and iv and III are a step down.

But:

V7/iv - iv - V7/III - III not only highlights the nature of this pattern which we call a Sequence, but it highlights the functional nature of each chord's V-I idea.

Now the next chord is tricky:

C/E - for two measures no less!

Is this in Bm?

Well, it's not a V7, but it could be a V. What Key is C the V chord in? F Major. But there's no F Major in Bm. It's not a "secondary" key, it's like "tertiary" or worse! So it's actually not a Secondary chord at all.

But it's a "special" class of chord.

It's a Major Triad built on the LOWERED 2nd SCALE DEGREE. And it almost always happens in First Inversion. Remember I told you about the inversion symbols and the old names for chords like "sixth" chords.

Well, this is a "sixth" chord.

We call it:

Neapolitan Sixth.

Some analysts call it "bII6". That's a "flat" for being built on a lowered scale degree, a "two" for it being lowered 2, and a superscript "6" for it being in first inversion (or in this special case, a "sixth chord" held over from earlier music).

Kostka and Payne, in their text, "Tonal Harmony" like to name structures like this that are slightly different from "regular" chords in the Key with "name" names instead of Roman Numerals, call this "N6" for Neapolitan Sixth. I'm going to follow their lead here.

The N6, while not "officially" in the Key, is considered to be used "as if it were" and it typically appears in a very special context:

N6, as a type of "II" chord, still operates as a Pre-Dominant Chord, and moves to the Dominant.

Here, it almost does:

C/E - C/E - E#o7 - F#

N6 - N6 - ? - V

See how how it goes there?

So what about this E#o7.

Is it in Bm? No. The only o7 in Bm would be A#o7 (built on the Leading Tone A#).

But Fully Diminished 7th chords (which this E#o7 is) are built on Leading Tone. So you have to ask yourself, what Key is E# the Leading Tone to.

The answer is F#. And F# is in fact in the key of Bm - it's V.

So this IS a Secondary chord - a Secondary Leading Tone chord - it's viio7 of the key of the V chord, or:

viio7/V - and it goes to V as it should.

This "interjection" of the viio7/V between the N6 and V doesn't really "mess up" the move from Pre-Dominant to Dominant. In fact, it's a common enough occurrence and we see this as a "Pre-Dominant" moving to a "Dominant of the Dominant" to the Dominant.

Therefore:

III and it's V7, is Mediant, which moves to the Pre-Dominant (N6) which moves to a "Dominant of the Dominant" which still has a Dominant-Prep function (viio7/V) then finally to the Dominant.

So this is all pretty much Functional Harmony except for the Sequence of V7/iv to iv moving to V7/III to III.

iv to III isn't exactly "functional" - it's not on our chart.

But look at the Roots of those chords - B-E-A-D - up in 4ths! It is still a functional progression overall! And the roots are in the Key!

So this kind of Sequence is still "mostly functional" if not "directly functional".

Let's look at this:

i
V-i
iio-V-i
VI-iio-V-i
III-VI-iio-V-i
bVII-III-VI-iio-V-i
iv-bVII-III-VI-iio-V-i
i-iv-bVII-III-VI-iio-V-i

This is all 7 chords in the key, moving "up in 4ths". The only differnce is "i" is replaced with "I7", or V7/III, and instead of VI and iio we just get N6 (bII) instead.

So it STILL moves from Tonic (ish) to Mediant to Pre-Dominant to Dominant.

BTW, bVII is used in Sequences like this as a non-Dominant (though it's the Secondary Dominant of III), while viio is used as a Dominant chord.

Finally, remember I said not all progression have to be Functional. Our Sequence here is somewhat Functional in following the up a 4th root movement. But, one of the main places non-Functional harmony appears is in Sequences. The "Pattern" of a Sequence over-rides the need for Functional Progression becuase it "makes sense" in it's own way. It doesn't hurt it, like here, it also is close to Functional moves anyway.

So the whole section is:

V7/iv - iv - V7/III - III - N6 - N6 - viio7/V - V

Now, basically the beginning repeats in Measures 33-40.

The only change is in Measure 40, the V chord adds a 7th at the end of the measure, making it a V4/2.

Where did I tell you the 7th should resolve? That's right, DOWN. Usually a V4/2 moves to a i6 (or I6 in Major of course). Does it?

It does!
So measure 41 = i6

What about 42? It's C#-E#-G#-B

Is that in Bm? Nope.

But it is a Dominant 7th Structure (and that's why it's important to know your chord forms!)

So it could be a Secondary Dominant.

If it was, what Key is C#7 the V7 of? F# correct? Is F# in Bm? Yes, it's V.

So this is the Dominant of the V chord, or the Dominant of the Dominant. V7/V (five-seven of five).

Where does it go? It goes to V, as all good V7s/V should :-) But really, if you think it's a V7/V and it DOESN'T go to V, then you might be wrong. But since this one goes to V, it being V7/V is a safe bet.

i6 - V7/V - V - VI - there's that Deceptive Progression again.

ii%6/5 (that's "two half-diminished 7 in first inversion) to i6/4 to V (7 at the end) to i.

So the last 8 measures:

i6 - V7/V - V - VI - ii%6/5 - i6/4 - V - i

Do you see the Mediant (VI) to Pre-Dominant (II) to Dominant (V) to Tonic (i) progression again? Functional Harmony (remember, i can go anywhere).

Here's the whole piece, broken up into 8 measure segments:

i - i - V7 - i6/4 - V - i6/4 - iv6 - V
i - i - V7 - VI - iio6 - i6/4 - V - i

i6/4 - V7 - i6/4 - V - i6/4 - V7 - i6/4 - V
V7/iv - iv - V7/III - III - N6 - N6 - viiio7/V - V

i - i - V7 - i6/4 - V - i6/4 - iv6 - V---4/2
i6 - V7/V - V7 - VI - ii%6/5 - i6/4 - V7 - i


Throughout this entire piece, aside from the middle section where it just focused on the Dominant and toggled between V(7) and i6/4, every 8 measures Sor does the following:

1. Establishes Key Center by using Tonic chord and Dominant chord in the initial measures of each line.
2. Moves to either a IV-V or II-V, or N-V, or a VI-II-V progression that ultimately leads to the Tonic.

He goes a little farther afield in the middle, which as we found in Sonata Form is common to do in a "developmental" manner. This is NOT Sonata Form, but it's still a common procedure to focus on the dominant and use more "episodic" or "developmental" material once you've established the Key pretty well. This piece doesn't modulate, but the focus on V in the middle and Sequence provide some change for us and focus on Keys other than Bm, albeit briefly. It's "relief" and a "change of sound" if not a "change of Key" per se (remember this is an "exercise", not a concert work).

This my friends, is textbook Functional Harmony.

Not all pieces *always* do it this way - this is but one way to do it - but Sor does it masterfully. He even goes so far as to resolve all of his 7ths and leading tones as they should, with one exception (and an idiomatic one - can you find it?).

I have a few other things to discuss but will hit those in the next thread.
Last edited by stevel on Mon Aug 10, 2015 4:49 am, edited 1 time in total.

stevel
Posts: 558
Joined: Thu Jan 06, 2011 2:15 pm

Re: Let's Learn Functional Harmony (with Analysis)!

Post by stevel » Mon Aug 10, 2015 4:37 am

Okay, that was a lot to digest so I'm going to let that all sink in.

So as a diversion, I want to discuss one little note some of you may have gone, "hey, what about that note?"

It's the E# in Measure 7.

It' happens again in the same place later in the piece.

E# is found two other places - in the viio7/V and the V7/V.

In that case, it's the Leading Tone to F#, and part of either the viio7 (E#o7) or V7 (C#7) chords in F#.

E#-G#-B-D, or C#-E-G#-B

But if you try to make a chord out of this, you get E#-G-B.

That might look like a chord at first, because it's every other letter, but E#-G is an interval called a "diminished 3rd", and chords aren't built with those.

Rookie Mistake:

Oh, E#, that's F, so this is G-B-[D]-F - it's a G7 chord.

Wrong.

Composers and Editors spell notes according to their FUNCTION. Since we're dealing with Functional Harmony, composers and editors want the right note that tells you what the function of the chord is! NOtice the E#o7 later in the piece. You might have said "geez, E#o7, why didn't they just make it Fo7 (or Bo7 or Do7 which all sound the same). It's because E# is the Leading Tone to F#, and the note in the Key of Bm is F#. Fo7 leads to Gb. Do7 leads to Eb. Bo7 leads to C.

Now there are some rare and specific exceptions where a chord is spelled one way and acts another, but this ain't one of them.

But here, in Measure 7 we have the E#-G-B structure. What is it?

Important Fact:

Not everything is a chord tone!

We said it last time, but it's worth repeating.

The first melody note is E, and in the next measure, it's F#. The E is a chord tone in m.7 and the F# is in m.8. One interpretation of this note is it's simply a Passing Tone, passing between the E and F#. Wait you say, how's that happen - E and F# are both in the scale already.

That's OK, you can have Chromatic Passing Tones. That's what this is.

Important Fact:

Non-Chord Tones (NCTs) may be Diatonic (belong to the scale) or Chromatic (outside of the Key at hand).

Because this piece contains a Neapolitan Sixth chord, I do want to discuss another chord we often encounter in Keys, that uses chromatic notes, but is so often used, it can be considered "part of the key" in the same way the Neapolitan is (and Secondary chords are not).

Some "chords" in CPP music are not really "chords" at all, but merely most of a chord, with a NCT that could be counted as a chord. Kind of like all of those notes I said could be interpreted two ways in the von Call piece.

In fact, all of our chords originally arose from COUNTERPOINT. Counterpoint is LINEAR. It involves combining music HORIZONTALLY - melodies combined to make harmony. This is how harmony began.

One of the major shifts in musical thought was to interpret sounds that resulted from combining melodic notes as VERTICAL entities - chords! Interestingly, this happens right around the same time the CPP begins!

But, not every note is part of a chord as we've discovered. Sometimes, in this more vertically-oriented music of "chords" we still have melodic tones that don't fit the chord - a NCT.

That's what this E# could be.

But as I said, all of chords actually started as horizontal elements - melodies.

What has happened, throughout the evolutionary process of musical history, is that many elements that originally were MELODIC, later become HARMONIC.

For example, a long time ago, 7ths were NCTs. They were Passing Tones, Neighbor Tones, Pedal Tones, or other types of NCTs we've not yet discussed.

But as time went on, they became accepted as part of the chord proper.

Whether a note is a Chord Tone or not largely depends on the context. Something that's a Passing Tone in one context - if it sounds for a really long time within a chord - might just as well be considered a chord tone. Also, it depends on the time period as well.

Consider this:

G - A - G
E - E - E
C - C -C

If we have a C chord, followed by another C chord in the next measure, and let's say the G melody note is 7 8th notes long, and the A note only appears on the last 8th note of the measure, followed by the G melody note in the 2nd measure, do we call the chord under the A an Am? Is it long enough to be heard as a "stand alone" chord, or is this all just a C Harmony with a little melodic Neighbor on top? Most analysts would say it's only a Chord tone.

But what if the A were 2 beats - or a whole measure? At what point does it become a chord?

So it's largely contextual.

This E# is pretty short, so I'm going to call it a Chromatic Passing Tone (the arpeggiated context lends some credence to this)

But it does afford us a chance to learn another new chord, that's a "Sixth" chord like the Neapolitan.

There is a family of chords called the "Augmented Sixth" chords.

In their usual context (there can be others) they appear on b6 of the scale (that would be G in Bm or B Major, or F in A Major or Am, etc.).

They also contain the interval of an Augmented 6th above, which happens to be #4 of the Key.

In Bm, this would be G and E#. See those notes :-)

b6 is a tendency tone. It wants to move down to scale degree 5. #4 is like the Leading Tone to 5 (E# in this key as already discussed).

The two together - man - lots of "push" to the Dominant scale degree.

So like the Neapolitan, the Augmented Sixth chord family is Pre-Dominant and wants to move to the Dominant.

So first, if we're thinking this might be an Augmented Sixth (+6 hereafter), it should go to V (or a Secondary of V, or the Tonic, which can go anywhere, ultimately moving to V).

Does it?

It does?

Also the b6 (G here) should resolve down (does it?) and the #4 (E#) should resolve up or to the 7th of the V7. Does it?

They do, so this just might be a +6 chord.

You will find the +6 chords in 4 common flavors:

The +6 interval, which contains b6 and #4.

Then three "nationalities" with the interval "filled" in with other notes:

German +6
#4
b3
1
b6

French +6
#4
2
1
b6

Italian +6
#4
1 (doubled in 4 parts)
b6


Now, here's the funky part. The names were made up by some theorist a long time ago. He did it based on sound and prejudices about the countries.

But one way to remember them is "geographically" - if you look at the middle note, it "heads north" as you go from Italy to France to Germany (well, France reaches further south than Germany).

If we put this in letter form, on a C note (which would be b6 in the key of E/Em), we'd have:

Ger+6
A#
G
E
C

Fr+6
A#
F#
E
C

It+6
A#
E E
C

See how the E middle note moves from scale degree 1 in E to 2 to b 3 (E - F# - G)?

This is Bm.

We have G, B, and E#. What scale degrees are they?

b6 - 1 - and #4

So this is an Italian +6 if we want to call this a "chord proper".

It does resolve "like it should" so there's a very good case for calling it that.

I'd say the only real mark against it is that Sor has pretty consistently given us 1 harmony per measure.

That's why I go with the Chromatic Passing Tone analysis (on the other hand, that makes it the only NCT in the piece the two times it appears, which could be evidence the other way).

I don't think it's all that important which you choose - but hey, you learned two things - Chromatic Passing Tone and +6 chords!

cPT is easier though too ;-)

OK, I'm going to do one more post for this one, about the Form of the piece, so we can learn everything we need to know for the next analysis we'll undertake.

Continued...

tom2977
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Re: Let's Learn Functional Harmony (with Analysis)!

Post by tom2977 » Mon Aug 10, 2015 6:00 pm

I'm loving this Steve......putting together systematically things i have come across but not worked through before. Many thanks. You are a great communicator and teacher.

1st Question going back to Carulli in lesson 1: Bar 9 - i don't think you dealt with that at the time but i think you have covered this sort of thing now. i can see it a diminished 7 chord (tone-semitone between every note). My understanding is this would have a dominant function and next chord is iv6 (Dm6). So is it viio7/iv?? (ie C#o7). The leading tone and 7th seem to move correctly. Correct? Would i more correctly label it as viio4/3/iv due to the 2nd inversion?

2nd question.....regarding the augmented sixth and that E# (post just preceding this). To my ear that really pulls you into the next chord....so it does seem to serve a harmonic purpose not just melodic. Would that effect on the ear lend argument to the Augmented 6th rather cPT? I know both are correct but just found the relationship between what you hear and the analysis was interesting.

stevel
Posts: 558
Joined: Thu Jan 06, 2011 2:15 pm

Re: Let's Learn Functional Harmony (with Analysis)!

Post by stevel » Tue Aug 11, 2015 9:17 pm

tom2977 wrote:1st Question going back to Carulli in lesson 1: Bar 9 - i don't think you dealt with that at the time but i think you have covered this sort of thing now. i can see it a diminished 7 chord (tone-semitone between every note). My understanding is this would have a dominant function and next chord is iv6 (Dm6). So is it viio7/iv?? (ie C#o7). The leading tone and 7th seem to move correctly. Correct? Would i more correctly label it as viio4/3/iv due to the 2nd inversion?
100% Correct.

2nd question.....regarding the augmented sixth and that E# (post just preceding this). To my ear that really pulls you into the next chord....so it does seem to serve a harmonic purpose not just melodic. Would that effect on the ear lend argument to the Augmented 6th rather cPT? I know both are correct but just found the relationship between what you hear and the analysis was interesting.
100% Correct! You're getting it :-)

That's right, the ear is an imporant "decision-making tool" when it comes to things that could go one of two ways, or you have the need to justify one choice over another.

Play the melody without any chords. See if you still hear it as implying a harmonic change, rather than it just being a melodic tone. Context plays a huge role in making decisions like this, but it can also depend on what you're trying to point out in an analysis.

In my case, I'm trying to point out that in some cases, either or both analyses are valid, and in this particular case, I'm pointing to a "grey area" example on purpose - I want people to understand that many "chords" are not really "chords" at all and instead consist of NCT(s), and some "chords" evolved from the inclusion of NCTs that do eventually get accepted as a "chord proper". So you see why I left it open-ended!

One caution about ears though - remember we are conditioned - we hear things "chordally" more often today because not only has music evolved from a more linear construct to a more vertical one, but we are taught analaysis "chordally" for the most part and much of the music we play is chordally based.

As a result, we're a little more likely to hear something that - at the time of composition - may have been heard more clearly as a NCT, but we hear today as a chord. That doesn't make the analysis "wrong" per se, but it's like playing a transcription from keyboard or lute on the guitar - we just need to be understand that we may be adapting something to a modern thought process and that investigation into or comparison with the original thought-process might be helpful in revealing elements we may not have previously thought about.

Best,
Steve

stevel
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Re: Let's Learn Functional Harmony (with Analysis)!

Post by stevel » Tue Aug 11, 2015 11:42 pm

Now I want to use this "simple to analyze" Sor Exercise to talk more about Form, and more especially, "levels" of form.

Music is somewhat like literature:

A Novel consists of Chapters.
A Chapter consists of Paragraphs.
A Paragraph consists of Sentences.
A Sentence consists of Phrases.
A Phrase consists of a "thought" (for lack of a better term).

A Symphony consists of Movements.
A Movement consists of Sections.
A Section consists of Periods.
A Period consists of Phrases.
A Phrase consists of a "motive" (considered the smallest idea of musical thought).

Obviously, not all literature is a Novel - a short story is different. Instructions on how to Analyze a Piece of Music are different. Likewise, a Symphony is different than an Orchestral Suite is different from an Etude.

Just like communication (especially in the modern era with Texts!), music doesn't always have all of these elements. Nor is it supposed to. But obviously, you need to know how they work in order to define them when you encounter them.

Remember all that Iambic Pentamater and Rhyme Scheme junk from school? This is kind of like that for music (literature to music is not 1:1 analogy of course, but is often helpful to think in those terms).

Kostka/Payne, in their text "Tonal Harmony" describe a Phrase as "a complete musical thought terminated by a Cadence".

So we can't talk about what a Phrase is without understanding a Cadence.

A Cadence is like Punctuation - a period, comma, question mark, exclamation point, or maybe even semi-colon and colon.

It represents a "pause" or "rest" in the musical action. This doesn't literally mean a rest as in silence, but can. It implies a "hold" or "wait" within a piece (not necessarily a long note or fermata though) where the harmonic action takes a moment, and then springs back into action. Think about it like walking down the street 20 yards then turning around and coming back. You could literally stop, pause for a moment, take in the scenery, and then turn and return, or, you could simply do an about-face. But the act of stopping one direction and moving on another is what a cadence does.

Cadences are primarily Harmonic, though when a Melody comes to a resting point, it's a cadence as well - we just don't have the kind of definitions for melodic cadences we do for harmonic ones. So I'm focusing on the latter for now.

There are Four Types of Cadence:

Authentic
Half
Deceptive
Plagal

Important Note: In Europe or in British English, I've noticed that the terminology differs and people will use terms like "Full Close" for a Perfect Cadence and various other terminology. Before arguing about the terms I'm using here, please investigate how Cadences are defined in various systems so you know what one in one "language" means in another "language" to lessen confusion.

Many students learn a "basic" form of these, but Kostka/Payne define them further because in order to understand not only Phrases, but the Periods and Sections they are part of, one must be able to determine the *relative strength* or the "finality" of a Cadence. I fully agree because it's clear in music that composers definitely chose their cadences with intent. Note, the following discussions go for Major and Minor keys, unless specifically noted.

1. Authentic Cadence.

This is the "strongest" and "most final" sounding cadence. This represented by Dominant to Tonic motion. However, there are varying levels of finality in these motions as follows:

Perfect Authentic Cadence (PAC): V(7) - I with both chords in Root Position and the Tonic Note in the melody on the I chord.

Dominant to Tonic Cadence that doesn't meet the above requirements are categorized as follows:

Root Position Imperfect Authentic Cadence (IAC): Both chords are in Root Position, but the final melody note is not the Tonic note.

Inverted IAC: One or both chords are inverted.

Leading Tone IAC: viio(7) is used instead of V(7).

2. Half Cadence.

This is not a final cadence at all, and "leaves you hanging", and creates an expectation. A phrase that ends with a Half Cadence is like a Sentence that is a Question - "What do you think about this phrase of music?" Aren't you all now dying to find out?

The textbook Half Cadence is "? - V" where "?" could be any chord.

? - V

There is a special type of Half Cadence found in Minor Keys called the Phrygian Half Cadence:

iv6 - V

3. Deceptive Cadence.

A "trick" cadence that sounds like it's going to be a V-I, but "deceives" you and instead goes to VI instead. Because VI shares two notes with I in their respective Keys, this "make sense", but you realize something's wrong.

It too is an inclusive cadence, but almost always appears before a true Authentic Cadence not long after.

V-VI

4. Plagal Cadence.

The Plagal Cadence is familiar to most as the "Amen" Cadence. This is

IV-I

Plagal Cadences are often "tagged on" after the main Authentic Cadence.

Any cadence that doesn't follow these patterns are usually fit in depending on what they do and how they work. For example, V-IV would be considered Deceptive, and "? to X" where X is not V or I would be considered a Half Cadence. Let's worry about the "textbook" ones first and we can hit the others later.

Let's now look at the Sor and try to identify some Cadences, and thus the Phrases, and ultimately, any Periods, Sections, etc.

You should be aware that Phrases can be of varying lengths, but are also very often 4 or 8 measures long so it's often easiest to start there and see that fits.

Let's look at the first 8 measures (see, there was a reason I laid them out that way in the previous post!)

i - i - V7 - i6/4 - V - i6/4 - iv6 - V

Now you might say, hey Steve, I see a V7-i6/4 move in measures 3 and 4, is that an Inverted IAC.

No.

Something you need to know to help you with this: 6/4 chords - second inversion triads, were "special" in CPP music. They were considered "unstable" sonorities and thus could not be a "Tonic". In fact, this goes back to the NCT versus "chord proper" issue raised earlier in this thread. Despite the way we're taught, 6/4 chords are not really chords at all, and more the result of voice leading. We don't necessarily treat them that way when we analyzed them (though there are some instances we'll learn about where you do) but one needs to know that 6/4 chords just don't appear willy-nilly. They are reserved for specific purposes, and being a "Stable Tonic" is not one of them.

I think if you play this through, even though you might feel there could be a possible cadence at m. 4, the 6/4 chord should tell you it's not at rest and there's a need to go on (but it's not a Half Cadence as that would ordinarily be V). Play on through the first 8 bars. Hopefully you'll feel it "coming to rest" on the V chord. Firstly, notice that the arpeggio pattern changes here, and the melody note is all 3 beats long - there's no additional note here on beat 3 like there has been. So the melody "stops" and the arp changes - both significant evidence something is happpening. In this case, it's a cadence.

But what type?

It's a Half Cadence.

And this is, specifically iv6 - V in minor, thus a Phrygian Half Cadence (which carries no more importance than the specific name). BTW, this is more evidence on the side of calling the E# a cPT, because iv6-V is a familiar Phrygian Half Cadence, but iv6 - It+6 - V is just a plain old Half Cadence. That's OK too, but less common overall.

1 - 8 HC

Now, by Kostka/Payne's definition, this is a Phrase. A musical "sentence" terminated by a cadence.

There's a special name for this type of Phrase though. It's called an Antecedent Phrase.

This implies that it will be followed by something else, called a Consequent Phrase.

Phrases may appear individually, in pairs or even in a group of three (called a Phrase Group) but an Antecedent is always paired with a Consequent.

An Antecedent Phrase will always have a weaker cadence than the Consequent Phrase that follows (which is why the distinction between types of Authentic Cadences, because sometimes you'll get a Root Position IAC followed by a PAC and the only difference in finality is the melody note).

So measures 9 to whatever should be another Phrase, should probably be about 8 measures, and should be stronger.

Sure enough, at measure 16, 8 bars later, we have a ROOT POSITION TONIC chord with the Tonic Note in the melody on the downbeat (the fact it goes higher for the arp is ignored here). It's preceded by a Root position V chord. Notice also we have a double bar, so that should tell you something too.

This is a Perfect Authentic Cadence.

1-8, HC, Antecedent Phrase
9-16, PAC, Consequent Phrase

These two Phrases together make up what's called a "Period". Ant. and Con. together are often compared to a "question and answer" form, but it's better to think of it as a "dependent clause" where you have two clauses on either side of a comma (the HC being the comma) to make a full sentence (the PAC being the period).

Periods are called "Parallel" or "Contrasting" based on if the beginning material is similar.

I have often wondered what is the meaning of life?
I have often wondered about things that I can't answer.

That's a Parallel Period.

I have often wondered what is the meaning of life?
Purple Cows dancing on Tulips is the meaning of it all.

That's a Contrasting Period.

Yes, I know, my grammar sucks.

So what are these first 16 Measures, Parallel or Contrasting. They start the same so it's a Parallel Period.

1-8, HC Antecedent Phrase
9-16, PAC Consequent Phrase

1-16, Paralle Period (also, "section 1" since we hit a double bar).

Let's assume for argument's sake he's probably going to continue in 8 measure Phrases.

17-24 HC. Do you see that?

Is it an Antecedent Phrase? Don't know yet.

25-32 HC again.

Since HC are both "weak" and we don't further define a stronger or weaker HC, this is not a Period, nor an Ant/Con pair of Phrases.

It's simply two Phrases, or a "Pair of Phrases.

1-8, HC Ant.
9-16, PAC Con.

1-16, Parallel Period, "section 1".

17-24, HC phrase 1
25-32, HC, phrase 2

17-32, pair of Phrases.

Now, is this a section of its own? If you look back to how I laid them out in the earlier posts, you might notice I hinted at that.

So let's move on.

What happens in m. 33 and onward?

33-40 is pretty much just like 1-8 isn't it? Same HC. Yes it "moves on" with the added 7th at the end of the measure, but it's still a "measure of rest" harmonically and with the long melody note again, just like before.

33-40, HC
41-48, PAC again isn't it.

So this is another Ant/Con pair, and a Period again. It's a Contrasting Period this time, because the two Phrases begin differently.

1-8, HC, Ant
9-16, PAC, Con

1-16, Parallel Period, "section 1"

17-24, HC phrase 1
25-32, HC, phrase 2

17-32, pair of Phrases. possible "section 2"?

33-40, HC Ant
41-48, PAC Con

33-48 Contrasting Period

Now, if the first Period was a "section" we could call this last 16 bars a "section" too.

Usually, when naming sections, we call them "A" "B" and "C" as high as we need to go.

1-16 is an A Section.
17-32 is a B Section (because the material is new and decidedly different).
33-48 is a repeat of the A Section with a variation, which we call "A' " or "A Prime".

If we have additional variations of sections, we'll call them "A Double Prime", and notate it A'', etc.

We don't really care that the first A is Parallel and the 2nd is Contrasting, or that they end differently. It's basically "a repeat of the A section, with a varied ending". So we still call it an "A section" generically, and more specifically, "A Prime" (A').

So here's our formal layout, in 16 measure blocks:

| A | B | A ||

This is called "Ternary Form" because it's 3 sections.

There is, by the way, no Ternary Form that goes A-B-C - that's called "through composed" and not very common.

Also, the repeat bars don't affect anything. Some of you might say, hold on there Steve, with the repeats, it's:

A - B - A - B - A

isn't that a Rondo?

Nice guess, but a Rondo typically alternates its A sections (usually exact or continually varying versions) with continually changing material.

A-B-A'-C-A would be a Rondo

A-B-A-C-A would be a Rondo

A-B-A'-C-A'' would be a Rondo.

So analysts don't put too much emphasis on repeat bars (or written out repeats) in terms of formal analysis, other than mentioning a few specific types (which we don't have here).

A-B-A

A-B-A'

Those are Ternary.

It doesn't mater if each section repeats (A-A-B-B-A-A) or only portions of it repeat (like here) it's still though of as if the repeat bars were simply not present.

So, Sor's Exercise 22, Opus 35, is

Ternary Form

A Section is a Parallel Period, consisting of an Ant/Con pair of Phrases that end with a HC and PAC respectively.
B Section is a pair of Phrases, both ending with a HC.
A Section (or A' if you prefer) is a Contrasting Period, consisting of an Ant/Con pair of Phrases that end with a HC and PAC respectively.

Couple that with the Harmonic Analysis and you have a fairly complete picture of a "textbook" CPP work.

BTW, remember I mentioned that the B section was "developmental" not unlike the middle section of a Sonata Form work. This obviously doesn't meet those requirements but very often, "middle" or "B" sections are developmental, exploratory, episodic, or otherwise are in different keys or focus on a key area (as we have here).

And if you think about this for a moment:

A Section - begins on i, ends on i. "About" the Tonic.

B Section - focuses on V (i chords are 6/4 chords), ends on V, and has other "non Bm" forays. It's really "Dominant" or at least "not about the Tonic".

A Section - "about the Tonic" again.

So this idea of "Tonic-Dominant-Tonic" or "Tonic - Not Tonic - Tonic" or "Set up a Home Key - Visit Other Keys - Come back to Home Key" is a "large scale" version of our basic harmonic motion of I-V-I that establishes Tonality.

IOW, we can see Tonality happening at many levels in CPP music - in chord progressions within a piece, and even with sections in a piece. In fact, if you look at some 3 movement pieces, you'll often find Movement 1 in a Key like C, the 2nd movement in G, and the final movement in C. Tonic-Dominant-Tonic again!

This "nested" T-D-T idea is one of the things that makes Tonal music unique especially in the CPP.

It's not true of all pieces on all levels of course, but it's certainly present in abundance.

Hope you enjoyed this analysis.

I'll post links to all of them so people can navigate back and forth amongst them at a later date.

Steve

tom2977
Posts: 227
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Location: Manchester, UK

Re: Let's Learn Functional Harmony (with Analysis)!

Post by tom2977 » Wed Aug 12, 2015 9:56 pm

Yes, enjoyed it thanks.......any homework yet? ;)

stevel
Posts: 558
Joined: Thu Jan 06, 2011 2:15 pm

Re: Let's Learn Functional Harmony (with Analysis)!

Post by stevel » Sun Aug 14, 2016 10:24 pm

I had a few questions about and references to this series that I'm going to bump them in hopes for more visibility.

Best,
Steve

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