(Note: this is a level IV topic that assumes familiarity with scale degree triads and their functions.)

The dominant/tonic relationship has been called the single most defining concept in Western music. A cadential dominant followed by a tonic cements one's perception of the tonality of a passage in a way that few other cadential formulas can. Since the dominant/tonic relationship is based on one of the simplest of pitch frequency ratios (2:3), the affinity of the dominant for the tonic is straightforward and usually fairly predictable. Additionally, the almost irresistable inclination of the leading tone (the the third of the dominant chord) to rise to the tonic creates a sort of double-whammy of predictable behavior of the dominant.

In the extension of tonal harmonies, this predictability of the the dominant/tonic relationship became a useful tool for adding harmonic interest. Whereas diatonic harmonies rely strictly on the pitches available in the scale corresponding to the tonic, it was found very early on that additional, non-diatonic pitches could be used to imply a temporary dominant/tonic relationship without actually leaving the key of the tonic.

Let's start by looking at a simple progression using entirely diatonic harmony:



The V7-I cadence is very strong and clearly establishes the passage as being in F Major. Not only is there a rather predictable motion from dominant to tonic in the bass, the resolution of the tritone between the E in the alto and Bb in the tenor to F and A, respectively, further solidifies the cadence.

Now, let's take that same progression, but instead of using an inverted IV chord in the second measure, we'll try something a little different:



As you may be aware, ii7 is a common dominant preparation, and in the above example, that's what we would have had, if only the B had remained the diatonic Bb. Instead, it has been raised a half step to B natural. Look closely at the chord's structure, notice that even though it is in first inversion, it is a dominant seventh chord!

OK, so if it's a dominant seventh chord, does it act[/b] like a dominant seventh chord? Let's look at it a little closer. If it's truly a dominant seventh, the third (B natural) should be a leading tone; this one leads to C, so that part checks out fine. The tritone between the bass and alto resolves in just the manner we would expect in a dominant seventh chord, so that part works as well. So, then yes, this chord appears to be functioning in exactly the same manner as a diatonic dominant V7 chord. And, as it turns out there IS a diatonic dominant V7 that's spelled GBDF, but it only occurs in the key of C.

Well, is it really any surprise then that the chord that follows our mystery chord is a C chord? (Yes, it's a dominant C7, but its root is still C.) The mystery chord functions as a dominant to C. Since this passage is in the key of F, this dominant is not the dominant of the tonic, so we call it a secondary[/b] dominant. It functions as the dominant to a secondary pitch, not the tonic. In the case of the chord in the second example, we would call this a secondary dominant to V (since C is scale degree V in F Major). Thus, we would call this "five of five," and it would be harmonically notated like this:



It is important to note that secondary dominants can be used in anticipation of any[/b] diatonic harmony. Thus, one will encounter secondary dominants of harmonies rooted on every scale degree. In nearly all cases, these secondary dominants will contain at least one non-diatonic note. The exceptions, however are that the secondary dominant to IV in a major key is the same as I, and in a minor key, a bVII is the dominant to III.

The secondary dominant used in this example is a first inversion dominant seventh chord. However, a simple major triad will function just as well, as will a more complex ninth chord. Just as a diminished vii chord performs a dominant function, the concept of secondary dominants can also be extended to include diminished triads and seventh chords built on the leading tone to the following harmony. The dominant function of such chords is, naturally, correlative to the function of normal dominant triads and seventh (and ninth) chords.

Now, if you want to get truly and utterly confused , the possibility also exists to create strings of secondary dominants in preparation for a chord. They can be strung together just like going through the circle of fifths. While doing so is relatively uncommon in 18th and 19th century practice, it is quite common in jazz and jazz-based popular music, where the concept is often referred to as a "slide".

I know that the concept of secondary dominants is a difficult one for most people to grasp at first. Nevertheless, if you haven't been completely thrown off by any of this, try your hand at building the following secondary dominants:



(answers on Friday)

P.S - When deciding on the placement of trees and shrubs, always consider the full mature size of the variety being planted. There's nothing worse than having a tree planted so close to the house that its branches scrape the building when it's windy!

Next week's topic: CADENCES -- Sound off... 1,2... Sound off... V, I?[/b]

lost me.

I still liked your plant tip tho.

I'm going to have to read this several times, think about it, then read it several more times. Hopefully I'll figure it out before Friday. We'll see.

Matt G:
i am confused with your notations. what do you mean by V(6,5)/V, dominant of dominant (as supposed 'secondary dominant')? also, same question to V7/VI, and etc (as you listed above).

I think I understand signa's 2nd question, (V7/VI ), but his first question is one I am also not clear on.

signa, I think the V7/VI (in the Fminor scale) means go to the VIth step of the Fminor scale, then using that note as the "temporary" root, build the V7 of THAT root.
The "minor" part of it throws me a little, though. Not the Fminor scale part, but rather finding the Vth of a minorII. (exercise #2).

In the example Matt gave, it was an Fmajor scale and the chord in question(the secondary chord) was a G7. G is the Vth of C , and C is the Vth of F.

So it looks like the example he explained may be the most symmetrical or elegant or easiest...some quality like that. Then the rat bast*** gives US these odd looking cursed things to worry about all week.

Well, one can play THAT game!
I hacked his web site and heres the answers.
#1. 14.7 tons
#2. Can't be done. No matter HOW fast he drives the last quarter mile the minute is already UP!!
#3. The Righteous Brothers
#4. Error 404, file not found.


Bob

thanks, bob, i will try to absorb it. have to read the post a few times more.

OK, maybe what I wrote is a bit esoteric. (You were warned!) Let's try this in a bit less theoretical sphere and venture into the real world. How about this: based on what little you could grasp of this lesson, see if you can identify all of the secondary dominants in the following passage:



This is from L. v. Beethoven's Sonata #10, Op. 14 No. 2, the beginning of the Andante section.

I just printed off the lesson today. Perfect timing since my group piano class teacher at the college told us we'd be covering secondary dominants in class next Tuesday! Maybe I can be ahead for once!

Ok, here is my input, correct me if i am wrong!

Def. secondary dominant = dominant of another key.

Hamony progression of op.14.2 andante's bar1-17 (regardless of inversion):

1) I V7 I V
2) V II V (V7)
3) I V7 I III7aug
4) I13(A) IV V
5) I V7 I V
6) I II7aug V
7) I I7aug V
8) II7aug II7 V
9) I V7 I I7dim
10) IV I7aug IV
11) IV VIaug II Idim
12) II IIaug V11 V
13) I V7 I V
14) I II V V7
15) I Idim IV9
16) I V7 I
17) V7 I I13 II

So, secondary dominants are:

III7aug = dominant 7th of A (V7/VI?)
IIaug/II7aug = dominant (7th) of G (V/V or V7/V?)
VIaug = dominant of D (V/II?)
Idim/I7dim = dominant of ?? (no idea of this chord, maybe not a secondary dominant at all)

Bob, regarding your confusion about the minor part: just break it down. For V/ii

1. Think of a 2 minor scale. (The ii part.)
2. Think of the 5th degree of that scale. (Half of the V part.)
3. Now think of the major triad built on the note that is that 5th degree. (The other half of the V part.)

For example, V/ii in the key of G.

1. The A minor scale is A B C D E F G#. (2 is A minor in G.)
2. The 5th degree of the A minor scale is E.
3. The E major triad is E G# B.

Or, more succinctly, our secondary dominant is the major traid built on the 5th degree of the key of 2.

Another example: V7/ii in the key of Db.

In this case we're looking for the dominant 7th built on the 5th degree of the key of Eb minor.

1. The Eb minor scale is Eb F Gb Ab Bb Cb D.
2. The 5th degree of the Eb minor scale is Bb.
3. Bb dominant 7th is Bb D F Ab

Are you going to drop one quiz grade at the end of the semester Mr. G? If so, I'm sitting this one out. (Though I almost thought I nearly latched onto an idea here reading the thread last night about what all those hieroglyphics might mean. Is it just me or does this weeks lesson actually build on last week's lesson in a very really complicated way? Maybe I was just dreaming that it did.)

Well, this has been a tough lesson for lots of people, it seems. Not to worry, though, next lesson will be a bit simpler. For those of you who were brave enough to tackle the exercises, here are the "answers". Note that in each case, your answer needn't be identical to this, only the chords should contain the same notes and the bass notes should be the same. I have included the resolution for each of the secondary dominants.

#1:



#2:



#3:



#4:



So, how did you do?

#1 = V7/VI in Fminor:
VI in Fminor scale is Db. V of Db is Ab. Ab7 = Gb, Ab, C, Eb Nailed it so I could delete this part of the post.


#2 = Vmaj/ii in Dmaj.
II in D is E, don't know what to do about the minor, so forget it. V of E is BMaj, B, D#, F#
Yea, I win! (but don't "get the "minor" thing for sure yet)


#3 vii/iv in Bminor;
IV in Bminor is E, forget the minor thing
vii of E is D#minor (say Eb minor ) = Eb, Gb, Bb = D#, F#, A# which still misses your answer by the A# A natural problem.


#4, vii7/Vmaj in EbMajor ... next easiest I thought due to Major Scale.
V of Eb is Bb. vii of Bb is A, ok Aminor7 = G, A, Cnatural (the minor part), E
Your answer includes the Flat of E which I would normally call a A-halfDiminished 7th instead of (an) A minor 7th.


#1: got it right, understood it too.

#2: got it right, but don't know why minor didn't throw me

#3: wrong, still confused about the minor

#4: I thought I had it right. Is you is or is you ain't sure about your proof-reader, Matt?

Bob, your confusion (or consternation) regarding the "vii" notation is understandable. Let me see if I can explain it to make it somewhat clearer. In any scale, major or minor, the triad built on the leading tone is always diminished. As there is no other diatonic form of the triad, it is usually presumed unnecessary to notate it as such. In those cases where the 7th is not diatonic, it is notated as such (e.g., vii°7 for a "fully" diminished seventh chord), whereas if the seventh is the diatonic minor seventh (forming a "half" diminished chord), no additional notation is usually given.

I hope that helps clear things up. It should be noted, however, that there is no real standard, correct harmonic notation to which everyone adheres, and other notational practices may vary considerably from those I learned. Accept my apologies for any deviation from the perceived norm of others.

Hey Matt G.,

Thanks for the info about vii. (viz. it usually meaning viidim.) I didn't know that either.

I've got a couple of questions.

Wouldn't vii/iv be called a secondary leading tone?

Also, would iii/vi in A be ACE, or would it be A# C# F? (I'm trying to test whether or not my generalization for how to construct secondary dominants (or other secondary chords) is correct.) Or is it nonsensical to use "secondary notation" for a chord like this? Is the idea restricted to use with certain chords?

Ack! Nested parens.