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What is a secondary dominant chord? What's the theory behind them? How are they used in composition?

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    "Mahna Mahná (duh duh dudúduh)" (E7 A7 D) The E7 here is a secondary dominant chord (dominant of dominant). – leonbloy Jul 15 '14 at 15:12
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    You can have secondary dominants of secondary dominants too. That is, not just V (dominant) of V, but V of V of V. Mr. Sandman does this to an extreme: the chord progression (after the bum bum introduction) is: I, V of V of V of V of V, V of V of V of V, V of V of V, V of V, V, I. It's a little weirder because the Vs are also augmented, but the dominant motion is undeniable. youtube.com/watch?v=VNUgsbKisp8 – Scott Wallace May 12 '18 at 7:05
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    V of V of V of V of V is a bit much to follow. I think it's the same thing as V/III. If it doesn't resolve to the III chord, you can call it "deceptive resolution". So in the key of C, V is G, V/V is D, V/V/V is A, V/V/V/V is E, V/V/V/V/V is B. B7 in the key of C is V/iii. It's easier and more sensible way to analyze it IMO. – Garrett Mar 5 '19 at 21:52
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In common-practice theory, secondary dominant chords are chromatic harmonies used to approach a non-tonic chord with greater urgency. Let's use C major for examples:

I might want to approach the V chord (G) with a secondary dominant to give greater direction or "color" to the approach. I construct the secondary dominant by going to the V chord of the V chord. In other words, I briefly pretend I'm in G Major, and borrow its V, which is a D major chord. The standard Roman numeral notation is V/V, and the chord is chromatic to the original key of C major due to the third (F#). Just as often, I might borrow the V7 from the target chord's key, and this would be labeled V7/V and would be a D dominant 7th chord. Generally only major or minor non-tonic diatonic chords are used as targets, but obviously one could extend this to other qualities and to chromatic chords.

In some cases, particularly V/IV, the secondary dominant would not be chromatic. In C major, the target chord IV would be F Major, and its key's dominant would be C major, which isn't chromatic to the original key. In such cases, composers will almost always use the V7/IV instead, which in C major would have the chromatic note Bb.

The concept is easily extended to vii° chords, since they also have dominant function. In C major vii°/V would be F#dim for example. Most theorists distinguish between the two by calling secondary vii° chords secondary leading tone chords instead of secondary dominants, but the concept is precisely the same.

In all cases, their purpose is to highlight the target chord, and create a sharper resolution to it.

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    Really interesting answer, but what do you mean by chromatic/not chromatic here? – JonnyRaa Nov 13 '15 at 12:23
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    @JonnyLeeds I'm using the standard meaning: chromatic notes are notes that aren't in the key. It's the opposite of a diatonic note which is a note that is in the key. A chromatic chord is any chord that contains at least one chromatic note. – Pat Muchmore Nov 13 '15 at 12:36
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    Concise & clear, Thank you! "viio" was the only challenge for me, I guess that means that 'o' is means '0' or diminished chord? – inger Sep 27 '16 at 7:43
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    @inger Yes, the "o" is a degree symbol which would ideally be a superscript after the "vii" and it means "diminished." – Pat Muchmore Sep 27 '16 at 9:27
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As the other answers have said, a secondary dominant is a 7th chord that resolves to a chord other than the tonic. The classic example is a D7 chord in the key of C: the D7 resolves to G, which itself resolves to C.

Dominants create tension

To understand the theory and practice behind secondary dominants, you have to understand that all dominant chords serve a functional purpose, namely to drive the harmony forward by creating tension. That tension demands release and resolution, and so dominant chords provide the music with momentum and forward drive.

Sustaining tension is a tricky business. Obviously, music with no tension (and subsequent release) is dull and lacks momentum. But you can't just play the same V chord over and over hoping to draw out the tension as long as possible, because eventually the excitement dissipates and the listener is left with an unsatisfied, unresolved feeling.

So secondary dominants are used to extend the harmonic drive. They create some tension and offer the composer the opportunity to resolve it, but because they resolve to a non-tonic chord, the resolution itself creates new tension that can then be itself resolved later.

Example

Suppose (again) you're in the key of C. You could write a progression that goes something like C-C-G7-G7-C. The first two chords establish a key center (C), the second two chords establish tension relative to that key center, and the final chord resolves that tension.

Now consider this progression: C-C-D7-D7-G7-G7-C. The same basic principle applies: establish a key center, create tension, resolve it—but now the portion of the music that creates tension is twice as long. Playing C-C-G7-G7-G7-G7-C is just as long, but not really effective (try it!), but using the secondary dominant allows the tension to extend without losing its power.

And you can keep this idea going: C-C-A7-A7-D7-D7-G7-G7-C. Now the harmonic tension is three times as long as in the original chord progression, but by using secondary dominants, it manages to sustain interest without dissipating. This is an extremely popular chord progression; in the key of Bb, it goes Bb-Bb-G7-G7-C7-C7-F7-F7-Bb, which you may recognize as the progression behind "I Got Rhythm" and countless other tunes.

And that's the idea. Dominants create tension and make the listener anticipate the coming resolution. Secondary dominants allow the composer to extend that tension, thus raising the emotional stakes of the music.

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Theory

Secondary Dominants are chords that are the Dominant (V) chord of a certain key other than the Tonic (I) key.

For example, let the current key be C Major. An F Major chord is the Subdominant (IV) of the current key (C Major). How about a C Dominant 7th chord? That is not in the current key, but you know it's the Dominant 7th (V7) of F Major, and F Major is in C Major.

That C Dominant 7th chord is therefore the a Secondary Dominant.

Please note that Secondary Dominants can work in all valid forms (including the Root form and its 2 inversions, and the Dominant 7th form and its 3 inversions).

Why "Secondary Dominant"? It's because it's the Dominant of a key other than the original key (as stated in the first sentence). Please note that if a chord that appears to be secondary chord leads to a key change, that chord is NOT considered a secondary chord.

The Secondary Dominant can be the Dominant of any key other than the Tonic. If the current key is C Major (again), then:

  • The Secondary Dominant of the Supertonic (ii) key, which is d minor, will be A Major
  • The Secondary Dominant of the Mediant (iii) key, which is e minor, will be B Major
  • The Secondary Dominant of the Subdominant (IV) key, which is F Major, will be C Major
  • The Secondary Dominant of the Dominant (V) key, which is G Major, will be D Major
  • The Secondary Dominant of the Submediant (vi) key, which is a minor, will be E Major
  • The Secondary Dominant of the Leading Tone key with the root lowered a half step (♭VII), which is B♭ Major, will be F Major.

Remember that Secondary Dominants can also be used in Dominant 7th form. For the 3rd condition (Secondary Dominant of Subdominant), the C Major chord can be C Dominant 7th (and in this case, should be).

How are they used in composition?

Secondary Dominants add harmonic color to the music.

Please note that each Secondary Dominant usually is followed by the Tonic (I) chord of the Secondary Dominant's key. If the Secondary Dominant chord is F Dominant 7th, and the current key is F Major, then the Tonic of the chord is B♭, so the following chord should be a B♭ chord.

Let's do an exercise!

Given that the current key is B Major, and there is an A# Major chord, what chord will most likely follow that A# Major chord?

Well A# Major is clearly not in B Major, and we can see that it's the Dominant key of D# Major and d# minor, and we can see that d# minor is in B Major (the current key), so the d# minor chord will most likely follow that chord.

Notation

Since Secondary Dominants are the Dominant of a certain key, Secondary Dominants are written as V/?, where ? is a Roman Numeral such that the Secondary Dominant is the Dominant of the ? of the original key.

For example, V/V means that the Secondary Dominant is the Dominant of the Dominant of the original key (we'll use C Major again; it's easy to work with). That translates to the Dominant of the Dominant of C Major. The Dominant of C Major is G Major, so V/V translates to the Dominant of G Major, which is D Major.

Let's do another one, where the current key is D Major this time. V/ii of D Major means that the Secondary Dominant is the Dominant of the Supertonic (ii) of D Major, which is the Dominant of e minor, which is B Major. Get it?

In real notation, you don't need to go "V/IV of E Major". Instead, you only need to go "V/IV", because the key is already given in the music score.

Let's do an exercise!

What is the V/VI of a minor?

Well the VI of a minor is F Major, and the Dominant of that is C Major, so the V/VI of a minor is C Major.

Conclusion

That's it! I hope you learned what Secondary Dominants are! Feel free to comment if you have any questions or comments (duh)!

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    A good, thorough answer. When writing for example 'a minor' I find 'A minor' easier to read.Could come across as 'any old minor'! Still like II7 rather than V/V7 (or is it V7/V?) to represent say D7 in key C.There's no difference in the meaning, it's less to read, and therefore is better.I've asked this before - lets take A7 in C. That then becomes V/V/V. What's the point ? VI7 works, doesn't it ? – Tim Jul 15 '14 at 20:08
  • For the minor part, it's more proper to write it in lowercase, but good point. For your V/V/V question, think about if A7 will ever appear in C. If it does, it will usually lead to a key change, and then as said in my answer above, it wouldn't be considered a secondary chord anymore (in this case, maybe not "secondary" anymore, but you get the point). Continued... – user8886 Jul 16 '14 at 0:16
  • For your II7 and VI7 point, please understand that vi7 is A MINOR 7th, not A MAJOR 7th, and ii7 is therefore D minor 7th. For the A7 in C, think about if A7 would work in C. If there was an A7, then it should lead to a key change, and therefore wouldn't be a secondary chord anymore, as stated in the question (maybe not "secondary", but you get the point). If the A7 was put in without a key change, then the A7 would be a vi7#3 (vi7 sharp 3). – user8886 Jul 16 '14 at 0:26
  • Taking a tune like Sweet Georgia Brown, usually in G, starts with E, then A, then D and back to G (maj. or 7ths). Cycle of 4ths.On the E bit, it hasn't changed key, don't even think it has modulated.I see the E and A as secondary dominants, if in a strange way. I understand that lower case represents minor, but if one qualifies it with the word, it's not necessary to put lower case.None of the music I've ever played has used that.A bar of C (c) would be too confusing to read - yes, of course, the context may give a clue as to whether it's supposed to be maj. or min., but caps all round ..... – Tim Jul 16 '14 at 5:06
  • ...with 'm' if necessary is far better to read. You actually used capitals in the last comment, which to me at least looks better.The vi7#3 is a bit of a contradiction in terms.It can't be a maj. AND a min. That to me hints of the Hendrix chord, which of course, it isn't. – Tim Jul 16 '14 at 5:07
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A secondary dominant chord is when you turn a minor or major 7th chord into a dominant chord, in order to make another chord the tonic chord. I can't tell you exactly what's the theory behind this, but I can tell you a bit about how they're used, not so much for composition but for arrangements:

Take for example a typical chord progression I-VI-II-V. If we use the C scale, then it's CM7-Am7-Dm7-G7

First of all, any degree can turn into a secondary dominant, except the IV.

Now, in this progression, if we take the third chord, D, and imagine for a moment that it's the tonic, then the previous chord, A, happens to be the V grade of D, so we can turn Am7 into A7. This will give the sensation of resolution that happens with the V-I so commonly used in jazz and other genres, but right in the middle of the progression.

But, D also happens to be the V grade of G (if G were the tonic), so we can turn Dm7 into D7 and have yet another feeling of resolution. So we turn the progression into CM7-A7-D7-G7. This is known as extended secondary dominants.

But, that's not all... any dominant can be accompanied by the II degree that precedes it in a full cadence (II-V-I). Using the same example progression (the original one), if we once again turn Am7 into A7 because it's the V degree of D, then the II degree of D would be Em7, so we can squeeze Em7 before A7 and play those 2 chords in the same timeframe in which A7 was played before.

So if you're playing quarter notes, then CM7 for 1/4, then Em7 for 1/8, A7 for 1/8, Dm7 for 1/4 and finally G7 for 1/4. The same can be done when turning Dm7 into D7: squeeze in the II degree of G which happens to be Am7. So now we have:

CM7, Em7+A7, Am7+D7, G7

There are other things you can do with secondary dominants, such as replacing a dominant with the dominant born from its tritone; this means that instead of playing G7, which is G-B-D-F (the tritone is B-F), you can switch the order of B-F to F-B and that would be the tritone of Db7.

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What is a secondary dominant chord?

There are two parts to the question:

  • what is a dominant chord?
  • secondary to what?

In major/minor tonal system the tonic and dominant chords are the two most important chords which define a key.

A tonic chord can be any major or minor triad. The tonic chord is the "home" chord of the key, the principle chord of stability. The tonic chord is usually the first chord of - or prominent at - the beginning of a composition, and it usually is the final chord for the ending.

A dominant chord is a major chord (triad or various types of dominant sevenths) rooted on the dominant degree of a key, a perfect fifth above the tonic.

It's important to emphasize the dominant chord is always fundamentally a major triad. It can be extended with a minor seventh to make a dominant seventh chord, or extended and altered with other intervals, but the basic dominant chord is a major triad a perfect fifth above the tonic.

The third of the dominant chord is always one half step below the tonic degree of the key. That half step below the tonic is the seventh degree of the key and is called the leading tone. So, with a tonic of C the dominant chord is G major. The third of G major is B natural which is the leading tone of the key, one half step below C.

An important concept in the major/minor system is the dominant chord leads to the tonic chord and that progression defines or confirms what key the music is in. That can be regarded as the primary dominant to tonic relationship in any given key. So, with a tonic of C the primary dominant to tonic relationship is a G major chord to C.

The tonic chord can be either major or minor. So, for example, the G major dominant could lead to either a C major triad in the key of C major, or it could lead to a C minor triad in the key of C minor. It's important to understand that regardless of whether the tonic chord is major or minor the dominant chord is always a major chord.

Now that we have defined what are the primary tonic and dominant chords of a key we can look at secondary chords.

In any major or minor key there are always three diatonic major chords and three diatonic minor chords (diatonic meaning chords of the key signature.)

The dominant chord was defined as a major triad a perfect fifth above the tonic, but we could modify that and say a dominant could be a major triad a perfect fifth above any of the major or minor triads of the key. The dominant above the tonic is the primary dominant, but dominants above any of the other major or minor triads in the key are secondary dominants. Again, being dominant chords, secondary dominants are always fundamentally major triads.

So, in the key of C major we have these major and minor triads:

  • C major, in Roman numerals I the tonic of the key
  • D minor ii
  • E minor iii
  • F major IV
  • G major V (the primary dominant of the key)
  • A minor vi

The odd chord out is B diminished, the leading tone triad.

A secondary dominant can be constructed above any of the five non-tonic major or minor triads. Examples: the secondary dominant of E minor is an B major chord, the secondary dominant of A minor is an E major triad.

While the label secondary is applied to these dominants secondary is not applied to the term tonic. There are no secondary tonics. However, the term tonicize is used to describe this special treatment. The secondary dominant B major tonicizes E minor in the key of C major. The secondary dominant E major tonicizes A minor in the key of C major.

In Roman numerals the chords will be labeled like C: V/iii iii or C: V/vi vi where the secondary dominant is indicated with a slash and is read as "five of three" or "five of six."

Secondary dominants are typically chromatic (using tones that don't belong to the key signature.) Notice that those secondary dominant must be spelled with chromatic sharps and flats: B D# F# and E G# B. The secondary dominant triads of IV in major and VI in minor are I and III respectively. Both chords are diatonic to their key signatures. In those cases the secondary dominant identity is a bit ambiguous so a minor seventh could be added to those chords to bring in a chromatic tone for the characteristic chromatic feel of a secondary dominant.

It's worth while to point out that when all the possible secondary dominant of a key are considered (including those secondary dominant seventh chords V7/IV and V7/VI) all twelve tones of the chromatic scale will be used! So, in any major or minor key the whole 12 chromatic tones are immediately related to the key either directly via the key signature or indirectly via secondary dominants (and the special handling of the dominant chord in minor keys.)

Some people misrepresent "classical" style harmony as purely diatonic. That simply is not true. Chromaticism is the norm in classical style. Even the simplest classical pieces often include some chromatic chord, like the secondary dominant V/V.

How are they used in composition?

A very common way to encounter secondary dominants is within the interior of a composition after the initial tonic has been established. (That isn't always the case, but it's common.) From a structural point of view they offer options for building phrases to elaborate and extend the music between the opening and final close.

Being secondary and tonicizations they occur within an established key rather than constituting an complete change of key (which is called a modulation.) The secondary function is brief. Often it's just the two chord progression from secondary dominant to the target, tonicized chord, then the music returns to the established key.

A very common pattern in classical music is for music in a major key to shift emphasis to other tonal regions in a particular order: the dominant, the modal regions of the supertonic and submediant, and then the subdominant. Those shifts can be achieved by modulation or secondary tonicization. This is not an absolute rule, but a common pattern.

Chroma - the root of chromatic - means "color." So the use of these chromatic secondary dominants is often described as colorful.

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What is a secondary dominant chord?

Let's say we are in C:

V7-I => G7 = dominant7 of C: G7 - C

V7/V => D7 secondary dominant of C: D7 - G (spelling D-seven is five seven of five of C)

etc. following the circle of 5ths and "running" counter clockwise back to C

Example 1 : V7/V (five seven of five)

C => B7-E7-A7-D7-G7-C = I-V7/V7 (B7-E7)-V7/V7 (E7-A7)-V7/V7 (A7-D7)-V7/V7 (D7-G7) V-I (G7-C)

(spelling one (C=tonic=1st degree) five seven (B7) of five seven (E7) of five seven (A7) of five seven (D7) of five -> one

**Example 2: ii-V7/I: (two minor seven - five seven of one)

ii-V7-I = dm-G7-C

ii-V7/V7 = am-D7-G7 (G7=dominant of C, am = ii of G)

etc.

Example 3: secondary dominants of all degrees:

analog all secondary dominants of some other degrees are:

A7-dm = V7/ii

B7-em = V7/iii

C7-F = V7/IV

D7-G = V7/V

E7-am = V7/vi

F#7-bm = V7/vii

What's the theory behind them? How are they used in composition?

They are used to embellish the harmony. "Primitive" folk music like Swiss music, Yodeling, children songs often are based (or arranged) only on a simple cadence: I IV-V-I or I-V,V-I etc) (e.g. Frère Jachues, Sur le pon d'Avignon, London Bridge is falling down, Good night, Ladies)

To embellish the harmony there are short extensions to another tonal center (this can last only one measure!) or we have a repeated phrase with first ending on the dominant (introduced by a secondary dominant) or a form AABA whith an extension in section B to the dominant (also by a secondary dominant e.g. "Au clair de la lune")

My favorite examples are:

The Preludes by Bach: e.g. C-major, D-major and C#-major (s. my newest question ... link will follow)

You're a Lady (Peter Skellen)

but there are hundreds and thousands more as examples of course!

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