​Become a better composer!​

Dominant Intervals used as Secondary Dominants​

​A Secondary Dominant is (probably) the most common way to modulate to a new tonal center. It's a basic concept and should be part of every composer's palette. In this article, we not only show how to use Secondary Dominants most efficiently but also go into the application of dominant intervals as substitutions for Secondary Dominants. Sounds intriguing? Well, keep reading and find out more about the secret of dominant intervals and how you can use this knowledge to spice up your compositions as well.

​Secondary Dominants set up the transition to a new tonal center. Typically, they fall on scale-step V (related to the new tonic) and resolve in an authentic cadence (V - I). Secondary Dominants first showed up in the Baroque era, and since then, they became part of the standard repertoire of composers in the Western culture.


​The Application of ​a Secondary Dominant

​When we look at the function of a Secondary Dominant, it's quite apparent that it's "just" an authentic cadence that resolves to the new tonic and, therefore, helps to transition from one tonal center to the next.

In terms of building blocks for composition, Secondary Dominants are easy to find on the Circle of Fifths (or the Root Cycle 5 [RC5], how we call it in Interval Theory). Choose your new tonal center and move into it via the neighboring step in a clockwise direction. We'll illustrate this concept in an example in a minute.

But first, here's a quick general formula that you can apply to modulate from one tonal center to the next using Secondary Dominants. As we follow simple steps based on technique, this process is easy to apply, no matter the musical genre or the arrangement. It's almost like connecting the dots. So, here we go.

  1. ​Know your current tonal center.
  2. Choose the new tonal center that you want to modulate to.
  3. From the new tonic, move up seven chromatic steps (or a perfect Diatonic fifth), and you'll arrive at the Secondary Dominant.
  4. Optional (but very important): Find a good transition from a chord structure on your current tonal center so that you can move elegantly into the Secondary Dominant (via chromatic movement, for example).

​​Following the formula from above, let's pretend we want to modulate from C major to E major. We can gather all the information by looking at the RC5. We just have to move from C major to the Secondary Dominant of E major and use that as a smooth transition into the E tonic.

​Now, here's what this modulation looks like on paper. These few chords are going to serve as source material for a short musical idea.

Because we are all about writing music, let's create a quick sketch that shows the modulation in action. And to give you a bit of a reference, something like the sketch below shouldn't take you longer than around 5-10 minutes.

If it does take significantly more time, then you should re-think your process. That is also part of what we teach at the Academy. Just stick to your first musical ideas combined with technique, and you'll see how quickly you get something going that inspires you to expand.

​That's your basic recipe of modulation - the Diatonic way! You simply have to follow the formula from above, and you'll be able to module FROM any tonal center TO any other tonal center.

​​Remember this concept and use it, but as it is the go-to-method by most composers out there, let's dive into some more advanced techniques based on Interval Theory.


​Exploring the Dominant Intervals

​Talking about dominant structures, the central question that one should ask is: "What makes a chord structure dominant?"

Let's begin our explorations from the Diatonic-point of view. Two scale tones are crucial for any dominant-type structure, and those are scale tones 3 and -7. As we already know from our studies about cadences, dominant structures want to resolve to their related tonic. Now, let's switch our perspective to the intervals and see what happens.


​The Nature of a 6-interval

Scale tones 3 and -7 create a 6-interval, like a tritone as the Diatonic system calls it. And this 6-interval has some properties you should know about. It wants to contract chromatically in opposite directions. Finally, a 6-interval intends to go to a 4-interval; that's your authentic cadence, by the way. Here it is.

The two tones of this interval act as leading tones into the new tonality. That's actually not new as the Diatonic system explains these relations pretty well.

But here comes the first interval trick: Have you ever tried to reflect this movement? So, instead of moving inwards, let's expand it outwards using the same chromatic movement. This opens up a second tonal center that we can modulate to!

​But why does this work and sound good to our ears? Well, look at the final intervals that we just moved into. It's either a 4-interval or an 8, which are complementary intervals. They add up to one octave.

This whole musical connection becomes more apparent when we look closer at the root tones. Remember, that a dominant structure needs to have scale tones 3 and -7? In our case, the E is scale tone 3, and the Bb is -7.

Now, let's split the bass and go from a C root to an F#. According to the Diatonic system, are we still creating a dominant structure? ​- Yes, we do. The function of the scale tones switch, but the actual pitches stay the same, see it?

​​Let's come back to the Secondary Dominants and the RC5. A 6-interval involves two different root tones, which are equal and located six chromatic steps apart from each other. You can always resolve this dominant 6-interval in two different ways! When you think about that, it becomes apparent that a 6-interval lives on two various tonal centers at the same time!​

This musical door is not easy to find from a Diatonic-point of view and, therefore, you want to remember the following concept.

​A 6-interval is dominant, bitonal, and wants to resolve chromatically - either via contraction or expansion.

​Now you'll be able to modulate elegantly to more than one tonal center using a dominant 6-interval. That's a fantastic tool in line-writing with two or more parts. Here's a quick demonstration that shows how musical and versatile this method is in the application.

​This all looks quite complex on paper, but actually, it's simple. Let your lines weave together so that they create a 6-interval, and you've just given yourself the option to either contract or expand chromatically to a new tonal center.

​But we are not done yet as there are more great things to explore.


​The Nature of a 2-interval

​I want to take you even a bit deeper into the fascinating world of Interval Theory. Let's have a look at a 4p-dominant chord structure in its position of the seventh; that is scale tone -7 on top (see the picture below). From this structure, we only use the Outside Interval (OI), which is a 10 (from C to Bb).

This 10-interval or its Position Change, the 2, is not stable and wants to resolve as well. Listen to the resolution and how natural that sounds - again, the movement is mimicking the authentic cadence.

​I want you not to think of any musical key right now, just relate the 2-interval to itself, no matter how you got there. Generally, this 2-interval wants to resolve, and here is how.

​Think of a 2 or 10 as the root and its scale tone -7, no matter the key or the scale. The root wants to move up five chromatic steps and scale tone -7 intends to move down one chromatic step.

Just for fun, let's pick the C Ionian scale and see where we can create such a 2-interval on it. All of these 2s are musical doors that can emulate a Secondary Dominant and, therefore, lead to a new tonal center.

This knowledge is very beneficial as it enables the composer to set up new tonal centers with only two voices. And those voices can be individual lines that weave together to a vertical interval.

Now you start seeing how quickly and elegantly you can move through different tonalities without even worrying about a modulation via harmony! Don't miss adding this knowledge to your bag of tricks, as it will serve you very well.

​Below, we show those opportunities for modulation in more detail. Using 2s and 10s as substitutes for Secondary Dominants also works amazingly well on the guitar. It very quickly brings up this feeling of Baroque music.

​So, whenever you manage to run over a 2-interval, be aware that you can use that musical door to modulate to a new tonal center. It's like you drive on a highway, and those exits pass by. You may take any of those exits at any time. The only point is, you have to spot them first, or you'll miss them.

​You see that we always resolve the 2s to an 8-interval, right? As we know from the 6s already, we can always resolve into a 4-interval as well. This gives us even another option for modulation and results in chromatic movement in both voices!

​Really pay attention to the number of possible modulations from the C major scale! This is remarkable, and we want to give you a clear listing of all the potential tonal centers that you can move into via 2s! There are 8 in total!

  • ​Db​
  • ​D
  • ​E (via two different ways)
  • ​F#/Gb
  • G
  • Ab
  • A
  • B

​ii-V-I Cadences with Interval Substitutions

Next, let's focus on one of the highly overused elements in music, the ii-V-I progression (or cadence). Yes, it's a cliché, and it works, but you should want to separate yourself a little bit from what everybody else is doing. Otherwise, you'll end up sounding like everybody else.

So, let me point out that you SHOULD be using this cadence - but the smart way, and that is by bringing in alternations and variations. We'll step into some combinations of intervals and cadences in a minute, but first, I want to make clear that everybody knows what a standard ii-V-I progression over a C tonic sounds like.

​Next, we want to bring in some substitutions for those vertical structures. You'll see that, although we are using different notes, the overall emotional direction stays the same. That means that your audience won't be confused when they come across these variations. 2s and 6s are great opportunities to add color and set up interesting musical turning points.

​​As you can tell, the reduction in the number of voices involved does not take away anything from the emotional level. In fact, the opposite takes place. The whole line sounds more sophisticated, and besides all of that, the dominant intervals can be used to tell the musical story more interestingly. You see that our starting structure and the endpoint stay the same in both versions of the ii-V-I. So, basically, the plot remains the same, but the second version of the story is way more exciting!

Did you notice how this reduction of voices gives an excellent parameter that lets you control the density of your vertical structures? As a composer, orchestrator, or arranger, you always have to deal with a set number of instruments. Part of your job is to arrange and develop a sketch for any given amount of players.


​Advice for performing Musicians

​Don't underestimate the power of using the OI (the outside interval of any vertical structure) or just a dominant interval as a substitution for a dominant chord. Especially when the tempo is fast, and the chords fly by quickly, you might have a hard time performing on your instrument.

In this case, temporarily switch to the OIs (outside intervals) or just a middle interval to bridge to the next strong chord in the progression, which should sound full again. Nobody will recognize that, and you make your life as a performer a lot easier. In fact, you might want to use fewer voices to create transparency or simply stay out of a particular register.

That is one efficient way to make your performance look easy and effortless! And if you are a guitar player, we even have another goodie for you. Make sure to check out the article about "Under the Bridge" as we go deeper into the application of this technique on the guitar.

  • ​OIs are easier to play than full chords
  • ​OIs still give the most important notes to the listener, that's the top note and the bottom one; the middle notes are very hard to catch anyway
  • ​place your OIs on chords that work as transitions to stronger rest points; those chords on the weaker upbeats are also great candidates for OIs​

Summary

This all is very valuable knowledge for music composition that is not covered in basic Diatonic theory. ​Only by studying this article, you'll walk away with a ton of practical knowledge that will help you sound unique and more advanced than so many other composers out there.

​​Dominant intervals are not only mighty engines that can lead to new tonal centers, but they also give you a more elegant and defined musical vocabulary. Look at them as opportunities that open up regularly, just like the various exits on a freeway. You decide what exit door is best for you.

In conclusion, here's a summary of what we went over in this article.

  • ​Secondary Dominants are the Diatonic way to harmonic modulation​
  • ​Scale tones 3 and -7 create a 6-interval which can bring you to two different resolutions
  • A 2-interval is also dominant and can also work as on OI (outside interval) of a full dominant chord structures​
  • ii-V-I cadences are a great starting point, but bring in variations and alterations later​
  • ​Performing musicians can benefit big-time from using the OIs in their playing​

​Advice

​Whenever you learn something, don't force this technique into your process. Instead, write out your usual progressions first and look for opportunities to bring in dominant intervals later. It's more efficient to connect new concepts to existing knowledge without trying to replace anything that has worked for you in the past.


Frank Herrlinger​

Co-founder and instructor at Music Interval Theory Academy