Intervals: Diatonic Expression, Part 2

Introduction:

I don't want to leave the topic of intervals without clarifying a couple concepts. It's worth a reminder that we're still only dealing with a singular voice at this point so distance between voices and chords aren't a concern just yet. We've already covered some guidelines for writing melodies/motifs so for now we'll focus on things like considerations for stepping and leaping and inversions.

Considerations for Stepping and Leaping:

Stepping:

Stepping is always a safe move, but also not particularly interesting over the course of longer pieces of music. Steps can either be M2 or m2, but technically staying on the same note can also be a kind of stepwise "movement" (this will be especially important when we get to the topic of oblique movement in voice leading). The more interesting use of steps is to fill in leaps. These types of steps will later be described as non-chord tones when we get to functional harmony, but for now they'll be generically referred to as steps.

Leaping:

Leaps are a generally a more interesting way of getting around, but come with far more pitfalls and footguns. For one it's easy to reach and exceed the range of a particular voice, and as mentioned in a previous blog many instruments will have significant changes in sound character at different ranges. Not to mention the conflicts that can be created in the mixing process. Like steps, the over use of leaps like 3rds can quickly become boring so it is necessary to mix up what leaps are used just as it's necessary to not constantly step around. We'll dig through some specifics.

Thirds:

Thirds are generally safe, but can be easily overused with it being easy to create music that is too "thirdy". Unless you're going for a very specific effect it's usually better to avoid more than 2-3 leaps of a third in the same direction. It will become more common when we get to part writing harmonies, but for now in a singular melodic voice it's better to keep a firm constraint on their use.

Fourths and Fifths:

Jumping to and from fourths/fifths can either help reinforce the root of the mode, or can even be a way to steer towards a new root. After this size of a leap it's usually best practice to have some stepwise movement in the other direction, or a descending third. You can also reach this interval indirectly via 4 steps of a second or 2 leaps of a third. For now leaps of this size and larger will be used sparingly as they are generally more used in bass writing which will be explored in detail later.

Sixths and Sevenths:

These are far more dramatic leaps, and in very few instances will they be used for melodic/motif purposes. Two occasions when they are used is to either shift into a lower part of the voices range when nearing the upper/lower limit or to provide a dramatic start/end to a phrase. Beyond those two cases I suggest avoiding their use until we get into topics of harmony.

Octaves:

While these are the largest interval used so far they can almost be treated as unisons, but with less frequent use. I wouldn't suggest doing octaves leaps too often, but they are easy ways to shift register or to simply keep the same note and relationships while shifting pitch.

Inversions:

Inversions are a topic of great confusion in music theory classrooms. Not because they're especially complicated, but because they're not particularly intuitive. A simple way to conceptualize inversions is to first think of an octave. In this case let's go with A4 down to A3. Now starting at A4 leap down a P4 which puts us at E4, and now if we consider the interval between E4 and A3 we'll see that it's a P5. We have the same note (A) at different pitches (A4 and A3) at two different intervals (P4 and P5) from the same root note/pitch(E4). Let's make some observations about what we have so far.

1) If we look at the interval values (4 and 5) we see that we can add them to get 9. This is, in part, why inversions are not intuitive because the math we use to check them doesn't add or subtract to a value we would associate with an octave which was our starting interval.

2) We now have a practical situation where our root can be both below and above the note we're moving to. This means our root acts as a kind of zero or pivot point

Let's now invert our inversion process starting with a root note. Again, our root in this case will be the E4, but let's change the leap to a m3 upward to the G4. Based on our previous observation we know that the inversion of this leap will be a 6th, but unlike the Perfect intervals we also see a change in quality. Leaping down to the G3 from E4 gives us an interval of a M6. With that we can add to our observations.

3) Inversions also invert the quality of major and minor. Thus, major intervals going in one direction will be minor intervals going in the other. In our case the m3 from E4 to G4 is also a M6 going from E4 to G3. This same feature is also true of other major/minor inversions

Thus;

m2↨ = M7↨

M2↨ = m7↨

m3↨ = M6↨

M3↨ = m6↨

P4↨ = P5↨

Tritone is similar to P4/5

Conclusion:

In most of your writing at this point it's generally better to stick to seconds and thirds with some leaps of a P4/5, and occasionally usage of sixths and sevenths for dramatic leaps or practical leaps to a different register. We've also seen how intervals relate as inversions of each other.