Voice Leading: Control Through Counterpoint (Part 1: Consonance vs. Dissonance)
Intro:
So far we have only been working with concepts as they apply to individual voices. This doesn't make for very interesting musical ideas, but it removes a lot of the complications that come with having multiple voices. Starting now we will begin looking at how two voices can interact, and our first topic will be how to deal with consonance vs dissonance. We'll continue to avoid topics such as harmony and scales and we will still be using our established modes.
Consonance vs Dissonance:
This topic is a slippery slope as it kind of depends on who and "when" you're asking. Early music had very clear distinctions between what is consonant and dissonant, and even declared the tritone "forbidden". However, as you move through different eras there's a gradual transition to a more welcoming attitude of dissonance to even being considered "distant consonances" (this is especially true for composers such as Charles Ives and Arnold Schoenberg). While I don't hold a particularly strict attitude about the distinction and usage, for now we will have some limitations on how to use certain intervals which will eventually be loosened as functional harmonic structures are introduced, and concepts become more complex.
Invoking the Overtone Series:
The overtone series is simultaneously a mathematically perfect description while also being somewhat impractical in implementation. As a mathematical formula it allows us to map out the frequencies that make up naturally occurring sounds by dividing a fundamental (root) into smaller and smaller ratios which (1/2, 1/3, 1/4, etc.) which results in a layering of smaller intervals. However, in regards to tuning systems certain adjustments had to be made (tempering) to allow the resulting scales to be useful in a more and more chromatic, musical world. This is can be a hugely complicated topic, but for now we'll only cover it as it relates to the current discussion.
Starting on C2 (two octaves below middle C) the overtone series is represented as the following pattern:
C2 -> C3 -> G3 -> C4 -> E4 -> G4 -> Bb4 -> C5 -> D5 -> E5 -> F#5 -> G5 -> Ab5 -> Bb5 -> B5 -> C6
How does this relate to consonance and dissonance? A basic observation of the pitches gives a good hint as to why certain pitches will sound more 'in tune' than others. For example, the overtone of C occurs 4 times, making up a significant portion of the overtones. There are also 3 instances of Gs. It's no accident that the resulting intervals (P8 and a P5) are two of the most consonant pitches in common practice harmony. The next most common pitch being Es with the resulting interval being a M3. If we then apply our understanding of inversions we get unisons, thirds, fifths, and sixths as our consonances, and seconds and sevenths as our dissonances. Fourths are kind of an exceptional case. While it is considered a perfect interval within a singular voice, it's still often considered dissonant between voices.
For our purposes we will only treat unisons, thirds, fifths, and sixths as consonant
The First Species:
In traditional theory training there's an entire sequence that involves working through the various species (types) of counterpoint, and they're all distinctly useful for practicing specific concepts. We'll do a little bit of that here, but a lot of the practices and rules are outdated so there's no particular reason to take a deep dive into counter point exclusively.
First species counterpoint consists of note against note writing along a pair of staves called a system. This is usually done in a non-metered format with one whole note length per measure, and each exercise can range from 8-16 measures long. In formal training you are provided an already written part called the 'cantus firmus' (fixed voice), and for this introduction I'll provide a series of pitches to use. However, I encourage the reader to spend some time writing their own fixed parts, and then writing their own counter point above/below it. For now the fixed voice will be the lower part, and the upper part will be written no more than an octave above any given fixed note.
This can be done either in a daw or on staff paper. Regardless of the format the goal should be to either play or listen to the final result. Ideally, you should also be able to sing both parts to some degree even if not in the exact range. To prepare the introduction example we're going to setup a short 9 measure phrase starting and ending on C4 (just below the treble clef). If you're working in a daw set your piano roll to whole notes only. The sequence will be as follows.
C4 -> G4 -> F4 -> E4 -> D4 -> C4 -> E4 -> D4 -> C4
The first and last notes will be easy in this case since they will both be C5 or C4. Moving through the rest of the exercise we won't be concerned with things like parallel movement just yet since the focus is on controlling for dissonance. However, save this exercise since it will be the basis for the next example for voice independence. At this point we're only concerned with the intervals between the voices. Below are the possible correct notes that can be used above the given fixed voice, but I would encourage you to try working through this on your own; only checking below when you feel like you've worked through it correctly.
Octave C5 -> G5 -> F5 -> E5 -> D5 -> C5 -> E5 -> D5 -> C5
6th E5 -> D5 -> C5 -> B4 -> A4 -> B4 -> C5
5th D5 -> C5 -> B4 -> A4 -> G4 -> A4 -> B4
3rd B4 -> A4 -> G4 -> F4 -> E4 -> G4 -> A4
Unison C4 -> G4 -> F4 -> E4 -> D4 -> C4 -> E4 -> D4 -> C4
Root C4 -> G4 -> F4 -> E4 -> D4 -> C4 -> E4 -> D4 -> C4
Based on the current rules there's a wide variety of ways to map through this problem as long as you're starting and ending on either C4 or C5. Parallel intervals and other rules aside the results should sound relatively pleasant. This is because we've limited the intervals between notes to only those that sound consonant. Technically, you could do something like only using thirds or 6ths, but that wouldn't particularly interesting over the course of longer pieces of music, and you would quickly find many of your instruments/voices becoming part of a blob of sound rather than having any distinct character.
Conclusion:
We'll get to more complex scenarios not far from now, but until then I encourage you to play around with this provided example and possible solutions. Maybe even play around with having each voice always move in opposite directions. However, don't stress over every small detail just yet, and try to explore how various solutions sound while making some basic observations. You can use the following questions:
Does each interval sound like it needs to move somewhere or does it already sound resolved?
What happens if I switch out one of the consonant intervals for a dissonant one?
Is there a distinct difference between the sound of parallel vs opposing movement between the voices?
Is the part I wrote singable?
What happens if I let the top voice go farther than an octave higher?
The goal here isn't to necessarily write perfect counter point, but to establish a baseline of knowledge about how writing in certain ways effects the outcome. It's still helpful to have a strong understand of what good counter point is even if you don't plan to implement it in your own music because it does give you some perspective at which to make decisions, and understand their consequences.
P.S.
If it hasn’t been obvious already, all the examples I provide will have to be constructed on your own on staff paper or in a daw, and it's up to you, the reader, to not only work through the exercises as provided, but to also play around with them; explore possibilities beyond what is immediately discussed here.
