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Polytonality is when music uses more than one Key simultaneously. It isn't Modulation (where we go from one Key to another), but two or more separate Keys occuring at the exact same time! This might sound bizarre, but it is possible to put together different Keys in a way where they all complement in some way. Here, we will talk about a couple of concepts that can help us to do this effectively...
A Different Way of Thinking
To be a little more specific, Polytonality is a type of "Non-Functional Harmony". In other words, we don't really pay attention to the Function of individual Chords within this context. Instead, we will think of Chord Progressions as creating an overall "mood", rather than expressing a journey from point A to point B like they would in Functional Harmony.
This is similar to the distinction that we made between Tonal and Atonal music (i.e.: Melodies can follow the Tone Tendencies inside of Scales, or they can be written as Tone Rows that eschew them entirely).
Please keep in mind that Functional and Non-Functional Harmony are not necessarily at odds with one another. Just like Tonal and Atonal music, there are different situations in which we might decide to use one or the other. Even if we mostly stick with making pieces which are Tonal and Functional in nature, understanding how to make Atonal and Non-Functional pieces can be useful.
An Easy & Useful Point of Entry
"Polychords" can be made by putting multiple Chords together. For example, when we looked at the Upper Extensions, we saw that we could form giant Chords like the C Major Thirteen. This Chord has all of the Notes within the C Major Scale inside of it:
However, we can also think of this as a combination of two different Chords being played simultaneously. For example:
CM7 [C-E-G-B] + Dm [D-F-A]
If we were at a piano, we could play the Chord on the left with our left hand while also playing the Chord on the right with our right hand.
This is a Polychord! It would be notated similar to how it is played, as two Chords stacked on top of one another. The lower Chord is on the bottom and the higher Chord is on top, with a line separating the two. Do NOT confuse this with a Slash Chord. While there is a line separating both types of Chords, Polychords are always written as one above the other, not side-by-side like a Slash Chord. For example:
Photo Credit: Music Theory for the 21st-Century Classroom by Robert Hutchinson
Oftentimes, pieces which use Non-Functional Harmony do one of these two things:
1. They do not create full Chord Progressions but repeatedly oscillate between two Chords. This is very common within Ambient music. Each Chord is made as interesting as possible on its own (e.g.: using lots of different Intervals gives a "lush" feel, like with the Tone Clusters of Neo-Soul). The Chord selections are usually Harmonically ambiguous as well (e.g.: no strong V → I movements).
2. They make Chord Progressions where every Note within each Chord shifts by a particular Interval. This is called "Planing" (pronounced as "plane-ing", also known as "Harmonic Parallelism").
The musician JJay Berthume gives a very useful framework that he calls "Harmonic Relativity", which demonstrates how Chords can combine to create certain moods and how to connect these Chords together without considering their Function. To give a simple summary of it...
Let's take any two different Chords and pay attention to both their type (i.e.: Major or minor) and the Interval between them (i.e.: the distance between the Root of each Chord when Ascending). JJay calls this a "Chord Relationship" (or "CR" for short). For example:
||C → F♯
||C → E♭
||C → A♭
The "M"'s represent Major Chords, while the red text represents the Interval between them. [Please keep in mind that JJay comes up with his own notation that uses Roman numerals to describe the Intervals, but we will just use their regular names here to avoid confusion with Chord Functions!]
Any two Chords with the same CR will evoke a similar mood. The emotions induced by the Chord pairings are completely subjective. What does it sound like to you? Taking some time to think about this can help us to Compose music by recalling all of the CRs that are assoicated with the feeling(s) that we want to convey. JJay points out that this is particularly useful when it comes to Composing for media (like movies and video games). For example, need to make some music for a jungle scene? Then, gather all of the CRs that evoke that quality for you!
Further, we can build Chord Progressions by linking together a sequence of CRs. Therefore, the type of Chord on the ends of each CR are important. They have to be the same if we want to link those two CRs together! For example, here is a very unique Progression with eight Chords built out of the above three CRs. In this case, since all of these CRs begin and end with a Major Chord, we don't have to think about the type of Chord on each end. We can mix and match them however we want:
Usually, we do not use more than 3-5 different CRs at a time. Using too many at once makes it seem like the music is jumping around all over the place without reason.
While we have been talking about Non-Functional Harmony here, similar approaches can also be used for creating unique Modulations. Notice that the above method is almost like Modulating to a new Key with every Chord! Techniques like this are particularly common within Jazz. A very good example are the famous "Coltrane Changes". [Vox gives a longer explanation, while 12Tone gives a shorter one.]
Basically, any sort of ambiguity about what Key that we are in can be used to move in and out of multiple Keys at will!
If we are bouncing back-and-forth between a couple of Chords, then we simply have to make sure that the Melodies and Chord Tones mesh like we normally would within the context of Functional Harmony. If there are more Chords involved, then we must do something similar to what we did with Modulations (i.e.: look at the Common Tones across all of the Keys that we are using).
In other words, how many Notes does each Key share? Usually, the more Notes that differ between the Scales, the more tension that is created when they are used at the same time. Because they use fewer Notes, we can often use Pentatonic Scales to form Melodies that work within multiple Keys without it being too jarring (unless, of course, that is an effect that we want to create). [8-Bit Music Theory gives some great examples of Non-Functional Harmony within the soundtrack of the video game, Chrono Trigger.]
We hope all of this was simple to understand and gave some useful tools for Composing. Along with concepts like Negative Melodies and Harmonies, we are starting to reach the outer periphery of Music Theory as it is currently taught in the west.
Thank you for reading!