Jazz and Musical Symmetry

It’s probably not a surprise that music has a lot to do with patterns (the scale, the note progression, the time signature used). However, these alone aren’t enough to make beautiful and interesting sounding cadences, as too much repetition can make a piece boring to listen to. Enter jazz theory, and music suddenly becomes more colorful (and more complicated lol). It would probably take me forever to talk about all the different harmonization techniques available (and most of you probably won’t get it anyway), so for this post, I will just focus on the tritone substitution method often used in improv jazz.

(this is also just an excuse for me to geek out about music theory hue)



Music is in essence, the art of placing notes or tones together and making them sound good. Not all note combinations sound nice (to some extent), so it is important for an instrumentalist to know which notes go well with each other.

Some of you may be familiar with the octave sequence (DoDo, if that makes any sense), the triad (Do-Mi-So), and the complete major chord (Do-Mi-So-Do). You can already go a long way just by using these, but to generate more interest in repeated sections of a song, variations may be done. Sometimes, removing some notes to create a cleaner sound (e.g. only using the fifths instead of the full triad, like Do-So), or you can replace some notes with relative notes. For example, you may opt to play a G octave when playing a C major chord (as G is the relative fifth of C). Tritone substitution takes this a step further by using a symmetric substitution instead of its fifth.

Most of you are probably confused at this point, so I’ll try to explain this as simply as possible, using the Circle of Fifths. Below is a graphical representation of the Circle of Fifths (or Circle of Fourths, but to avoid confusion, lets stick with Circle of Fifths).


Image from Wikimedia Commons

To put it simply, the clockwise neighbor of any note is considered the fifth of the note. From the circle, you can see that G is the clockwise neighbor of C, meaning that G is the fifth of C. The reason this works is because the key of C and the key of G are so close together in terms of notes (C has C-D-E-F-G-A-B, G has G-A-B-C-D-E-F#, a one note difference). The same is true for C and F, but their relationship is called a fourth (hence the alternate name of the circle). F however, is usually not substituted for C, but rather the other way around (because F does not want to “resolve” to C, but C wants to “resolve” to F.)

Tritone substitution works by taking the direct opposite of the note you are using (C’s tritone, for example, is F#). You may have already noticed similarities with another circular chart (one that has more color than this one, wink wink), and that’s because that’s the concept behind it: complements. C and F# are so far away from one another note-wise that because of this, substituting one of them for the other will make the melody stand out (the same way that complementary colors make both colors pop).

And that’s one way symmetry is used in jazz music. If you want to learn more about this topic, I suggest starting from the basics of music theory, as some of the concepts discussed in Jazz are very advanced, and would probably confuse you a lot (much like how I confused you guys lol)

(I’ll probably add some music snippets later so you guys can better appreciate this concept :D)