The circle of fifths is a visual tool that demonstrates the geometric relationships between the twelve distinct pitches used in western music culture. These pitches can also be classified as members of the chromatic scale.
A circle is an amazing tool to teach and to conceptualize musical ideas that would otherwise be terribly complicated. Before delving into the deeper truths about music that the circle keeps, let’s familiarize ourselves with its inner workings.
First of all, at its core, the circle of fifths is just that. A circle. In the same way, as an analogic clock does with numbers that represent time, the circle of fifths possesses 12 equally distributed pitches ordered by the interval of the perfect fifth, thus cycling through the twelve distinct pitches of the chromatic scale in twelve steps. Each of these notes carries a lot of information within it. Not only do they represent a particular note in the projection of fifths, but they represent different keys.
A musical key is essentially a definite system of relationships between musical sounds that dwells around a particular key center which is always represented by a single note, in a similar way to how the solar system works, with several different planets orbiting around the sun. Every key possesses a unique key signature which, as the name indicates, is its own individual or signature collection of notes. For example, C major contains no accidentals or altered notes, meaning it contains the seven distinct syllables used to name pitches or the total content of the diatonic system, C D E F G A B, thus its key signature contains no sharps or flats, putting on the top part of the circle. Every time we move up or down (clockwise or counterclockwise respectively) the circle, we change the tonal or key center to a new tonic and thus change the key signature. By going up, we add sharps, by going down, flats. Furthermore, each successive fifth adds a single sharp or flat to the previous collection, meaning that the first note to either side of C will contain either one sharp or one flat, the second, two, and so on.
The circle of fifths is also a great resource to explain some of the properties that arise between key centers. Namely the two main relationships, that of relative and parallel keys.
The relative relationship arises between two keys of opposite mode that share the same collection of sounds but poses a different key center or tonic. For example, C major and A minor. To represent this relationship in the circle we produce a second smaller one within the first one.
Parallel keys are those who share the same key center or tonic but poses different collections, for example, C major and C minor. This relationship has a distance of three accidentals and it is represented by using the same color.
Last but definitively not least, the circle of fifths is by far, the best method to picture the distance between keys. These distances refer to the total amount of common tones between two given key centers. The larger the number of fifths that separate two given key centers, the less common notes between them. Yet, when we cycle through the circle in any direction, we eventually return to the original key center, therefore, there must be a turning point somewhere along the circle, a point of furthest detachment from the original key in which the least possible amount of notes are shared. Curiously enough, that point seems to be the exact opposite side of the circle, the bottom key, F# major or its enharmonic equivalent G flat major, a pair of tritone-related keys which have six sharps and flats respectively. Nevertheless, since there are only twelve distinct pitches and each key should have seven, there is no way to have more than 5 different pitches between any two given keys, this is due to the enharmonic principle which declares the idea that musical sounds with a distinct name can sound the same due to the nature of sharps and flats and how they alter the seven basic syllables. For example, the equivalency between C# and D flat, or between E# and F. Therefore, although C# major has seven sharps in its key signature and C major has none, two of the notes in C# major (E# and B#) are enharmonically equivalent to some notes in C major (F and C respectively). Furthermore, both C# major (7 sharps) and C flat major (7 flats) can be simplified to key signatures which are enharmonically equivalent that contains fewer accidentals, namely, D flat major and B major, both containing five accidentals respectively.
In summary, the circle of fifths is a central pedagogical resource for music education. It can be extremely useful to understand the tonal distance between different sections of a piece, to figure out the key signature, and even to learn a thing or two about the enharmonic principle. Yet, it is not limited to the instruction of harmony and basic theory, but it can serve as a starting point for deeper and more complex dwellings into the wonderful and mysterious set of properties and characteristics of the tonal system.
If you are looking for an interactive Circle of Fifths, feel free to check out our Piano Companion for iOS, Android, macOS. Additionally, if you want to learn notes, chords, theory then you can check ChordIQ for iOS, Android.