How to use the Circle of Fifths for Scales & Modes

Introduction

The Circle of Fifths is one of the most powerful tools we half to represent our 12-tone system. By stacking perfect fifths you get all the notes in western music. Using the circle of fifths to show scales allows us to find very interesting properties of that scale, from determining key signatures, to finding all its related modes and symmetric properties of scale, and much more.

The Circle of Fifths (In the Key of C)
How to use the Circle of Fifths for Scales & Modes as shown in The Universal Encyclopedia of Scales

How to use the Circle of Fifths for Scales & Modes

  1. Choose a Scale and write the root on the top node (12 o’clock) of the circle
  2. Go around the circle (clockwise) and add all the other notes in our 12-tone system. Remember each node is a perfect fifth above the previous node.
  3. Mark the notes in the circle that belong to the scale and draw a polygon by joining the notes in the scale.
  4. Get the scale in all keys by rotating the note labels, without rotating the polygon, one node at a time. Make sure the top note in the circle is always a vertex of the polygon.
  5. Get all the related modes of a scale by rotating the entire circle, note-labels and polygon together, one node at a time. Make sure the top note in the circle is always a vertex of the polygon.
The C major scale
One rotation (only note labels) gives us the G major scale. The F moves out of the polygon and the F# comes in. That’s why key signature for G major has one sharp (F#)
One rotation (note-labels and polygon) gives us a mode of the C major scale: G Mixolydian
By rotating the polygon (making sure the top note always belong to the polygon) we get all possible modes of that scale.
Symmetric scales (i.e. The Augmente Triad. Yes, it is also a scale with 3 notes) have less modes than notes. Because the polygon looks the same under rotation.
The Symmetrical Augmented is a scale with 6 notes but only 2 modes, and it can only be transposed to 4 different keys. Symmetric scales are also known as “Scales of Limited Transpositions”
Here’s the complete method on “How to Use the Circle of Fifths for Scales”. We take a random number and turn it into a polygon which should represent one of all the scales in music.

Finding All Scales in Music

This method was used in The Universal Encyclopedia of Scales to find all possible scales in music and organize them by groups of related modes and symmetry. Every group of related modes is shown in an page dedicated to that group, and each scale is shown in its own page in all keys: As music notation, on a piano keyboard and a guitar fretboard

The Universal Encyclopedia of Scales by mDecks Music was created by using a mapping technique that graphs scales over the circle of fifths.

The Universal Encyclopedia of Scales


This technique in conjunction with mathematical principles allowed us to reveal, organize and catalogue the entire universe of musical scales.
The Universal Encyclopedia of Scales contains all 2048 scales in music (2036 scales with three or more notes plus 12 scales of two notes also known as intervals.)
Since graphing allows us to determine which scales were related modes of each other, we were able to establish the amount of source scales of three or more notes which is 344 (not considering intervals which are trivial scales of two notes)

The amount of scales in music will never change. It will always be 2048 (in a twelve tone system). The catalogue ID used in the encyclopedia is also universal and eternal. Standard names for scales including the three other alternative names were created by using different naming techniques consistent with music theory (such as Omit, Add, Truncation, etc)  that facilitate the recognition of a scale based on well-known scale names.

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