The Circle of Neutral Thirds

In standard, 12-tone music, we can visualize all notes by creating a circle of fifths, starting with C as the top note, followed by G, D, and the rest, until we loop back to C. You can then draw lines between notes within the circle to visualize relationships between notes, such as fourths, thirds, tritones, and similar.

With quarter tones, in 24-tone music, we can expand upon this idea. The interval of a neutral third, which is the quarter tone between a minor third and major third, is exactly halfway between the interval of a fifth, so we can add each neutral third interval in-between each fifth interval in the circle.

The diagram below is an interactive circle of neutral thirds. By default, it shows connections between each note and its neighbors one quarter tone apart. You can select one or more intervals to see how the connections align geometrically. Different combinations yield different patterns. You can also hover over a line to highlight it and see which notes it connects.