The Circle of Fifths: An Ongoing Exploration of the Map
This is a new section on our site, requested by, and evolving dynamically in response to the interaction of those who engage in our circle building sessions. Thanks for your patience as we build it.
You’ve probably heard that circle of fifths is a reference chart, and can function as a method and visual resource. It is all these, and it’s an ancient map woven from math, geometry, physics, and human wonder, that offers a portal constructed of connection.
The circle’s twelve-step version is a zoomed-out view of the universe of possible intervals, set into a twelve note system. We zoom out like this for ease and the sake of simplicity. Intervals are generated by multiplying or dividing frequencies, resulting in observable cyclical patterns. In this format, the circle is arranging the 12 tone chromatic scale in a sequence of perfect fifths.
The circle serves as a reference for understanding harmony, key signatures, and modulation. It is a representation of the relationships and interaction of frequencies, of the ratios that describe how sounds resonate together.
- In its classic form, at each step we advance around the circle in an interval of 5. Starting at one position, we land at the fifth step away in the next, either ascending or descending (pitch, alpha, and numeric).
- Defined by the frequency ratio 3:2, this 5th interval relationship is not an arbitrary invention; it’s a natural, physical phenomenon that musicians, along with scientists, philosophers, and mathematicians have recognized across cultures and time.
The image on the right, and description that follows, are from Joe Dubs & OmniCore Tech
This image unveils the profound geometric structure underlying musical harmony, revealing a sacred order woven into the fabric of sound itself.
At its core, this “Musical Geometry” diagram illustrates the harmonic relationships between fundamental intervals—the perfect octave (1:2), perfect fifth (2:3), and perfect fourth (3:4). These ratios are not arbitrary but are intrinsic to the very physics of vibration, echoing through nature, celestial mechanics, and human perception of consonance.
The circles interwoven in the central diagram reflect harmonic progression, where geometric relationships mirror the resonance of frequencies. This sacred design reflects the harmonic lattice, an ancient concept recognizing that music is not just an art but a mathematical and cosmic principle. The Fibonacci sequence, the Golden Ratio, and sacred geometry all find expression in these vibrational relationships.
For an incredibly simple and useful tool, visit Rand Scullard’s Interactive Circle
