Circle of Fifths
tightens right, settles left
As old as human civilization itself, the Circle of Fifths maps the 12 distinct tones within an octave in a circular form, like a clock.
It is built on the perfect fifth interval, the first harmonic ratio (3) that introduces a new pitch beyond the root, and with it the starting point of “change”.
The circle contains symmetry. With any tone at the center, the relationships between tones remain fixed.
Top tone as the center, the harmonic relationship weakens as you move downward on either side. Major intervals fall to the right, while minor intervals fall to the left.
TextBook
‘Music’ is the sum of vibrations created by an intelligence. ‘Theory’ is the evaluation of the bonds between these vibrations.
This book proposes a new theoretical model, Tritonet, that provides a unique approach to music theory by reintroducing the ‘Circle of Fifths’. It offers additional components that turn the circle into a musical calculator, which can be used to construct musical structures visually.
Inspired by a three thousand year-old tablet, the book pays homage to past and present music, while looking towards the future with ‘ResTens’ (modular voice leading) and ‘Cyclic Music’ (tonality cycles).
Cambridge Scholars Publishing
ISBN : 978-1527503779
Dec 2017
Personal Note
Only later did I realize that its origins reach back to my childhood. My first formal encounter with the Circle of Fifths took place in 2007. While studying ancient music tablets, I noticed a recurring numerical sequence. These numbers pointed to the series of fifths as a structure that has existed for thousands of years. My initial motivation was to follow the trail of such deeply ancient knowledge.
When I began teaching music theory at university, the Circle of Fifths confronted me once again. The educational approach in use was both time-consuming and bound to a single aesthetic viewpoint. Yet music theory can be approached within a far broader framework. Beginning with ratios and grasping the underlying structure first opens faster and more flexible paths toward any aesthetic direction. That realization led me to decide to write a book. This was the period when the Tritonet diagram first took shape. I cannot recall how many times I began writing, only to stop again, telling myself it was not yet the right moment. Eventually, the book was completed and published in 2017.
After 2017, my focus shifted toward transforming this method into a digital compositional tool. The first version was released in 2021. It was highly innovative, yet clearly incomplete. The second version followed in 2022. It reached a new level, but lacked stability. The version you see today took three years to develop, and it was worth every moment.
My next ambition is to turn this into a scientific measurement instrument, capable of performing harmonic analysis on any band of the electromagnetic spectrum. If I am unable to complete this journey myself, I hope others will carry it forward.
First, it is time to enjoy playing with it.
Thank you,
Tolga Zafer Özdemir
18 December 2025 / London