RESEARCH

Harmonic Geometry & Heptatonic Scales

Tom began researching the relationship between geometry and music during his Masters Degree in 2017, spending countless hours studying the harmonic series, tuning systems, musical interval ratios and their relationships to 2D shapes, the Platonic Solids and organic mathematics.

Tom gradually began to apply this knowledge to musical practice, by formulating a system of categorizing, accessing and teaching all 266 heptatonic scales in 12-Tone Equal Temperament. 

Tom has taught this new system to all of his current students with breathtaking results. Tom's method breaks down the vast amount of mathematically possible scales and modes into an easy system of Parent Scale groups.


Employing perspectives such as Primary Triads and Tetrachords, the student receives a deep and prophetic grasp of this advanced music theory. These two areas of research, harmonic geometry and heptatonic scale pedagogy, will together form the backbone of a PhD proposal.

The system has been born, gradually, over a decade-long study into exotic scales, flamenco harmony and jazz theory. It draws and expands upon George Russell's Lydian Chromatic Concept (1953) and the ideas found in Ernst Levy's A Theory of Harmony (1985), such as tonal gravity and negative harmony, which were recently popularized online by Jacob Collier in a viral interview.

Interview: Jacob Collier (Part 1) - YouTube

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PhD proposal and Journal Article

In July 2021, Tom's friend and mentor, Professor Alan Burns, passed away suddenly. Alan was one of the most gifted mathematicians of his generation and taught extensively after studying at Cambridge University. He was also a polymath, a proficient guitarist and a lover of folk music. 

Alan and Tom had been working on an article on musical geometry that they were hoping to publish together in an academic journal, which was going to add significant weight to Tom's PhD proposal. Tom is currently in touch with Alan's family, as well as academics in the music department at the University of Salford, about how best to proceed.

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Booking Info

  • Private tuition in Manchester, UK or online via Zoom/Skype/What's App.

  • Workshops and lectures in schools, college and universities. 

  • Join the Gold Tier of Tom's Patreon and you can book a free 30 mins private lesson per month, as well as access to all research and documentation.

www.patreon.com/tommetcalfemusic

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