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Harmonic Geometry
See harmonies in a whole new way
Harmonic Geometry is a visual music theory application designed to bridge the gap between abstract mathematical patterns and intuitive musical performance. As an engineer and musician, I developed this tool to move beyond the "black box" of traditional notation, which often obscures the structural logic of harmony. By projecting the twelve notes of the chromatic scale into a geometric space, the app allows users to visualise chords and scales as distinct, repeatable shapes. Whether you are navigating a fretboard or a keyboard, these visual "blueprints" transform complex harmonic relationships into clear, spatial patterns that are easier to internalise and recall.
My pedagogy is rooted in the belief that music should be learned like a language — through immersion and relationship-mapping rather than rote memorisation of sheet music. In my coaching practice, I often see students struggle with "imposter syndrome" because they can play the notes but don't understand the "why" behind the sound. Harmonic Geometry serves as a Rosetta Stone for these players; it provides a visual anchor for the ear. By seeing a Major 7th chord as a specific geometric symmetry, students can bypass the mental hurdle of counting intervals and instead recognise the "flavour" of the sound through its visual form.
One of the most powerful features of the application is its cross-instrument "Matrix" view. Since the geometric logic of music remains constant regardless of the interface, the app allows users to translate ideas instantly between the piano and the guitar. For example, a student who understands a specific voicing on the fretboard can see its geometric equivalent on the keyboard, fostering a "whole-brain" understanding of the instrument. This spatial reasoning approach is particularly effective for analytical learners, such as engineers and tech professionals, who naturally excel at identifying patterns and systems.
Beyond simple chord-mapping, Harmonic Geometry includes interactive features for exploring voice-leading and modal relationships. Users can rotate shapes to discover how a single geometric pattern transforms as it moves through different modes, such as turning a bright Lydian sound into a dark Locrian one with a simple visual shift. With integrated audio feedback and a colour-coded interval system, the app turns the often-dry study of music theory into a tactile, exploratory experience. It isn’t just a reference tool; it’s a sandbox for musical discovery that empowers players to find their own unique voice.
Try it out!
Harmonic Geometry is free and open-source for anyone to try or contribute to (under the MIT license). Great for music students and teachers alike to explore harmonies visually.
Note Navigation
Connect the dots between staff and instrument
Note Navigation is a targeted musical fluency application designed to bridge the gap between physical intuition and visual literacy. While many musicians develop a strong "shape-based" understanding of their instrument, they often struggle to translate that physical knowledge into traditional notation. Note Navigation addresses this disconnect by providing a real-time environment where motor movement is immediately mapped to its visual representation on the staff. By turning the relationship between physical execution and musical symbols into an intuitive feedback loop, the tool helps musicians demystify sheet music without losing their ear-first foundation.
A core pedagogical feature of the application is the visualisation of the Grand Staff as a logical mirror around Middle C. Traditional engraving often obscures this relationship, but Note Navigation makes it obvious by showing how hand positions radiate symmetrically from the centre of the keyboard. This "mirroring" approach allows students to see the staff not as two disconnected grids, but as a single, cohesive map. By reinforcing this spatial symmetry through MIDI interaction, students can develop a more instinctive grasp of ledger lines and stave transitions, turning what is usually a mental calculation into a natural motor association.
For guitarists, the application tackles the challenge of the "fluid" fretboard, where the geography shifts with alternate tunings and scale lengths. Note Navigation provides a dynamic map that adapts to these changes, helping players move beyond memorised box patterns and towards a structural understanding of the neck. Furthermore, the app includes a dedicated section for exploring the relationship between fundamentals and overtones. This allows students to visualise "critical band interference" in real-time. By seeing how identical voicings create "muddy" textures in lower registers versus clarity in higher ones, musicians can develop a more sophisticated approach to arrangement and harmonic spacing.
Ultimately, Note Navigation is a sandbox for understanding the physics and architecture of sound. Whether you are an engineer looking to see the data-driven reality of acoustic interference or a creative player trying to break out of shape-based ruts, the app provides a clear path to mastery. It offers specialised modules for drilling staff-to-motor mapping, tuning-specific navigation, and register-dependent harmony. It isn't just about finding notes; it’s about developing the "pre-conscious" fluency required to see a pattern on a page and feel it in your fingers - or hear a sound in your head and know exactly where it sits on the staff.
Try it now!
Note Navigation is free and open-source for anyone to try or contribute to (under the MIT license). Great for music students and teachers alike to map out notes on the sheet and instrument.
Frequency Perception
Understand where "notes" come from
Frequency Perception is an interactive acoustics and psychoacoustics tool designed to close one of the most persistent gaps in music education: the disconnect between the physics of sound and the experience of hearing it. As both an engineer and a musician, I built this application because I found that students could often describe what a note is theoretically, but had no framework for understanding why it feels the way it does. By walking through five sequential layers — Physical, Theoretical, Cultural, Biological, and Psychological — the app traces the full journey of a sound from raw air pressure to conscious perception.
Each layer reveals a different truth about the same pair of frequencies. The Physical layer shows the exponential reality of Hz — the raw mechanical world where octaves pack double the frequency range yet feel perceptually identical. Compress that axis logarithmically and you arrive at the Theoretical layer: the stable, interval-consistent grid that music notation and harmony theory actually live in. This transition alone is a revelation for students who have never questioned why a piano's layout looks the way it does. The Cultural layer then confronts a fundamental musical negotiation: how do human civilisations carve a finite set of playable notes out of an infinite frequency continuum? By comparing tuning systems such as 12-Tone Equal Temperament against pure harmonic ratios, students can hear and visualise the compromises embedded in every instrument they have ever played.
The final two layers take the journey inward. The Biological layer introduces the Bark scale and the cochlea's critical band model, explaining why two notes that appear well-separated on a keyboard can still clash when their harmonics compete for the same auditory hair cells. The Psychological layer completes the picture with the Mel scale — the brain's own non-linear remapping of pitch distance, which explains why a bass line feels spacious and grounded even when the Hz gap is modest. Throughout, contextual Insight panels surface the musically relevant implications of each phase, bridging the science back to the listening experience.
My core teaching philosophy is that musical intuition should be earned through understanding, not inherited through convention. Students who grasp why equal temperament is a compromise — rather than simply accepting it as the way things are — develop a far more flexible ear and a deeper respect for the tonal choices embedded in non-Western traditions. Frequency Perception gives those students a single, coherent visual and interactive thread to pull, from the physics of a vibrating string all the way to the subjective sensation of pitch. It transforms acoustics from an abstract science elective into the foundational language of musical decision-making.
Give it a go!
Frequency Perception is free and open-source for anyone to try or contribute to (under the MIT license). Great for music students and teachers alike to understand the nature of sound and how it is represented in music.