Interactive Tools
The Lab
A suite of web-based tools for exploring the mathematics underneath music. Built on provable number theory, psychoacoustic science, and real frequency data. Every calculation is transparent — no black boxes, no mysticism.
Vortex Explorer
Visualize the 9-class digital root system that underlies all musical intervals. See how octave doubling creates loops and feeders — and why certain notes are structurally stable while others are transitional.
Scale Explorer
Browse all four Sacrifunk scales, their modes, and chord families. Compare Just Intonation and Equal Temperament side by side. Hear the difference in real time.
Cymatics Lab
Generate visual patterns from frequency input. See how different tuning systems produce different geometric forms — real physics, not decoration.
Frequency Explorer
Look up any note, any octave, across all five tuning systems. Compare frequencies, cent deviations, and spectral roughness values.
Frequency Designer
Design custom frequency sets and tuning tables. Export as Scala files, Peterson tuner offsets, or raw frequency data for studio use.
Five Laws Tutorial
An interactive walkthrough of the Five Laws of Loop-Feeder Decomposition — provable mathematical theorems about musical intervals.
The Science
What’s Underneath
These tools are built on three pillars of verifiable mathematics and physics. No claims are made that cannot be demonstrated with a calculator or a spectrum analyzer.
Vortex Mathematics
The 9-class digital root system. Every positive integer maps to a class 1–9. Musical intervals inherit this structure: octave doubling creates a cycle (1→2→4→8→7→5→1) that governs note stability.
Just Intonation
Pure frequency ratios (5:4 for major thirds, 3:2 for perfect fifths) produce zero-beating consonance. Equal Temperament compromises every interval to enable modulation.
Spectral Coherence
Sethares roughness analysis measures the psychoacoustic “smoothness” of any chord. In Sacrifunk scales, A♭ Major in JI produces the lowest roughness score (0.197).