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. A visualization of the mathematics of each tuning ratio — a way to see how systems differ geometrically. It is a pattern generator, not a physics simulation of a vibrating plate (real plate modes need measurement or FEA). No claim is made that these images predict physical cymatics.
Frequency Explorer
Look up any note and octave in Just Intonation (5-limit, C = 256 Hz) — intervals, cent deviations, and spectral-roughness values.
Frequency Designer
Design and export tuning tables for all five Sacrifunk systems plus both True-Temperament sets — Scala (.scl / .kbm), Peterson strobe-tuner offsets, a frequency CSV, and an MTS SysEx dump. Every value is generated from the self-tested tuning atlas.
Five Laws Tutorial
An interactive walkthrough of the Five Laws of Loop-Feeder Decomposition — provable mathematical theorems about musical intervals.
Vortex Explorer v2
The multi-generator successor to the Vortex Explorer. Overlay any scale on the 12-class circle, combine generators ×2 through ×11, and read JI frequencies, stability scores, spectral coherence and cymatics side by side.
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. Note: a note’s vortex “stability” is a number-theory property (its digital-root class structure) — distinct from spectral roughness, which is psychoacoustic. The Lab reports both and never treats one as the other.
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. Among the Sacrifunk scale’s Just-Intonation triads, A♭ major ranks among the smoothest — the full ranking is being finalized directly from the dissonance computation.
True Temperament — Thidell Formula 1
Sacrifunk’s movable-fret guitars (Taylor T5-C, refretted) use the Thidell Formula 1 (TF1) temperament — per-note microtuning that cleans up triads in every key without breaking free modulation. These are the exact offsets, verified against the manufacturer’s tuning sheet and the studio’s Logic Pro tuning table.
Chromatic offsets (cents from equal temperament, A = 0)
Open-string offsets (for tuning the strings)
7-string adds B1 −4
8-string adds F♯1 −8
On A = 432 vs A = 430.04
The same fret geometry, anchored two ways on the C = 256 spine. Anchor A to 432 (a spine harmonic, since 27/16 × 256 = 432 exactly) → TT-A432 (primary recording system). Anchor C to 256 exactly → TT-A430.04 (A lands at 430.04 Hz). One guitar, one spine, two reference notes.