Where toroids, tone curves, and ancient grids collide
🔄 The Full Feedback Loop
We began with a keypad walk.
From that, we derived:
- The Preston Toroidal Scale (3PTS)
- A recursive relationship between digits
- A match to both angel and Solfeggio numbers
- Harmonic groupings based on 3, 6, and 9
We then explored:
- PTS extensions to 1-, 2-, and 4-digit domains
- Magic square overlays and numeric sums
- A resonance with 12TET musical curves
- Recursive Lo Shu fractal expansion to rank-n matrices
Each discovery wasn’t random—it interlocked.
The result? A system. One that behaves with structure, rhythm, recursion, and constraint.
A numeric harmonic engine.
🔬 Axioms of the PTS–LoShu System
This emerging system appears to obey:
- Toroidal iteration yields digit-root harmonics (3, 6, 9)
- Gridwalk-derived numbers can be arranged into magic squares
- PTS-derived values scale logarithmically when sorted
- Recursive expansion of Lo Shu preserves symmetry at any rank
- The 3×3 base grid—whether Pythagorean or Lo Shu—is one of only two that satisfies the complete set of toroidal harmonic rules
It walks like math and hums like music.
🎼 From Digits to Frequencies
Let’s recall:
- 1PTS → 45
- 2PTS → 495
- 3PTS → 4995
- 4PTS → 49995
Every level up multiplies structure. Digit roots remain constrained.
The curve of PTS values resembles musical octaves. Recursive grids echo harmonic resonance.
Is this a universal tuning mechanism? A symbolic artifact of ancient pattern recognition? A beautiful mathematical coincidence?
Maybe all three.
💡 Future Explorations
This system invites deeper dives into:
- Modular number theory and symmetry groups
- Acoustic sonification of toroidal walks
- Machine learning applied to magic square evolution
- Hypercubic analogs of Lo Shu matrices
- Integrating this system into music composition tools or generative art
The “woo” has become structured. The mystery has become modular.
And we’ve only scratched the surface.
🌀 Closing Thought
Harmony is not just a sound. It is structure made audible.
This was a system hiding in plain sight—from keypad grids to tone charts, to 81-number loops and magic matrices.
Whether you’re here for the math, the music, or the metaphysics, there’s room in this system to explore.
More posts will follow. But this marks the close of Phase 1.
Next up: code, demos, experiments, and your own interactions with the harmonic engine.
Until then:
Don’t just listen for patterns—walk them.
Product | Category | Details | Link |
---|---|---|---|
Sony WH-1000XM5 Wireless Headphones | Best Overall | Top-tier noise cancelling and exceptional sound quality — perfect for travel, work, and music lovers. | View on Amazon |
Samsung Galaxy Tab S9 Ultra | Premium Pick | A stunning 14.6″ AMOLED screen and powerhouse specs — the ultimate Android tablet for professionals. | View on Amazon |
BenQ EX3501R Ultrawide Monitor | Editor’s Choice | This 35-inch curved monitor offers stunning visuals and eye-care tech — ideal for creators and multitaskers. | View on Amazon |
iRobot Roomba j7+ Self-Emptying Robot Vacuum | Smart Home Pick | Avoids obstacles like pet waste and cords while learning your home’s layout — the smartest Roomba yet. | View on Amazon |
Anker 757 PowerHouse Portable Generator | Best for Outdoors | Huge 1229Wh battery perfect for camping, backup power, or road trips — charge anything, anywhere. | View on Amazon |
Sony Alpha a6400 Mirrorless Camera | Best for Creators | Fast autofocus, 4K video, and a flip screen — this is the perfect vlogging and photography camera for serious creators. | View on Amazon |
Apple Watch Ultra | Premium Smartwatch | Built like a tank for adventure athletes — insane GPS accuracy, sapphire crystal display, and 36-hour battery life. | View on Amazon |
DJI Mini 4 Pro Drone | Best Drone | Lightweight, under 249g, with pro-level 4K video, obstacle avoidance, and 45-minute flight time — no pilot’s license required. | View on Amazon |
Bose Smart Soundbar 900 | Top Soundbar | Dolby Atmos support + legendary Bose audio clarity = one of the best cinematic upgrades for any living room. | View on Amazon |
Garmin fenix 7X Solar Multisport GPS Watch | Adventure Watch | Solar charging, topo maps, and extreme durability — built for endurance athletes, hikers, and survivalists alike. | View on Amazon |