Structured multiplicative, recursive systems as explained in Market Resonance Theory by LJ Parsons

[Hedgehog Cottage]

Abstract​

Market Resonance Theory (MRT) reinterprets financial markets as structured multiplicative, recursive systems rather than linear, dollar-based constructs. By mapping price growth as a logarithmic lattice of intervals, MRT identifies the deep structural cycles underlying long-term market behaviour. The model draws inspiration from the proportional relationships found in musical resonance, specifically the equal temperament system, revealing that markets expand through recurring octaves of compounded growth. This framework reframes volatility, not as noise, but as part of a larger self-organising structure.

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1. Introduction​

When most people look at a price chart, they see a story told in dollars, up, down, sideways, repeat. Yet the numbers themselves are deceiving. Price is merely a projection of growth through a measurement lens we happen to call “currency.” The underlying system is not linear, nor is it “Price” it is a recursive and self-amplifying measurement.

Market Resonance Theory begins from a simple but powerful observation, Financial markets behave more like harmonic oscillators than arithmetic progressions. Their movements, when properly scaled, reveal recurring structural patterns that resemble musical intervals more than random walks.

Conventional analysis tends to flatten these dynamics into trendlines, moving averages, and regression fits. MRT, by contrast, introduces a structural language for growth, one that identifies markets as evolving through a hierarchy of resonant intervals.

2. Core Framework​

2.1 The Limits of Standard Logarithmic Scaling​

Conventional log price charts compress data to show proportional change, but they rely on whole-number scaling—typically powers of ten. This assumes a neat exponential growth function, implying that markets expand smoothly across numeric decades. The problem is that markets don’t.

In reality, market growth evolves through compound proportional steps, nested ratios that form fractal patterns, not simple curves. Whole-number scaling flattens these relationships, hiding the resonant structures that actually drive market behaviour.

It’s a bit like tuning an instrument only by octaves and ignoring the notes in between, you’ll hit the broad strokes but miss the music. MRT replaces this coarse scaling with a “harmonic” logarithmic scale which are not to be confused with traditional harmonic trading models. This framework is based on equal temperament intervals, which captures the natural rhythm of compounded growth.

2.2 Octaves and Intervals​

Each market “octave” in Hz represents a doubling in structural scale, subdivided into 12 logarithmic intervals of roughly 5.9463 percent. This mirrors the 12-tone division of Hz in equal-temperament tuning. Within each octave, prices resonate between these proportional zones, forming repeating patterns that persist across timeframes.

Rather than tracking absolute prices, MRT tracks the structural rate of change between harmonically consistent levels. The result is a chart that exposes where the market “sings” (zones where energy builds, releases, and transitions predictably.)

2.3 Recursive Multiplicatory Transition​

Every octave’s completion seeds the next. The growth achieved through one harmonic cycle compounds to form the base frequency of the next higher octave. This recursive behaviour explains why market dynamics appear self-similar across vastly different scales, minutes echo years, and bull markets hum the same tune as intraday rallies.

2.4 Harmonic Resonance​

In markets, as in acoustics, resonance occurs when frequencies align. MRT observes that when price movements across timeframes converge on shared intervals, significant inflection points arise. These resonances, (periods when daily, monthly, and decadal structures synchronize) often precede major market shifts.

3. Empirical Structure​

Applying MRT to the S&P 500 and Nasdaq between 2010 and 2025 reveals recurring octave boundaries that correspond to major consolidation and breakout zones. Each successive octave follows the recursive growth law, doubling in structural magnitude while preserving interval spacing.

Periods traditionally described as “irrational exuberance” or “bubble phases” often coincide with the upper boundaries of an octave, points of resonance where compounded energy reaches structural saturation before transitioning into the next cycle.

4. Discussion​

Traditional finance interprets markets through additive change. Prices rise or fall in response to external stimuli. MRT views them instead as resonant systems, self-referential entities that express growth in predictable proportional layers.

This reframing resolves several persistent anomalies:

• Why bull markets accelerate geometrically rather than linearly.
• Why volatility clusters occur near specific proportional levels.
• Why long-term consolidations appear where no clear external cause exists.

The reason is structural, not psychological. The market is behaving like a resonating body, its energy naturally redistributing as it approaches each harmonic threshold.

5. Implications​

For portfolio construction, MRT suggests an entirely new reference frame. Instead of anchoring valuation to nominal currency units, investors can anchor to harmonic growth levels, intervals that define the system’s natural expansion rhythm.

• Quantitative Analysts: can incorporate MRT lattices into multi-scale prediction models.
• Strategic Investors: can identify octave boundaries as zones of systemic transition.
• Complexity Researchers: can extend MRT as a formal recursive growth function applicable to other nonlinear domains.

6. Conclusion​

Market Resonance Theory recasts financial systems as self-organizing harmonic structures. By abandoning the flat logic of whole-number logarithms and adopting a recursive harmonic scale, we expose the geometry of growth itself {a geometry that repeats, compounds, and resonates.}

If the market is a symphony, MRT provides the score: a framework where price, time, and structure play in tune.

Author’s Note​

Market Resonance Theory was conceived and developed by LJ Parsons. It is presented here not as speculation but as a record of discovery: that financial markets grow through recursive harmonic structures analogous to musical resonance. Whether or not it finds recognition today, it stands as a marker of observation. Time, as ever, will decide the rest.