From Empirical to Derived

The 110 Hz Convergence

Paul Samuel Guarino | September 6, 2026

The measurements established a convergence. The cascade gives that convergence a mathematical relationship.

For decades, researchers studying ancient chambers have documented resonances around 110 Hz. These measurements come from structures built long before modern acoustic instruments—places where stone, space, and the human voice interact in ways people can hear and experience.

In their six-site investigation, Robert Jahn, Paul Devereux, and Michael Ibison reported strong resonances between 95 and 120 Hz. Their 1996 study established an empirical range for investigating the recurring response around 110 Hz. [1]

My research asks how that convergence relates to the cascade. The development presented here is specific: the observed acoustic range has a mathematical counterpart within my framework.

From measurement to mathematical relationship

An empirical value comes from measurement. A derived value follows from a specified mathematical structure. The cascade anchor is:

700/17 Hz ≈ 41.176 Hz

Applying the framework’s binary–ternary ratio of 8/3 gives:

8/3 × 700/17 Hz = 5600/51 Hz ≈ 109.80 Hz

The calculation falls within the observed 110 Hz region. It gives that acoustic convergence a mathematical position in the cascade.

My compilation contains 16 archaeoacoustic site measurements drawn from published resonance data by multiple researchers. It spans seven regions and more than 2,000 years of independent architectural development. The reported comparison is:

The calculated value and the survey mean are within half a percent of each other. That is the transition I am describing: empirical in the measurements, derived within the cascade.

Why the ratio is 8/3

The ratio uses the binary and ternary operations of the framework: 8 = 2³ represents three binary factors, while 3 supplies one ternary factor. Together, they give 8/3.

The cascade's binary–ternary structure generates a family of ratios of the form 2ᵃ/3ᵇ. Applied to the anchor, that family is sparse in the region of interest.

Across every member with a ≤ 15 and b ≤ 11 — 192 candidate ratios — exactly one falls within a single standard deviation of the survey mean: 8/3, at 109.80 Hz, which sits 0.10 SD from the observed mean of 110.25 Hz. The nearest competing member is 2¹¹/3⁶. It requires seventeen factors and still lands 1.17 SD away, at 115.68 Hz.

The family does not offer a ratio for every target. In the 110 Hz region it offers one, and that one is the simplest member available: three binary factors and one ternary factor.

The structure narrows the field to a single low-complexity candidate. The measurement confirms it.

My broader cascade analysis follows a mixed ladder of binary and ternary steps from the Fröhlich scale toward the gamma band. The 8/3 relationship is the local expression examined here. It gives the observed convergence a mathematical form within that framework.

The chamber and the person inside it

Newgrange offers a recognizable example. My compilation lists its resonance at 110 Hz. Watson and Keating’s 1999 study provides related analysis of how prehistoric monuments shape sound through standing waves, resonance, and the relationship between chambers and passages. [2]

A chamber has a shape, and that shape influences its acoustic response. My framework asks whether the recurring response around 110 Hz corresponds to a particular relationship in the cascade.

The Ħal Saflieni Hypogeum adds another dimension. Rupert Till’s study describes a complex acoustic environment with multiple resonances and interactions between connected chambers. My compilation lists the Hypogeum at 111 Hz. [3]

Within my framework, the proposed coupling extends from sound in the chamber to vibration experienced through the body, including skeletal transmission. The architecture responds; the person experiences that response. The research question therefore includes the interaction between the room and its occupants.

The neuroscience connection belongs here. In a 2008 pilot study, Ian Cook, Sarah Pajot, and Andrew Leuchter examined EEG responses in 30 healthy older adults listening to tones at 90, 100, 110, 120, and 130 Hz. At 110 Hz, they reported differences in left temporal EEG measures and a shift toward right-sided prefrontal dominance relative to several comparison conditions. [4]

My framework proposes a relationship between stimulation in the 110 Hz region and the 41.176 Hz anchor. That gives the physiological investigation a specific question: do the acoustic input and measured neural response exhibit the coupling the cascade proposes? The pilot findings provide a reason to investigate; that proposed coupling still needs to be measured.

Could experience come before the equation?

David Lubman’s work at Chichén Itzá offers a related architectural precedent. He proposed that the Kukulkan pyramid’s quetzal-like echo reflected intentional acoustic design, with the staircase geometry shaping a distinctive sound. In his interpretation, the structure itself becomes an instrument. [5]

Ancient builders could have recognized an acoustic effect through listening, returned to it, and refined a space around it. The Klein Spiral framework asks whether some ancient chambers could have been tuned to acoustic targets corresponding to the cascade’s proposed frequency relationships.

Lubman’s interpretation provides a precedent for investigating acoustic intent. The 8/3 relationship provides a specific mathematical target. The experience could come before the equation.

What independent validation must establish

The 110 Hz convergence sits within my broader investigation of cascade relationships across EEG, Schumann resonance, and Riemann prime-side analysis. Here, the focus is the acoustic convergence and its relationship to the anchor.

The advance is a derived mathematical expression within the framework. Independent validation must determine what that relationship explains in the physical world.

That means testing additional sites with geometries, measurement conditions, and comparison criteria defined in advance. It means examining the full acoustic response and reporting where the relationship succeeds and where it fails. For the physiological proposal, it means measuring whether exposure near 110 Hz produces the proposed coupling to the anchor.

I welcome acousticians, archaeologists, signal-processing researchers, and neuroscience teams interested in an independent assessment. The methodology, survey dataset, and mathematical development are available on request.

The measurements brought 110 Hz into the investigation. The cascade gives it a relationship. From empirical to derived describes that development within the framework. Independent validation will determine its reach.

Paul Samuel Guarino
East Northport, New York · Independent Researcher
Lead Theorist, SEIS-UGFM Framework | Patent Pending
Full methodology and datasets available on request.

Research cited

1. Jahn, R. G., Devereux, P., & Ibison, M. (1996). Acoustical resonances of assorted ancient structures. Journal of the Acoustical Society of America, 99(2), 649–658.
2. Watson, A., & Keating, D. (1999). Architecture and sound: an acoustic analysis of megalithic monuments in prehistoric Britain. Antiquity, 73(280), 325–336.
3. Till, R. (2017). An archaeoacoustic study of the Ħal Saflieni Hypogeum on Malta. Antiquity, 91(355), 74–89.
4. Cook, I. A., Pajot, S. K., & Leuchter, A. F. (2008). Ancient Architectural Acoustic Resonance Patterns and Regional Brain Activity. Time and Mind, 1(1), 95–104.
5. Lubman, D. (1998). Archaeological acoustic study of chirped echo from the Mayan pyramid at Chichén Itzá, in the Yucatán Region of Mexico. Acoustical Society of America meeting presentation.