19 November 2021
Certain hieroglyphic sequences at Karnak resist standard linguistic parsing. When analyzed as frequency notation — mapping symbol geometry to acoustic wavelengths — a secondary layer of meaning emerges that corresponds to the temple's measured resonant properties.
I completed my doctoral dissertation in 1987 at the Oriental Institute of the University of Chicago. The title was Anomalous Glyph Sequences in New Kingdom Hieratic: A Structural Analysis of Non-Standard Notation in Theban Temple Inscriptions. It was, and remains, the least-read dissertation to emerge from the Oriental Institute in the decade of the 1980s, a distinction I hold with a certain resigned pride.
The subject of the dissertation was a set of hieroglyphic sequences — approximately three hundred forty individual groupings — found on interior walls and columns of the Karnak Temple Complex in Luxor, Egypt. These sequences share several properties that distinguish them from standard Middle Egyptian hieroglyphic text:
First, they resist translation using the established phonetic and logographic values of the signs they contain. The individual glyphs are recognizable — they belong to the standard repertoire of New Kingdom hieroglyphs. But their combinations do not produce coherent readings in Middle Egyptian, Late Egyptian, or any known phase of the language. They are not names. They are not titles. They are not offering formulas, hymns, or administrative records. When parsed using the standard grammar established by Gardiner (1927), Loprieno (1995), and Allen (2000), they produce nonsense.
Second, they occur exclusively in specific architectural contexts. The anomalous sequences are not distributed randomly across the temple. They appear on interior surfaces of enclosed chambers — particularly the hypostyle hall and the inner sanctuaries — and are positioned at consistent heights relative to the floor. They do not appear on exterior walls, pylons, or any surface exposed to open air. This distribution pattern is architecturally specific in a way that standard inscriptional text is not.
Third — and this is the observation that consumed the second half of my career and eventually removed me from it — the geometric proportions of the anomalous glyphs differ subtly but measurably from their standard counterparts. The same sign, when used in a translatable text elsewhere in the temple, has slightly different proportional relationships between its component strokes than when it appears in one of the anomalous sequences. The differences are small enough to be invisible to casual inspection but consistent enough to be quantified. I measured them. It took four years.
My dissertation committee accepted the structural analysis. They did not accept my proposed explanation. I do not blame them. The explanation was, at the time, unsupportable. It has taken me thirty-four years and a career spent in circumstances I did not anticipate to develop it to a point where I believe it is ready to be presented, if only on this modest platform.
The anomalous glyph sequences at Karnak are not text. They are notation. Specifically, they are acoustic frequency notation — a symbolic system for encoding information about sound.
The Karnak Temple Complex is the largest religious structure ever built. Its construction spanned approximately two thousand years, from the Middle Kingdom (circa 2055 BCE) through the Ptolemaic period (circa 30 BCE), with the most significant building campaigns occurring during the New Kingdom, particularly under Hatshepsut, Thutmose III, Amenhotep III, and Ramesses II. The complex covers approximately two hundred acres and contains, among other structures, the Great Hypostyle Hall — a forest of 134 massive sandstone columns, the tallest of which stand approximately twenty-three meters high, enclosed within walls that create one of the largest covered spaces in the ancient world.
The Hypostyle Hall is one of the most acoustically extraordinary rooms on Earth.
This is not a subjective assessment. Acoustic engineers and archaeoacousticians who have measured the hall's properties — including work by Miriam Kolar (Stanford), whose research on ancient acoustic architecture is among the most rigorous in the field, and Chris Scarre (Durham), whose edited volume Archaeoacoustics established the discipline's methodological foundations — have documented a space with resonant properties that are, by any standard, exceptional.
The hall's dimensions, column spacing, and ceiling height create a complex pattern of standing waves, reflections, and resonances that would be difficult to achieve accidentally. The columns are not uniformly spaced — they are arranged in rows with two distinct column diameters (the central twelve columns are significantly larger than the surrounding 122), creating what acousticians describe as a coupled resonant system: the central nave and the flanking aisles function as distinct but interacting acoustic chambers with different resonant frequencies.
The measured resonant frequencies of the Hypostyle Hall cluster in the range of 90 to 150 Hz, with a strong fundamental around 110 Hz. This frequency range overlaps with the human vocal range and with the frequencies produced by the ritual instruments known to have been used in Egyptian temple ceremonies — specifically the sistrum (a metal rattle with a characteristic frequency profile centered around 120 Hz) and various forms of chanting and recitation.
I want to be careful here. The observation that the Hypostyle Hall has favorable acoustics does not, by itself, prove that acoustics were an intentional design parameter. Large enclosed stone spaces tend to have strong acoustic properties regardless of intent. The question is whether the specific acoustic properties of Karnak — the frequency ranges, the standing wave patterns, the relationship between the nave and the aisles — are the incidental byproduct of a space designed for visual and ceremonial grandeur, or evidence that the builders deliberately shaped the acoustic environment.
The anomalous glyph sequences, I believe, answer this question.
What follows is a summary of the analytical framework I developed between 1988 and 2002, refined during the subsequent years, and which I present here for the first time in any public forum.
During my doctoral research, I made detailed measurements of 147 anomalous glyph groups across eight interior chambers and passages at Karnak, working from both direct observation (during three field seasons in 1984, 1985, and 1986) and high-resolution photographs taken with measurement scales included in each frame. For the remaining 193 groups identified in my survey, I worked from published photographic records and, where available, the detailed drawings produced by the Oriental Institute's Epigraphic Survey — an ongoing project that has been documenting the inscriptions at Karnak and Luxor since 1924 with extraordinary precision.
For each glyph in an anomalous sequence, I measured the following geometric properties:
The height-to-width ratio of the sign as inscribed. The angular relationships between major strokes (where applicable — many hieroglyphs contain diagonal or curved elements whose angles relative to the vertical and horizontal can be measured). The proportional spacing between the sign and its neighbors in the sequence. The proportional relationship between the sign and the cartouche or register boundary enclosing it.
These measurements produced a dataset of approximately nine thousand individual values across the 340 glyph groups.
The hypothesis emerged, I confess, not from rigorous deduction but from an accident of perception.
In 1995, I was examining a set of anomalous glyphs from the inner chamber of the Akhmenu — the Festival Hall of Thutmose III, a structure within the larger Karnak complex. I had been measuring glyph proportions for hours, and I had also, that same week, been reading T.C.W. Blanning's The Triumph of Music, which includes a discussion of acoustic theory and the mathematical relationships between musical intervals.
I noticed that the height-to-width ratios of two adjacent glyphs in the sequence I was examining were related by a factor of approximately 1.498 — very close to the ratio of 3:2, which in acoustic terms represents a perfect fifth interval. The next pair of glyphs had a proportional relationship of approximately 1.334, close to the 4:3 ratio of a perfect fourth.
This could, of course, be coincidence. Two data points establish nothing. But it was enough to make me go back through my measurements systematically, examining the proportional relationships between adjacent glyphs in every anomalous sequence in my dataset.
The results were not coincidental.
Across 340 anomalous glyph groups, the proportional relationships between adjacent signs cluster around simple integer ratios with a consistency that cannot be attributed to chance. The most frequently occurring ratios, in order of prevalence, are:
3:2 (the acoustic interval of a perfect fifth) — present in approximately 34 percent of adjacent glyph pairs.
4:3 (a perfect fourth) — approximately 22 percent.
5:4 (a major third) — approximately 14 percent.
2:1 (an octave) — approximately 11 percent.
The remaining 19 percent of adjacent pairs show ratios that are either more complex integer relationships or do not correspond to standard acoustic intervals. This is expected in any real dataset — perfect correspondence would suggest fabricated data, not authentic results.
I want to state what this means plainly. The geometric proportions of the anomalous glyphs encode harmonic ratios. The relationships between adjacent symbols in a sequence correspond to the mathematical relationships between consonant acoustic intervals — the same ratios that define the structure of virtually every musical tradition in human history, from Pythagoras's monochord to the Indian shruti system to the overtone series that is a physical property of vibrating strings, columns of air, and resonant chambers.
The glyphs are not words. They are intervals.
If the anomalous glyph sequences encode harmonic relationships, the next question is: harmonic relationships between what?
This is where the architectural specificity of the glyph placement becomes critical. The sequences do not appear randomly on any available surface. They appear in enclosed chambers, at consistent heights, and in spatial relationships with architectural features — columns, doorways, niches — that are specific and repeatable.
My hypothesis: the glyph sequences encode the resonant properties of the spaces in which they appear. They are, in effect, acoustic specifications — notations that describe the frequency relationships that the space was designed to produce or that are produced by the space as built.
Testing this hypothesis requires acoustic measurements of the specific chambers where anomalous glyphs appear, correlated with the harmonic ratios encoded in the glyphs at those locations.
I conducted this correlation during my field season in 1986, using portable acoustic measurement equipment that was, I freely admit, not sophisticated by current standards. I generated test tones at measured frequencies, recorded the room's response at the locations of the anomalous glyphs, and compared the measured resonant relationships to the harmonic ratios encoded in the glyphs.
The correspondence, at the seven locations where I was able to conduct measurements before my funding was terminated, ranged from 78 to 94 percent agreement between encoded ratios and measured acoustic properties. This is a high degree of correspondence. It is not proof. Seven locations is not a statistically robust sample. But seventy-eight percent agreement at the worst-performing location, and ninety-four percent at the best, is enough to warrant the further investigation that I have not been in a position to conduct.
Before the reader dismisses the notion that hieroglyphs could encode non-linguistic information, it is worth noting that this is not without precedent in Egyptological scholarship.
The use of hieroglyphic signs as mathematical notation is well established. Egyptian mathematical texts — the Rhind Papyrus, the Moscow Papyrus — employ hieroglyphic and hieratic signs to represent numerical values and mathematical operations using conventions that differ from their linguistic usage. A sign that means “mouth” in linguistic context means “part” or “fraction” in mathematical context. The same symbol carries different information depending on the system in which it is embedded.
The use of hieroglyphic signs in astronomical notation is similarly documented. The “star clocks” found on New Kingdom coffin lids — the diagonal star tables used to mark the passage of nighttime hours — employ hieroglyphic notation in a non-linguistic, observational mode. The signs represent celestial positions and temporal intervals, not words or sentences.
The concept I am proposing — that a subset of hieroglyphic signs was used to encode acoustic information — is, structurally, no different from these established precedents. It is a notational system embedded within but distinct from the linguistic system that uses the same symbols. The difference is that mathematical and astronomical applications of hieroglyphs have been recognized and studied for over a century, while acoustic applications have not. This may reflect a genuine absence. Or it may reflect the fact that Egyptologists, as a discipline, do not typically possess training in acoustics, and acousticians do not typically read hieroglyphs.
I read hieroglyphs. I have spent twenty-three years in a facility where acoustic phenomena are a daily reality. The convergence is accidental. The analysis is not.
If the anomalous glyph sequences are acoustic notation, what does this tell us about the builders?
It tells us that they possessed a sophisticated understanding of the relationship between spatial dimensions and acoustic properties — that they could predict the resonant behavior of an enclosed space before or during its construction, and that they had a symbolic system for recording and communicating that knowledge.
This is not as remarkable as it may initially seem. Any culture that builds enclosed ceremonial spaces and uses those spaces for chanting, singing, and instrumental performance will develop, over time, an empirical understanding of how room dimensions affect sound. The question is not whether the Karnak builders understood acoustics — the acoustic properties of the Hypostyle Hall make that self-evident — but whether their understanding was systematic enough to be encoded in notation.
The glyph sequences suggest that it was. And the specificity of the notation — encoding not just the presence of resonance but the harmonic relationships between resonant frequencies — implies a level of acoustic knowledge that is quantitative, not merely intuitive.
This has implications beyond Karnak. If one New Kingdom temple complex employs acoustic notation, the question immediately arises: do others? The temples at Luxor, Abydos, Dendera, Edfu, and Philae all contain interior spaces with documented acoustic properties. Some of these temples contain anomalous glyph sequences that have resisted standard translation. I have examined published photographs of inscriptions at Dendera and Luxor and have identified preliminary evidence of proportional relationships consistent with harmonic encoding, but I have not conducted the detailed measurements necessary to make a definitive claim.
The further implication — and here I venture beyond what my data can directly support — is that if acoustic notation was a feature of Egyptian temple construction, then the builders' tradition included not just architectural knowledge and religious symbolism but a technical vocabulary for describing the behavior of sound. This vocabulary was encoded in a form that only someone trained in both the hieroglyphic system and the acoustic system could read. It was, in other words, a specialist notation — legible to the initiated, invisible to everyone else.
I find this possibility both exhilarating and melancholy. Exhilarating because it suggests that the inscriptions at Karnak and elsewhere contain a layer of information that has been visible for three thousand years and has never been read. Melancholy because I suspect that the tradition of reading them — the knowledge of what the notation means and how to apply it — was lost long before the last hieroglyphic inscription was carved.
I presented a preliminary version of this analysis at the American Research Center in Egypt (ARCE) annual meeting in 1992. The response was courteous, skeptical, and final. The primary objection was that my proposed frequency mapping relied on measurements of glyph proportions that were too fine to be reliably distinguished from natural variation in carving technique. Different hands, different tools, different qualities of stone — all of these introduce variation in glyph proportions that could, in the view of my critics, account for the patterns I had identified.
This objection has merit. It is the same objection I would raise if presented with similar data by someone else. The rebuttal — that the proportional clustering around simple harmonic ratios is too consistent across 340 separate glyph groups, carved in different periods by different hands on different stones, to be explained by carving variation alone — was not sufficient to overcome the objection in the room. Statistical arguments rarely prevail against disciplinary consensus in a single presentation.
I had intended to develop the rebuttal through further fieldwork — larger sample sizes, more precise measurements using photogrammetric techniques that were becoming available in the early 1990s, and comprehensive acoustic surveys of the chambers where anomalous glyphs appear. This fieldwork required funding and access. By 1993, I had neither. My career had taken a turn that removed me from academic life, and my subsequent employment, while affording me certain advantages in terms of time and acoustic environments, did not include field seasons in Upper Egypt.
I have continued the analysis from a distance, working with published photographic records and measurements taken by others. The dataset has grown. The patterns have held. The proportion of adjacent glyph pairs falling within 5 percent of simple harmonic ratios has remained above 80 percent in every sample I have examined, across every chamber, across every construction period represented in the anomalous corpus.
I cannot compel anyone to take this work seriously. I can only continue it, and present it, and hope that someone with the means to test it in the field — with modern photogrammetric measurement, modern acoustic instrumentation, and the access to Karnak that I no longer possess — will find the question worth asking.
The inscriptions are on the walls. They have been there for three thousand years. They are not going anywhere. Neither am I.
I am aware that this paper bridges two fields — Egyptology and acoustics — in a way that neither field is likely to find entirely satisfactory. Egyptologists will object that I am overreading the geometric data. Acousticians will object that I am underqualified to evaluate the acoustic data. Both are correct, in the narrow sense that specialists always are when confronted with work that crosses their boundaries.
But the anomalous glyph sequences cross boundaries. That is why they have remained anomalous — they sit at the intersection of linguistics, archaeology, architecture, and acoustic physics, and no single discipline has the tools to evaluate them alone. My analysis is incomplete. It is the best I can do from where I sit. The completion requires collaboration that has not been available to me and that I continue to seek.
I will note, as a final observation, that the practice of encoding technical information in symbolic systems that double as decorative or ceremonial elements is not unique to ancient Egypt. Medieval European cathedrals — built by guilds with closely guarded construction knowledge — contain stonework markings and proportional systems that have been shown to encode structural and acoustic information legible only to trained masons. The compagnonnage tradition in France maintained technical knowledge across centuries using symbolic systems embedded in the architecture itself. The parallel is not exact, but it is suggestive. Traditions of specialized building knowledge, transmitted through symbolic notation and understood only by initiates, have existed across cultures and across millennia.
The question is not whether such traditions could have existed in ancient Egypt. The question is whether we are equipped to recognize them when we see them. The glyphs are on the wall. The frequencies are in the air. What remains is the willingness to listen.
Correspondence: leh [at] 442423N1042233W.com
Acknowledgment: My doctoral committee at the Oriental Institute — Professors [redacted], [redacted], and [redacted] — deserve credit for accepting my structural analysis even when they could not accept my conclusions. They taught me to measure carefully. I have tried to honor that teaching, even when the measurements led me to places they did not intend.