Method & limits

Model boundaries

Numerical precision cannot establish fidelity to the real theatre.

The study

Roman reconstruction hypothesis (A) and Ruin configuration as simulated (B) share one parametric Blender script. Their parts carry acoustic material classes, independent of rendered appearance.

COMSOL Multiphysics geometric acoustics treats sound as rays that reflect, scatter and lose energy to the air. Ray energy is collected in volumes at named receiver ranks and on a grid.

This edition presents one fixed comparison: D50 at 1000 Hz, with empty seating, source S1 at mouth. Other study configurations and bands are not interchangeable with it.

S1 is a modelled directional voice at normal vocal effort, facing the seating from the centre of the stage deck. ‘Mouth’ is the modelled talker’s mouth position above that deck.

Conditional uncertainty

Direct sound is computed deterministically.

Finite reflected rays give conditional u₂

Excluded uncertainty: Geometry, material, model-form and calibration.

A/B contrasts and their uncertainties come from matched-ray computation, not subtracting rounded values or comparing the two configurations’ uncertainties.

The median’s uncertainty, U_M, uses matched replicate medians, unlike a value’s u₂. Resolved differences exceed matched conditional uncertainty; resolution is not an audibility, confidence-interval or significance result.

The site formats published values and keeps statuses, without acoustic calculation, estimation or gap-filling.

Geometry limits

The acoustic results use the solver’s automatic geometry representation. The surfaces that rays meet can differ from the flat faces in the input mesh.

A limited comparison using explicitly flat faces changed local results and reversed some A/B differences. The reported ray-sampling ranges exclude this effect; the comparison supplies neither a correction nor an uncertainty estimate here.

The display model is separate from the acoustic input. Details added for visual clarity were not simulated and cannot explain the acoustic differences.

Studied model ranges

The wider study varies one factor at a time and reports the resulting sampled ranges.

Structural and material factors were varied only for REF-ISO, a reference source at the orchestra centre that emits equally in all directions. For S2 at mouth, the voice source at raised vocal effort, only the source height was varied. For source S1 at mouth, the study compares empty and occupied seating only; that comparison is not a material or geometry range.

These ranges are the extremes observed under declared assumptions. They are not calibrated measurement uncertainty, confidence intervals or joint model uncertainty, and they do not transfer to other sources or positions.

Sources: Sensitivity (section 4) and Model envelope coverage records.

Scope limits

The model is uncalibrated. Measured theatre impulse responses were unavailable for calibration. This project excludes listener studies and on-site measurements.

A/B compares whole configurations, without attributing effects to damage or reconstructing ancient sound. Neither speech-intelligibility index nor absolute speech level is established.

No moving-source result is qualified or shown. Private diagnostics and unqualified calculations are excluded; see the study statements.

Rendering

Each pair shows the two model configurations from one camera. These are renderings, not photographs: greyboard terrain, surface colours, contours and lighting describe the model, not historical materials or illumination.

Blender 5.2.0 LTS rendered the model with Cycles and the Khronos PBR Neutral view transform. For this edition the architecture and terrain layers of those renders were recombined on a transparent background, so the images sit directly on the page. The architecture keeps its original shading. The terrain fades out towards the edge of each image, without the edge darkening of the original framed composite.

Within each pair, A and B share one crop and the same resizing and encoding; the stage-wall detail uses a second shared crop. None of this changes the model geometry, the camera or the lighting. Full-image links open the complete frame on a paper-coloured background, and the link-preview image shows the Overview pair in two equal paper-coloured frames.

The images are architectural interpretations; their light and shading are neither measured weather nor acoustic data.

Image and terrain source credits

A layered history

The Hellenistic theatre preceded Roman rebuilding and later arena conversion. Changing uses and architecture, loss and restoration shaped the surviving monument.

A is a Roman reconstruction hypothesis, not its Hellenistic predecessor. B combines periods: no single event connects A to B, and neither represents a complete historical moment.

Historical sources and reconstruction scholarship

Selected source records

This unchanged JSON subset comes from the study’s release; metadata may reference omitted records.

Original study statements

These statements are quoted unchanged from the wider study. References to future verification or publication concern additional measures or private diagnostics not presented in this edition. Technical identifiers are retained for traceability. Read the first quotation with its qualification.

What the model can establish

This model has not been calibrated against measured impulse responses from the Teatro Antico di Taormina; no public per-position dataset exists. Materials are literature values for comparable Greco-Roman theatres, cited individually. Ray acoustics does not model edge diffraction; low-frequency results near the scaenae-frons gap and seat rows carry extra uncertainty. Results are a physically consistent reconstruction with stated sensitivity ranges — what our model predicts, not what it sounded like.

Qualification of the quoted statement

Two points in the quoted statement need qualification.

The material coefficients are modelling assumptions, including values set by the project and stand-in values for missing or rough structure; they were not measured at the theatre for this study. The project’s material table refers back to the study plan and does not give a verified external citation for each coefficient.

The study does report sampled model ranges, but only for limited source positions and factors; those ranges do not set material or geometry uncertainty bounds for this example (source S1 at mouth, empty seating). Here, u₂ and U_M describe only the conditional uncertainty from ray sampling; they do not include material, geometry or calibration uncertainty.

Which model ranges were studied

Conditional ray uncertainty

How precise these numbers are, and what that does and does not mean (ADR 0012 D9). The direct sound is deterministic. The reflected energy is sampled by a FINITE DETERMINISTIC release lattice, and the uncertainty published beside every D50, C50, C80, Ts and G is conditional internal release-ray resampling of that run's own rays: an approximate expanded uncertainty u2 = 2 sigma_N, NOT an ISO compliance statement and NOT total model uncertainty - geometry, materials, model form and calibration are outside it, and a bias shared by every resample is invisible to it. Precision misses stay visible: a value whose u2 exceeds its target is published and flagged, never withheld or quietly smoothed. A pooled layer, where one is shown, is a separately labelled regional estimate and is not 2.5 m-resolved. Echogram EDT is published only where its fit passes the decay-linearity and trusted-range gates; a failed fit is null with its reason, while a valid EDT remains numeric. The echogram estimator does not produce T20 or T30: their null reason is metric_not_produced_by_estimator, not a claim that their decay fits failed. An A/B or occupancy contrast needs matched-ray resampling: two bars whose intervals overlap have not been shown to differ, and two that do not overlap have not been compared correctly either until the same rays are used on both sides.

Timing convention

TIMING (ADR 0014, contract v0.4). D50, C50, C80, Ts and t0 are the POINT-EQUIVALENT EVENT estimator: contiguous pieces of one ray in one cell are coalesced into complete visits (D1), each visit is booked at the energy-weighted centroid of its in-cell chord (D2), t0 is the exact unbinned energy-weighted centroid of the visible direct quadrature nodes - or the earliest complete reflected-visit centroid where there is no direct energy (D3) - and the four parameters come from exact E / E50 / E80 / sum(E t) accumulators over strictly half-open windows [t0, t0+50 ms) and [t0, t0+80 ms) (D4). G carries the D5 reference taken IN THE RUN'S AIR, which is +alpha_b*10 dB above the air-free reference a v0.3 document used. The 1 ms entry-booked histogram is UNCHANGED and is kept for the ADR 0011 D5 IR synthesis and for EDT, on its own frozen origin synthesis_histogram_t0_s; the legacy value of each metric travels beside the exact one as <metric>_histogram with the signed <metric>_hist_minus_exact difference, so the change is auditable from this document alone. Energies, the direct/reflected split, both visit counters, the histograms and EDT did not move. A v0.3 document and a v0.4 document of the same run must never be mixed in one view: the producer SCHEMA ID, never a date, is how a renderer tells them apart.

Impulse-response energy closure

CLOSURE, NARROWED (ADR 0014 D7). The ADR 0011 D5 energy closure of a synthesised impulse response holds for TOTAL ENERGY, for the direct/reflected split and for the HISTOGRAM window partitions of that waveform. It does NOT claim that those histogram partitions equal the published D50 / C50 / C80 / Ts, which are the exact point-equivalent event values of ADR 0014 D1-D4 on a different origin. The signed difference between the two is published per cell and per seat (<metric>_hist_minus_exact), so the gap is a number a reader can see rather than an assumption. Nothing may be read back off a synthesised waveform and quoted as a published parameter.

Reverberation in an open-air theatre

Reverberation-time metrics are unreliable outdoors: G/D50/C50/C80/Ts are the headline; T30 only with a validity caveat (PLAN section 6.5).

Air absorption

Every run in this publication propagated in the audited air-absorbing medium of ADR 0009 (the pre-2026-09-02 theatre numbers, which had no air absorption, are not published here).

Uncertainty and unavailable measures

The study is uncalibrated (PLAN §6.5). Conditional ray precision is not total model uncertainty; EDT is conditional; T20/T30, absolute speech levels and STI are not produced.

Private listening diagnostics

Same-seat listening: accepted products are band-selectable private mono responses. No combined broadband waveform, HRTF, playback/device validation or publication admission exists (playback_available=false).

Unqualified stage motion

Stage motion: state A was computed and compared but is unqualified (all four precision allowances unknown; recorded arithmetic shows every state-A context already exceeds at least one unchanged target); state B halted on a preserved release mismatch. No moving-source, interpolation or held-out-accuracy claim exists; the common-normalization application is still REFUSED_MISSING_ACTUAL_PROVENANCE.

Separate private diagnostic band

A-occupied seat-3S03 has six accepted private diagnostic bands. Its 2000 Hz band is the root-adopted standalone 1.6M result: a private named diagnostic with no confidence, total-ear, point-limit, HRTF, playback, broadband, seed-independence or sqrt-N claim and no publication authorization. The four 800k refusals stand as dated history and nothing is pooled. No 2000 Hz value is shown before its own publication admission.

Geometry representation

Geometry representation: the bounded A/B screen found locally material effects, including some reversed architectural contrasts; the original ranges do not include it.

Strength for a directional source

Strict ISO G assumes an omnidirectional source, a claim still to be verified against the standard before publication; the directive voice sources' G is therefore published as source-normalised basis strength (VERIFICATION §4, ADR 0010 D7).