Proof that girdle faceting changes sparkle density and nothing else.
Global score against Tolkowsky 1919, measured the same way in the same material.
Diamondn = 2.417−1.80Behind
Moissaniten = 2.65−1.82Behind
Cubic zirconian = 2.16−1.82Behind
−2Tolkowsky 1919 = 0+2
The short version
Tolkowsky 73 is the 1919 ideal with sixteen girdle facets added and nothing else touched. It sits 1.80 points below the 185-facet standard in diamond, 1.82 in moissanite and 1.82 in cubic zirconia, a gap that barely moves across three different refractive indices, because it is essentially one term.
Scintillation: 80.3 against 98.4, worth 1.81 points. Everything else nets to zero to within a hundredth of a point.
The ledger
Where the points come from
Global is a weighted sum of six terms. Subtract the standard's figure from this cut's,
term by term, and the six differences add back up to the published gap. Nothing is hidden in the total,
so you can see exactly which part of the stone is doing the work.
In diamond n = 2.417
Behind
89.85 against the standard's 91.65. Five terms cancel to zero; scintillation accounts for the entire 1.80-point gap. The tightest control result in the registry.
TermThis cut / standardPoints
Useful lightweight 0.3492.992.6+0.10
Fireweight 0.2078.378.7−0.08
Tiltweight 0.1692.292.5−0.05
Scintillationweight 0.1080.398.4−1.81
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓1.912.17+0.03
Sum of the six terms−1.81
Published Global gap −1.80. The six terms reconstruct it to
0.01 of a point. The difference is rounding in the source figures, not a second method.
In moissanite n = 2.65
Behind
91.04 against the standard's 92.86. Identical behaviour at a different index: fire matches the standard exactly (97.2), leak lands within 0.06%, and scintillation again carries the whole gap.
TermThis cut / standardPoints
Useful lightweight 0.3486.086.1−0.03
Fireweight 0.2097.297.2+0.00
Tiltweight 0.1694.194.0+0.02
Scintillationweight 0.1080.398.4−1.81
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓7.407.46+0.01
Sum of the six terms−1.82
Published Global gap −1.82. The six terms reconstruct it to
0.00 of a point. The difference is rounding in the source figures, not a second method.
In cubic zirconia n = 2.16
Behind
92.77 against the standard's 94.59. Useful light is identical to the standard's, to the decimal (98.4). The gap is 1.81 points of scintillation and 0.01 of everything else.
TermThis cut / standardPoints
Useful lightweight 0.3498.498.4+0.00
Fireweight 0.2086.887.0−0.04
Tiltweight 0.1687.487.1+0.05
Scintillationweight 0.1080.398.4−1.81
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓0.600.58−0.00
Sum of the six terms−1.80
Published Global gap −1.82. The six terms reconstruct it to
0.02 of a point. The difference is rounding in the source figures, not a second method.
What it's doing
This is the cleanest experiment in the registry. Same crown, same pavilion, same angles as the standard. The only variable is how finely the girdle is faceted.
In diamond, useful light goes up 0.3, fire goes down 0.4, tilt goes down 0.3 and leak improves 0.26: five terms that cancel each other to +0.00. The whole 1.80-point gap is the scintillation term.
It is worth sitting with that: two stones with effectively identical optical behaviour, separated on the Global scale by facet count alone. It is also the reason the registry publishes all six terms rather than a single number. The number can be moved without the stone changing.
Where it gives ground
Nothing optical: that is the point. It is behind the standard in the registry because the registry counts sparkle density, and this stone has 112 fewer facets to produce it with.
How to read this
The protocol
Monte-Carlo ray census on exact facet geometry: 3,200 rays face-up plus 2,200 at
20° tilt, cosine-weighted from a 7° near-vertical cone. Every cut is scored against Tolkowsky's 1919 ideal,
measured the same way in the same material.
These are engine estimates, ± 2 points, not lab-certified grades.
A lead of under half a point sits inside the engine's resolution, so we don't claim it as a win. A deficit is reported as a deficit, however small.
Symmetry
Reads 100 for every cut, because each is modelled from exact geometry rather than
a finished stone. It contributes nothing to any comparison here: it cancels, and we show the row anyway.
The rest of the registry
Behind the standard in all three materials. Read the decomposition for why.