The 1919 ideal with a real girdle instead of a knife edge, and slightly better for it.
Global score against T57, Tolkowsky’s 1919 ideal, measured the same way in the same material.
Diamondn = 2.417+1.24Ahead
Moissaniten = 2.65+1.22Ahead
Cubic zirconian = 2.16+1.00Ahead
−6T57 = 0+6
The short version
T73 is the standard with sixteen girdle facets added and nothing else touched, so the pair isolates one variable: what happens when the knife edge Tolkowsky specified is replaced by a girdle a cutter can actually finish.
It finishes 1.24 points ahead in diamond, 1.22 in moissanite and 1.00 in cubic zirconia. Most of that is sparkle density, at +0.85, but not all: the girdle also buys +0.29 of tilt stability and +0.20 of brightness, and gives back 0.10 of fire. A knife edge is an idealisation, and it costs a little light.
The full account of what Tolkowsky calculated, and what each cut in the T-series changes about it, is on the 1919 ideal.
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
Ahead
89.85 against the standard's 88.61. Scintillation is +0.85 of the +1.24, tilt +0.29 and useful light +0.20, against −0.10 of fire. The knife edge is the only thing that changed.
TermThis cut / standardPoints
Useful lightweight 0.3492.992.3+0.20
Fireweight 0.2078.378.8−0.10
Tiltweight 0.1692.290.4+0.29
Scintillationweight 0.1080.371.8+0.85
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓1.911.88−0.00
Sum of the six terms+1.24
Published Global gap +1.24. The six terms reconstruct it exactly.
In moissanite n = 2.65
Ahead
91.04 against the standard's 89.82. Near-identical behaviour at a different index: fire matches the standard to within 0.3, leak lands within 0.36%, and scintillation again carries most of the gap.
TermThis cut / standardPoints
Useful lightweight 0.3486.085.3+0.24
Fireweight 0.2097.297.5−0.06
Tiltweight 0.1694.193.2+0.14
Scintillationweight 0.1080.371.8+0.85
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓7.407.76+0.04
Sum of the six terms+1.21
Published Global gap +1.22. The six terms reconstruct it to
0.01 of a point. The difference is rounding in the source figures, not a second method.
In cubic zirconia n = 2.16
Ahead
92.77 against the standard's 91.77. Useful light is identical to the standard's, to the decimal, at 98.4%. The margin is +0.85 of scintillation and +0.15 of everything else.
TermThis cut / standardPoints
Useful lightweight 0.3498.498.0+0.14
Fireweight 0.2086.886.8+0.00
Tiltweight 0.1687.487.1+0.05
Scintillationweight 0.1080.371.8+0.85
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓0.600.51−0.01
Sum of the six terms+1.03
Published Global gap +1.00. The six terms reconstruct it to
0.03 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 that the knife edge Tolkowsky specified has been replaced by a girdle a cutter can actually finish.
Sixteen girdle facets are worth +0.85 of scintillation, which is expected. What is less expected is the rest: tilt improves 1.8 points (+0.29) and useful light 0.6 (+0.20), against 0.5 points of fire given back. A knife edge is an idealisation on paper, and on this engine it costs a little light.
What it costs
Fire, and only fire: 78.3 against 78.8, worth −0.10. It is the single term where the knife edge was genuinely better.
Everything else about this stone is the standard, which is exactly what makes it useful. Read T57, T73 and T185 as one design at three densities and you can price a facet count directly.
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.