Ahead of the 1919 ideal in all three materials, and the widest margin in diamond of any cut in the registry.
Global score against T57, Tolkowsky’s 1919 ideal, measured the same way in the same material.
Diamondn = 2.417+4.68Ahead
Moissaniten = 2.65+2.49Ahead
Cubic zirconian = 2.16+3.28Ahead
−6T57 = 0+6
The short version
In lab-grown diamond, BL-Miliano holds the largest margin over the 1919 ideal of any cut in the registry: 93.28 against 88.61. Read it honestly and +2.71 of that +4.68 is scintillation, which is to say 201 facets against 57.
Strip the facet count out and it still leads on optics by +1.99, more than any other cut manages: +0.85 of brilliance, +0.84 of fire and +0.34 of tilt, against 0.04 given back on leak at 2.25% to the standard’s 1.88%. It is ahead in cubic zirconia and in moissanite too.
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
93.28 against the standard's 88.61. Of the +4.68, scintillation is +2.71: facet count doing what facet count does. Take it out and the optics still lead by +2.14, the largest genuine margin in the diamond column, with brilliance at +0.95 and fire at +0.82.
TermThis cut / standardPoints
Brillianceweight 0.3494.892.3+0.85
Fireweight 0.2083.078.8+0.84
Tiltweight 0.1692.590.4+0.34
Scintillationweight 0.1098.971.8+2.71
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓2.251.88−0.04
Sum of the six terms+4.70
Published Global gap +4.68. The six terms reconstruct it to
0.02 of a point. The difference is rounding in the source figures, not a second method.
In moissanite n = 2.65
Ahead
92.31 against the standard's 89.82. Scintillation carries +2.71 of the +2.49. Brilliance adds +0.44 and tilt +0.30, while fire gives back −0.94: at n = 2.65 the 1919 angles disperse better than these do.
TermThis cut / standardPoints
Brillianceweight 0.3486.685.3+0.44
Fireweight 0.2092.597.5−1.00
Tiltweight 0.1695.193.2+0.30
Scintillationweight 0.1098.971.8+2.71
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓7.587.76+0.02
Sum of the six terms+2.47
Published Global gap +2.49. 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
95.06 against the standard's 91.77, top of the zirconia table. Scintillation +2.71 and fire +0.62 do the work, while brilliance slips −0.31 against a standard already returning 98.0% of its light usefully.
TermThis cut / standardPoints
Brillianceweight 0.3497.198.0−0.31
Fireweight 0.2089.986.8+0.62
Tiltweight 0.1689.287.1+0.34
Scintillationweight 0.1098.971.8+2.71
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓1.170.51−0.07
Sum of the six terms+3.29
Published Global gap +3.28. The six terms reconstruct it to
0.01 of a point. The difference is rounding in the source figures, not a second method.
Against the control
How much of this is facet count
Global gives scintillation a tenth of its weight, and scintillation is a closed formula on facet count rather than a ray measurement. T57 carries 57 facets, fewer than anything else published here, so any finely cut stone banks that term before a single ray is traced. Miliano is the cut that survives having it taken away.
The facet-count term
Of the +4.68 diamond margin, +2.71 is scintillation, a formula on 201 facets rather than a measurement. The optical margin, the part traced ray by ray, is +1.99, the largest in the registry.
Against BL-Vitruvio
Vitruvio carries Tolkowsky’s own angles at 185 facets, so it is the fair control for a finely cut modern stone. Miliano finishes +1.63 above it on Global and +1.61 on the optical terms alone. That is the largest genuine margin published here.
What the angles buy
Put Miliano’s angles on a plain 57-facet pavilion, crown 31.5°, pavilion 40.9°, table 56.2%, and brilliance rises 2.0 points over the standard while fire falls 3.9 and tilt falls 2.3. A shallow crown buys brilliance and gives fire away. On the angles alone, Miliano would be on the wrong side of that trade.
What the tiling buys
The 201-facet pavilion hands the fire back and more: fire +7.6, tilt +3.7, brilliance level. That is the design. The tiling recovers what the crown angle spends, and the finished cut is ahead on brilliance and fire at once, for 0.37 of a point more leak at 2.25% against 1.88%.
Where it departs from 1919
It keeps his pavilion and rewrites his crown
Miliano’s pavilion sits at 40.92°, seventeen hundredths of a degree off Tolkowsky’s 40.75° and inside the plateau the sweep gives for diamond. Its crown sits at 31.53°, three degrees off his. The departure is almost entirely crown.
Pavilion: +0.17°
Already where the refractive index puts it. Re-aiming it to exactly 40.75° on Miliano’s own pavilion is worth −0.29 of Global, so the cut gains nothing by moving and loses nothing by staying.
Crown: −2.97°
Re-aiming the crown to his 34.5° costs 1.78 of Global. This is the parameter the cut was designed on.
What the crown bought
Against the same 201-facet pavilion carrying 1919 angles: brilliance +4.7 and leak 4.5 points lower, paying 1.1 of fire and 4.3 of tilt. A shallow crown banks brilliance and light budget. Miliano then takes the fire back out of the facet pattern, which returns +7.6 of it.
Why that is allowed
The pavilion is pinned by the critical angle: on this engine Global holds its value across only 0.75° of pavilion, 40.00° to 40.75°. The crown holds across 2.5°, 33.0° to 35.5°. Tolkowsky derived the first rigorously from the refractive index and the second loosely from appearance. This cut leaves the pinned one alone and moves the loose one.
The facets
Where the 201 facets are, and what each group is for
Facets
Count
Angle from the girdle plane
Share of surface
Table
1
–
11.6%
Stars
8
20.6°
3.5%
Bezels
8
32.0°
20.1%
Upper girdle halves
16
40.0°
8.5%
Girdle
120
–
4.4%
Pavilion, outer tier
16
43.8°
6.5%
Pavilion, middle tier
16
42.5°
39.3%
Pavilion, inner tier
16
38.3°
6.0%
Total
201
–
100%
The crown is a standard crown
32 facets above the girdle, the same eight stars, eight bezels and sixteen upper halves the 1919 stone carries. Nothing was added up here. Miliano’s crown is a change of angle, not of count.
The pavilion is where the facets went
48 against the standard’s 24, in three tiers. Their combined girdle-to-culet slope is 40.91°, which is Tolkowsky’s 40.75° to within a sixth of a degree. The tiers are what return the fire that the shallow crown gives away.
The girdle buys roundness, not light
Rebuild the same stone with a 16-facet girdle and brilliance, fire, tilt and leak all move by less than half a point, inside the engine’s resolution. What does change is the outline. Sixteen flats leave the girdle 1.96% out of round between a flat and a corner, 0.13 mm on a 6.5 mm stone. At 120 facets it is 0.03%, two microns. It also runs thinner, 3.4% of the diameter against 5.1%, so less weight sits in the girdle. A round girdle measures true and sets true.
And it flatters the scorecard
That same rebuild costs 0.96 of Global, and 1.04 of it is the scintillation term, a closed formula on facet count. So the girdle band is worth about a point of Global that it does not earn optically. We publish the figure because it is the one the protocol produces, and we publish this note because it is the honest way to read it.
What it’s doing
Miliano carries 201 facets against the standard’s 57, and the honest way to read the margin is to split it. Scintillation is worth +2.71 of the +4.68, and that is facet count, not design.
The T-series makes the comparison exact. BL-Vitruvio carries Tolkowsky’s own angles at a comparable facet density and scores +3.04. Miliano scores +4.68. The +1.63 between them is what these angles add over Tolkowsky’s once facet count is held roughly level: +0.95 of brilliance, +0.82 of fire and +0.37 of tilt, with a light budget that matches the standard’s at 1.83% against 1.88%.
Where it gives ground
Moissanite, and not for the reason you would expect. At n = 2.65 Miliano leaks marginally less than the standard (7.32% against 7.76%) and returns marginally more light. What it loses is fire: 92.8 against 97.5, worth −0.94.
The crown geometry that lifts dispersion 4.1 points in diamond lifts it not at all in moissanite, where Tolkowsky’s own angles already reach 97.5. Miliano still finishes 2.79 ahead, but BL-Vitruvio finishes ahead of Miliano there. In that one material, the old angles win.
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.
Scintillation
The one term that is not ray-traced. It is a closed formula on the cut’s active facet count, 100(1 − e−n/45), at a tenth of the weight. Planes buried inside the solid form no facet and are not counted. The standard has 57 facets, fewer than anything else here, so every finely cut stone banks this term before a ray is traced. Each cut page reports its margin with the term removed.
Tilt
A retention figure, the share of face-up return the cut still delivers at 20°, capped at 100. It is a ratio, so read it beside the absolute return rather than on its own: a dim cut has less to lose and keeps a higher share of it.
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.