Marcel Tolkowsky’s 1919 ideal, exactly as he specified it. The zero on every chart in the registry.
Global score against T57, Tolkowsky’s 1919 ideal, measured the same way in the same material.
Diamondn = 2.417+0.00Level
Moissaniten = 2.65+0.00Level
Cubic zirconian = 2.16+0.00Level
−6T57 = 0+6
The short version
This is the zero on every chart here, and it is worth knowing exactly what it is: Marcel Tolkowsky’s 1919 proportions as he published them. Table 53%, crown 34.5°, pavilion 40.75°, girdle a knife edge, depth 59.2%, 57 facets.
We measure against it because it is the one benchmark on this site we did not design. Most modern cuts clear it, and a good deal of what clears it does so on facet count rather than optics: scintillation on this scale is a direct function of how finely a stone is cut, and nothing here is cut more coarsely than a 1919 stone. The margins are published term by term so you can see which part is which.
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
Level
88.61, the reference condition. The geometry as Tolkowsky specified it, performing as designed at the index he designed it for: brilliance of 92.3, 1.88% leak and 78.8 points of fire.
TermThis cut / standardPoints
Brillianceweight 0.3492.392.3+0.00
Fireweight 0.2078.878.8+0.00
Tiltweight 0.1690.490.4+0.00
Scintillationweight 0.1071.871.8+0.00
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓1.881.88+0.00
Sum of the six terms+0.00
This cut is the standard, so every term is measured against itself and the ledger is zero by construction.
In moissanite n = 2.65
Level
89.82. At n = 2.65 the 1919 angles disperse unusually well, returning 97.5 points of fire, second in the registry only to BL-M5. Leak rises to 7.76% and brilliance falls to 85.3.
TermThis cut / standardPoints
Brillianceweight 0.3485.385.3+0.00
Fireweight 0.2097.597.5+0.00
Tiltweight 0.1693.293.2+0.00
Scintillationweight 0.1071.871.8+0.00
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓7.767.76+0.00
Sum of the six terms+0.00
This cut is the standard, so every term is measured against itself and the ledger is zero by construction.
In cubic zirconia n = 2.16
Level
91.77. Its cleanest light budget: 98.0% useful and 0.51% leak. Seven of the eight other cuts still finish above it, almost entirely on facet count.
TermThis cut / standardPoints
Brillianceweight 0.3498.098.0+0.00
Fireweight 0.2086.886.8+0.00
Tiltweight 0.1687.187.1+0.00
Scintillationweight 0.1071.871.8+0.00
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓0.510.51+0.00
Sum of the six terms+0.00
This cut is the standard, so every term is measured against itself and the ledger is zero by construction.
The angle
Nothing here beats his pavilion on his own stone
The registry measures every cut against T57, so it is worth asking whether the standard’s own angle is the right one. We swept it.
On his architecture
Swept at four times the standard ray count, Global holds its value from 40.00° to 40.75° and peaks at 40.25°. His 40.75° is 0.05 of a point off that peak, well inside the engine’s resolution.
Across materials
Repeat the sweep at other indices and the optimum tracks the critical angle: 41.25° in cubic zirconia (n 2.16), 40.25° in diamond (2.417), 38.25° in moissanite (2.65). A 3° range, in the direction Diamond Design predicts from the index alone.
What does move it
Only the facet layout, and only by about a degree: a 145-facet pavilion shifts the plateau to 41.00° to 41.50°. Every house cut in this registry stays within three quarters of a degree of his pavilion. They depart on the crown instead, by up to three degrees.
Why the line is here
Every benchmark on a maker’s own website has the same problem: the maker chose it. This one is the exception we can point at. Marcel Tolkowsky published these proportions in 1919, they are the most-cited cut specification in the trade, and we did not get to pick them.
The cost of that choice is that the bar is not high. Six of the eight other cuts in the registry clear it in all three materials. We publish every term rather than the total precisely so that is visible, because most of what clears it does so on facet count.
What it cannot do
Sparkle density. At 57 facets there is no route to a higher scintillation figure, and scintillation on this scale is a direct function of facet count: 71.8 here against 98.4 at 185 facets, worth 2.66 points of Global before a single angle is reconsidered.
That is the number to hold in mind when reading any margin on this site. A cut at 145 or 201 facets banks roughly +2.4 to +2.7 against this standard before its optics are assessed at all. Subtract it, and what is left is the part the cutter actually designed.
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.
The rest of the registry
This cut is the standard. Every figure in the registry is measured against it.