3.32 points ahead of the 1919 ideal in diamond, and the most fire of any cut measured here.
Global score against T57, Tolkowsky’s 1919 ideal, measured the same way in the same material.
Diamondn = 2.417+3.32Ahead
Moissaniten = 2.65+0.67Ahead
Cubic zirconian = 2.16+2.10Ahead
−6T57 = 0+6
The short version
Girandola is the most single-minded of the house diamond cuts. It carries 85.4 points of fire against the standard’s 78.8, the highest diamond figure in the registry.
Of its +3.32 margin, +1.55 is scintillation and +1.32 is fire, which is the term it was designed around. It pays in leak: 4.42% against 1.88%, worth −0.25. If you want coloured flash rather than white light, that is the trade, made deliberately, and on the record.
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
91.92 against the standard's 88.61. Scintillation is +1.55 of it, facet count doing what facet count does. Fire is the real work at +1.32, the largest fire contribution in the registry, paid for with −0.25 of leak.
TermThis cut / standardPoints
Brillianceweight 0.3493.192.3+0.27
Fireweight 0.2085.478.8+1.32
Tiltweight 0.1693.190.4+0.43
Scintillationweight 0.1087.371.8+1.55
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓4.421.88−0.25
Sum of the six terms+3.32
Published Global gap +3.32. The six terms reconstruct it exactly.
In moissanite n = 2.65
Ahead
90.49 against the standard's 89.82. The whole margin is scintillation: +1.55 against a +0.67 result, because brilliance and fire both go backwards, at −0.44 and −0.90. Brilliance of 84.0 is the lowest figure anywhere in the registry.
TermThis cut / standardPoints
Brillianceweight 0.3484.085.3−0.44
Fireweight 0.2093.097.5−0.90
Tiltweight 0.1696.293.2+0.48
Scintillationweight 0.1087.371.8+1.55
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓7.907.76−0.01
Sum of the six terms+0.67
Published Global gap +0.67. The six terms reconstruct it exactly.
In cubic zirconia n = 2.16
Ahead
93.88 against the standard's 91.77. Fire lifts again at +0.96, and 91.6 tops the zirconia column, while tilt hands back −0.30 at 85.2, the lowest tilt figure in that column.
TermThis cut / standardPoints
Brillianceweight 0.3497.898.0−0.07
Fireweight 0.2091.686.8+0.96
Tiltweight 0.1685.287.1−0.30
Scintillationweight 0.1087.371.8+1.55
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓0.510.51+0.00
Sum of the six terms+2.14
Published Global gap +2.10. The six terms reconstruct it to
0.04 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. Girandola banks less of it than the other house cuts, and loses least when it goes.
The facet-count term
Of the +3.32 diamond margin, +1.55 is scintillation, a formula on 93 facets rather than a measurement. The optical margin, the part traced ray by ray, is +1.77, and it is the highest share of any house cut.
Against BL-Vitruvio
Vitruvio carries Tolkowsky’s own angles at 185 facets, so it is the fair control for a finely cut modern stone. Girandola finishes +0.27 above it on Global, and +1.39 on the optical terms alone, because Vitruvio outscores it on facet count and nowhere else.
What the angles buy
Put Girandola’s angles on a plain 57-facet pavilion, crown 35.1°, pavilion 41.2°, table 54.0%, and fire rises 5.5 points over the standard on its own. Brilliance falls 3.5 and leak rises 4.3. On that plain pavilion the fire is the angles, and so is the light it costs.
What the tiling buys
The 93-facet pavilion pays that bill back: brilliance +4.3, leak −1.8, and a further +1.1 of fire on top. The dispersion is designed and the brilliance is recovered. It is a trade made deliberately, and on these numbers it holds.
Where it departs from 1919
The closest of the house cuts to 1919
Girandola sits nearest Tolkowsky on both angles: pavilion 41.22° against his 40.75°, crown 35.10° against his 34.51°. It is also the only house cut that steepens the crown rather than shallowing it. Its whole angle departure is worth +0.19 of Global, and the fire it is named for turns out to be over-determined.
Pavilion: +0.47°, crown: +0.59°
Both inside the band the sweep gives for a pavilion of this facet count. Re-aiming the crown to 34.5° costs 0.52 of Global and the pavilion 0.24, the smallest angle contributions of the three house cuts.
What the angles bought
Against the same 93-facet pavilion carrying 1919 angles: fire +2.0 and tilt +1.3, paying 2.0 of brilliance and 1.3 of leak. A small, deliberate trade in the direction the cut is named for.
The fire is over-determined
Against the standard, the angles on their own are worth +5.8 of fire and the facet pattern on its own is worth +5.4. Doing both yields +7.4, not +11. The two deliver dispersion by overlapping means, so they do not add. Either half would give most of this cut’s fire; together they give a little more.
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.
What it’s doing
The ledger is unusually lopsided. Brilliance barely moves, at +0.27. What Girandola does is take dispersion up 6.6 points, worth +1.32, the largest fire contribution in the registry, and accept the consequence: light that travels further inside the stone before it returns is light that more often does not return at all.
Two and a half points of extra leakage cost it −0.25. Set against the +1.55 it banks on facet count, the fire is the part of this cut that is actually designed, and it is the part worth paying for.
Where it gives ground
Leak, and moissanite. At 4.42% it holds less light than the standard, than Miliano, or than either of the shorter T-series references.
And the geometry that buys fire in diamond stops buying it at n = 2.65: in moissanite Girandola returns less fire than the standard does, 93.0 against 97.5, worth −0.90. Its +0.67 there is the weakest showing of the three house diamond cuts, and every point of it comes from facet count. The trade only works in the material it was drawn for.
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.