Absurdly Optimized Gelato: A Calculator Built on the Italian Bilanciamento

· Absurdly Optimized ·

51 min read Original article ↗

A dense quenelle of peach sorbetto in a glass bowl, its surface glossy and finely textured

This is what the arithmetic is for: peach sorbetto, dense enough to tear rather than crumble, glossy instead of icy, and soft straight out of a home freezer. There is no stabiliser gum in it and no dextrose either, because the peach brought its own antifreeze, which took the longest to work out and is the part I am proudest of.

Gelato is churned with far less air in it than ice cream and carries less fat (Caviezel), so the flavour arrives with nothing standing in front of it. A pistachio one tastes overwhelmingly of pistachios; a strawberry one of strawberries, rather than of cold sweet cream. The best I have ever eaten was at Cremeria Cavour in Bologna, and I came home wanting to be able to make it whenever I felt like it. I had by then already researched gelato makers to the point of buying the one that won, a Musso, so I considered the equipment question comprehensively settled. I looked up GialloZafferano’s gelato alla panna and ran a batch through it (GialloZafferano). The texture was perfect. It was also far too sweet.

A scoop of vanilla-flecked gelato in a red ramekin with a spoon, the GialloZafferano gelato alla panna the article starts from

The starting point: my first batch of GialloZafferano’s gelato alla panna, vanilla flecks and all. Very good, a shade too sweet, and the reason for every gram that follows.

The obvious move is to use less sugar. The obvious move gives you a brick. That is because gelato never actually freezes solid: some of its water turns to ice and the rest stays behind as a cold syrup, and the ratio between the two is what you feel when the spoon goes in. Sugar sets that ratio, because dissolved sugar drops the freezing point, so at any given temperature less of the water has gone over to ice (Caviezel). Which means the sugar in a gelato is holding down two jobs at once, and firing it from one fires it from both.

Finding that out turned into reading a literature I had not known existed, and then into an unembarrassed love for Luca Caviezel’s six hundred and eighty-six pages on the science of artisan gelato (Caviezel, 2016), which is now, straightforwardly, my favourite book. Professionals do not accept that trade; they use two sugars. One of them is dextrose, which I had spent years avoiding on the grounds that it sounded like something out of a factory. It is glucose, the same sugar already sitting in fruit and honey, sold as a white powder because that is what a sugar looks like once you dry it. Per gram it pulls the freezing point down about twice as hard as table sugar and tastes about three-quarters as sweet (Caviezel). So a gelatiere hands part of the sugar’s work to dextrose and the two jobs come apart: the dextrose holds the gelato soft, and the table sugar is left deciding nothing but how sweet it is. The ingredient I had been refusing was the one that would have let me use less sugar.

By then I had a second gelato to chase. Osteria La Sangiovesa is my favourite restaurant in Italy, and its own cookbook prints the gelato di crema it serves (La Sangiovesa), which is a different animal again: no cream in it at all, and enough egg yolk to carry the whole thing on its own. Two gelati, then, and twenty more behind them, each one the same handful of percentages solved over again around whatever it has to dissolve. Doing that by hand, once per flavour, is not a reasonable way to spend an evening. Building something to do it for me took far longer than doing it by hand ever would have, which is obviously the wrong trade, and I would make it again tomorrow: it means the Bologna version is something I can have in February without leaving the house.

What actually matters

Underneath the flavour, a gelato is a handful of fractions and one curve. Get both right and it comes out denser, colder and more intense than any ice cream, and it melts almost as soon as it lands. Get either wrong and no amount of good milk will rescue it.

The fractions are what the Italian trade calls the bilanciamento, the balance: total solids, sugars, fat, and the milk solids that are not fat, which in Italian are the sostanza secca, the zuccheri, the grassi and the SLNG. Each is a percentage of the finished mix by weight, and each has to land inside a band the trade agrees on. The bands here are Luca Caviezel’s, out of Scienza e tecnologia del gelato artigianale, the field’s reference text (Caviezel, 2016), and they are what the Carpigiani university teaches to most of the gelatieri in Italy (Carpigiani).

The second lever is a curve rather than a temperature, because the mix does not freeze all at once. The first water to freeze leaves its sugar behind, so the syrup that remains is more concentrated than what you started with and has to go colder still before any more of it will freeze, and then colder again. Every degree you take away turns a little less water to ice than the degree before it did. The craft is picking a sugar mix that puts about three-quarters of the water into ice at the temperature you actually serve at and leaves the last quarter as syrup (Caviezel). That last quarter is the difference between a scoop that gives under the spoon and a block you could level a table with.

The bands are not mine, and neither are the sugar numbers nor the freezing rule. All of it comes out of one 686-page book that Italian gelatieri actually train on, and what sits on top of it here is a compression, a lossy one. If you want the real thing rather than my summary, buy Caviezel (Caviezel, 2016). My own contribution is the arithmetic: every ingredient sized in grams to hit those targets, and the sugar solved rather than scaled, so the gelato comes out soft at the temperature you serve it and no sweeter than it ought to be.

The Italian classics fall into three bases, and the calculator makes all of them. The milk base is milk and cream and sugar with no egg in it at all, which is what fior di latte and gelato alla panna are (Caviezel). Fold yolks into that and you have gelato alla crema, the cooked custard, and Osteria La Sangiovesa’s Romagna version goes further by dropping the cream entirely and leaving a generous dose of yolk to do the work on its own (La Sangiovesa). Fruit is the third, and in Italy fruit means sorbetto: fruit, sugar and water, and no dairy at all, because cream mutes fruit and pales it, and the trade’s own definition of a fruit gelato is one that carries no dairy fat (Carpigiani). Everything else on the list is one of those three with something stirred into it, twenty-five flavours from dark chocolate through pistachio to zabaione, each re-solving the same fractions around whatever it brings with it.

One thing is missing on purpose, and it is the one an Italian gelateria would never leave out: stabiliser. Carob and guar gums are standard there, and they do real work, binding up the free water so the ice crystals cannot coarsen (Zeppa). But nearly all of that work goes on fighting what a week in a freezer does. A powerful batch freezer freezes fast, a fast freeze grows many tiny crystals instead of a few big ones, and the gelato is smooth the moment you draw it whether there is gum in it or not (Zeppa). Eaten within a day or two it never misses the stabiliser. Left for a week it does, and if you want it to keep that long, use carob, which is a bean rather than an industrial blend.

Background: the Italian system

Nobody invented gelato, and Caviezel is the one who says so. He opens his history by refusing to award the thing to any country at all, borrowing Odysseus telling the Cyclops his name is Nobody: it was many, many Nobodies, he writes, who made what we now call gelato (Caviezel, 2016). The technique moved the way techniques do, from China to India to Persia to the Arabs, then to the Greeks and the Romans. When the Arabs took Sicily in the ninth century they brought cane sugar and citrus with them, and it was there that the sorbetto stopped being a drink and became something you ate with a spoon (Caviezel).

Two Italian moves after that do matter. Bernardo Buontalenti staged frozen creams for the Medici court in sixteenth-century Florence, which makes him the ancestor of crema rather than of the egg-free fior di latte (Treccani). The bigger one is mantecatura: churning the mix while it freezes so it never sets into coarse crystals, tied to the Sicilian Francesco Procopio dei Coltelli and his Paris café in the 1680s (Treccani). A court spectacle and a café, four centuries ago, and the machine on your counter now out-freezes both of them without being asked.

Italy’s contribution was the discipline, and the two desserts part company on fat and on air. American ice cream is required by law to carry at least 10% milkfat (21 CFR §135.110), where Caviezel bands a gelato at 6 to 12% and calls 8% a good average (Caviezel). Air is where they diverge furthest. Caviezel puts a milk-base gelato at 35 to 40% of its own volume, with 35% the level he says not to push past, and a fruit sorbetto lower still at 20 to 30%, since it has neither the egg nor the fat to hold a bubble (Caviezel). That is where the density comes from, and why a gelato goes soft on the tongue faster than an ice cream does. American law, for its part, regulates the air only by weight: a gallon of ice cream may not come in under 4.5 pounds (21 CFR §135.110).

Those differences are written down as bands, and the calculator aims at them. For the milk base: 16 to 22% sugar, 6 to 12% fat, 8 to 12% milk solids, and 32 to 42% total solids. For the fruit base, 26 to 31% sugar and no dairy fat at all (Carpigiani).

Balancing the sugars stops being guesswork once each one carries two numbers. POD (potere dolcificante) is sweetening power and PAC (potere anticongelante) is freezing-point-depressing power, both scored against sucrose at 100 (Calzari). They do not move together, which is what makes the split possible: fructose is far sweeter than sucrose per gram but drops the freezing point by the same amount, while dextrose gives up sweetness to buy antifreeze. The Italians built a small two-number bureaucracy on that fact, and I mean that admiringly.

And none of it is law. Neither Italy nor the EU defines gelato or fixes what goes in it, which the trade concedes in its own paperwork: the industry’s voluntary code exists, by its own preamble, precisely because no specific rule does, and the one milkfat figure it sets is 8% for crema alla panna (IGI). A 2018 bill would have put minimum total solids into actual law. It died in committee (Camera dei Deputati). The 3.5% minimum you will find repeated online is not a law either; it is the fat content of whole milk, transplanted into gelato lore by somebody and never checked since. So the whole apparatus is a trade agreeing with itself, which is exactly why I was not willing to take its most important number on faith.

The freezing curve, derived and then checked against Caviezel

This is the number I was least willing to take on trust, and happily it is the one you can derive. The freezing point of a liquid depends on how many separate particles are dissolved in it and not at all on what those particles are. Raoult’s law puts that in an equation: the freezing point falls in proportion to the moles of sugar dissolved per kilogram of water (Treccani).

\Delta T_f = K_f \, \frac{n_{\text{sugar}}}{m_{\text{water}}}

Only one term in it is yours to set. K_f is 1.86 °C kg/mol, a constant of water rather than of your recipe, and the kilograms of water are whatever you poured. That leaves the moles of sugar, and moles are not grams. A gram of a small sugar holds more molecules than a gram of a big one, so it pushes the freezing point further down. Sucrose weighs 342 g/mol; glucose and fructose weigh 180. Divide one by the other and you get 1.9. So a gram of either of the small sugars should depress the freezing point about 1.9 times as hard as a gram of sucrose, which is exactly the PAC of 190 the Italian craft tables hand them (Calzari). Lactose is a disaccharide like sucrose and duly comes out at 100. The convention and the physics agree because the convention is the physics, written down by people who had a refractometer and no patience for theory. Nothing else in the mix contributes anything: fat and protein do not move the freezing point at all, only sugars and salts do, and that is why whole milk freezes at just −0.55 °C with almost all of that owed to its lactose (Caviezel).

From that one idea the whole curve follows. Model the water freezing out and the syrup left behind concentrating as it goes, and you can say how much of the water is ice at any temperature you like. I did not expect this to survive contact with a real measurement, because two molar masses and one equation is not much to bring to a dessert that people have spent four centuries getting right by hand. Caviezel measured the curve for a standard mix and printed it as his fig. 109, so I laid mine over his. About 54% of the water frozen at −6 °C against his 55 to 57%, about 80% at −14 °C against his roughly 80% (Caviezel). That is a closer agreement than I had any right to expect, and it means the scoopability the calculator reports is not a rule of thumb but physics landing on the reference text’s own measurements. Every mix here is balanced so that about three-quarters of the water is ice at the −11 °C an Italian gelateria scoops at, which sits between Caviezel’s two measured points. What the physics will not tell you is which sugar to reach for.

Dense white gelato being churned in a Musso batch freezer, the dasher and paddle cutting a furrow through the stiff mix

Seven-tenths of the water in there has already turned to fine ice, which is about the point where the dasher starts to labour. The mix is stiff enough to hold the trough the paddle cut, and the ridges it shouldered up against the wall are standing exactly where they were left.

The sugar blend: two sugars, two jobs

Nobody decides how the sugar splits; the solver does, and it works to one instruction: hold the sweetness at a fixed target and let the freezing point do all the moving. That is only possible because the two come apart by ratio. Trading a gram of sucrose for a gram of dextrose buys a lot of softness for a little sweetness (Caviezel), so the solver spends dextrose until the curve reaches the −12 to −14 °C an Italian gelateria holds its case at (Carpigiani), then stops. Osteria La Sangiovesa’s crema does exactly this, carrying dextrose alongside its sucrose, which is why it scoops soft without tasting any sweeter (La Sangiovesa).

You can reach the same softness on sucrose alone. The mix freezes harder without dextrose in it, and the only lever left is to add more sugar, which is more sweetness, which is precisely why the GialloZafferano recipe reads the way it does: it is all sucrose, and that one sugar is carrying the freezing and the tasting at the same time (GialloZafferano). Dextrose is the only purified thing in this entire recipe, and if you would still rather not, skip it. The calculator will balance on sucrose alone and tell you to temper the gelato on the counter instead, which is the same scoop ten minutes later.

A jar of dextrose on a pantry shelf between Bob's Red Mill milk powder and a box of Sugar in the Raw, its label printed with a glucose molecule

The only purified thing in the recipe, sitting between a bag of nonfat milk powder and the box of raw cane sugar it is there to out-work. It looks industrial and it reads industrial, which is exactly the reaction that kept it out of my kitchen for years.

That box of raw cane sugar raises its own question, since it is what I actually cook with, and for a long time I assumed it was quietly doing something the white bag would not. It is not. Caviezel settles it in one flat line: however different the grades look, it is always the same disaccharide, sucrose (Caviezel). Cane against beet is the same non-answer, because Codex holds white sugar of either origin to a polarisation of at least 99.7, which is as close to pure sucrose as the measurement gets, and the USDA puts the ordinary bag at 99.8% sucrose (Codex Alimentarius; USDA). Raw cane is that identical crystal wearing a film of cane molasses, about two parts in a thousand of it (USDA), which is an aroma rather than a number.

One grade does move the arithmetic. Soft brown sugar is about 95% sugar rather than the white bag’s 99.8, the balance being molasses and the water molasses carries, and roughly a fortieth of the sugar it does have arrives as glucose and fructose instead of sucrose (USDA). Those two weigh a little over half what a sucrose molecule weighs, so gram for gram they depress the freezing point nearly twice as hard. Tell the calculator which box you opened and it puts about 3% more of it on the scale to reach the same sugar, then reports a mix that scoops a fifth of a degree softer. Neither correction is one you would taste. The molasses is not small at all, and it will walk straight over a peach.

How much dextrose a mix gets is set by your machine rather than by your palate, which is the part nobody warns you about. Caviezel draws when about 70% of the water has frozen (Caviezel), and every batch freezer has a floor, the coldest the mix will reach before the dasher stalls: about −11 °C for a prosumer compressor, −9 for a home one, and only −5 for a frozen-bowl canister (Porto). I expected the expensive machine to matter here and it barely does. A fior di latte hits 70% frozen at around −9 °C, so any compressor gets there and the calculator leaves the full dextrose in; a cheap home compressor makes essentially the same gelato as my Musso Lussino, a couple of minutes slower. The frozen bowl is the real exception. It tops out at −5 °C, where the full-dextrose mix is barely 45% frozen, so it draws a slush that coarsens into ice in the freezer. For that machine the calculator strips the dextrose out entirely and lets sucrose alone set firmer at the warmer temperature the bowl can actually reach, which is what the all-sucrose GialloZafferano recipe was doing by accident all along (GialloZafferano). It does not buy that firmness with sweetness, though: it holds the sweetness where it was aimed and takes the total sugar down instead. The bill is texture, and you get a leaner mix that sets harder and wants a longer temper on the counter.

Fat, body, and the two ways to make a gelato sandy

Fat is the number everyone reaches for, and in a panna base the cream has already settled it: about 10.7%, the rich classic level, all of it from the cream (GialloZafferano). Body is a different number and comes from the other solids. Milk proteins hold the air and the water, and a gelato short of them tastes thin no matter how much cream went in, which is why the trade bands them separately at 8 to 12% milk solids-not-fat in the milk base (Carpigiani). Here is the trap. Richness lives in the cream, so more cream looks like the fix, but cream is fat-rich and solids-poor: another ladle pushes the fat past where you wanted it and leaves the milk solids exactly as short as they were. What fixes it is a spoonful of skimmed milk powder, which is milk with the water taken out. The calculator never sets that powder by hand. It holds a total-solids target and works backwards to the powder that reaches it, so the milk solids are derived rather than dialled. With no yolk and no cocoa to help bind the water, fior di latte is the tightest balance on the list, and I hold its milk solids low in the band.

Those solids have two ceilings, and crossing either turns body into grit. Lactose is only weakly soluble, and the syrup left behind concentrates as the water freezes out, so past a point the lactose drops out of it as crystals that the tongue reads as sand: the defect Italians call sabbiosità (Zeppa). Caviezel’s rule keeps lactose under about 10% of the water in the mix, and the calculator checks it on every batch (Caviezel). The second ceiling is hydration. Milk solids can only take up so much water before the rest of the powder sits there undissolved and reads sandy for a different reason, and that limit is near 15 g of solids per 100 g of water (Caviezel). So a mix can carry only as much powder as the water left over from the sugar and the fat will actually hydrate. Both ceilings get checked on every batch, because they are the two ways to wreck a gelato by trying to make it richer.

No stabiliser, and the yolk as its own emulsifier

A professional mix carries two things this one does not, and neither is an oversight. The emulsifier is already in the eggs: yolk is full of lecithin, and Caviezel reckons about 8% yolk in the mix makes a separate emulsifier superfluous (Caviezel). The crema here runs at 12.8% yolk, comfortably past his number, so it emulsifies itself. Fior di latte has no yolk at all and leans on milk protein and a fast freeze instead, which is one more reason it is the fussiest thing on the list. The stabiliser is the other, and the thing to understand about a gum is that it does nothing for you on day one. It is there for week three, turning free water into bound water so a tub survives the freezer door opening and closing (Caviezel). Add carob if you mean to keep the gelato past a few days; carob gum is ground seed. The emulsifier I left out is called mono- and diglycerides of fatty acids, and I would sooner put a seed in a dessert than something I have to spell twice.

Maturazione: the wait that does the most

The least glamorous step in this method is the one that decides the texture. The mix goes into the fridge at about +4 °C and sits there four or five hours at the very least; overnight is better. Caviezel gives that rest two jobs: the fats crystallise, and the proteins from the milk and the eggs take up the free water as water of hydration (Caviezel). Free water freezes fast in the machine and hydrated water is much slower to go, so an aged mix runs less risk of big crystals and comes out smoother for it (Caviezel). A lean mix needs the rest more than a rich one, because fewer solids mean less in the mix to hold the water down (Caviezel), which is why fior di latte, carrying less of everything than anything else here, is the flavour the wait does the most for. It would be tidy if this explained a sandy gelato too, and it does not. Sand is lactose dropping out of the syrup, or milk powder past what the water can hydrate, and both of those are settled at the scale rather than in the fridge; Caviezel keeps the two faults in separate rows of his defect tables under separate remedies (Caviezel).

The rest has a ceiling as well as a floor. Stabiliser blends hydrate fast enough now that Caviezel puts the optimum at four to six hours, though his own habit runs wider: into the maturation tank in the evening, out in the morning, twelve to fourteen hours by his count. Before those blends existed the trade held its mixes two or three days (Caviezel). Past the overnight mark there is nothing further to collect, but the risk keeps accumulating. Sour flavour has a row of its own in the defect tables, and two of its causes are process rather than ingredient: an ageing that ran too long, or one that ran too warm. A mix held past the maximum can turn sour in otherwise ideal conditions, and the tank is not to go above +4 °C (Caviezel). So the useful window runs from about four hours to about a day, and stretching to the full day needs a fridge that genuinely holds +4 °C. A door shelf at +7 trades a night for hours that add nothing.

The third thing the rest does needs no chemistry at all: it makes the mix cold, and going into the machine cold is what decides how fine the ice comes out. Crystal size is set by how fast the water freezes, and the band Caviezel treats as critical runs from the freezing point down to −8 °C, to be crossed as fast as the machine can manage (Caviezel). These mixes freeze at around −2 to −3.5 °C, so there are only a few degrees to cross. A mix poured in at room temperature spends its first minutes merely getting to the top of that band; a mix at +4 °C is nearly there when it goes in, which is why Caviezel lists pre-cooling the freezing cylinder among his precautions (Caviezel). Run a compressor machine empty for a few minutes first, and freeze a canister bowl solid the whole way through.

The draw itself is a consistency rather than a temperature, and I know that because I once spent an evening proving the opposite. An earlier version of this recipe printed −11 °C as the target, and I churned toward it until the Musso seized. That figure is the machine’s stall floor, not anything to aim at. The dasher never scrapes the barrel completely clean, so the last two degrees never reach the gelato at all: they go into the frozen crust on the wall, and the crust thickens until it grabs the blade. What you actually want is the mix standing thick and matte with the dasher still turning easily, which on my machine lands near −8 or −9 °C if I bother to probe it, and Caviezel draws at around −7 to −8 and leaves the rest to the hardening cabinet (Caviezel). So watch the mix, not the probe. This is the only recipe that has ever jammed my machine, and I wrote it.

Fior di latte: the plainest base has nowhere to hide

Every other flavour on the list arrives with something to hide behind. Fior di latte does not, which makes its balance the fussiest here. The bowl takes milk, cream, sugar and a spoonful of skimmed milk powder, and there is nothing else in it to cover for a number that came out wrong. So the calculator holds the sweetness at 18%, low in the band and low deliberately. Caviezel keeps every one of his base mixes down at 16 to 18% sugar because the flavouring pastes that follow carry sugar of their own and lift the finished gelato to the 19 or 20% he actually wants (Caviezel). No paste is coming for this one, so the base has to arrive at the spoon already right. Get the fat and the solids inside their bands as well and what you have is cold sweet cream and almost nothing else: milk, tasting more like milk than milk does. That is the exam, and a bad one has nowhere to hide. Neither does the cook.

Fior di latte also has the shortest history here, and for most of that history it did not exist at all. Antonio Latini’s milk ice of 1692 was already egg-free, but it carried about 37% sugar with candied citron through it (Latini), close to double what this calculator puts in. Two centuries later Pellegrino Artusi still had no plain milk or cream ice whatsoever: his cream flavour was a custard on eight yolks, and coffee or coriander or toasted almond went into that same custard (Artusi). The egg-free white base is a modern category, settled by the trade long after the tradition it now sits inside (Caviezel). The plainest thing on the menu turns out to be the youngest.

Recipe (era) Egg yolk Sugar Fat Milk solids Total solids
Latini, 1692 (first milk ice, no egg) none ~37% ~2% ~4%
Artusi, 1891: no plain milk or cream ice. His cream flavour is the egg crema, though his chocolate and caffe-latte ices are egg-free milk (Artusi).
Caviezel, modern panna base none ~17% ~9% ~9% ~35%
This calculator none 19.5% 10.7% 8.3% 38.5%

Every figure here is a percentage of the finished mix. The sugar row is a weight and part of that weight is dextrose, so the mix reads 19.5% on the scale and tastes like the 18% it was balanced to. The one honest outlier is the fat, which at 10.7% sits near the top of Caviezel’s 6 to 12% band and above every panna base he prints (Caviezel) – on purpose, because this is a generous fior di latte rather than the middle of his range. Latini’s figures are converted from period Neapolitan units, so read them as approximate (Latini).

Crema: the Romagna custard, no cream at all

Cook yolks into milk and sugar and you have crema, the egg base. The Romagna version I took from Osteria La Sangiovesa leaves out the cream and the milk powder, which means the yolk has to supply the fat, hold the mix together and carry the flavour, all three, by itself (La Sangiovesa). That takes a startling quantity of yolk: the calculator uses La Sangiovesa’s own dose, 12.8% of the mix, against the barely-half-that in Caviezel’s own crema, which gets to the same fat by leaning on cream (Caviezel). Take the cream away and the yolk is the only thing left to carry it. Because La Sangiovesa weighed that dose with Italian eggs, the calculator models an Italian yolk at about 32% fat, which is fattier than a US one (Caviezel), and it gives the dose as a weight rather than a count, since a yolk is not a standard size; it converts to US-large yolks at 17 g each, where an Italian large runs nearer 19. At that dose the fat lands at 6.2%, the lean end of Caviezel’s 6 to 12% band, so no cream is needed to reach it, and the yolk sails well past the 8% at which its own lecithin makes a separate emulsifier pointless. The powder is the one thing you cannot also drop: without it the milk solids stop at 6.3%, which is Caviezel’s floor rather than his median (Caviezel). And you can taste every bit of it. Crema comes out rounder than fior di latte, with a savoury edge that stops just short of eggy, and it is the one I keep going back for.

Its paper trail runs three centuries. The first milk ice anyone wrote down, Latini’s cooked-milk sorbet of 1692, had no egg in it at all and buried the dairy under sugar (Latini). By Artusi’s 1891 recipe the yolk had arrived and the sugar had halved, a litre of milk to eight yolks (Artusi). Caviezel’s two cremas bracket that: a lean modern one reaching its fat through cream and powder, and a rich Sicilian base of cream and a dozen yolks, the one that made the Swiss pastry houses of Palermo famous (Caviezel). This calculator lands on Artusi’s egg and Artusi’s fat, and leaves him only on sugar, carrying nearly half again as much and eating a quarter sweeter for it.

Recipe (era) Egg yolk Sweetness (POD) Fat Milk solids Total solids
Latini, 1692 (first milk ice, no egg) none ~37 ~2% ~4%
Baldini, 1775 – a medical treatise that first classified the sorbetti (the milk family, plus the aromatic chocolate, coffee, and pistachio ones) but fixed no doses (Baldini).
Artusi, 1891 (lean egg, no cream) ~11% ~16 ~6% ~7% ~30%
Caviezel, modern crema (cream + powder) ~7% ~20 ~8% ~9% ~38%
Caviezel, rich Sicilian base (cream + yolk) ~13% ~19 ~11% ~6% ~38%
La Sangiovesa, this calculator (yolk only) 12.8% 20 6.2% 6.3% 36.6%

Every figure here is a percentage of the finished mix, and the sweetness column is POD, sucrose-equivalent rather than sugar by weight. Read down that column and this crema sits level with Caviezel’s modern one, even though it carries 21.7% sugar by weight against his 19%, because dextrose is about three-quarters as sweet as sucrose gram for gram (Caviezel). Three caveats: the historical POD figures are worked out from each recipe’s sugar and milk solids rather than quoted, Latini’s row is converted from period Neapolitan measures, and the 32% fat for an Italian yolk is an assumption.

Dark chocolate: softer and richer, not darker by starving it

Chocolate is the flavour that fights back, and it is reckoned one of the hardest in the trade to get right, because cocoa butter hardens at freezer temperature and the fibre in the powder stiffens everything else (Caviezel). Faced with that, the instinct is to pull the sugar down until the cocoa reads dark and serious, and the instinct is exactly backwards. Caviezel’s four chocolates say so plainly: the darkest of them is also the least sweet, with its sugar sitting inside the same 16 to 18% band he holds a plain cream base to, and what he adds against the hardness is more sugar rather than less, a higher percentage of it and preferably of the alternative kinds (Caviezel). So the calculator does what it does everywhere else and splits the two jobs apart. Sweetness is pinned at 18% POD, level with the white base, while the softness comes off the freezing curve instead: the mix is balanced to leave more of its water liquid at serving than any other cream flavour here, which pushes the dextrose share up on purpose and costs nothing in sweetness, because the dextrose is doing that work (Caviezel). What makes it dark is what goes in, not what is left out. The yolk runs to 7% against the crema’s 12.8%, a custard stopped short; the fat lands where his richest chocolate’s does (Caviezel); and the cocoa is a low-fat 10/12, the grade he recommends for carrying the least cocoa butter (Caviezel), alkalised and cooked into the mix rather than steeped, so it blooms. A dark bar melts in on top of that for the gloss its cocoa butter gives. What comes out is dense and very nearly black and softer under the spoon than any of the cream flavours at the same temperature. Starving the sugar does not make a chocolate gelato sophisticated. It makes a brick, cold and bitter.

Recipe (era) Egg yolk Sugar Fat Milk solids Total solids
Latini, 1692 & Baldini, 1775: Baldini calls cioccolata the finest of the aromatic sorbetti and prescribes it as medicine, but fixes no dose; Latini’s chocolate sorbetta survives only with its snow-and-salt freezing bath, not a weighable mix (Latini; Baldini).
Artusi, 1891 (egg-free) none ~15% ~7% ~7% ~33%
Caviezel, gelato di cioccolato ~5% ~19% ~8% ~9% ~40%
This calculator 7% 20.5% 10.3% 5.6% 46%

The basis is the finished mix, as before. Caviezel’s column is his gelato di cioccolato con latte condensato, fig. 184, one of the four chocolates he prints, and across those four the sugar runs from 17.8 to 22.5% and the fat from 6.6 to 10.3%, so no single row of his is the standard (Caviezel). Artusi’s sugar is not sugar he added: most of it arrived inside the 200 g of grated eating chocolate, taken here as roughly half sugar, and what he spooned in himself came to just under 8%, a figure that holds however the bar was made (Artusi). Read the last two columns together and this recipe is the densest of the three on the fewest milk solids, because what went in instead was cocoa and fat and yolk.

Coffee: a lean crema al caffe

Coffee is where more fat stops helping and starts hiding the thing you came for. Caviezel holds an ordinary cream gelato between 6 and 12% fat and calls 8% a good average, but warns that an excess of fat easily covers the aromas (Caviezel), and his own four coffee recipes duly run between 4.7 and 6.7%, leaner than every base mix he prints and three of them under his own floor (Caviezel). The calculator follows the leanest and loudest of the four, the one he calls ricco: fat at his 4.7%, cream down to about a third of what the plain base carries, and a 4% yolk doing the enriching in its place, its lecithin and protein giving the roundness that more cream would have bought at the coffee’s expense (Caviezel). The espresso is not a flavouring stirred into a base. It is half the mix. Espresso runs about a tenth dissolved solids by weight, so at half the mix it carries roughly 5% coffee solids into the gelato, which is exactly what his ricco prints (Caviezel); it goes in hot, straight into the warm custard, and nothing else in the recipe is there to taste of coffee. Only the cheapest of his four reaches for a jar of freeze-dried (Caviezel). Coffee also wants more sugar than the white base does, so the mix is balanced to 20% sweetness, two points above fior di latte and at the top of the 19 to 20% Caviezel calls the habitual level for a finished gelato (Caviezel). Those two points are there to pay for the bitterness. Caviezel says a coffee gelato sits as happily on an egg base as a cream one (Caviezel), and Artusi was flavouring his egg crema with burnt coffee a century before him (Artusi).

You do not need an espresso machine to get there. The balance only asks that the coffee arrive at that strength, and it does not care how you got it there. Boiling a press or a moka down is the obvious route, and it does concentrate the coffee. Heat also drives off the reason you brewed coffee. In a direct comparison on coffee extract, freezing the water out kept all nine of its flavour compounds, and gentle vacuum evaporation at 50 °C lost almost all of them (Gunathilake). A sensory panel rated block freeze concentration statistically identical to the untouched extract on eight of its ten attributes (Moreno). At home, that is a freezer and a strainer. Freeze the brewed coffee solid, drip-thaw it at room temperature over a strainer, and keep only the first half of the melt, because the dissolved coffee lowers the freezing point and runs out ahead of the near-pure ice. Repeat on what you collect until a Brix refractometer reads about 11.5, which is roughly 10% dissolved solids, coffee sitting a little under sucrose on that scale. The method is slow, and some of the coffee always leaves with the discarded ice. It takes two days of freezing and thawing to avoid ten minutes of boiling, which is plainly absurd. It also tastes better.

Recipe (era) Egg yolk Sugar Fat Milk solids Total solids
Latini, 1692 & Baldini, 1775: Baldini classes coffee among the aromatic sorbetti but fixes no dose, and Latini gives no quantified coffee ice (Latini; Baldini).
Artusi, 1891 (coffee crema) ~11% ~15% ~6% ~7% ~33%
Artusi, 1891 (caffe-latte, egg-free) none ~17% ~2% ~5% ~24%
Caviezel, gelato di caffe “ricco” 4% ~19% 4.7% ~8% ~38%
This calculator (crema al caffe) 4% 21.4% 4.7% 6.3% 38.1%

Caviezel’s row is a choice rather than an average: it is his gelato di caffe ricco, the leanest and most coffee-forward of the four he prints, built on a 4% yolk at only 4.7% fat (Caviezel). The two Artusi rows are two different desserts, an egg custard he flavoured with burnt coffee and a separate coffee-milk ice with no egg in it at all (Artusi). And the sugar column is a weight, not a sweetness: ours reads 21.4%, higher than any row above it, but about a third of that weight is dextrose, lighter on the tongue than sucrose gram for gram, so the mix eats level with them rather than sweeter.

The nut gelati: nocciola, pistacchio, mandorla, gianduia

The four nut flavours are the white base built around a paste, and the paste is roasted nuts ground to butter with nothing whatever added: no oil, no sugar. Caviezel tabulates them himself, hazelnut the fattiest, pistachio and almond a few points behind (Caviezel). Gianduia is the odd one out, pulling the paste back to put cocoa in the gap, and he is firm that neither flavour should win (Caviezel). The paste brings more than fat, though: its non-fat solids bind water the way milk powder binds it in a plain base, which is why the nut flavours take no powder at all, and why a fior di latte comes out of the calculator with skimmed milk powder in its list while none of these four does. The fat is what it costs. Nut fat sets hard at freezer temperature much as cocoa butter does, so these mixes get the chocolate’s answer rather than a new one: Caviezel picks nocciola out by name as the one that comes out compact and hard at the same sugar as everything else, and hands part of the sucrose’s job to invert sugar (Caviezel), which is the job dextrose does here. Then roast the nuts darker than feels reasonable, because cold takes the top off everything, which is why Caviezel’s own scale runs light for a chocolate, golden for a cream, and higher again for anything that will be eaten frozen (Caviezel). Take them to a shade you would call a mistake in any other dessert. Frozen, it reads as restraint.

Mascarpone and the variegati

Mascarpone gelato is fior di latte with mascarpone standing where the cream usually stands. Because it is cream set with acid it arrives with a tang, and that tang is the entire flavour; the fat is only what carries it. Caviezel puts mascarpone at about 47% fat and describes it as cream set with citric acid rather than milk set with rennet (Caviezel), so the calculator treats it as a cream that happens to be that rich and re-solves the milk dose around it. The variegati are not mixes at all. The ribbon goes in at the draw, so the base underneath stays plain fior di latte and the only thing that changes is what runs through it: Caviezel’s own recipes call for the variegatura in estrazione, after the churning is done and never in the balance (Caviezel). Amarena is whole candied sour cherries in their dark syrup, malaga is raisins left to swell in rum, croccantino is caramel-nut brittle crushed to grit. Stracciatella belongs to the same family, a thin drizzle of melted dark chocolate poured in while the gelato is still turning, which sets and shatters on contact, so what ends up in the tub is not chips but splinters thin enough to snap under the spoon and be gone before you have swallowed the bite.

Zabaione: letting the wine do the freezing

Zabaione is the crema again with sweet Marsala poured into it, and it is the one flavour here whose antifreeze is not a sugar at all. Ethanol dissolves in the water and drags the freezing point down harder than anything else on Caviezel’s scale, which puts it at 743 against sucrose’s 100, the top of his table (Caviezel). So the calculator has nothing left to add and the dextrose line comes out empty. Take the dextrose out of a plain crema and it freezes hard; take it out of the zabaione and nothing moves at all, because the wine has already done the entire job. Which makes more Marsala look free, the same bottle carrying the flavour and the softness at once, and it is not free. Ethanol has no ceiling: every extra splash softens it further, and Caviezel’s own gloss on that enormous number is that alcoholic gelati melt in the tub (Caviezel). So the dose stays small, and what you get is the dessert it is named after, only cold: yolk, sugar and sweet wine. Pour in too much and the gelato never firms up at all, which is the one property the wine passes on reliably to whoever finishes the bottle.

Fruit sorbetti: solving around the fruit

The sugar in a sorbetto is not a dose, it is a total the finished mix has to hit, and the fruit walks in already carrying part of it. Carpigiani bands that total at 26 to 31% of the finished mix, counting the fruit’s own sugar alongside whatever you weigh out (Carpigiani), so the arithmetic runs backwards from every other flavour here: measure what the fruit brought, then add the difference. A peach sorbetto comes out around 55 parts fruit to 22 of sugar and 23 of water, and about a sixth of that sugar was inside the peach before anything went on the scale. Which is why the calculator asks which fruit before it asks anything else, and why the strawberry mix ends up with more added sugar than the peach one while carrying less fruit: strawberries simply brought less of their own. None of the fruit fractions are roundings either. Each is a dose some named Italian maestro already works to: 45% strawberry is Andrea Soban’s (Soban), 55% peach is Geppy Sferra’s (Sferra), and 65% blueberry is where the puree house Adamance works a fruit that brings hardly any acid of its own (Adamance).

Here the rule governing every other flavour in this article turns over: a fruit sorbetto gets no dextrose whatsoever. Caviezel rules dextrose and invert sugar out of a sorbetto on the grounds that either would drag the freezing point down further still and force a cabinet colder than any shop wants to keep (Caviezel), and the reason he can afford that ban is that the fruit has already done the work: the glucose and fructose arriving with it hold the freezing point down about twice as hard per gram as sucrose does (Caviezel). So the fruit is not only the flavour. It is where the freezing curve starts, and it starts somewhere different for every fruit, because a fruit’s sugar is never all one sugar. Peach is about three-quarters sucrose (Robertson), strawberry almost entirely glucose and fructose (Souza), blueberry very nearly pure monosaccharide (Mikulić-Petkovšek), which is why a blueberry sorbetto sits softer than a peach one at identical sugar and identical freezer temperature. Several of them turn up carrying a second antifreeze nobody added: pear (USDA), sweet cherry (USDA), plum and pluot hold real sorbitol at around two to three percent of their own weight, the very thing Caviezel has a gelatiere stirring into a sorbetto for creaminess and scoopability (Caviezel). The fruit supplies it free, better than a percent of the finished weight, and the curve hands back half a degree of softness or more. Mango (USDA) and lemon (USDA) are entered off the same kind of composition table, so there is no generic fruit anywhere in here. None of which is needed to make a sorbet. Fruit and sugar and water in a cold machine will give you something good, and this is a great deal more arithmetic than anybody needs. It is also the difference between a sorbetto you put a spoon through and one you have to chip.

The plum is easy and the pluot is where I got stuck. A plum is in the USDA tables like everything else here, half its sugar glucose, and a chromatographic run over eighty-six of them puts sorbitol at about a seventh of the flesh sugar on top of that (Xiao), which is enough to drop it in beside the pear. A pluot is in no table at all. It is a plum crossed with an apricot that mostly came out plum (Crisosto), it has been sold for thirty years, and nobody has ever put one on a scale for a composition database.

So I went looking for the two of them measured against each other, and there is exactly one such study: twelve plum and four pluot cultivars, same orchards, same seasons, ripened to the same firmness and read on the same refractometer. The plums came in at 14.0 Brix and the pluots at 16.4, with the pluots very slightly less sour (Crisosto). That is the whole difference between them, and it is the whole difference here: the pluot in this calculator is the USDA plum with its sugar and its sorbitol multiplied by 16.4 over 14.0, and every other number, the split between the three sugars included, held identical, because there is nothing measured to change it to. A pluot is a plum bred sweeter. It makes the sorbetto you would expect from that – a sixth more of the fruit’s own sugar, so about 4% less added to reach the same Brix, and a scoop that gives way a third of a degree sooner.

Peach gelato being churned in a batch freezer, pale orange, a spatula lifting a dense scoop from beside the dasher

The sorbetto banks up against the blade: matte and faintly dusty, packed into a smooth mound on one side and climbing the bowl in thick ridges. There is no dairy anywhere in a sorbetto to pale it, so that colour is the peach’s own. More than half of it was peach.

Even at the low end of that band a sorbetto tastes sweeter than a cream gelato does, and the low-acid fruits have the worst of it. The culprit is the fruit’s own fructose, half again as sweet as sucrose per gram (Caviezel), so a fructose-heavy fruit reads above its Brix, and pear and mango and blueberry bring the least acid of anything here to cut it. The trade’s answer is a little glucose syrup alongside the sucrose, which trims the sweetness without trimming the sugar (Caviezel), and since that is not something a home kitchen keeps, the added sugar here is plain sucrose and the fix is acid rather than less sugar. Caviezel writes lemon juice into every fruit sorbetto he prints, always with the same instruction, quanto basta, as much as it takes (Caviezel). He will not give a weight because every fruit’s pH is different, and it goes in at the last possible moment, immediately before the churn, because acid stirred in early destabilises the mix. Carpigiani puts the whole squeeze between nothing and 2% of the mix (Carpigiani), a dose worth a few hundredths of a degree on the freezing point, which is to say nothing at all: the sugar is the curve, and there is no fat and no milk solids in a sorbetto to prop the texture up in its place. Lemon is the same trick at its limit, a fruit with almost no sugar of its own, so the sucrose carries the entire sweetness and the juice’s acid is the only thing keeping it from cloying.

Which leaves the milder lemon, and it is the one fruit here with a paper to itself. A Meyer is a lemon crossed with a mandarin or a sweet orange, and in 1965 two researchers squeezed 82 of them, grown across California, to find out what was actually in the juice: 4.6 g of sugar and 3.5 g of citric acid per 100 mL, and not a trace of sucrose in any of them (Kennedy). Against the ordinary Eureka’s 2.5 and 4.8 (USDA) that is nearly twice the sugar and about seven-tenths of the acid, which sounds like a gift and is really a bill, because the acid was doing a job. Give a Meyer the same weight of juice the Eureka gets and the sugar has nothing to push against, and the ice goes flat and sweet at the same 27%. So the calculator sizes it by acid rather than by weight: enough juice to land the mix where the Eureka lands it, which is 28% of the mix against 20%. The extra juice walks in carrying its own sugar, every gram of it glucose or fructose, so a little less goes on the scale and the scoop gives way a fifth of a degree sooner.

The sweetness leaves the same paper trail the crema’s did. Artusi printed four fruit ices in 1891, running from about 24% to about 32% of the finished mix (Artusi): his raspberry at 27 and his strawberry at 26 land inside the modern band, while the other two step outside it, the lemon above and the sour cherry below, each in the direction a balancer would still push it today (Artusi), since more sugar carries a fierce acid and a tart fruit-heavy ice wants less. So the 1891 ices sit where the modern band does, and the calculator aims at its floor, 27%, which is the sweetness of Artusi’s own berries. The modern norm runs sweeter than a fruit ice actually needs.

Recipe (era) Fruit Sugar
Latini, 1692 & Baldini, 1775 – the first sorbetti and the first classification of them, but neither fixed a weighable fruit dose: Latini quantified only his milk ice, and Baldini’s book is a medical treatise, not a recipe collection (Latini; Baldini).
Artusi, 1891 Lemon ~32%
Artusi, 1891 Raspberry ~27%
Artusi, 1891 Strawberry ~26%
Artusi, 1891 Sour cherry ~24%
Carpigiani, modern band any fruit 26–31%
This calculator (all sucrose) any fruit 27%

Every figure here is total sugar as a percentage of the finished mix, with the fruit’s own sugar counted in alongside the added. Artusi’s four are computed from the gram doses he printed rather than quoted off a page, which is what lets an 1891 ice be set against the modern band at all (Artusi). The fruit’s own share is estimated from composition tables, so the estimate carries most weight in the rows with the most fruit in them: the sour cherry takes nearly a quarter of its figure from the fruit alone, which is the row to read most loosely.

Sugar is one axis and how much fruit the ice carries is the other, and the two authorities treat that second one completely differently. Caviezel will not fix a fraction at all: in his telling it swings widely with the quality you are after, and more juice or pulp gives a sorbetto more flavourful and more prized (Caviezel). His own nine sorbetti sit mostly between a third and two-fifths fruit, with a melon at half and a lemon down at 18% because that one goes in as juice rather than pulp (Caviezel). Carpigiani does band it, and bands it by how loudly the fruit tastes: 15 to 35% for a strong one, 35 to 55 for a middling one, and 55 to 75 for a fruit that whispers (Carpigiani). Every fruit in this calculator sits inside those. Peach is the worked example, because a peach is nearly nine-tenths water before you do anything to it, which makes the fruit fraction really a question about how watery the ice will read.

Recipe (era) Fruit Sugar
Latini, 1692 & Baldini, 1775: neither fixes a weighable fruit dose (Latini; Baldini).
Artusi, 1891 (peach) ~31% ~24%
Caviezel (fruit sorbetto) 18–50% ~33%
This calculator (peach) 55% 27%

Fruit and sugar are both percentages of the finished mix. Artusi’s row is his own dose worked out: 400 g of peaches with the stones still in them, 250 g of sugar and half a litre of water, which lands near 31% fruit (Artusi). The calculator’s row is a deliberate trade of more peach for less sugar, and the 55% is not ours either – it is Geppy Sferra’s (Sferra), more fruit than Artusi’s ice carries and more than any sorbetto Caviezel prints, while the 27% sits under the 31 to 33 Brix Caviezel asks for (Caviezel). So the ice comes out peach-forward and lightly sweetened, and the price is water: a peach is nearly nine-tenths water to begin with, so this much of it at this little sugar finishes a shade over seven-tenths water itself. The lemon is what answers that, rather than another spoon of sugar.

Conclusion

What Cremeria Cavour had was never one secret ingredient. It was that every number was already in its place, and this calculator is my attempt to put them there on purpose across three bases and twenty-five flavours: the sugar low enough that what you taste is milk or fruit or roasted hazelnut rather than sweetness, the solids high enough for body and under both of the ceilings that turn body to grit, the freezing point set so a scoop gives way under the spoon. The antifreeze comes from dextrose, or from a fruit’s own fructose, or from a splash of Marsala, whichever the flavour asks for, and there is nothing anywhere in it you would hesitate to call food. So pick a flavour and a batch size, weigh it out, age it overnight, and give it a few minutes on the counter before you serve it. The physics is done. What is left is a spoon.

References

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  2. Caviezel, L. Scienza e tecnologia del gelato artigianale. Chiriotti Editori, 2016.
  3. Osteria La Sangiovesa. Ricette e storie: la Romagna in trent’anni di cucina. Maggioli Editore, 2022.
  4. Carpigiani Gelato University. “Corso base di gelateria.” Carpigiani Gelato University.
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  10. Treccani. “Crioscopia.” Enciclopedia Treccani.
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  13. Adamance. “Sorbetto mirtillo.” Adamance.
  14. Sferra, G. “Il sorbetto alla pesca di Geppy Sferra.” MangiaeBevi.
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  16. Souza, V.R. et al. “Compositional variation in sugars and organic acids in selected small fruits.” 2012.
  17. Mikulić-Petkovšek, M. et al. “Comparison of sugar profile between leaves and fruits of blueberry and strawberry.” 2019.
  18. United States Department of Agriculture. “Mangos, raw (SR Legacy, 169910).” FoodData Central.
  19. United States Department of Agriculture. “Cherries, sweet, raw (SR Legacy, 171719).” FoodData Central.
  20. United States Department of Agriculture. “Pears, raw (SR Legacy, 169118).” FoodData Central.
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  22. Latini, A. Lo scalco alla moderna. Napoli, 1692–94. (Sorbetta di latte, the first documented milk ice.)
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  28. U.S. Food and Drug Administration. “21 CFR §135.110: Ice cream and frozen custard.” Code of Federal Regulations.
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  30. Xiao, Q.; Ye, S.; Wang, H. et al. “Soluble sugar, organic acid and phenolic composition and flavor evaluation of plum fruits.” Food Chemistry: X 24:101790, 2024.
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  33. United States Department of Agriculture. “Sugar, turbinado (SR Legacy, 170674).” FoodData Central.
  34. United States Department of Agriculture. “Sugars, brown (SR Legacy, 168833).” FoodData Central.
  35. Kennedy, B.M.; Schelstraete, M. “Ascorbic acid, acidity, and sugar in Meyer lemons.” Journal of Food Science 30(1):77–79, 1965.

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