Pull too little out of the bean and the cup is sour and thin and weak, with the sharpness of an unripe plum, and pull too much and it turns bitter and drying, like the black edge of burnt toast, and leaves your tongue feeling like a wool sweater. There is a band in the middle where most people, most of the time, find that the coffee tastes right, and the rule for finding it fits on a matchbox:

• Sour means go further.

• Bitter means stop sooner.

Everything else in this note is about doing one or the other on purpose, with your hand on the right dial and your tongue on the cup.

Where does that band come from? It comes from a chart that home brewers and roasters have used since the fifties, drawn from work at a coffee institute in the United States, and it is a convention, a habit of the trade hardened by sixty years into scripture, and it does not appear in the current standards of the trade body that everyone cites for it. A chart everyone uses is a different creature from a standard, and it took me an embarrassingly long time to see it.

Strength is a different thing

Strength confuses nearly everyone who has ever called a coffee too strong, and it confused me for years. Strength is how much of the finished drink is coffee rather than water, and extraction is how much of the dry coffee dissolved, and the two move independently, the way the volume knob and the tone knob on an old stereo move independently.

A cup can be strong and under-extracted at once, which is the sour, intense, unpleasant cup you get from too much coffee ground too coarse, and a cup can be weak and over-extracted, which is the thin, bitter cup from an office machine that dripped too long over too little coffee, the cup that tastes like the smell of a photocopier.

An espresso and a filter coffee should end up with roughly the same extraction, and the espresso simply carries far less water, which is why it hits the tongue like a struck match while the filter coffee arrives like a warm bath; when I understood this the two drinks stopped being different subjects and became the same subject with the water changed.

The three dials

Three dials move extraction, and they are as unequal as the brothers in a folk tale, where the eldest inherits most of the land.

Grind size is the big one by a long way, because grinding finer exposes more surface and extraction runs faster, and halving the size of the particles roughly quadruples the speed, the way a sugar cube takes an age to dissolve in tea while a spoon of caster sugar vanishes before you have stirred. This is why the grinder, more than the brewer, is the purchase that changes your coffee, which is a whole note of its own later in the series.

Contact time is the second, and longer contact means more extraction. In a French press you control this directly with a clock, and I love the French press for exactly that plainness, and for the oils it lets through; in a pour-over the water flows through a bed of coffee and the dials are tangled, since a finer grind also slows the water, so that it extracts faster and for longer at once, the way a wet sponge both holds water and drips, which is why pour-over feels unpredictable at first and rewards a notebook more than any other brewer.

Temperature is the third, and hotter water works faster; caffeine comes out even in lukewarm water, but some of the harsh, drying compounds only come out near the boil, which is why most advice keeps the water a few degrees under it. I would leave this dial alone until the other two are settled, and the note on water explains why the dial reads differently a mile above the sea.

After those three come the small ones: how much you stir, and what is dissolved in your water, which is its own note, and how fresh the coffee is, because very fresh beans give off enough gas to hold water away from the grounds like a raincoat, which is another note.

When a coffee is good in two places

Some coffees taste wonderful extracted a little below the band, bright and clean and fruity, like biting into a cold green apple, and the same coffees taste wonderful again a little above the middle of it, jammy and sweet, like the last spoonful at the bottom of a pot of stewed plums, and, strangely, they can taste flat and grey in between. Nobody I have read can fully explain this, and the writer whose book I lean on for the chemistry compares it to a cocktail that is good dry and good sweet and dull halfway between, which I have to take on trust, having never drunk one.

So I treat the band as a lamp at the head of a road, and when a cup tastes good outside it I believe the cup; I will always take my own dark, oily, slightly-over-the-line cup over anyone's chart.

Ratio, and the trap inside it

The other number people argue over is the ratio of coffee to water, and the usual starting points show how different the drinks really are.

The trap is that ground coffee holds on to about twice its own weight in water and never gives it back, the way a bath sponge keeps the last of the bathwater however hard you squeeze, so that three hundred grams of water poured over twenty grams of coffee gives you less than three hundred grams of coffee, and the missing part is sitting in the wet grounds. When people compare ratios they are often comparing different things without knowing it, and if you weigh what ends up in the cup, or at least remember that the two numbers differ, half the internet's arguments about ratio dissolve like sugar.

What it costs to measure

I assumed measuring would be expensive, and it cost less than a bag of good beans: two kitchen scales, one that reads to a tenth of a gram for the coffee and one that reads to a gram and goes up to a few kilos for the water, and a phone with a timer. That is the whole instrument upgrade, and after the grinder it is the best money you will spend.

There is a device that measures strength properly, a refractometer, which reads a drop of coffee by how much it bends light, and it costs several hundred dollars, and I have never owned one. I mention it because the instinct to buy the instrument is strong and usually a way of putting off the tasting, and because the most famous measurement ever made in the city I grew up beside was made with almost nothing at all.

In 1928, at the Indian Association for the Cultivation of Science on Bowbazar Street in Calcutta, a short walk from the College Street book stalls of my teens, C. V. Raman and his student K. S. Krishnan found that when light scatters in a liquid, a tiny part of it comes out a different colour, changed by the molecules it has brushed against, like a song returning from a far room in a new key. Their first observations were made with sunlight gathered through a lens, and coloured filters, and the naked eye: a beam of filtered light went through the liquid, and they looked at it through a second filter that should have blocked it entirely, and a faint glow came through anyway, a colour that had not gone in, and they saw it with their own eyes before any spectrograph wrote it down. Two years later Raman had the Nobel Prize in Physics, the first given to an Asian in any of the sciences, in the years when Calcutta sent the world its physics the way Darjeeling sent it tea; and the eye came first, and the instrument followed and served it, which I remember whenever someone tells me their coffee cannot improve until they own the right machine.

What the mathematicians say

There is a line every mathematician knows, that a mathematician is a machine for turning coffee into theorems, and everyone attributes it to Paul Erdős, though Erdős himself, in print, gave it to his friend Alfréd Rényi, and Rényi had died the year before the paper came out, so he never saw his joke become famous under another man's name. A third mathematician, handed a weak cup, is supposed to have said that it was fit only for lemmas, and I cannot verify that one and have no wish to, because it is perfect.

A postscript, added in the new year because it arrived too late for this note and was too good to leave out: a group of chemists and mathematicians has now published a real mathematical model of espresso, and their theory said grinding coarser should always lower extraction while their experiments found an optimum, a point past which going finer makes things worse, because at very fine grinds the water finds channels through the bed and leaves the rest of it dry, the way rain finds the gutters and leaves the garden thirsty. Their practical conclusion was that many cafés could use a little less coffee, ground a little coarser, and pull a more repeatable shot, and one of them has said that solving the full physics of water moving through a bed of ground coffee would need more computing power than the largest technology company owns, which I find comforting, since it makes the notebook the one instrument in the house the right size for the problem.

The confession

I spent a year measuring everything, dose and water and time and temperature, all of it written in a small black notebook in handwriting that got worse as the mornings got earlier, and the coffee stayed exactly as it was. It got better when I started tasting first and writing second, deciding with my mouth whether the cup was sour or bitter or right, and only then writing down what I had done. Raman looked before his spectrograph did, and I should have tasted before my notebook did, because the instrument is downstream of the eye and the tongue, and its job is to help you repeat what worked, and a notebook kept in place of the tasting is only a diary of guesses.

My father, who has taught measurement to engineering students most of his life, used to say, and I remember it only in half, like a hymn from school, that every meter takes a little of what it measures, that a voltmeter draws its own small current from the circuit it reads and so reports a circuit slightly changed by being read; and I think a notebook does the same to a morning if you let it speak before the tongue. I should have known all this, since it is how I work when I work well, and somehow I forgot it in my own kitchen, where a man with a doctorate in measuring invisible things needed a one-year-old to show him the order of operations; my son tastes everything he picks up before he decides what it is, the remote and a shoe and the edge of the table, and I have started to think he has it right.

One page

What I would do this morning:

• Take one page of a notebook.

• Write the dose, the grind setting, the water weight, the time, and one word for how it tasted.

• Do it again tomorrow, and change one thing, only one.

• After ten entries, read the page back; you will know more about your own kit than any review will tell you.

I still do not know which of Manish and Mayank was right, and I suspect the coffee on the eighteenth floor was bad for a reason neither of them had thought of, a bag that had been open since the spring and smelled, when you put your nose in it, like the inside of a cardboard box, which is the next question, and it has a note of its own.