F-Stop Timing and the Mathematics of Print Exposure

Add two seconds to a four-second exposure and the print changes a great deal. Add the same two seconds to a forty-second exposure and almost nothing happens. Both additions are two seconds; one is 0.585 of a stop and the other is 0.070 of a stop, and the ratio between those two numbers is more than eight. That is the whole problem with counting a print exposure in seconds, and everything on this page follows from fixing it.

By the end you should be able to generate an exposure series for any base time and any step size, work out what to add to a strip band by band, say how many useful steps your paper actually has, convert a burn or a dodge into an instruction that survives a change of enlargement, and state what this course has not been able to establish about the two ends of the scale.

Why seconds are the wrong unit and ratios are the right one

Photographic paper plots its density against the logarithm of exposure, and Part XIII owns that curve. The consequence for the timer is one sentence: a fixed ratio of exposure moves the print by a fixed amount of tone wherever on the curve it is applied, and a fixed number of seconds does not.

A stop is a factor of two in exposure, which is 0.301 in log exposure. So any change of exposure time converts into stops by taking a base-two logarithm of the ratio.

s = log₂(t₂ ÷ t₁)

A change of exposure, expressed in stops

t₁ is the exposure you gave, t₂ the one you are giving instead, and s the change in stops: positive is more exposure and a darker print, negative is less and a lighter one. Run the two examples through it. Four seconds to six is log₂(1.5) = 0.585 stops. Forty seconds to forty-two is log₂(1.05) = 0.070 stops. The eye reads those as a large change and a change it would struggle to see at all, because the eye is reading the paper, and the paper is reading the ratio.

This is also why a printing record in seconds decays. “Burn the sky eight seconds” is a true statement about one print at one enlargement under one lamp. Move the head up, change the paper, replace the LED module, and the eight seconds mean something different, while “burn the sky half a stop” means exactly what it always meant.

🧮Why the base-two logarithm rather than base ten

Nothing physical distinguishes them; a stop is a unit of convenience laid over the same logarithmic axis sensitometry already uses. One stop is log₁₀ 2 = 0.301 in log exposure, so stops and log exposure units convert by a constant: stops = log exposure units ÷ 0.301, and log exposure units = stops × 0.301. Keep that number in your head. It is the bridge between the printing bench, where people speak in stops, and Part XIII’s axes, where the same quantity is ruled at 0.30 intervals — and it is the conversion that turns a manufacturer’s published range figure into a number of test-strip steps later on this page.

Stops, and the geometric series that follows from them

If equal visible steps are equal ratios, then an exposure series is geometric: each term is the previous term multiplied by a fixed number. Choose how many divisions of a stop you want — call it n — and the multiplier is fixed for you.

r = 2^(1 ÷ n)

The step ratio for n divisions per stop

tₖ = t₀ × 2^(k ÷ n)

The general term of the series

t₀ is the base exposure, k counts the steps away from it (negative for lighter, positive for darker), and n is the number of divisions per stop. Everything else on this page is that expression applied to something.

Step size	Divisions per stop, n	Ratio r	What one step does
Whole stop	1	2.0000	Doubles or halves the exposure
Half stop	2	1.4142	Adds 41 per cent
Third stop	3	1.2599	Adds 26 per cent
Quarter stop	4	1.1892	Adds 19 per cent
Sixth stop	6	1.1225	Adds 12 per cent
Twelfth stop	12	1.0595	Adds 6 per cent

The four ladders below all start at a base of 12.0 seconds and all end one stop up at 24.0 seconds. They differ only in how many rungs they put between the two.

Series	Terms from 12.0 s to 24.0 s
Whole stops	12.0, 24.0
Half stops	12.0, 17.0, 24.0
Third stops	12.0, 15.1, 19.0, 24.0
Sixth stops	12.0, 13.5, 15.1, 17.0, 19.0, 21.4, 24.0

Two things are worth noticing. The sixth-stop series contains every term of the third-stop series, which contains every term of the half-stop series: a finer series is the coarser one with rungs added between, never a different set of numbers. And the gaps grow along every ladder — 1.5 s at the bottom of the sixth-stop series and 2.6 s at the top — because a constant ratio is a growing difference. A timer that steps in seconds cannot produce any of these ladders; a timer that steps in stops produces all of them from one number.

The additive test strip, and the arithmetic nobody enjoys

A test strip is the series made visible on one sheet. There are two ways to make one, and they are not equivalent.

The additive strip is the usual method because it uses one piece of paper. Expose the whole strip for the shortest time in the series; cover one band with card and expose the rest for the difference to the next term; cover a second band and expose for the next difference; and so on. Each band ends up with the cumulative total of everything given while it was still uncovered, and those totals are the terms of the series. The arithmetic is entirely in the differences, and it is where strips go wrong.

Here is a five-band, third-stop strip centred on a base of 12.0 seconds, so the series runs from two thirds of a stop under to two thirds over.

Band	Steps from base	Ideal cumulative	Cumulative, to 0.1 s	Add at this step
1	−2/3	7.5595 s	7.6 s	7.6 s
2	−1/3	9.5244 s	9.5 s	1.9 s
3	base	12.0000 s	12.0 s	2.5 s
4	+1/3	15.1191 s	15.1 s	3.1 s
5	+2/3	19.0488 s	19.0 s	3.9 s

Read the last column downwards and that is the session: 7.6, then 1.9, then 2.5, then 3.1, then 3.9, covering one more band before each. Nineteen seconds of lamp time in total — the sum of the additions is, necessarily, the last band’s cumulative exposure — and it yields five exposures spanning one and a third stops.

🧮The rounding rule: round the cumulative, never the increment

A timer that resolves a tenth of a second has to round somewhere, and where it rounds decides whether the error accumulates.

The wrong way. Round each ideal increment to a tenth and add them up: 7.6 + 2.0 + 2.5 + 3.1 + 3.9. The running totals are 7.6, 9.6, 12.1, 15.2, 19.1, against ideal totals of 7.56, 9.52, 12.00, 15.12, 19.05. Every band inherits every earlier rounding, and the middle band — the one you will read the base exposure from — lands 12 millistops high.

The right way. Round the ideal cumulative to a tenth first, then take differences of the rounded values. The totals are then exactly 7.6, 9.5, 12.0, 15.1, 19.0, each within half a tenth of its ideal and none of them carrying anybody else’s error. The worst band is 8 millistops out and the errors do not compound as the strip grows.

Neither error is visible on a print: a third of a stop is 333 millistops and the worst case here is a fortieth of that. The rule earns its place elsewhere. It is what keeps a twenty-band strip honest, and it is the rule the firmware implements, in integer milliseconds, so that the rounding happens once per band rather than once per addition.

The same one-stop interval, stepped in seconds and stepped in stops

1. 1Equal seconds: 12, 15, 18, 21, 24 — the first gap is 0.32 stops, the last is 0.19
2. 2Equal thirds of a stop: 12.0, 15.1, 19.0, 24.0 — every gap is 0.333 stops
3. 3The tone patches — drawn to show equal and unequal steps, not measured from a paper

Both rows are drawn to teach the difference between equal differences and equal ratios; neither is a measurement from a material.

The single-band strip, and when it is worth the paper

The alternative is to give each band one exposure of its own, masking everything else, so that band three receives a single continuous 12.0 seconds rather than 7.6 + 1.9 + 2.5 in three instalments. It costs more time and, if you use separate offcuts, more paper.

Two reasons to spend it. The first is mechanical and certain: on an additive strip the card has to be moved four times without moving the paper, and a strip that shifts by a millimetre between bands is worthless in a way that is not obvious when you look at it. The second is a question the course cannot yet answer. Whether a paper responds identically to five separated exposures totalling 19.0 seconds and to one continuous 19.0 seconds is an intermittency question, and no manufacturer figure for it on a developing-out paper was found in this course’s corpus. If your additive strip and your single-band strip disagree, that disagreement is data, and the place it gets tested properly is the sensitometric check on the calibration page.

How many steps your paper actually has

The step size is not a matter of taste. It is set by how much exposure range the paper has to spend.

Manufacturers publish that range as a range figure to ISO 6846, which ILFORD and Foma both print on their sheets: the figure is one hundred times the log exposure range, so R90 means 0.90 log units. Part XIII owns what that means; this page only converts it.

stops = R ÷ 100 ÷ 0.301

A paper's exposure range in stops

Paper and grade	Published range figure	Log exposure range	In stops
MULTIGRADE RC DELUXE, filter 00	R160	1.60	5.32
MULTIGRADE RC DELUXE, filter 2	R90	0.90	2.99
MULTIGRADE RC DELUXE, filter 5	R50	0.50	1.66
MULTIGRADE FB CLASSIC, filter 2	R95	0.95	3.16
ILFOBROM GALERIE FB, grade 2	R110	1.10	3.65
ILFOBROM GALERIE FB, grade 4	R70	0.70	2.33
FOMASPEED, normal	R80	0.80	2.66
FOMASPEED, hard	R60	0.60	1.99

A grade 2 resin-coated paper has about three stops in it, from the first useful density to maximum black. That single number decides the step size.

• Third-stop steps put nine rungs across the paper’s entire scale. A five-band strip covers a stop and a third, which is a substantial fraction of everything the paper can do, and each band differs from its neighbour by an amount you can see without hunting.
• Twelfth-stop steps put thirty-six rungs across the same scale. One step is then a thirty-sixth of the paper’s whole range: below what most people can distinguish on a print, and — as the calibration page will show — potentially below what the timer and the lamp can repeat. A step smaller than your instrument’s scatter is not resolution; it is a way of printing noise on purpose.
• Whole stops are for finding the neighbourhood when you have no idea, and for nothing else.

Notice the third and fifth rows. Going from filter 00 to filter 5 on the same sheet of paper takes its range from 5.32 stops to 1.66 — the hard grade has less than a third of the soft grade’s latitude, so a strip that was comfortable at grade 00 is a coarse instrument at grade 5. Match the step size to the grade, not to habit.

📷What the step size feels like at the easel

On a three-stop paper a third-stop step moves a mid-tone by about a tenth of the paper’s whole scale. That is roughly the smallest change most printers will confidently identify on a dry print seen next to its neighbour, which is why third stops became the working default rather than because of any property of the arithmetic. Half stops are quicker and coarse enough that the right exposure often falls between two bands; sixth stops are the finish, used once the neighbourhood is known.

Reading a strip as data rather than as a set of candidates

Most people read a test strip by choosing the band they like. That answers one question and throws away the second one, which is the more useful of the two: a strip in stops measures your negative.

Read it twice.

First pass, the highlight. Find the band at which the important highlight — the textured white you are not willing to lose — first shows a tone distinct from the paper base. Call that band’s exposure t_H. Below it the highlight is empty paper; above it the highlight is closing up.

Second pass, the shadow. Find the band at which the deepest shadow you want as a true black first reaches maximum black. Call it t_S. Below it the blacks are grey, and no contrast grade retrieves what was never exposed.

Those two bands are rarely the same band, and the gap between them is not a nuisance. It is the difference between what the paper can hold and what the negative is asking it to hold.

negative’s range in stops = paper’s range in stops − log₂(t_shadow ÷ t_highlight)

Reading the negative off the strip

If the two readings land on the same band, the negative’s density range and the paper’s exposure range already fit and every band between is a decision about the picture rather than about the grade. If the shadow needs more exposure than the highlight will tolerate — t_S above t_H — then at the exposure that places the highlight the shadows are still grey: the negative is flatter than the grade, and it wants a harder one. If the shadow blacks before the highlight has any tone, the negative is asking for more range than the grade has, and it wants a softer one.

🧮A five-band strip, read as a measurement

The strip above, on MULTIGRADE RC DELUXE through filter 2. The highlight comes right at band 3, 12.0 s. The shadow does not reach maximum black until band 5, 19.0 s.

log₂(19.0 ÷ 12.0) = 0.66 stops — which, on a third-stop strip, is exactly the two bands you counted.

Filter 2 on that paper is published at R90, so 0.90 ÷ 0.301 = 2.99 stops of range. The negative is therefore 2.99 − 0.66 = 2.33 stops, which is 2.33 × 0.301 = 0.70 in log exposure, or a range figure of 70.

Look up 70 in the same published table and it is filter 3. Print it at grade 3 and both readings should collapse onto one band.

That is precisely the instruction ILFORD give from the other side — measure the negative’s effective density range, multiply by a hundred, pick the nearest range figure — except that the strip did the photometer’s job with a sheet of paper you were going to expose anyway.

Burning and dodging, expressed so that they travel

A local adjustment is an exposure change applied to part of the print, so it obeys exactly the same arithmetic. Two formulas cover everything.

Δt = t × (2^s − 1)

Extra time for a burn of s stops

Δt = t × (1 − 2^(−s))

Time withheld for a dodge of s stops

t is the base exposure and s is the size of the adjustment in stops. The two are not symmetrical, and the asymmetry is the point: a burn of one stop doubles the exposure in that area, so it adds the whole base time again, while a dodge of one stop halves it, so it withholds only half.

Adjustment	Burn: add	Dodge: withhold
One third of a stop	0.26 × base	0.21 × base
Half a stop	0.41 × base	0.29 × base
Two thirds of a stop	0.59 × base	0.37 × base
One stop	1.00 × base	0.50 × base
Two stops	3.00 × base	0.75 × base

Now watch it travel. At a base of 12.0 s, half a stop of burn is 5.0 s. Raise the head, re-focus, and the same negative now needs 24.0 s: half a stop of burn is 9.9 s. The instruction did not change and the seconds did. That is why a printing map written in stops is still usable a year later, and one written in seconds is a record of an evening rather than of a print.

A repeat function on a timer is this formula with the base remembered. Ask for “the last exposure again, plus a third of a stop” and the firmware multiplies the stored base by 0.26 and runs that interval; ask for it as a burn on a 24-second base and it multiplies the same 0.26 by 24. The printer never does the arithmetic and never has to remember which print the seconds belonged to.

✦Record dodges and burns separately, never netted off

A sky burned two thirds of a stop and a face dodged a third of a stop are two instructions, not one third of a stop of net exposure. They act on different parts of the sheet, and netting them off destroys the record. The glossary’s printing map keeps them as separate lines for this reason, and so does the timer’s log.

Dry-down, and what this course will not tell you

Prints look lighter wet than dry. A print judged in the tray under a bright inspection lamp is being judged against the wrong reference, the highlights close up as it dries, and a base exposure chosen wet is wrong by a fixed amount on every print you make.

The obvious fix is to expose a little less and call the difference a dry-down correction. The course will not give you a number for it, and the reason is Rule 1 rather than caution. A manufacturer’s statement of the effect was found for printing-out paper, where prints are described as getting significantly darker as they dry. No published figure for a developing-out silver gelatin paper was found in this course’s corpus at all. A number invented here would be repeated into thousands of prints, and it would be wrong for most of them, because the size of the effect belongs to a paper, a surface, a developer and a drying method together.

What the page can give you is the method, and it is one evening’s work.

1. Make a print at your chosen base exposure and cut it in half.
2. Judge the wet half in the tray, under the light you normally judge by, and write down the exposure you would have given had you been choosing again.
3. Dry the other half by the method you actually use — air, heat, glaze, whatever it is — and judge it dry, under the light the print will be seen in rather than the light it was made in.
4. Print again at a series of third-stop steps around the base, dry every one, and find the exposure whose dry print matches your wet judgement.
5. The difference, in stops, is your dry-down correction for that paper, that developer and that drying method. Record all three beside the number, because it does not travel between them.

A timer can then carry it as a standing offset: you type the exposure you judged wet, and the firmware subtracts the correction before it opens the shutter. That is a convenience and a trap at the same time, which is why the firmware logs the commanded exposure and the offset it applied, rather than quietly delivering a different number from the one on the display.

Recalculating a base exposure when something changes

Four things routinely change between one print and the next, and all four are exposure changes, so all four are additions in stops. Convert each to stops, add them, and apply the total once.

The enlargement. Raising the head lengthens the projection and spreads the same light over more paper, and Part XVI owns the relation: exposure goes as (1 + m)², not as m². Going from 3× to 5× at the same aperture takes 6.0 s to 13.5 s, which is 1.17 stops. Do not re-derive it here; take it from the page that established it.

The aperture. One stop on the lens is one stop of exposure, by construction. This is the cleanest of the four and the one worth using when the required change is large, because it does not lengthen an already long exposure.

The paper speed. ILFORD publish an ISO speed figure for each paper at each filter, and a speed ratio converts to stops the same way everything else does. MULTIGRADE RC DELUXE reads 240 through filters 00 to 3 and 500 unfiltered — so taking the filter out makes the paper 1.06 stops faster, which is very nearly a whole stop of exposure you must give back.

The grade. This one deserves care, because ILFORD’s own sheets do not say the same thing, and the difference matters to anybody building a timer.

⁇How much extra exposure does grade 4 need? Three ILFORD statements, and they disagree

The contrast control sheet states it flatly: the exposure time for filters 00 to 3½ is the same, and that for filters 4 to 5 is double — one stop.

The MULTIGRADE FILTERS sheet hedges: grades 00 to 3.5 are speed matched, and grades 4 to 5 will generally require more exposure, in practice between 0.5 and 1 stop depending on the product.

The MULTIGRADE RC papers sheet gives numbers instead of advice, and for the current emulsion they are not a stop. MULTIGRADE RC DELUXE (NEW) has an ISO speed of 240 through filters 00 to 3 and 220 through filters 4 and 5, which is a ratio of 1.09, or 0.13 of a stop. The same table gives MULTIGRADE IV RC DELUXE as 200 dropping to 100 — exactly one stop — and WARMTONE and COOLTONE likewise.

The course’s reading: all three are correct about different products. The doubling rule was true of the older emulsions and is still true of Warmtone and Cooltone; the current Deluxe and Portfolio papers are speed-matched across all seven grades to within an eighth of a stop, and the filter sheet’s “0.5 to 1 stop depending on the product” is the manufacturer acknowledging that spread. What follows for you is not which sheet to believe but that the correction belongs to the box of paper in front of you. Print a grade 2 and a grade 5 strip from the same negative, find the exposure that puts an identical mid-tone on both, take the ratio in stops, and write it on the box. That measurement takes twenty minutes and outranks all three sheets for your paper.

The order to apply them in. Because they are additions in stops, the total does not depend on the order. The decision does. Take them in the order of how free you are to choose: the enlargement is usually forced by the picture, so compute it first; the aperture is a free choice within the lens’s good range, so spend it next if the total is large; the paper and the grade come last because changing either changes the print’s contrast as well as its exposure, and you should not be paying for exposure with contrast by accident.

🧮One worked recalculation, start to finish

A negative printed well at 8.0 s, f/8, 3×, grade 2, on MULTIGRADE RC DELUXE. You want it at 5×, and you have decided it wants grade 3½.

• Enlargement, 3× to 5×: (1 + 5)² ÷ (1 + 3)² = 2.25, which is log₂ 2.25 = +1.17 stops.
• Grade 2 to grade 3½: both are inside the speed-matched band 00 to 3½, and the published ISO speed is 240 for both, so 0.00 stops. (Had you gone to grade 4 on this paper the sheet’s own speeds would give +0.13, and on MULTIGRADE IV they would give +1.00.)
• Aperture unchanged: 0.00 stops.

Total +1.17 stops, so t₂ = 8.0 × 2^1.17 = 18.0 s. Now make a three-band, third-stop strip centred there — 14.3, 18.0, 22.7 s — because a computed exposure is a starting point and not an answer, and because the arithmetic knows nothing about your negative’s density range or your developer’s temperature tonight.

The metronome, and why an audible beat beats a bright display

During a five-second dodge your eyes belong on the easel and your hands are holding a card in the light path. They are not available for reading a display, and a display bright enough to read across a dark room is a light source sitting next to unexposed paper — which is why the hardware page puts the display through the same fog test as a safelight.

So the timer counts out loud. A beat on the half second and a distinct tone on the second gives you position without looking, at a resolution of half a second, which is the resolution a hand moving a dodging card actually works at. The last second is marked differently so that the end of the exposure is not a surprise, and every accepted keypress is confirmed audibly so that you know in the dark whether the instrument heard you.

The counting must not drift, and how it is made not to drift is a firmware matter rather than a printing one: beats are scheduled against the exposure’s own start tick rather than counted out with sleeps, so a beat that arrives late does not push the next one later. That is the firmware page’s problem and it is solved there.

Reciprocity at the two ends, and the limit of a tenth of a second

Everything above assumes that doubling the time doubles the effective exposure. That assumption fails at both ends of the scale for every photographic material, and the honest position on paper is short.

ILFORD publish a low-intensity reciprocity failure correction for their films, as an exponent in a formula, and state that exposure times of one second or less need no compensation at all. That is a film document. No equivalent published correction for their papers was found in this course’s corpus, and none is quoted here.

What that means for a timer is specific rather than vague. At very short exposures the arithmetic on this page describes what the timer did, and three separate effects can make the paper disagree with it: the lamp takes time to rise and fall, so the light delivered is the area under a curve rather than a rectangle; the timer’s own scatter is a larger fraction of a short interval than of a long one; and the paper’s reciprocity behaviour below about a second is unpublished. Those three have different signatures and the calibration page separates them — the first by measuring light against time at the easel, the second by repeating an exposure ten times, the third by comparing a strip made at short exposures with one made at long.

Until that has been done on your build with your head, a tenth of a second is what the instrument commands and not what the paper receives, and this course will not claim otherwise. The useful working rule in the meantime is to keep printing exposures in the range where the lamp is comfortably settled and the strip is comfortably readable — for most LED heads that is a few seconds upwards — and to reach for the aperture rather than the timer when the required exposure falls outside it.

Recap

• Paper answers to ratios, so exposure changes are counted in stops: s = log₂(t₂ ÷ t₁), and one stop is 0.301 in log exposure.
• An exposure series is geometric, tₖ = t₀ × 2^(k ÷ n), and n — the divisions per stop — is the only choice you have to make.
• On an additive strip, round the cumulative and take differences, never round the increments and add them, or every band inherits every earlier rounding.
• A grade 2 resin-coated paper holds about three stops, which is why third-stop steps are useful and twelfth-stop steps are below both the eye and the instrument.
• Read a strip twice, for the highlight and for the shadow: the gap between them measures the negative against the paper and chooses the grade.
• A burn of s stops adds t(2^s − 1) and a dodge withholds t(1 − 2^−s); both survive a change of enlargement, and eight seconds does not.
• The course gives no dry-down figure and no grade-4 exposure factor for your paper, because the published sources disagree or are silent. It gives the measurement instead.
• A tenth of a second is a specification until the calibration page has measured it.

Check your understanding

Question 1. A print is made at 20.0 s. You want it two thirds of a stop darker. What exposure do you set, and what would you have set if the base had been 5.0 s?

• 31.7 s and 7.9 s, because two thirds of a stop is a multiplier of 1.5874 applied to whichever base you have
• 31.7 s and 16.7 s, because the adjustment is the extra 11.7 s and it goes on either base
• 33.3 s and 8.3 s, because two thirds of a stop means two thirds more exposure
• 40.0 s and 10.0 s, because two thirds of a stop rounds to a whole stop in practice

Show the answer and why

Answer: 31.7 s and 7.9 s, because two thirds of a stop is a multiplier of 1.5874 applied to whichever base you have

Two thirds of a stop is 2 raised to the power 2/3, which is 1.5874: applied to 20.0 s that is 31.7 s, and to 5.0 s it is 7.9 s. The second option is the error this whole page exists to prevent — it carries the seconds of the adjustment to a different base, where 11.7 s added to 5.0 s is not two thirds of a stop but 1.74 stops. The third confuses a ratio with a fraction added on: 1.667 is not 1.5874, and the difference is a twelfth of a stop, which a sixth-stop strip would show. The fourth throws away the resolution the timer exists to provide.

Question 2. You are building a nine-band strip in sixth stops. Your timer rounds to 0.1 s. Which rounding rule keeps the ninth band honest?

• Round each increment to 0.1 s and add them, because that is what you actually type into the timer
• Round the ideal cumulative exposure of each band to 0.1 s and take the differences of the rounded values
• Round only the base exposure, and give the increments to the nearest millisecond
• It makes no difference over nine bands, because a tenth of a second is far below what the paper can show

Show the answer and why

Answer: Round the ideal cumulative exposure of each band to 0.1 s and take the differences of the rounded values

Rounding the increments makes each band inherit every earlier error, and over nine bands the drift compounds; rounding the cumulative and differencing bounds every band at half a tenth, independently. The third option is not available on a timer whose display and control resolution is a tenth. The fourth is the tempting one and it is wrong in principle rather than in this example: the error here is invisible, but the rule that makes it invisible is the one that also works on the twentieth band.

Question 3. A paper is published at ISO range R60 at its hardest grade. How many stops of exposure does that grade have, and what does it imply about step size?

• Six stops, so twelfth-stop steps are appropriate
• About two stops, so a five-band third-stop strip already spans two thirds of everything the grade can do
• About 0.6 of a stop, so only whole-stop steps are usable
• The range figure describes density rather than exposure, so it says nothing about step size

Show the answer and why

Answer: About two stops, so a five-band third-stop strip already spans two thirds of everything the grade can do

R60 is a log exposure range of 0.60, and 0.60 divided by 0.301 is 1.99 stops. A five-band third-stop strip covers one and a third stops, which is two thirds of the whole grade — so on a hard grade the strip is a coarse instrument and the bands run off both ends quickly. The range figure is an exposure range, published to ISO 6846; the density range is a different quantity and Part XIII keeps them apart.

Question 4. A printer records "burn the corner 6 seconds" on a 12-second print, then reprints the same negative larger at a 30-second base and applies the same 6 seconds. What has happened to the burn?

• Nothing: 6 seconds is 6 seconds of extra light either way
• It has grown, because the larger print needs proportionally more of everything
• It has shrunk from 0.58 of a stop to 0.26 of a stop, so the corner is now about a third of a stop lighter than intended
• It has shrunk to nothing, because 6 seconds is inside the timer's rounding at 30 seconds

Show the answer and why

Answer: It has shrunk from 0.58 of a stop to 0.26 of a stop, so the corner is now about a third of a stop lighter than intended

On the 12-second print the burn took the corner to 18 s, which is log2(18/12) = 0.585 stops. On the 30-second print the same 6 s takes it to 36 s, which is log2(36/30) = 0.263 stops. The instruction has lost more than half its size without anybody changing it, which is exactly the failure that recording it as a fraction of the base — 0.41 times the base for half a stop — prevents. Six seconds is nowhere near the timer's rounding; the arithmetic, not the instrument, is what moved.

Question 5. Why does this course publish no dry-down correction in stops, when nearly every printing text gives one?

• Because dry-down is a myth produced by viewing prints under different lamps
• Because the effect belongs to a paper, surface, developer and drying method together, and no published figure for a developing-out silver gelatin paper was found in this course's sources
• Because the timer cannot apply a correction smaller than a tenth of a second
• Because Part XIII has not yet established the paper characteristic curve

Show the answer and why

Answer: Because the effect belongs to a paper, surface, developer and drying method together, and no published figure for a developing-out silver gelatin paper was found in this course's sources

The effect is real and is the largest systematic error in print judgement, so the first option is wrong. The course found a manufacturer statement for printing-out paper, where prints are said to darken significantly on drying, and nothing published for developing-out papers — so a number here would be an invention repeated into every print a reader makes. The page gives the five-step measurement instead, and tells you to record the paper, the developer and the drying method beside the answer, because it does not travel between them.

Question 6. On the current MULTIGRADE RC DELUXE, what exposure change do the published ISO speeds imply when you move from filter 3 to filter 4, and why does that not match the contrast control sheet?

• One stop, and the sheets agree
• About 0.13 of a stop, because the published speeds are 240 and 220; the contrast control sheet's doubling rule is true of the older MULTIGRADE IV and of Warmtone and Cooltone, whose speeds do halve
• About 0.13 of a stop, because ILFORD have withdrawn the doubling rule as an error
• No change at all, since all seven grades are speed matched

Show the answer and why

Answer: About 0.13 of a stop, because the published speeds are 240 and 220; the contrast control sheet's doubling rule is true of the older MULTIGRADE IV and of Warmtone and Cooltone, whose speeds do halve

The RC papers sheet publishes 240 through filters 00 to 3 and 220 through 4 and 5, a ratio of 1.09 or 0.13 stops; the same table gives MULTIGRADE IV as 200 dropping to 100, and Warmtone as 100 dropping to 50, both exactly one stop. So all three ILFORD statements are correct about different products, which is why the filters sheet says "between 0.5 and 1 stop depending on the product" rather than naming a figure. Nothing has been withdrawn, and the speed matching runs 00 to 3.5 rather than across all seven grades — which is why the course tells you to measure the pair on your own box.

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