What scale of shutter speeds actually lies behind the numbers? [duplicate]

On nearly every camera I've used, the scale of shutter speeds goes something like:

1s, 1/2s, 1/4s, 1/8s, 1/15s, 1/30s, 1/60s, 1/120s, 1/250s, 1/500s, 1/1000s, 1/2000s

whereas clearly a scale of halves actually runs:

1s, 1/2s, 1/4s, 1/8s, 1/16, 1/32s, 1/64s, 1/128s, 1/256s, 1/512s, 1/1024s, 1/2048s.

That's close enough, but still, there's a difference, and I imagine that with high-precison electronic shutters it's quite possible to be right on the mark with timings.

Where on the scales are the marked, nominal values generally intended to be true (i.e. where are the shutter makers aiming for true accuracy, even if it's only an aim):

• along the up to 1/8s range (where they match the actual scale of halves)
• along the 1/15-1/120s range (where they are off at a ratio of 0.9375)
• along the 1/250s and faster range (where they are off at a ratio of 0.9765625)?

I am well aware that mechanical and even electronic tolerances may in most circumstances render quibbles over tiny fractions of a second moot. I am equally well aware that many of the scales and numbers used in photography are convenient approximations, and not intended to be taken at face value.

Even so, the fact remains that in design and manufacture an approximation of an ideal still requires a conception of that ideal. Just because a standard is an ideal and can't be met, or it doesn't really matter if it's not met, doesn't mean that design and manufacture don't need ideals, or don't work with them.

I guess that the point of truth in the shutter timings scale is 1s=1s, and all the other numbers are allowed to be approximations if necessary, but it would be nice to know.

• Neither that question nor its answers address the issue raised here: Since they can't all be true to life, at which point along these scales are the nominal values intended to represent reality? – Daniele Procida Oct 14 '18 at 14:10
• It is addressed from a photography point of view: it doesn't matter. – Philip Kendall Oct 14 '18 at 14:27
• @DanieleProcida Correct. Consumer (including "professional") digital cameras are not precison measuring devices. – mattdm Oct 14 '18 at 15:04
• But why are those gaps bad? If you're shooting a time lapse, those gaps will hardly matter in the end. What are you shooting where it would matter? Is there an actual photographic context (I'm curious) or are you simply using a consumer product as a precision (haha) measuring device? – OnBreak. Oct 14 '18 at 15:15
• What part isn't covered by, say, Wayne's answers to both this question and the other one? – mattdm Oct 14 '18 at 18:05

For each stop to be precisely 2x steps, the only possible actual precise shutter speed goals are necessarily these:

1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024 etc seconds.

For full seconds: 1, 2, 4, 8, 16, 32 seconds (sequential powers of 2)

The camera markings are just nominal numbers for convenience (close, but existing in name only, but not actual or real). The camera shows us humans the nominal numbers, but it always tries its best to meet the exact goals of precise 2x steps.

I am NOT saying the camera mechanisms are always precisely accurate, but their goal is these precise numbers. And shutter speeds are pretty accurate today, via digital computer chips and focal plane shutters.

This "nominal marking" concept is true of shutter speed, f/stops, and ISO values. We are shown rounded approximate markings, but the camera goals are the precise 2x steps. Probably we humans can more easily recognize 2x steps by using the nominal numbers.

Complete charts of all of those exact numbers
and the plan to compute them (third stops, etc),
and the answer to your precise question, are shown at my site at
https://www.scantips.com/lights/fstop2.html

• I don't know whether to +1 for the accurate answer or -1 for making me read a page of numbers I'm never going to really need to know ;)) – Tetsujin Oct 14 '18 at 16:52
• Thanks. :) I'd guess everyone has wondered about the jumps in the nominal shutter speed sequence, like this OP's question. But you're right, it does not affect our taking pictures, nominal is a good enough concept. However any time we attempt computing things, like EV, or tenth f/stops, or even Guide Numbers, the accurate numbers actually used do become important. – WayneF Oct 14 '18 at 17:50
• As a 'modern, computer-aware human' I grok powers of two & work with them all day, every day, even to question if someone means GB or GiB . As a photographer, I don't give a sh... if the numbers are 'accurate' ;) – Tetsujin Oct 14 '18 at 18:17
• @WayneF "any time we attempt computing things... the accurate numbers actually used do become important" - one prompt for my question is that I have built a Canonet QL17 GIII simulator in Python, in a Jupyter Notebook. I have assumed the scale's nominal 1s is intended to be an actual 1s, and that the other figures follow from that. – Daniele Procida Oct 14 '18 at 19:10
• It is of course already the answer, and powers of 2 is specifically tediously included in the link, but suit yourself if you don't understand it. Curious, what other shutter sequence base choice would you possibly consider? Zero maybe might seem superficially reasonable as a generic base of a sequence of numbers, except zero is not a satisfactory shutter exposure, and for a sequence of powers of 2, 2 to power of 0 is instead 1. – WayneF Oct 14 '18 at 21:17

For technical reasons and aesthetics, a 2X increment of exposure change is considered the “norm”. This doubling or halving of the exposure energy applies to both the aperture and the shutter speed adjustments. However in modern times a finer increment is often used.

To appreciate the shutter speed number set, one should reflect on the fact that initially the mechanisms of the shutter are escapements. In other words, they are akin to the pocket watch which uses an impulse action called an escapement driven by spring action. These mechanisms used various gear ratios that present various possibilities for an exposure duration. Simplicity of design takes precedence.

So what is the error percentage setting 1/30 of a second vs. 1/32 of a second or 1/60 vs. 1/64? The error is about 6% ,which is zilch. Also note, it is likely impossible to set either shutter or aperture any finer that 1/3 of an f-stop.