A time-lapse can show a fresh photograph at every playback step and still jump over an unusually long part of the original scene. Imagine photographs intended to begin ten seconds apart. One never happens. If the surviving photographs are placed in consecutive movie frames, the jump across the missing photograph covers twenty seconds of scene time in the same playback interval that normally covers ten. The output keeps its regular rhythm, while the amount of original time represented by one step changes. This is a hypothetical example about complete photographs, with no camera experiment behind it.

Real documentation gives a reason to take the distinction seriously: Canon's EOS R7 time-lapse guide warns that an unavailable scheduled shot is skipped and may shorten the resulting movie [2]. The example below does not reproduce that camera's internal assembly. We choose our own capture log and two explicit ways to arrange its surviving images. That lets us answer a practical reading question: does a movie's frame rate describe how evenly its original moments were sampled? To find out, we need the capture times and the assignment of photographs to playback slots, as well as the frame rate.

A constant presentation period does not imply a constant interval between the acquisitions represented by consecutive frames. Let t denote elapsed scene time at the start of a complete hypothetical exposure, and p denote the start of its assigned presentation slot. The local ratio of an acquisition-time difference to a presentation-time difference describes how that pair of sampled moments is compressed. If consecutive surviving captures are separated by different amounts of scene time but assigned equal presentation intervals, this ratio varies. It is a property of the chosen temporal mapping, rather than a measurement of subject velocity or perceived smoothness.

The EOS R7 manual documents skipped scheduled shots and possible shortening of a time-lapse movie [2]. That motivates the question without establishing a universal camera implementation. Our original model will explicitly stipulate a missing interior exposure, complete retained images, exact presentation rates, and no further frame conversion. We then compare consecutive assignment with a deliberately held image. These constructions separate acquisition evidence from editorial timing. The result is independently checkable arithmetic, not a device benchmark, an Adobe application test, or an assertion that every camera automatically fills or removes an empty position in the same way.

Our imaginary plan has 61 photographs, with exposure starts at 0, 10, 20 seconds and so on through 600 seconds. Each successful exposure lasts two seconds and produces one complete image. We stipulate that the exposure due at 300 seconds never occurs; every other planned exposure succeeds and its image is retained. The retained collection therefore has 60 capture records. Around the missing event, the starts read 280, 290, 310 and 320 seconds. These timestamps label our invented exposure starts. They are not file modification dates, camera menu estimates, or times measured from real equipment.

The distinction between a requested schedule and completed shots matters. Nikon's Z 8 interval-timer guide says exposure and processing need time, and an interval that is too short can result in skipped intervals and fewer shots [1]. Our example chooses no particular cause. It also distinguishes an exposure that never happened from a photograph that was captured and later lost. Those histories can leave the same surviving files but support different statements about acquisition. A record with a missing number alone cannot settle which history occurred. Keep the original identity of each surviving photograph, even if you later give the files new names for editing.

Define scheduled indices i = 0 through 60 and exposure starts t_i = 10i seconds. A successful image integrates over the two-second window beginning at t_i. Remove the exposure at i = 30 entirely, retaining all other images. This yields 60 retained records, 59 intervals between their starts, 58 intervals of ten seconds and one interval of twenty seconds. The first and last retained starts remain 0 and 600 seconds. Exposure duration is specified to make acquisition meaning explicit; the calculations will use start timestamps and will not treat a photograph as an instantaneous measurement of every event during its integration window.

Nikon's documented short-interval limitation supports separating the intended schedule from completed shots [1]. The missing event here is an assumption, not a diagnosis from a file list. Under that assumption, total exposure duration is 60 × 2 = 120 seconds; the two-second exposure at 300 seconds never contributed information. If it had occurred and its file had merely been discarded, the acquisition history would instead contain 61 completed exposures. Both histories could have the same retained subset. A sound time map therefore preserves acquisition identity, timestamp definition and retention status as separate fields, rather than using a consecutive filename index as evidence of elapsed time.

The compact sequence has 60 equal slots at 30 fps, so its modeled playback duration is two seconds. The first and last capture starts are ten minutes apart. Dividing 600 by two produces a tempting headline: 300 times faster. Yet the local calculation has already found one 600-to-one step. A total-duration quotient can be arithmetically correct for its named endpoints while saying little about where time is compressed more strongly. To explain the actual arrangement, report the usual gap and the longest gap alongside the total. That tells a reader something a single headline cannot.

There is also a small endpoint distinction. The last photograph begins its playback at 59/30 seconds and occupies the final slot until two seconds. Thus the capture-start span and the full playback duration do not end at corresponding kinds of event. Comparing first-to-last starts on both sides gives 600 divided by 59/30, or about 305.08. Even that matched average hides the one larger step among 58 normal ones. These are different descriptions of the same invented sequence, not contradictory measurements. Our concern is the distribution of time jumps; the last frame's own display duration cannot reveal the missing scene interval.

For K retained images in K equal slots, the stipulated slot duration totals K/f, whereas the first-to-last presentation-start span is (K−1)/f. In our compact example these are 2 s and 59/30 s respectively. The quotient 600 s / 2 s = 300 compares the scene's capture-start span with the full presentation duration. It is valid as that defined summary, but it is not the common value of every local C_j. Endpoint conventions are necessary background; the new issue is that a scalar summary cannot specify how the capture-time increments are distributed across the output slots.

Using corresponding start endpoints instead yields 600/(59/30) = 18000/59, approximately 305.0847. Because every presentation gap has equal duration here, this also equals the arithmetic mean of the 59 local ratios: (58 × 300 + 600)/59. The maximum remains 600. A complete report can therefore state a mean, a maximum and their underlying counts without confusing them. This calculation does not claim that a movie player reports that ratio or that a camera's menu uses our endpoint convention. It is an original analysis of the specified finite mapping. With unequal presentation intervals, an unweighted average of local ratios would generally require a different justification.

Return to the compact collection with 60 retained photographs and the missing exposure at 300 seconds. Change our playback rule from exactly 30 fps to exactly 24 fps, while keeping every photograph in the same order and giving each one slot. The duration becomes 60 divided by 24, or 2.5 seconds. That is 25 percent longer than the earlier two-second sequence. The usual ten-second capture gap now corresponds to one twenty-fourth of a second, giving a local ratio of 240. The twenty-second gap gives 480. Everything plays more slowly under this rule, while the larger time jump remains twice the usual jump.

Adobe's footage-interpretation documentation distinguishes changing frame duration from changing frame content [4]. That distinction supports the logic, but the numbers here come from our own chosen rates. They are not instructions to set only a final export option and assume every earlier stage will change identically. A source sequence, an editing composition and a final output can use different rates [4]. If a later stage repeats, removes or generates frames, the simple one-photograph-per-slot calculation no longer describes the whole path. Write down which stage you changed and inspect the resulting assignment before claiming that a new rate repaired missing information.

Holding acquisition records and consecutive image order fixed, change f from 30 to 24 s⁻¹. The local formula C_j = fΔt_j scales every ratio by 24/30 = 0.8. The values 300 and 600 become 240 and 480, preserving their ratio of two. Total duration scales inversely: (60/24)/(60/30) = 30/24 = 1.25. Thus a 20 percent reduction in the chosen rate yields a 25 percent increase in duration; the percentages use different denominators. This exact transformation cannot replace a missing capture, and it does not establish any specific subjective improvement in the movie.

Adobe documents conforming a footage item's rate as changing frame duration while retaining frame content, and distinguishes footage interpretation, composition rate and output rate [4]. Our arithmetic assumes those later stages introduce no additional resampling, interpolation, trimming or holds. It therefore describes the explicit mapping being evaluated, rather than an arbitrary export preset. For unequal but positive acquisition gaps, multiplying every C_j by the same positive factor leaves the ratio of maximum to minimum unchanged. A global rate change can alter overall duration without equalizing local compression. Equalization would require changing individual presentation assignments, and the absent acquisition would still remain absent.

Suppose an object appears farther along its path in the photograph after the gap. The larger change could reflect more elapsed time, a change in the object's motion, or both. Our known timestamps let us identify the longer interval, but the photographs do not show everything the object did between them. It might have stopped, turned or moved out and back. Even a held image provides no additional view of that period. For a creative movie, choosing a compact sequence or an obvious hold can be an editorial decision. For an explanatory movie, describe the choice so a viewer can distinguish a change in the scene from a change in its presentation.

This article treats each complete photograph as one retained unit. Timing across rows inside a photograph is a separate subject, covered in our rolling-shutter explainer, Why a Fast Shutter Can Still Bend a Moving Shape. Here the useful result is a table of scene-time gaps and their playback assignments. A regular frame rate alone leaves that table unknown. A repeated photograph can preserve an intended position without recovering the missing observation, and a slower rate can lengthen the movie without equalizing its time jumps. Keep those limits beside any speed claim, along with the records that make the particular calculation possible.

The ratio C_j describes temporal compression between two acquisition-start labels; it is not a reconstruction of the scene between exposures. Recovering motion would require an additional observation and motion model. For example, equal endpoints could be compatible with a stationary object or with an unobserved excursion that returns to the same position. Our finite capture record cannot choose between those histories. Likewise, unequal displacements in retained images cannot be attributed solely to timing without accounting for the scene's own dynamics. Exposure integration further limits treating a captured image as an instantaneous state. None of the mathematical checks performed here establishes a camera's measured behavior or a perceptual response.

The novelty of the analysis is the mapping between complete-image acquisition and presentation when captures are absent or unevenly spaced. Within-frame row offsets belong to the separate rolling-shutter explanation; repeated refreshes of a source image belong to display-cadence analysis. Their general lesson about naming events is relevant background, while this model supplies different records and calculations. State whether a reported ratio uses consecutive output slots, consecutive retained captures or whole-sequence endpoints. Then preserve the acquisition evidence and explicit presentation policy. That combination allows another reader to reproduce the timing conclusion while leaving unrecorded scene content and untested implementation details open.