NTSC Cuts US TV to 29.97 FPS to Stop Color Signal Interference

Why is TV 29.97 frames per second? — Stand-up Maths

Stand-up Maths

Broadcasters slowed North American television from 30 to 29.97 frames per second to cancel color carrier interference while preserving backwards compatibility with existing black-and-white sets.

AI-assisted summary of Why is TV 29.97 frames per second? — original source. Check the original for full context.

Source published:

Key ideas

  • North American television originally adopted 30 fps because 60 Hz domestic AC power naturally synced with two interlaced fields of 262.5 lines per frame on CRT sets. (0:00)
  • Introducing color in 1953 forced engineers to avoid visual cross-talk by ensuring the 4.5 MHz active payload window divided into an exact integer multiple of the horizontal line rate. (2:57)
  • Dividing 4,500,000 Hz by the original 15,750 Hz line rate yielded approximately 285.714, forcing engineers to round up to 286 and lower the frame rate by 0.1% to 29.97 fps (30 / 1.001). (5:15)
  • European PAL avoided fractional frame rates by using 50 Hz power grids, 625 lines, and a 6.0 MHz bandwidth window, cleanly yielding an exact integer quotient of 384 at 25 fps. (7:51)
  • NTSC engineers prioritized backward compatibility for existing monochrome sets, as CRT circuitry could tolerate a 0.1% frame rate drop but would have broken under line count changes. (9:13)

Detailed notes

## Background Published on YouTube by Matt Parker on his channel Stand-up Maths on October 3, 2016, this video investigates the historical and technical quirks that led to North American television running at 29.97 frames per second. The video description notes that while North America settled on this odd fractional frame rate, Europe uses a comfortable 25 frames per second, and includes links to Parker's Patreon and a spherical video project that originally prompted his research.

## TL;DR The video explains how North American television ended up with the bizarre frame rate of 29.97 frames per second, tracing its origins back to cathode ray tube (CRT) mechanics and the 60 Hz electrical grid. When color television was introduced in 1953, engineers had to squeeze a color subcarrier into the existing 4.5 MHz bandwidth without causing visual interference on black-and-white sets. To satisfy the mathematical requirements of phase reversal and avoid interference, they adjusted the horizontal line frequency slightly, which slowed the frame rate down by 0.1% to 29.97 fps. In contrast, Europe's PAL system benefited from a wider bandwidth and a 50 Hz grid, allowing for a clean 25 frames per second.

## Atmosphere & style The video has an enthusiastic, lighthearted, and deeply nerdy atmosphere, driven by Matt Parker's energetic and comedic presentation style. He explains complex mathematical and engineering concepts with playful exasperation, using self-deprecating jokes—such as redefining NTSC as 'Not The Smartest Choice'—to keep the technical history engaging. Watching feels like attending a fun, accessible lecture where historical engineering compromises are treated as amusing puzzles, ending with a warm, personal chat directly addressing his most dedicated viewers.

## Bulletin - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) North American television originally adopted 30 fps because 60 Hz domestic AC power naturally synced with two interlaced fields of 262.5 lines per frame on CRT sets. - [02:57](https://www.youtube.com/watch?v=3GJUM6pCpew&t=177s) Introducing color in 1953 forced engineers to avoid visual cross-talk by ensuring the 4.5 MHz active payload window divided into an exact integer multiple of the horizontal line rate. - [05:15](https://www.youtube.com/watch?v=3GJUM6pCpew&t=315s) Dividing 4,500,000 Hz by the original 15,750 Hz line rate yielded approximately 285.714, forcing engineers to round up to 286 and lower the frame rate by 0.1% to 29.97 fps (30 / 1.001). - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) European PAL avoided fractional frame rates by using 50 Hz power grids, 625 lines, and a 6.0 MHz bandwidth window, cleanly yielding an exact integer quotient of 384 at 25 fps. - [09:13](https://www.youtube.com/watch?v=3GJUM6pCpew&t=553s) NTSC engineers prioritized backward compatibility for existing monochrome sets, as CRT circuitry could tolerate a 0.1% frame rate drop but would have broken under line count changes.

## Key takeaways - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) Early CRT televisions relied on interlacing to conserve bandwidth and prevent noticeable display flicker. - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) Monochrome NTSC settled on 525 horizontal lines and 30 frames per second directly locked to North America's 60 Hz electrical grid. - [02:57](https://www.youtube.com/watch?v=3GJUM6pCpew&t=177s) Analog 6 MHz broadcast channels left an active transmission window of exactly 4.5 MHz between the video carrier and sound carrier. - [02:57](https://www.youtube.com/watch?v=3GJUM6pCpew&t=177s) Adding a color subcarrier within the existing 4.5 MHz window caused severe cross-talk and visual patterning with luminance and sound signals. - [02:57](https://www.youtube.com/watch?v=3GJUM6pCpew&t=177s) Line-by-line phase reversal eliminated visual interference by requiring internal carrier frequency separations to equal odd integer multiples of half the line rate. - [05:15](https://www.youtube.com/watch?v=3GJUM6pCpew&t=315s) Summing the two phase reversal requirements dictated that the entire 4.5 MHz active window had to equal an exact integer multiple of the horizontal line frequency. - [05:15](https://www.youtube.com/watch?v=3GJUM6pCpew&t=315s) The original monochrome horizontal line rate of 15,750 Hz resulted in a non-integer quotient of 285.714 when divided into 4.5 MHz. - [05:15](https://www.youtube.com/watch?v=3GJUM6pCpew&t=315s) Adjusting the quotient to the nearest whole integer of 286 reduced the horizontal frequency to approximately 15,734.27 Hz. - [05:15](https://www.youtube.com/watch?v=3GJUM6pCpew&t=315s) Dividing 15,734.27 Hz by 525 lines produced the standard 29.97 fps color broadcast frame rate, effectively 30 divided by 1.001. - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) Europe's PAL system was engineered from scratch with a 6.0 MHz active bandwidth and 625 lines at 25 fps, yielding a clean integer multiple of 384. - [09:13](https://www.youtube.com/watch?v=3GJUM6pCpew&t=553s) NTSC could theoretically have kept 30 fps by shifting to 625 horizontal lines, yielding an exact integer quotient of 240. - [09:13](https://www.youtube.com/watch?v=3GJUM6pCpew&t=553s) Increasing the line count was rejected because it would have rendered millions of existing monochrome televisions instantly obsolete. - [09:13](https://www.youtube.com/watch?v=3GJUM6pCpew&t=553s) Technological standards possess enormous inertia, meaning short-term engineering workarounds often persist as permanent technical debt. - [12:22](https://www.youtube.com/watch?v=3GJUM6pCpew&t=742s) Matt Parker soft-launches his Patreon page for dedicated viewers, offering behind-the-scenes footage to test reward tiers before a formal rollout.

## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) The CRT Legacy and the Origins of 30 Frames per Second

Matt Parker introduces the bizarre North American television frame rate of 29.97 frames per second, a number he ran into while trying to manually reassemble extracted video frames for a project. Unable to locate a concise, clear explanation online, he dug into the technical history. The odd frame rate traces directly back to the physical mechanics of cathode ray tube (CRT) television sets. Inside a CRT, a cathode ray fires a beam of electrons toward the back of the phosphor screen, causing it to illuminate at the point of impact while electromagnets steer the beam across the display. When this tiny glowing dot is swept across the display quickly enough while its brightness is modulated, human persistence of vision blends the raster lines into a coherent moving picture.

Rather than drawing the entire picture in a single pass from top to bottom, early television systems utilized interlacing to conserve bandwidth and prevent visible flicker. The electron beam would first scan the odd-numbered horizontal rows, return to the top, and then perform a second pass to fill in the even-numbered rows. North American analog television settled on 525 horizontal rows, an odd number chosen so that each alternating field scanned exactly 262.5 rows. The half-line offset allowed the beam's geometric flyback to take identical time for both passes, preserving vertical alignment. While matching standard cinema projection of 24 frames per second might have seemed intuitive, televisions were plugged directly into the standard North American domestic electrical grid, which supplied alternating current at 60 Hz. By locking the scan passes directly to the line frequency to avoid electrical hum and distortion, two passes per frame resulted in a clean 30 frames per second. As Matt Parker puts it: “What a perfectly logical, and sensible frame rate!”

- **Interlaced fields:** 2 passes per full image frame (odd field followed by even field). - **Line count:** 525 total horizontal lines per frame, split into two fields of 262.5 lines each. - **Power synchronization:** 60 Hz AC household power dictated 60 fields per second, creating 30 complete frames per second for black-and-white broadcasts.

```mermaid flowchart TD accTitle: CRT Interlaced Scanning Process accDescr: Diagram showing how a 60 Hz alternating current creates 30 interlaced frames per second on a 525-line CRT screen.

subgraph PowerGrid["Mains Power"] A["60 Hz AC Electrical Supply"] end

subgraph Fields["Interlaced Fields (60 fields/sec)"] B["Field 1: Odd Lines (262.5 lines)"] C["Field 2: Even Lines (262.5 lines)"] end

subgraph Output["Frame Output (30 fps)"] D["1 Full 525-Line Video Frame"] end

A --> B A --> C B --> D C --> D ```

---

[02:57](https://www.youtube.com/watch?v=3GJUM6pCpew&t=177s) The Color Crisis: Squeezing Color into an Analog Spectrum

The stable 30 frames per second standard ruled North American broadcasting until color television was introduced in 1953, disrupting the established transmission architecture. Analog television channels were allocated a 6 MHz slot of electromagnetic spectrum, but broadcasters could not utilize the entire width. The initial 0.25 MHz was reserved as a guard band buffer against adjacent channels, followed by roughly 1 MHz of signal ramp-up. The active picture information was transmitted across the central block, ending 4.5 MHz later where the audio carrier resided, capped by another 0.25 MHz guard band at the top edge. This left an active window of exactly 4.5 MHz (4,500,000 Hz) to carry all visual and audio information without bleeding into neighboring stations.

```mermaid flowchart LR accTitle: 6 MHz NTSC Channel Allocation accDescr: Visual breakdown of an analog 6 MHz NTSC channel spectrum showing guard bands and active 4.5 MHz payload.

subgraph Spectrum["6 MHz Broadcast Channel"] direction LR G1["0.25 MHz<br/>Guard Band"] RU["1.0 MHz<br/>Ramp-Up"] Active["4.5 MHz Active Payload Window<br/>(Picture Luminance, Color Subcarrier, and Sound Carrier)"] G2["0.25 MHz<br/>Guard Band"] end

G1 --- RU RU --- Active Active --- G2 ```

When the National Television System Committee (NTSC) designed the color standard, they had to place a new chrominance (color) subcarrier inside this existing 4.5 MHz window while maintaining compatibility with millions of existing black-and-white sets. Initial color tests created severe interference artifacts: the color subcarrier clashed with the existing monochrome luminance and sound frequencies, causing intolerable geometric patterning and distortion across the image.

To hide these visual artifacts from the viewer, broadcast engineers turned to a technique known as line-by-line phase reversal. Matt Parker explains that while the intricate physics can seem opaque, the mathematical constraint required to make it function is straightforward: the frequency separation between the luminance signal and the color subcarrier, as well as the separation between the color subcarrier and the sound signal, both had to equal an odd integer multiple of half the horizontal line frequency.

- **Total channel bandwidth:** 6.0 MHz allocated per television station. - **Active signal window:** 4.5 MHz (4,500,000 Hz) spanning from video carrier to audio carrier. - **Phase reversal condition:** Both frequency gaps must be an odd multiple of $(f_H / 2)$, where $f_H$ is the horizontal line scanning frequency.

---

[05:15](https://www.youtube.com/watch?v=3GJUM6pCpew&t=315s) The 285.714 Problem: Deriving 29.97 fps

The algebraic requirement of phase reversal leads directly to an arithmetic clash with 30 frames per second. If both internal frequency intervals are odd integer multiples of half the horizontal frequency, adding them together means summing two odd integers multiplied by half the horizontal frequency. Since the sum of two odd integers is always an even integer, multiplying that sum by one half yields a plain whole integer. Consequently, the total 4.5 MHz active transmission interval had to equal an exact integer multiple of the horizontal line frequency:

$$\text{Integer} \times f_H = 4{,}500{,}000\text{ Hz}$$

In the existing black-and-white system, each frame had 525 lines and ran at 30 frames per second, producing a horizontal line rate of:

$$525 \times 30 = 15{,}750\text{ lines per second (Hz)}$$

Dividing the 4,500,000 Hz active window by 15,750 Hz does not yield an integer; instead, it results in:

$$\frac{4{,}500{,}000}{15{,}750} \approx 285.714\dots$$

Matt Parker imagines the exasperation of the 1950s broadcast engineers: “And the poor engineers must be like ‘oh that's close, imagine.. imagine if that was 286 that would solve all of our problems!’ but it's not.”

To force the quotient to the nearest whole integer of 286, the required horizontal frequency had to be adjusted downward:

$$\frac{4{,}500{,}000}{286} \approx 15{,}734.2657\text{ Hz}$$

Dividing this new line frequency by the fixed 525 lines per frame yielded a frame rate of approximately 29.97003 frames per second (calculated as $30 / 1.001$). By slowing down the frame rate by a mere 0.1%, the color subcarrier sat precisely where phase reversal cancelled out visible beat frequencies. The NTSC committee locked this standard in 1953, prompting Matt to joke that NTSC really stands for “Not The Smartest Choice.”

- **Monochrome horizontal line rate:** $525 \times 30 = 15{,}750\text{ Hz}$. - **Quotient for 30 fps:** $4{,}500{,}000 / 15{,}750 \approx 285.714$ (non-integer; causes visible cross-talk). - **Target integer:** 286. - **Adjusted color horizontal line rate:** $4{,}500{,}000 / 286 \approx 15{,}734.25\text{ Hz}$. - **Resulting color frame rate:** $15{,}734.2657 / 525 \approx 29.97\text{ fps}$ (or $\frac{30}{1.001}\text{ fps}$).

---

[07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) How Europe Got It Right with PAL

In contrast to the awkward NTSC fraction, Europe adopted the Phase Alternating Line (PAL) standard, benefiting from later implementation and different infrastructure. European power grids run on 50 Hz alternating current, which, with two interlaced fields per frame, yielded a clean 25 frames per second. Furthermore, PAL utilized 625 horizontal lines—an extra 100 lines compared to NTSC, providing noticeably sharper image resolution.

European regulators also allocated a wider transmission space, providing a full 6.0 MHz active payload window for the signal data. When PAL engineers performed the identical calculation to eliminate color interference artifacts, dividing their 6,000,000 Hz window by their horizontal frequency ($625 \text{ lines} \times 25 \text{ fps} = 15{,}625\text{ Hz}$), the arithmetic worked out neatly:

$$\frac{6{,}000{,}000}{15{,}625} = 384$$

The division yielded exactly 384 with zero remainder. Matt Parker points out that this was not sheer luck, but deliberate engineering foresight: “PAL came into place because of color television. Europe had a look at North America went what a mess, let's just do a new system from the ground up and make it work.”

| Specification Parameter | North American NTSC | European PAL | |:--- |:--- |:--- | | **Grid Power Frequency** | 60 Hz | 50 Hz | | **Frame Rate** | 29.97 fps (originally 30 fps) | 25 fps | | **Horizontal Lines per Frame** | 525 lines | 625 lines | | **Horizontal Line Frequency** | 15,734.27 Hz | 15,625 Hz | | **Active Signal Bandwidth** | 4.5 MHz | 6.0 MHz | | **Harmonic Factor** | 286 | 384 (exact integer) |

---

[09:13](https://www.youtube.com/watch?v=3GJUM6pCpew&t=553s) Missed Alternatives and the Tenacity of Standards

Could the NTSC engineers have resolved the conflict without introducing a fractional frame rate? The 4.5 MHz carrier separation was legally locked by frequency allocations, ruling out expanding the active window. However, Matt argues that they could have altered the line count instead. If they had retained the original 30 frames per second rate and searched for the next odd line count greater than 525 lines to prevent resolution loss, 625 horizontal lines would have solved the problem:

$$625 \text{ lines} \times 30\text{ fps} = 18{,}750\text{ Hz}$$ $$\frac{4{,}500{,}000}{18{,}750} = 240$$

Under this alternative, the active window would divide into an exact integer of 240, and North America would have shared an identical line standard with Europe. Yet engineers chose backwards compatibility over mathematical elegance. Existing monochrome television sets had circuitry that could tolerate a 0.1% drop in frame rate without losing vertical sync, whereas changing the line count to 625 would have rendered every black-and-white receiver in America instantly obsolete. Reflecting on their philosophy, Matt notes: “Their theory was if they do their job correctly no-one would be sure they had done anything at all.”

Matt observes that technological standards possess extraordinary inertia because human societies resist disruptive shifts. He urges engineers and computer scientists in the audience to choose conventions wisely when designing foundational protocols, warning that future generations could be living with their workarounds decades later. He concludes by mentioning that this entire investigation stemmed from his own frustrations with 29.97 fps when building a spherical video project with Henry Segerman, where every frame had to be extracted, manipulated via custom Python scripts, and manually stitched back together.

[12:02](https://www.youtube.com/watch?v=3GJUM6pCpew&t=722s) Bodging Conventions and Future Consequences

Matt Parker reflects on the engineering philosophy that led to such an unusual frame rate in television standards. He points out that practical engineering often favors pragmatic compromises over theoretical perfection, as adopting a working system quickly is far more important than holding out for an ideal one. As Matt puts it: “A convention that exists is better than something that doesn't, so if you can bodge it together and it works, go for it.” He jokingly brushes aside any long-term technical debt created by these kinds of quick fixes, cheerfully assuring the audience that future generations will simply have to figure out their own ways to deal with the fallout.

[12:22](https://www.youtube.com/watch?v=3GJUM6pCpew&t=742s) A Special Announcement: The Patreon Soft Launch

Matt transitions to speaking directly to the remaining audience, citing his YouTube analytics to point out that only about thirty percent of viewers stick around to the very end of a video. He notes that the majority watch the interesting core topic and tune out once he starts rambling at the finish. Declaring the dedicated viewers who stay through to the end as his true people, he shares a special announcement just for them. For a long time, supporters have asked when he would create a Patreon page, and he reveals that he has finally set one up as a soft launch. While he intends to do a formal launch later with an introductory video explaining his plans and adhering to platform best practices, he wanted to debut it quietly here first.

Explaining the concept for those unfamiliar with the platform, Matt describes Patreon as functioning similarly to an ongoing Kickstarter. Supporters who have the means can contribute money on an ongoing basis to help him improve the production quality of his videos, and in return, he will provide a variety of rewards. He intends to have fun creating bonus material, starting with a behind-the-scenes look at the absurd technical setup surrounding him that was required to film this exact video. Since he has no patrons yet at launch, that behind-the-scenes clip will be freely viewable by anyone visiting the page. He encourages viewers to follow the link at the very top of the video description, test the waters, and provide feedback on the reward tiers so he can adjust what is offered before the official rollout.

- According to YouTube retention analytics, only about thirty percent of the total audience watches past the main content to the closing remarks. - The Patreon launch is intentionally soft-launched without fanfare to gather early feedback on rewards and features from core viewers. - A public behind-the-scenes video detailing the complex and ridiculous technical setup behind making this episode will be posted for everyone to view on Patreon.

## Notable quotes > [12:02](https://www.youtube.com/watch?v=3GJUM6pCpew&t=722s) A convention that exists is better than something that doesn't, so if you can bodge it together and it works, go for it. — Matt Parker

## Mentioned Matt Parker, Henry Segerman, Howard Carter, Simon Wright, NTSC, PAL, CRT, Patreon, Kickstarter, YouTube, Python

## Video description I look at the historical quirks which gave us TV at 29.97 frames per second. In North America at least. It's a comfortable 25 fps in Europe.

More on that thing I mentioned at the end of the video here: https://www.patreon.com/standupmaths

Here is the spherical video I was making with Henry Segerman which made me research NTSC frame rates in the first place: https://www.youtube.com/watch?v=Yp12c3-IL-I

Yes, technically, if you divide 4,500,000 by 286 you get a horizontal frequency of 15,734.26573 lines per second. That matches a frame rate of 29.97002997002997… and so old TVs used 30/1.001 = 29.97002997002997…

CORRECTIONS: - A lot of people pointing out that increasing the number of horizontal lines without increasing the bandwidth would be a loss of resolution. Which is a good point.

Music by Howard Carter Design by Simon Wright

MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/ Patreon: https://www.patreon.com/standupmaths Nerdy maths toys: http://mathsgear.co.uk/

[Source](https://www.youtube.com/watch?v=3GJUM6pCpew)

中文简报

NTSC将美国电视帧率降至29.97 FPS以消除彩色信号干扰 广播机构将北美电视帧率从每秒30帧调慢至29.97帧，以消除彩色载波干扰，同时保持对现有黑白电视机的向后兼容。 视频解释了北美电视为何最终采用了29.97帧/秒这一奇特帧率，其渊源可追溯至阴极射线管（CRT）的机械构造以及60 Hz电网。1953年推出彩色电视时，工程师必须在不引起黑白电视视觉干扰的前提下，将彩色副载波挤入既有的4.5 MHz带宽中。为了满足相位反转的数学要求并避免干扰，他们略微调整了行频，从而使帧率降低了0.1%，变为29.97 fps。相比之下，欧洲的PAL制式得益于更宽的带宽和50 Hz电网，得以维持25帧/秒的规整整数帧率。 北美电视最初采用30 fps，是因为60 Hz家用交流电能与CRT电视上每帧262.5行的两个隔行扫描场实现自然同步。 (0:00) 1953年引入彩色电视时，工程师不得不通过确保4.5 MHz有效负载窗口为行频的整数倍，来避免画面串扰。 (2:57) 将4,500,000 Hz除以原本15,750 Hz的行频约为285.714，这迫使工程师向上取整至286，并将帧率降低0.1%至29.97 fps（即30 / 1.001）。 (5:15) 欧洲PAL制式依托50 Hz电网、625行扫描线和6.0 MHz带宽窗口，在25 fps下刚好得出384的整除商，从而避免了分数帧率。 (7:51) NTSC工程师优先考虑了对现有黑白电视机的向后兼容，因为CRT电路可以容忍0.1%的帧率下降，但若改变扫描线数则会导致设备故障。 (9:13)

Reading summary

North American television operates at 29.97 frames per second due to a 1950s engineering compromise that eliminated color signal interference while preserving compatibility with existing black-and-white television sets, according to mathematician and presenter Matt Parker. Power Grid Synchronization and 30 fps Origins (0:00) The standard frame rate of North American television originated in the hardware requirements of early cathode ray tube (CRT) displays. To prevent visible image flicker and conserve signal bandwidth, analog television employed interlaced scanning, splitting each full frame into two alternating passes of odd and even horizontal lines. North American monochrome systems adopted a 525-line standard, meaning each interlaced field drew 262.5 lines. The half-line offset allowed identical flyback times for the electron beam on both passes. Rather than adopting standard film's 24 frames per second, television systems tied scanning rates directly to domestic mains electricity to eliminate visible hum and distortion. Because North American household power runs on 60 Hz alternating current, CRT displays refreshed at 60 fields per second. With two fields required to render all 525 lines, early black-and-white television operated at a clean, stable rate of 30 complete frames per second. The Phase Reversal Mathematical Constraint (2:57) When the National Television System Committee (NTSC) introduced color broadcasts in 1953, engineers had to fit a new color subcarrier within the existing 6.0 MHz analog broadcast channel. After subtracting guard bands and signal ramp-up buffers, the usable active transmission window between the video and audio carriers measured exactly 4.5 MHz (4,500,000 Hz). Initial attempts to transmit color within this window created severe visual cross-talk and distortion between the color, luminance, and audio frequencies. To cancel out these visible beat frequencies, engineers used line-by-line phase reversal. This technique required both the gap between luminance and color and the gap between color and sound to equal an odd integer multiple of half the horizontal line frequency. Adding two odd multiples of a half-integer produces a whole integer. Consequently, the entire 4.5 MHz active signal window had to equal an exact integer multiple of the horizontal line scanning rate. Deriving 29.97 fps to Prevent Interference (5:15) Under the original monochrome standard, 525 lines at 30 frames per second produced a horizontal line frequency of 15,750 Hz (525 multiplied by 30). Dividing the 4,500,000 Hz window by 15,750 Hz yielded approximately 285.714. Because this quotient was not a whole integer, the 30 fps standard generated intolerable visual interference. To solve the problem, engineers rounded the multiplier to the nearest whole integer, 286. Dividing 4,500,000 Hz by 286 yielded a required horizontal frequency of approximately 15,734.27 Hz. Dividing this new line frequency by the fixed 525 lines per frame produced a revised frame rate of approximately 29.97003 frames per second (exactly 30 divided by 1.001). This 0.1% reduction in frame rate aligned the phase cancellation precisely while remaining small enough that existing monochrome sets could maintain vertical synchronization without modification. European Alternatives and Lasting Technical Inertia (7:51) Parker notes that NTSC engineers could theoretically have avoided fractional frame rates by retaining 30 fps and increasing the line count to 625. At 30 fps, 625 lines creates an 18,750 Hz line rate, which divides into 4,500,000 Hz to produce an exact integer of 240. However, altering the line count would have rendered every existing black-and-white receiver instantly obsolete. In contrast, Europe later adopted the Phase Alternating Line (PAL) standard from scratch. Operating on a 50 Hz grid at 25 fps with 625 lines and a 6.0 MHz active bandwidth, PAL divided cleanly into 384 without fractional rates. Parker emphasizes that foundational standards frequently emerge from pragmatic compromises rather than theoretical purity. Because society naturally resists disruptive technological shifts, temporary workarounds become entrenched conventions that future engineers and computer scientists must support decades later. The 29.97 frames per second rate illustrates how the demands of backwards compatibility can institutionalize imperfect technical compromises, leaving modern digital workflows to inherit legacy synchronization rules originally devised for analog CRT electronics.

精炼阅读摘要

Matt Parker 阐释了北美电视采用 29.97 帧/秒这一反直觉标准的历史与数学成因：为了在 1953 年引入彩色电视时消除信号干扰，同时保持对数百万台既有黑白电视的向下兼容，工程人员被迫将原本整齐的 30 帧/秒基准精确降低了约 0.1%。 黑白电视基础：电网频率与30帧的诞生 (0:00) 电视帧率的最初设定源自阴极射线管（CRT）电视机的物理运作机制。CRT 内部通过向荧光屏发射受电磁铁偏转控制的电子束，借助人眼的视觉暂留效应将发光光点扫描成的水平行融合成动态画面。为了在节约信号带宽的同时消除可见闪烁，早期电视系统采用了隔行扫描技术。北美模拟电视选定 525 条总水平扫描线，每帧拆分为各含 262.5 行的奇数场与偶数场，半行偏移确保了电子束在场扫描回扫时具备相同的几何时间与垂直对齐状态。 尽管电影行业早已确立了每秒 24 帧的工业标准，但北美家用电视直接接入供电频率为 60 Hz 的民用交流电网。为防止电网工频干扰在屏幕上产生可见的交流声波纹与画面畸变，工程设计将场扫描频率与电网工频严格锁定为每秒 60 场。由两次隔行扫描场合成一个完整画面，便自然确立了黑白广播时代工整而符合逻辑的每秒 30 帧标准。 彩色兼容危机：4.5兆赫频宽与相位反转 (2:57) 1953 年美国国家电视系统委员会（NTSC）确立彩色电视标准，这一既有体系面临频谱重构。模拟电视频道每台仅分配 6.0 MHz 电磁频谱，除去两端各 0.25 MHz 的相邻频道防护带以及 1.0 MHz 的信号上升沿缓冲后，实际供图像亮度、色彩和伴音信号共同使用的有效载荷频宽严格受限于 4.5 MHz（即 4,500,000 Hz）。 为了在不干扰既有黑白电视接收的前提下挤入新增的彩色副载波，广播工程师在初期测试中遇到了严重的彩色副载波与既有黑白亮度及声音频率之间的交调失真，在画面上产生明显的几何条纹网纹。工程师引入了逐行相位反转技术来抵消人眼可见的干扰，但该技术强加了一个苛刻的数学约束：亮度信号与彩色副载波之间、以及彩色副载波与伴音信号之间的频率间隔，都必须严格等于水平行扫描频率一半的奇数倍。 285.714算术冲突与29.97帧率 (5:15) 逐行相位反转的物理条件直接与原有的 30 帧/秒参数发生代数冲突。由于两个半行频奇数倍间隔相加等同于一个整数乘以行频，这要求整个 4.5 MHz 的有效频谱窗口必须刚好等于水平行频的整数倍。在原黑白体制下，每帧 525 行且运行在 30 帧/秒时，水平行频为 15,750 Hz（即 525 乘以 30）。用 4,500,000 Hz 除以 15,750 Hz 得出的商约为 285.714，该数值非整数，必然导致频带内部出现可见的拍频干扰。 面对无法除尽的死结，1950 年代的工程师将目标商强行设定为最接近的整数 286。反向推导所需的新行频为 4,500,000 除以 286，约等于 15,734.27 Hz。随后将该行频除以固定的 525 行扫描线，最终推导出每秒约 29.97003 帧（精确表示为 30 除以 1.001）。通过将帧率放慢仅 0.1%，彩色副载波得以精确定位在相位反转能彻底抵消干扰的频点上，NTSC 遂于 1953 年正式锁定这一标准。 欧洲PAL对照与未采纳的625行替代案 (7:51) 与北美繁复的微调形成鲜明对照，欧洲稍晚推出的逐行倒相（PAL）制式展现了更为规整的数学结构。欧洲电网采用 50 Hz 交流电，天然对应两场合成 25 帧/秒的规整帧率；同时欧洲采用了图像解析度更高的 625 行扫描线，并将有效信号频宽拓宽至 6.0 MHz。当 PAL 工程师执行同样的相位反转无干扰计算时，用 6,000,000 Hz 除以行频 15,625 Hz（625 行乘以 25 帧），恰好得到无余数的整数 384。 Parker 指出，北美 NTSC 在当年并非没有其他数学解法。如果工程界在锁定 4.5 MHz 载波间距的同时，选择保留 30 帧/秒速率并将扫描线提升至 625 行，其行频将达到 18,750 Hz；用 4,500,000 Hz 除以 18,750 Hz 正好等于整数 240。此方案不仅能避免非整数帧率，还能使北美与欧洲共享 625 行的清晰度标准。 向下兼容的代价与技术标准的长期惯性 (9:13) 北美最终未采纳 625 行方案的核心原因在于保护既有硬件投资。如果改用 625 行扫描线，当时北美全境家庭中的所有黑白电视接收机将瞬间彻底报废；相反，模拟电视显像管内部的电子偏转电路具备足够的弹性容差，无需任何改装就能自动锁定仅降低 0.1% 的 29.97 帧/秒信号。工程师为了追求“让公众完全察觉不到技术更迭”的向下兼容性，选择了妥协方案。 Parker 强调，这一工程妥协反映了基础技术规范强大的历史惯性。工程师在特定历史约束下“拼凑实用方案”的快速决策，往往在几十年后演变为难以逆转的技术债务；非整数帧率的遗留问题跨越模拟时代，至今仍持续困扰着需要以脚本逐帧处理数字视频的现代计算机工作者。 电视工业史表明，技术标准的演进往往由现实的设备兼容性而非纯粹的数学优雅所主导；1953 年为了让第一代彩色电视平稳落地而对电网基准做出的 0.1% 微调，最终固化为现代数字音视频制作流程中难以抹去的技术惯性。

Detailed notes — zh

## Background 该视频由数学科普博主马特·帕克（Matt Parker）于 2016 年 10 月 3 日发布在 YouTube 频道 Stand-up Maths 上。视频简介指出，马特在制作球形全景视频时遭遇了帧率困扰，进而深入探讨了北美电视采用 29.97 帧每秒这一奇葩历史标准的来龙去脉，并与欧洲舒适的 25 fps 标准进行了对比。 ## TL;DR 视频深入剖析了北美电视标准 NTSC 为何最终定格在看似荒谬的 29.97 fps。马特首先解释了早期黑白 CRT 电视如何利用北美 60 Hz 交流电网进行隔行扫描，从而确立了每帧 525 线的 30 fps 标准。1953 年引入彩色电视时，工程师受限于 4.5 MHz 的既有核心带宽，必须采用逐行倒相技术避免信号串扰，这要求带宽必须是水平扫描频率的整数倍。在无法整除的情况下，工程师微调了帧率至 29.97 fps 以实现向后兼容；相比之下，欧洲吸取教训全新设计的 PAL 制式则维持了整数倍整除。马特借此反思了工程妥协如何演变为遗留至今的技术包袱，并在片尾低调公布了新开设的 Patreon 赞助主页。 ## Atmosphere & style 全片洋溢着马特·帕克招牌式的英式幽默与极客狂欢感，既是一场严谨的技术数学推导，也是一场妙趣横生的单口喜剧。马特带着一种被数字折磨后的无奈与戏剧性抓狂，绘声绘色地模仿当年工程师面对数学不吻合时的绝望神情，将枯燥的电磁频段与行扫描频率讲得跌宕起伏。观看体验既烧脑又轻松幽默，结尾面向仅存 30% 铁粉的促膝长谈更增添了一份亲切而诚恳的极客社区温情。 ## Bulletin - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) 北美最初采用的 30 fps 电视标准直接与 60 Hz 家用交流电网同步，利用隔行扫描技术将每帧分为两个 262.5 行的场进行刷新。 - [03:10](https://www.youtube.com/watch?v=3GJUM6pCpew&t=190s) 1953 年引入彩色电视时，为避免 4.5 MHz 有效频宽内的色彩载波干扰，工程师需使总带宽成为水平扫描频率的整数倍，最终选定 286 倍导致帧率微调为 29.97 fps。 - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) 欧洲 PAL 制式吸取了北美的教训，基于 50 Hz 电网从头设计了 625 行、25 fps 的标准，其 6 MHz 频宽恰好能被水平频率整除（384 倍）。 - [12:02](https://www.youtube.com/watch?v=3GJUM6pCpew&t=722s) 修改帧率的方案虽保留了对旧款黑白电视的无缝向下兼容，但这种工程妥协遗留的技术惯性在数字化时代的视频制作中依然造成了长期的处理负担。 ## Key takeaways - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) 传统 CRT 屏幕依赖电子束偏转扫描与人眼视觉暂留特性，在屏幕上快速重绘动态画面。 - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) 早期电视为避免电网杂波干扰，直接将场频锚定在北美 60 Hz 交流电网频率上。 - [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) NTSC 采用隔行扫描方式，将一帧 525 条扫描线拆解为两次各 262.5 行的半场扫描，原先合成为 30 fps 的整数帧率。 - [03:10](https://www.youtube.com/watch?v=3GJUM6pCpew&t=190s) 在 6 MHz 的模拟电视频道分配中，扣除前后隔离缓冲带与信号建立频段，留给图像与伴音的核心频宽仅有 4.5 MHz。 - [03:10](https://www.youtube.com/watch?v=3GJUM6pCpew&t=190s) 引入彩电信号时，为消除画面干扰所采用的“逐行倒相”技术，要求 4,500,000 Hz 必须是水平扫描频率的整数倍。 - [03:10](https://www.youtube.com/watch?v=3GJUM6pCpew&t=190s) 原本 30 fps 下的水平扫描频率为 15,750 Hz，与 4.5 MHz 相除结果约为 285.714，无法满足数学整除要求。 - [03:10](https://www.youtube.com/watch?v=3GJUM6pCpew&t=190s) 工程师退而求其次选择最接近的整数 286 倍，倒推得到约 15,734.26 Hz 的水平频率，进而将标准帧率微调为 29.97 fps。 - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) 欧洲 PAL 制式利用 50 Hz 电网匹配 25 fps，并预留 6 MHz 带宽，通过 625 行扫描线直接达成 384 的整倍数关系。 - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) PAL 相比 NTSC 额外多出的 100 行扫描线，为其带来了更高的垂直分辨率优势。 - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) 北美当年若想维持 30 fps 不变并实现频宽整除，理论上可行的唯一方案是将扫描线提升至 625 行（对应 240 倍），但会破坏对老设备的兼容性。 - [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) 北美选择微调帧率而非线数的核心考量是向下兼容，确保数以百万计的黑白电视用户无需更换硬件即可无缝收看彩电广播。 - [12:02](https://www.youtube.com/watch?v=3GJUM6pCpew&t=722s) 工程标准中的临时“凑合”方案往往会演变为难以撼动的行业惯例，将复杂的格式换算负担留给后世的数字技术人员。 - [12:22](https://www.youtube.com/watch?v=3GJUM6pCpew&t=742s) 视频结尾宣布软启动 Patreon 赞助主页，并以完全公开的形式发布首期关于拍摄现场复杂技术设备的幕后花絮。 ## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=3GJUM6pCpew&t=0s) 荒谬的帧率与老式 CRT 电视的工作原理 Matt Parker 开篇抛出了一个令人困惑的问题：为什么北美地区的电视帧率会是 29.97 帧每秒？他感叹道：“I mean what a ridiculous frame rate!”（我是说，多荒谬的一个帧率啊！）。最近他在制作一个视频时，需要手动将导出的单帧画面重新拼合成视频素材，期间深切体会到了这个非整数带来的巨大麻烦。为了查清楚这个数字的起源，他在网络上四处搜寻，却始终没能找到一个清晰易懂又准确的技术解释，于是决定深入底层技术细节，并亲自制作这期科普视频。 这个问题的根源可以追溯到传统的阴极射线管（CRT）屏幕。CRT 的背面装有阴极射线发射器，向前发射电子束，只要打在屏幕上，屏幕相应位置就会发光。后方的电磁铁则用于精确控制电子束在屏幕上的移动。为了呈现动态图像，光点必须在屏幕上飞速扫描。只要光斑足够小、移动得足够快，并在此过程中动态调整明暗亮度，利用人眼的视觉暂留特性，人类大脑就会将其感知为一幅完整的画面。Matt Parker 调侃着屏幕上不断刷新出现的自己：“In fact there are infinitely many of me. That is pretty good value!”（事实上这里有无数个我，这可真划算！）。 但电子束并不是单次扫描就能画出完整画面的，而是分两遍完成，即隔行扫描（Interlaced Video）。第一遍扫描顶部第一行以及之后的所有奇数行；第二遍扫描再回过头来填补所有偶数行。北美的电视广播标准设定为 525 条水平扫描线。由于这是个奇数，每一次扫描（一个场）实际上只扫描 262.5 行。之所以存在这半行，纯粹是因为电子束从屏幕底部返回顶部需要精确的几何对称路径，必须让两次扫描花费完全相同的时间以保持画面的严格对齐。在电视工业刚起步时，最合理的帧率本应是每秒完成两次扫描共 24 次（即 24 帧每秒），以匹配电影胶片的标准。然而，当这些家电接入北美 60 Hz 的家用交流电网时，工程师为了让电视更容易制造并避免受到电网杂波干扰，直接采用电网频率来同步扫描节奏。两次扫描合成一帧，正好造就了每秒 30 帧的黑白电视标准——一个合情合理且逻辑清晰的整数。然而到了 1953 年，彩色电视横空出世，彻底打破了原有的宁静。 ```mermaid flowchart TD accTitle: CRT 隔行扫描生成 30fps 画面原理 accDescr: 展示北美 60Hz 交流电如何驱动 CRT 电子束进行两次半场扫描，从而合成 30fps 黑白画面的过程。 subgraph Power ["电网同步"] AC["北美家用交流电<br/>60 Hz"] end subgraph Scanning ["隔行扫描 (Interlacing)"] Field1["奇数场扫描<br/>262.5 行"] Field2["偶数场扫描<br/>262.5 行"] end subgraph Output ["画面输出"] FullFrame["完整单帧画面<br/>525 行水平扫描线"] FPS30["黑白电视标准<br/>30 帧每秒 (fps)"] end AC -->|"驱动场频 60 次/秒"| Field1 AC -->|"驱动场频 60 次/秒"| Field2 Field1 -->|"合成"| FullFrame Field2 -->|"合成"| FullFrame FullFrame -->|"2次扫描 = 1帧"| FPS30 ``` - 北美家用交流电频率为 60 Hz，因此场频被设定为每秒 60 场。 - 采用隔行扫描后，每两场合成一帧，黑白时代的标准电视帧率正好为 30 fps。 - 每一帧画面包含 525 条水平扫描线，每场扫描精确执行 262.5 行。 --- ### [03:10](https://www.youtube.com/watch?v=3GJUM6pCpew&t=190s) 模拟信号瓶颈与 29.97 帧的数学推导 20 世纪 50 年代的电视信号是通过无线电波以模拟信号传输的。每个电视频道在电磁频谱中被分配了 6 MHz 的带宽窗口。然而这 6 MHz 无法被全额利用：最开头的 0.25 MHz 是防干扰缓冲区（频道隔离带）；紧接着的 1 MHz 属于图像信号的建立频段；之后是极为重要的图像信息；再往后 4.5 MHz 的位置则是伴音信号；最后还留有 0.25 MHz 的缓冲收尾。因此，留给图像和声音实际传输的有效频宽严格锁死在 4.5 MHz。当 1953 年引入彩色信号时，工程师必须把彩电数据塞进这狭窄的 4.5 MHz 窗口内，同时不能破坏原有的黑白图像和音频。如果不做处理，彩色信号会与原信号互相干扰，在屏幕上产生无法接受的严重伪影。 ```mermaid flowchart LR accTitle: 模拟电视频道 6MHz 带宽分配图 accDescr: 展示 6MHz 模拟信道中各频段的划分，重点标出图像与伴音之间 4.5MHz 的核心频带。 subgraph Bandwidth ["6 MHz 频道总带宽"] direction LR B1["前置缓冲<br/>0.25 MHz"] B2["图像建立带<br/>1.0 MHz"] Pic["图像信号载波"] CoreGap["核心有效频带<br/>4.5 MHz"] Snd["伴音信号载波"] B3["后置缓冲<br/>0.25 MHz"] end B1 --- B2 B2 --- Pic Pic --- CoreGap CoreGap --- Snd Snd --- B3 ``` 为了消除干扰，工程师采用了“逐行倒相”（Line-by-line phase reversal）技术。Matt Parker 直言自己虽未完全参透其深层机制，但完全清楚该技术成立的前提条件：图像载频与色彩载频之差，以及色彩载频与声音载频之差，这两段频隙必须同时是“水平扫描频率的一半”的奇数倍。将这两个差值相加，就必须等于整个 4.5 MHz（即 4,500,000 Hz）的窗口。数学逻辑非常直观：两个奇数相加必定为偶数，偶数除以 2 必然得到一个整数。因此，这项技术的最终铁律就是：**总带宽 4,500,000 Hz 必须是水平扫描频率的整数倍**。 在最初的 30 fps 设定下： $$\text{水平频率} = 525 \text{ 行} \times 30 \text{ 帧/秒} = 15,750 \text{ Hz}$$ 工程师尝试用 4,500,000 除以 15,750，期望得到一个完美的整数，但现实泼了冷水： $$\frac{4,500,000}{15,750} \approx 285.714\dots$$ Matt Parker 惟妙惟肖地模仿当时工程师的绝望神情： > “And the poor engineers must be like ‘oh that’s close, imagine.. imagine if that was 286 that would solve all of our problems!’ but it's not.” 如果这个倍数刚好是 286，倒推出来的理想水平频率应当是： $$\frac{4,500,000}{286} \approx 15,734.26573 \text{ Hz}$$ 再将这个水平频率除以每帧 525 行，得到的帧率正是令人窒息的 29.97 帧每秒！于是工程师微调了帧率，从而彻底消除彩电信号与旧黑白信号的杂波干扰。这套系统由国家电视系统委员会（National Television Systems Committee）在 20 世纪 50 年代确立，即 NTSC 制式。Matt Parker 借此大开嘲讽：“and so now you know what NTSC stands for, it stands for Not The Smartest Choice.”（所以你现在知道 NTSC 代表什么了吧，它代表‘绝非明智之选’）。 - 频道整体分配 6 MHz，但留给画质、色彩与音频的核心窗口仅有 4.5 MHz（4,500,000 Hz）。 - 逐行倒相技术要求：两个奇数倍半频相加，推导出 4,500,000 Hz 必须等于水平扫描频率乘以某个整数。 - 在 30 fps 下，水平频率为 15,750 Hz，比值约为 285.714，无法整除。 - 选定最接近的整数 286 后，计算得水平频率为 15,734.25 Hz，换算出的帧率恰好约为 29.97 fps。 --- ### [07:51](https://www.youtube.com/watch?v=3GJUM6pCpew&t=471s) 欧洲 PAL 制式的优越性与技术妥协的反思 欧洲的电视发展则走了一条截然不同的道路。欧洲电网使用的是 50 Hz 交流电，两次扫描对应每秒 25 帧。欧洲制式（PAL）拥有 625 条水平扫描线，比 NTSC 足足多出 100 行。每当有人争辩 PAL 的画质优于 NTSC 时，底气就在于这额外的 100 行扫描线带来了显著更高的纵向分辨率。欧洲为实际电视数据预留了整整 6 MHz 的传输通道。当欧洲工程师计算倍数关系时，惊人地发现其比值正好是完美的整数 384。这绝非侥幸中彩，而是欧洲吸取了北美的教训，全面审视了北美惨状后下定决心从头建立一个兼顾各方的数据标准：“Europe had a look at North America went what a mess, let’s just do a new system from the ground up and make it work.”。 当时北美是否还有更好的选择？Matt Parker 进行了假设： 1. **改变频宽窗口**：由于当时电磁频谱划分的标准已被法律和规范严格锁死，绝不允许超出 4.5 MHz 的界限，因此不可能通过拓宽频带来解决。 2. **更改水平扫描线数**：在 Matt Parker 看来，这才是当年最理想的解法。如果死守 30 fps 不变，并保证扫描线只增不减（避免降低清晰度）、且保持奇数以维持半线回扫几何形态，那么在 525 之上唯一能被整除的下一个兼容数字恰好是 625 行（对应倍数为 240）。这意味着 NTSC 完全有机会与 PAL 统一为相同的 625 行标准。 然而北美最终选择了修改帧率而非行数。Matt Parker 认为后人也不必过分苛责当年的设计者，因为他们当时的核心诉求是让数以百万计的旧黑白电视用户获得平滑无缝的过渡。微调帧率能够最大限度保留向下兼容性，让老电视用户甚至察觉不到任何变化——正如工程师当时的哲学：“Their theory was if they do their job correctly no-one would be sure they had done anything at all.”（他们的理念是：如果他们把工作做到了极致，根本不会有人意识到他们做过改动）。 这揭示了一个残酷的技术真理：由于人类对技术突变的抵触，工程标准必须具备极高的历史延续性，而这种惯性导致许多临时妥协变成了难以撼动的技术顽疾。最后，Matt Parker 呼吁所有从事科技工作及观看视频的年轻观众：在制定当下的新标准和新协议时，务必深思熟虑，因为你的孙辈未来很可能依然被迫受制于你今天留下的这套规则。他提到自己与 Henry Segerman 合作制作全景球面视频时，就因为要导出帧序列放进 Python 里批量处理再重新封装，被 29.97 fps 折磨得精疲力竭，这个数字带来的麻烦至今仍在数字世界中回荡。 | 对比维度 | 北美 NTSC 制式 | 欧洲 PAL 制式 | |:--- |:--- |:--- | | **电网基准频率** | 60 Hz 交流电 | 50 Hz 交流电 | | **原生/设定帧率** | 29.97 fps（原为 30 fps） | 25 fps | | **水平扫描线数** | 525 行（隔行扫描每场 262.5 行） | 625 行（隔行扫描每场 312.5 行） | | **有效信号带宽** | 4.5 MHz | 6.0 MHz | | **频宽/扫描倍数** | 286（经 29.97 fps 调整后凑整） | 384（全新设计直接整除） | | **向后兼容取向** | 牺牲帧率规整性，换取对旧款黑白电视的无缝兼容 | 推倒重来，兼顾画质与数学整除性 | ### [12:02](https://www.youtube.com/watch?v=3GJUM6pCpew&t=722s) “将就凑合”的技术哲学：留给后人的历史包袱 在探讨完电视标准为何最终定格在 29.97 帧/秒的技术细节后，马特·帕克（Matt Parker）对这种工程妥协背后的思维方式进行了精辟的总结与调侃。面对历史遗留的种种混乱，工程师和标准制定者的态度往往非常现实：现存的惯例哪怕再笨拙，也比根本不存在的规范要强得多。正如马特·帕克所总结的那样：“A convention that exists is better than something that doesn't, so if you can bodge it together and it works, go for it.”（一个已经存在的惯例总好过完全没有，所以只要你能把它凑合拼凑出来并且能用，那就尽管去做吧。） 在技术的演进史上，许多标准最初只是为了解决眼前的兼容性问题而打上的临时补丁，但一旦确立，便会被一直沿用数十年。马特戏谑地模仿当时工程师的心态说：“I mean don't worry, the people of the future will find out a way to deal with it.”（意思就是别担心，未来的人自会找到办法去解决它的。）这种把复杂的换算与同步问题直接丢给后世软硬件开发者的做法，恰恰生动解释了为什么直到数字化时代的今天，大家依然不得不在视频编辑软件里与 29.97 这个怪异的数字打交道。 ### [12:22](https://www.youtube.com/watch?v=3GJUM6pCpew&t=742s) 结尾特殊公告：Patreon 主页的“软启动” 话题告一段落后，视频进入了结尾阶段。马特向坚持看到最后的观众揭示了一组有趣的平台数据。根据他的 YouTube 后台统计，当视频播放到这个阶段时，通常只有大约 30% 的观众还在继续观看；大多数人看完正片中最有趣的核心知识后就会直接离开，并不会理会视频末尾的漫谈。马特亲切地将这些留存下来的核心铁粉称为“我的人”（my people），并专门为他们带来了一则筹划已久的特别公告。 长期以来，一直有观众询问马特何时开通打赏赞助主页，如今他终于正式迈出了这一步，建立了 Patreon 页面。这次宣告属于一次低调的“软启动”（soft launch），后续他还会按照规范制作专门的介绍视频进行正式发布。马特向不熟悉该平台的人解释道，Patreon 类似于一种持续性的众筹（类似 Kickstarter 但属于长期订阅机制），旨在让经济条件允许的观众提供资金支持，从而帮助他提升视频的制作质量与水准；赞助者则可以获得各类专属福利。目前，他计划在上面发布一些额外的趣味衍生内容，首期就是本期视频的幕后花絮（behind-the-scenes），展示现场为了实现拍摄效果而搭建的一整套令人难以置信的复杂设备。 - **留存数据**：YouTube 统计显示，在长视频尾声阶段，全片观众中仅有 30% 依然在关注画面。 - **Patreon 机制与规划**： - 运作模式类似于持续性的 Kickstarter 赞助，支持者可获得专属奖励回报。 - 目前处于软启动阶段，主页链接置于视频简介栏顶部，马特希望观众能提前访问并就回报设置提供建议与反馈。 - 由于刚刚建立页面且暂无赞助者，马特承诺即将发布的首个关于本期拍摄现场极端技术设备的幕后花絮视频将完全公开，所有人皆可免费浏览。 - 马特·帕克在谈及幕后内容时坦言：“I'm going to do a behind-the-scenes video of this video I've just made, because you wouldn't believe the ridiculous tech around me it took to make this all work, and because I haven't got any Patreon supporters yet I'm just going to put it on my Patreon channel and anyone can see it.”（我打算为刚制作的这期视频拍一个幕后花絮，因为你绝对想不到为了让这一切正常运转，我周围布置了多么离谱的设备；而且由于我现在还没有任何 Patreon 支持者，我会直接把它发在 Patreon 频道上，所有人都能看到。） ## Notable quotes > [12:02](https://www.youtube.com/watch?v=3GJUM6pCpew&t=722s) A convention that exists is better than something that doesn't, so if you can bodge it together and it works, go for it. — Matt Parker ## Mentioned Matt Parker, Henry Segerman, Howard Carter, Simon Wright, NTSC, PAL, CRT, Patreon, Kickstarter, YouTube, Python ## Video description I look at the historical quirks which gave us TV at 29.97 frames per second. In North America at least. It's a comfortable 25 fps in Europe. More on that thing I mentioned at the end of the video here: https://www.patreon.com/standupmaths Here is the spherical video I was making with Henry Segerman which made me research NTSC frame rates in the first place: https://www.youtube.com/watch?v=Yp12c3-IL-I Yes, technically, if you divide 4,500,000 by 286 you get a horizontal frequency of 15,734.26573 lines per second. That matches a frame rate of 29.97002997002997… and so old TVs used 30/1.001 = 29.97002997002997… CORRECTIONS: - A lot of people pointing out that increasing the number of horizontal lines without increasing the bandwidth would be a loss of resolution. Which is a good point. Music by Howard Carter Design by Simon Wright MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/ Patreon: https://www.patreon.com/standupmaths Nerdy maths toys: http://mathsgear.co.uk/ [Source](https://www.youtube.com/watch?v=3GJUM6pCpew)

Source quotes

[12:02] Matt Parker: A convention that exists is better than something that doesn't, so if you can bodge it together and it works, go for it.

Source quotes

[12:02] Matt Parker: A convention that exists is better than something that doesn't, so if you can bodge it together and it works, go for it.

Original transcript

[0:00] Did you ever wonder why in North America televisions run at a frame rate of 29.97 [0:08] frames per second? I mean what a ridiculous frame rate! I came across the [0:12] inconvenience of this number recently when I was making a video, and I was [0:17] trying to manually assemble some frames back to some footage, and it got me [0:20] thinking: [0:21] where did this come from? And I couldn't find a nice coherent concise explanation [0:26] online, so I had a bit of a dig into the technical details, and I thought I'd make a [0:30] video explaining how this came to be. It comes down to how these old CRT screens [0:37] used to work. At the back is a cathode ray it sends a beam of electrons [0:41] forward. Wherever they hit the screen the screen lights up, and then electromagnets [0:46] back here can steer that dot around on the screen. To produce an image, you need to [0:52] scan it across the screen. And if that dot is small enough, and if the dot is [0:57] moving fast enough, you can vary its brightness and because of the way the [1:02] human eye works, it will perceive the brightness as an image. And so as you can [1:08] see here a rapidly scanning dot is producing a picture of me, and then [1:13] another picture of me. In fact there are infinitely many of me. That is pretty [1:17] good value! The electron beam didn't actually do the whole image in one pass; [1:23] it took two passes. The first pass it would put the top row in and then every [1:28] second row all the way down: the odd positions. It would then do a second [1:33] pass and fill in the even positions. And this is what's called interlaced video. [1:38] Because of the human persistence of vision we wouldn't see two different [1:42] passes we would just see the complete frame. And in North America TV was [1:47] broadcast with 525 horizontal rows, which you may have noticed is an odd number. [1:55] Each pass of the beam would do 260 two-and-a-half rows. The weird half thing [2:03] was because of the geometry of how the beam gets back to the top, and you want [2:07] to take the same amount of time for both of the passes, so everything stays in [2:12] alignment. But that at the basics behind interlaced video. When TVs were first [2:17] built it would have made sense to do two of those passes 24 times a second, to match [2:23] what cinema movies ran at; they were 24 frames a second. [2:27] However these home appliances were plugged into the normal household [2:31] electrical supply. And in north america that's alternating current running at 60 [2:36] hertz, so to make them easier to build, and to avoid interference from other [2:40] things, they use the electricity to time the scans, and because it took two scans [2:46] of the beam for every image it meant your TV was running at 30 frames a second. [2:51] What a perfectly logical, and sensible frame rate! The problem was with the [2:57] introduction of color. The 30 frames per second system was for black and white TV, [3:03] and in 1953 color TV hit the airwaves and that ruined everything. [3:10] TV in the 1950's was sent as an analog signal over radio waves. Each [3:16] TV channel was given its own spot in the electromagnetic spectrum specifically a [3:20] six megahertz window to send all of its data. Now the first quarter of megahertz [3:26] it couldn't use, because it's kind of wasteland: a buffer between channels. It [3:30] couldn't really use the next one megahertz either because it was a build-up to the [3:35] picture signal. After that you get all the interesting data about the picture [3:39] and finally four-and-a-half megahertz later you get the audio signal and then [3:43] after that another wasted quarter of megahertz of wind down. Then above that [3:48] you would get another wasteland and the next station above it; they were packed [3:52] in fairly tight. So in reality each channel didn't get six megahertz they [3:58] just got this one four-and-a-half megahertz gap to send all of the image [4:03] and audio data when color TV came along in 1953, the color data had to be put [4:10] somewhere in that four-and-a-half megahertz window, but it needed to be [4:14] positioned carefully so it didn't disrupt the pre-existing picture and [4:19] sound information. It looked like this was going to be a major problem; the [4:24] color signal did [4:25] interfere with the picture and sound signals in a way that produced visible [4:29] artifacts. It was distorting the picture and that was not acceptable. [4:33] So the technicians had to find a way to fix that. And thankfully there's a thing [4:38] called line-by-line phase reversal. And even though I don't fully understand how [4:44] that works, [4:45] I do know what the criteria are to be able to use it. And it comes down to the two [4:50] gaps: the gap between the picture frequency and the color frequency, and [4:55] the difference between color and sound. In order for line-by-line phase reversal [4:59] to hide the artifacts both of these distances had to be an odd integer [5:05] multiple of the horizontal frequency divided by two. The horizontal frequency is the [5:11] number of horizontal lines being drawn every second. We know that if you add [5:15] these two differences together you get the complete four-and-a-half megahertz [5:20] window for the entire signal. And we can now do some simplification. Well we know [5:25] if you're adding two odd numbers together you're going to get an even [5:29] number out the other side. We can move the half over there, and if you halve any [5:33] even number you're just going to get some integer. And so the moral of the [5:38] story is that we need an integer multiple of the horizontal frequency to [5:44] equal our total interval of four-and-a-half megahertz. Which is of [5:48] course just 4,500,000. Well let's see if it works. The horizontal frequency is [5:55] equal to, well every frame is 525 horizontal rows, and we're running that [6:00] at 30 frames per second. If you multiply them together we get 15,750 out the [6:06] other side. That is our horizontal frequency. We can then try dividing both [6:12] sides up here by the horizontal frequency. And we hope to get an integer [6:17] out the other side. [6:18] Very sadly, we don't. We get 285.714 and then a bunch of other digits. And the [6:25] poor engineers must be like "oh that's close, imagine.. imagine if that was 286 [6:32] that would solve all of our problems!" but it's not. For that to be 286 we would need [6:38] a different horizontal frequency, and in fact we would need a horizontal [6:41] frequency of 15,734.25. And we haven't... well we would have that if... instead of a 30 [6:50] frames per second rate we had a... you got it 29.97 frames per second. And so that's [6:59] what they did they adjusted the frames per second, to make this number here an [7:05] integer and remove the interference between the new color signal and the old [7:10] picture and sound signals. So there you are, North American television has a frame [7:15] rate of 29.97 frames per second because if you multiply that by the number of [7:20] horizontal rows in each frame and then you multiply that by an integer, happens [7:25] to be 286, you get out a whole number which matches exactly the frequency [7:32] window [7:33] this data is sent over. This system of broadcast is called NTSC and it was put [7:38] in place in the 1950s by the National Television Systems Committee, and so now [7:43] you know what [7:44] NTSC stands for, it stands for Not The Smartest Choice. [7:51] surely there must be a better option than 29.97, well let's have a look what [7:56] happened in Europe. Europe has PAL television that's based on a 50 Hertz [8:01] power supply, and so at two scans a frame you get a 25 frame per second rate. [8:09] PAL has more horizontal lines, than ntsc it's got 625. Whenever you have someone [8:16] going on and on about how PAL is better quality than NTSC it's because it's [8:21] got an extra 100 horizontal lines; it has technically got better resolution. And in [8:27] Europe there's a slightly bigger window to send the data on. There's actually a [8:31] full six megahertz window, just for the data that's actually sending the TV [8:37] signals. So the PAL technicians must have been thinking oh come on how [8:41] close are we gonna be to an integer multiple? And it turns out exactly 384 [8:48] precisely [8:49] And you might think wow they got lucky, but in fact this was deliberate. [8:55] PAL came into place because of color television. Europe had a look at North [8:59] America went what a mess, [9:01] let's just do a new system from the ground up and make it work. And that's [9:05] why in Europe to this day we have a nice and tidy interlace standard whereas in [9:11] North America it's this ridiculousness. [9:13] The question now is was there a better option? Instead of changing the framerate [9:18] what if instead they changed the window over which the data is sent? What if they [9:23] just moved these out slightly to make these integer multiples. Unfortunately [9:29] that wasn't possible; the standards for this were immovable they were not [9:33] allowed to go outside of that four-and-a-half megahertz range. [9:37] The only other thing they could change would be the horizontal lines, and this [9:41] in my personal opinion is what they should have done. So let's say we want to [9:45] keep the frame rate at 30 frames per second, and we're going to change the [9:49] number of horizontal lines. How many are going to need? Well assuming we only want [9:54] to increase the number of lines, we don't want to decrease them and lose quality [9:57] in the new standard, and assuming we still need an odd number, so we get the [10:02] half line geometry for the beams movement, then the next compatible number [10:07] of horizontal lines about 525 is 625, with a nice multiple of 240. Yes [10:16] the NTSC standard could have been the same number of lines as PAL, we could [10:21] have had too much more compatible standards, if they had changed the [10:25] horizontal lines instead of the frequency. But they didn't, they change [10:29] the frame rate instead and we've been stuck with this ridiculous number ever since. [10:33] Although we can't be too harsh in judgment: their motivation at the time was [10:37] to make the transition as smooth as possible, and by slightly tweaking just [10:42] the frame rate, this was very backwards compatible, almost no one would notice [10:46] this change. Their theory was if they do their job correctly [10:51] no-one would be sure they had done anything at all. The final moral of the [10:56] story is just that conventions hang around for a very long time, because of [11:01] human nature [11:02] we can't have abrupt changes in technology, people need to be [11:05] transitioned from one to the next. Standards have to be continuous for some [11:11] definition of continuous, and that makes them incredibly tenacious. Now I know a [11:17] lot of people who watch my videos work in the tech sector, and you're [11:21] responsible for coming up with standards and conventions. And a lot of young [11:25] people watch these videos. You're going to come up with the conventions and [11:28] standards of the future. So all of you, please when you're coming up with new [11:33] ideas, just spare a thought that your grandkids may one day still be locked in [11:38] to the same standard. Although that said I still got my video may just by having [11:43] to deal with 29.97 frames per second. If you're curious it was the one I did with [11:48] Henry Segerman with the spherical cameras. Because we had to export all the frames, [11:53] mess with them in Python, and then put them back together. I'll put a link to [11:57] that video in the description, so you know, people come up with conventions I [12:01] guess [12:02] actually, we don't care. A convention that exists is better than something that [12:06] doesn't, so if you can bodge it together and it works, [12:09] go for it. [12:10] I mean don't worry, the people of the future [12:12] will find out a way to deal with it. [12:22] Okay, according to my YouTube statistics at this point in a video, of all the people [12:27] who've watched it only thirty percent of them are still paying attention. Most [12:31] people watch the interesting bit, and then they don't pay attention when I'm [12:35] just rambling on at the end. And so those of you who are still paying attention, [12:40] you are my people and so I have a special announcement just for you. [12:44] You're all incredibly supportive and a lot of people ask: "when am I going to set up a [12:48] patreon page?" And I've finally done it. I have set up a patreon page and this is [12:54] kind of a soft launch. I'll do a proper launch later, and I'll follow patreon [12:59] good practice by having a video about what I'll be doing. But for now I thought [13:04] I'll just mentioned it at the end of this video. If you'd like to, please do click [13:09] the link in the description; go and check it out if you're not familiar with [13:13] Patreon. [13:14] You can support me a bit like you would a kickstarter but it's ongoing. The idea is [13:19] people who can afford it [13:21] donate money so I can do these videos better, and in return I have all sorts of [13:26] rewards. So have a look at it, give me some feedback, let me know if there are [13:30] thing's there you do want things there you don't want. I'm going to have fun [13:34] making a bit of extra content for Patreon. In fact I'm going to do a [13:40] behind-the-scenes video of this video I've just made, because you wouldn't [13:44] believe the ridiculous tech around me it took to make this all work, and because I [13:49] haven't got any Patreon supporters yet I'm just going to put it on my Patreon [13:53] channel and anyone can see it. So do go check out my patreon, the link is at the [13:59] very top of the description unsurprisingly. I would love to make more [14:03] videos and do them better and so your support is hugely appreciated, so go [14:07] check it out and I'd love some feedback on it before I do the proper launch, let me [14:11] know if the rewards are what you want, or if there's anything else I can add in [14:15] there for you. I really appreciate you all supporting these videos.