It has been decades since I worked in the TV signal processing industry, but here's what I remember. Both NTSC and PAL/Secam have their frame rates based upon their electrical power grid's frequency. Europe's electricity runs at 50 Hz (cycles per second), so European TV broadcast systems scheduled one frame for every two cycles of electricity, or 25 frames per second. North America's frequency is 60 Hz, and the creators of North American TV also decided upon one frame for every two cycles of electricity, or 30 frames per second. When TV was first commercialized, both systems chose the first useful harmonic greater than the cinematic standard of 24 frames per second.
Things got messy only when color was introduced. The European governments decreed that color TV need not be backwards compatible with monochrome TV. PAL and Secam were developed from scratch, and retained their 25 frames per second rate. Europeans got to throw away all of their perfectly good black and white TVs in order to continue enjoying TV in the age of color. The US government stood firm on backwards compatibility (rejecting a color system by CBS in the process), so NTSC was designed to be backwards compatible. Engineers figured out how to inject color information into the spaces in between the lines of video, but this required refreshing the screen 0.1% more frequently than before, or 59.94 times per second. Painting a new frame at once every 'two beats' of the clock yielded 29.97 frames per second.
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