Por que os filmes foram filmados em quadros 24 por segundo?

De acordo com este site:

In the early days of film cameras were hand cranked, which caused inconsistencies from movie to movie. Even further still, projection houses would speed up frame rates of movies to get that one extra projection at the end of the day. It wouldn’t be until 1929, with the introduction of the optical sound track, that the standard of 24 fps was established. The 24 frames per second standard was the smallest number that was easily divisible by 2, 3, 4, 6, and 8 allowing editors to quickly find where to make their cuts; not to mention was the most cost effective.

Contudo, outro site explica dessa maneira:

In this Home Theater Geeks podcast, host Scott Wilkinson talks with television historian Mark Schubin to find out why. The first “standard” framerate for filming movies was about 16 frames per second, although they didn’t measure it in frames per second back then. The 24fps framerate basically boils down to an off-the-cuff compromise, as Schubin explains.

According to Schubin, movies weren’t initially measured in frames per second, but feet of film per minute. As an aside, this is where the term “footage” came from. 16fps came about because of the “60 feet per minute” standard. Filming was done at a rate of 60 feet per minute which provided around 16 frames of movie per second.

While filming was done at 60 feet per minute, playback was often anywhere between about 80-100 feet per minute (about 20-28 frames per second). This was in order to speed up the film. It allowed the theatre to be able to play more movies per day, and get more paying customers through the door.

When movies started to add sound, though, problems arose. The theatres were still able to play at pretty much any framerate they wanted to. But, 16fps movies sped up to 28fps would have actors sounding like Alvin and the Chipmunks. So, a new standard must be set.

Schubin says that an engineer from Western Electric named Stanley Watkins went to meet with the Warner Brothers chief projectionist, Frank Rich. Watkins asked Rich, “What rate do people show movies at?”. The answer showed quite a range.

The major first showings of movies typically played back at around 80 feet per minute (around 21.5fps). The little theatres that wanted to get more shows in would play back anywhere up to 100 feet per minute (about 27fps). Watkins thought for a minute and said “Ok, let’s compromise on 90 [feet per minute]”.

Esta segunda história parece ser suportado por esta postagem do blog, que oferece mais alguns detalhes:

Anyway, someone decided it would be a great idea to add sound. How hard could it be? In fact, several companies tried to be the first to bring sound to the movies, hoping to capture the market. Funny thing is they all insisted on capturing at the same frame rate they displayed at. If you didn’t, the pitch would be all wrong and everybody would sound silly. And forget about music. Some picked 80 feet per minute (the already established speed for projection), some picked 85 feet per minute, and some picked 90 feet per minute. First one to get a working system was Warner Brothers Vitaphone. It was used in the 1927 “The Jazz Singer” which was the first feature length film with sync dialog and is considered the official start of the “Talkies.”

The Vitaphone engineers had picked 90 feet per minute, or 24fps as their capture and projection speed. If one of the others had been first, we easily could be shooting 21.33fps or 22.66fp as a standard today. So sometimes you get lucky.

[...]

Movietone, which used technology that put the audio as an optical track on the film had many advantages, but it was a little late out of the gate. Because Vitaphone was first, the engineers of Movietone decided to match the Vitaphone frame rate.

Os fatos são que a menor taxa de quadros que pode ser usada para fazer as fotos se moverem é o 16 FPS, mas quanto mais, melhor e mais suave o filme fica. Thomas Edison acreditava que a taxa de quadros ideal deveria ser 46 FPS, no entanto, as câmeras e os projetores não eram tão rápidos e o filme no qual os filmes foram gravados era caro, para o 46 FPS era demais. A maioria dos filmes silenciosos foi filmada com o 14-26 FPS, mas projetada no cinema em velocidades que variam de 22 a 26 FPS. Quando os filmes começaram a incluir som, a filmagem não podia mais ser acelerada; portanto, a velocidade média de projeção do 24 FPS foi selecionada como padrão e, a partir de então, todos os filmes foram filmados no 24 FPS e projetados no 24 FPS.

Mais tarde, o que manteve o 24 FPS como padrão foi o fato de que as pessoas se acostumaram e nossos cérebros codificaram essa velocidade como a velocidade do filme. Se você observar um filme gravado com, por exemplo, o 48 FPS, como O Hobbit, ele parecerá "não natural" e não como um filme, mas como uma telenovela.

As fontes são as seguintes:

• Gary Elmer
• Wikipedia
• RedShark
• Independente de filme

Muito do que @BCdotWEB postado em sua resposta está correto, embora eu nunca tenha ouvido falar do requisito de taxa de quadros pares antes.

O 16-18 fps foi muito usado nos 1910s, mas no final do 1920s, a maioria dos cinegrafistas estava filmando em torno do 24 fps, se não mais. É claro que taxas mais lentas sempre foram usadas para efeito cômico em cenas de perseguição.

Tudo o que você sempre quis saber sobre taxas de quadros de filmes mudos está no arquivista vencedor do Oscar Kevin Brownlow artigo sobre velocidades de filmes mudos.

According to Stanley Watkins, head engineer for Western Electric, he and his team checked with the Warner Theatre for the average speed of projection in 1926. They were told 'between eighty and ninety feet per minute' in the big theatres- between 20 and 24 fps- and around 26 fps in the smaller theatres. They settled on 90 feet a minute (24 fps) as a reasonable compromise for the Vitaphone process. The other sound systems began at slower speeds (Fox-Case's first tests were shot at 21 fps), but they, too, adopted 24 fps as standard in November 1926.

E se você está se perguntando por que os filmes mudos (especialmente as comédias) foram projetados mais rápido que a velocidade em que foram gravados, visite O maravilhoso blog de Ben Model onde ele tem exemplos específicos de filmes que foram propositalmente filmados a uma velocidade menor do que foram projetados. Ben faz apresentações sobre arranque em festivais de cinema e na série Silent Clowns em Nova York. Dica: faz com que atores e comediantes pareçam mais graciosos e coreografados.

Como outros mencionados, o objetivo era minimizar a taxa de quadros e o 24 fps é (sem dúvida) a velocidade mais baixa que proporciona movimento suave. No entanto, minimizar a taxa de quadros não significa apenas minimizar o custo do filme (embora isso seja um fator). Manter o obturador aberto por mais tempo também maximiza a qualidade da imagem, como na fotografia.