How do you think the Arcade machine make sound, & make the long same sequence of sound each time in same time length everytime? (Possibly the same with video shown on the Arcade screen too)
The sounds including any music must be either stored in memory or synthesised as necessary, and the title or idling tune called up by a short programme that repeats itself until turned off by a command from the game-starting sequence.
The accompanying images would be controlled similarly.
I don't know if modern video-games live on the publisher's server and your computer calls the images and music over the Internet as necessary, or if you load the whole lot into your own computer beforehand.
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The early games were for very low-powered processors and memories by modern standards, so could play only short sequences of very simple notes. Those are quite easy to programme as a single whistle-like "beep" needs just its frequency and duration to describe it; provided the compiler has a signal-generator for the programme to call.
As a very simple example, I once did something similar for alert tones in a BASIC programme controlling a laboratory test-rig. Middle 'A' - 440Hz - told the operator the test sequence had finished. Two other beeps, at 'A' above (880Hz) and below (220Hz) alerted other functions, and each beep was 1 or 2 seconds long.
Those were single "beeps" but if I'd wanted something like an early Pakman game idling "tune", I'd have written several beeps as a sequence of commands, one per line, between [Start] and [Return], or similar, code-words - I forget the real language. So when it reaches the end, [Return] would send it back to [Start]. (I doubt Management would have approved though...)
The equivalent in the arcade-game would have some command written into the game programme itself that tells the idling tune and video to stop, calls it or other tones as needed during the play; and restores it at the end of play.
Modern, far more powerful games, must be somewhat similar at heart but are obviously many magnitudes more highly-developed.
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When the electronics developed enough to allow near-photographic, film-like videos, it also allowed enough memory to hold recordings of fully orchestral music for them alongside the pictures, as on the films. Again, the calls to the music would be triggered by appropriate cues in the game starting, playing and ending sequences.
The musical difference between films and videos, explained by a video-game composer I heard on the radio, is that while film scores are linear, following the action and mood depicted in a steadily-progressing, single narrative; the game music often has to follow the effects of players' choices and timings, and to do so seamlessly.
This parallel music development has grown to the point that BBC Radio Three has a monthly Saturday-afternoon programme of video-game music recordings. The same times in the intervening three weeks are devoted to film scores. Some of the music is composed and played on synthesisers; but a lot of both film and video music is of symphonic form and indeed played by "classical" symphony orchestras.