What is the the MOD music file format? Exactly how does it relate to the Amiga 1000 audio hardware?
Did the MOD format become popular on non-Amiga computers? If so, why?
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MOD is the file extension for SoundTracker modules. SoundTracker and its successors (NoiseTracker and ProTracker predominantly, although there are other derivatives) are sequencers, and load and save files in this format. It was originally designed for games and demo programmers - assembly code to play back the modules was commonly available and worked efficiently, and the module itself contained all the data needed.
Modules embed all the required sound samples, and the "patterns", essentially multiple 4x64 grids of musical notes and attributes. The 4 columns are matched to the Amiga's 4 audio channels; each of the 64 rows are a "beat" and the player steps through each row in time with the beat. Each cell has a musical note, a reference to the sample, and possibly some attributes which cause special behaviour. On each beat, the player takes the note and the sample reference in each column(channel) and tells the audio hardware to play it, and the frequency equivalent to the musical note. Also in the module file is the playlist, which tells the player in what order to play the patterns.
The format was very popular with game and demo writers, and later for musicians in general, so there ended up with a very large body of music modules that were freely available.
It is very closely tied to the Amiga's hardware, specifically the Paula chip which was largely unchanged throughout the Amiga's product line:
For a long time this format was exclusively tied to the Amiga - the Amiga's peers did not have an audio capability that matched or exceeded the Amiga's, so they were impossible to play. However, technology moved forward for other platforms and they developed audio systems that exceeded that of the Amiga. MOD players started to become available for these other systems. That allowed these other systems to play back this large collection of freely-available music modules.
As audio technology moved on and quality improved, new file formats took advantage. MP3 and its successors can represent higher resolution and higher bit rates, but a MOD file will always be 4-channel 8-bit sampled sound. There is still a "scene" for MOD files, similar to the demoscene and retro computing scene, and tools exist for modern platform to create and play MOD files.