I've just checked through my MP3 collection and these are all over 1 minute long (and, from memory, not looped);
Trollie Wallie, Super Space Invaders, Robozone, Artura, Avenger, Death Wish III, Deflektor, Footballer Of The Year, Future Knight, HATE, Krakout, Mask 3, Switchblade, Thing On A Spring, Blade Runner, Cyberbig, Prehistorik 2, Super Cauldron, Finders Keepers, BMX Simulator, Beverly Hills Cop, Beyond The Ice Palace, Crystal Kingdom Dizzy, Defcom, Dizzy Down The Rapids, Elektra Glide, Elevator Action, Gilbert (Escape From Drill), Glider Rider, Mr Heli, Shadow Of The Beast, Spellbound Dizzy, Stormbringer, Trantor, Treasure Island Dizzy, Xenon, Subbuteo, Xyphoe's Fantasy, Demon's Revenge, Energy, 1943, Bravestarr, Battle Valley, Cybernoid, Cybernoid 2, GI Hero, Herobotix, Marauder, Maze Mania, Nebulus, Netherworld, Radzone, Stormlord, Stormlord 2 (Deliverance), Turbo Boat Simulator, Zynaps, Gryzor, Mega Apocalypse, Out Run, Rastan Saga, Savage, Ball Breaker, Caecilia Metella, 3D Starfighter, Brainache, Dizzy, Super Robin Hood, (Bad Dudes Vs) Dragonninja, Burnin' Rubber, Daley Thompson's Olympic Challenge, Darkman, Robocop, The Vindicator, Mega-Phoenix, 1942, Airwolf 2, Duet, Great Gurianos, Space Harrier, Overlander, Hot Shot, Escape From The Planet Of The Robot Monsters, Pit Fighter, Batman (The Movie), Druid (Loader), Harvey Headbanger (Loader), Spiky Harold (Loader), Thrust (Loader), Stun Runner, Eliminator, Equinox, Exolon, Rampage, Silkworm, Prehistorik, Paladin, Barbarian, Cauldron 2, Stifflip & Co, The Sacred Armour Of Antiriad, Five-A-Side Soccer, Hydrofool, Knight Tyme, Monty On The Run, Nemesis The Warlock, Saboteur 2, Shockway Rider, Spellbound, The Human Race, The Last V8, Thundercats, Trans-Atlantic Balloon Challenge, Warhawk, Wriggler (Romantic Robot), Kettle, Turrican 2, Golden Axe, St Dragon, Batman (The Caped Crusader), Captain Blood, Purple Saturn Day, Double Dragon, Flimbo's Quest, Jet Set Willy, RBI2 (Baseball), Agent X 2, Gauntlet 3, Ghouls 'N' Ghosts, Cavemania, Las Tres Luces De Glaurung, Titanic, L'Aigle D'Or and Meltdown (SHALL WE PLAY A GAME?)
There are many, many others!
Amstrad game music was/is underrated (due to that CYD thing on the C64.)