Frequency, Harmonix first game-game. When they developed KR1 and it got popular, they figured they'd ask Konami if they'd buy the liscence off of Sony (at this point, Sony had no intention on making another one). Konami said no and Harmonix went on to finish their contract they had with Konami.
The "guitar hero" they say they asked Konami to do was just a demo. Since Konami was interested in the added revenue of peripherals, they added the fact that they could use a peripheral. They made up a demo of the game - the much fabled Weezer Dope Nose Demo - which was the Dope Nose level of Amplitude just straightened down to the guitar track.
Konami said no, Harmonix finished up their contract and went to Red Octane with the demo. Red Octane said "we just want the guitar", and hence Guitar Hero was born.