Here’s a band that went through several typefaces (as well as band members!) throughout its lifetime, but the most iconic logostyle associated with this band first appeared on the classic ‘Rainbow Rising’ album in 1976.
I think the redrawn ‘R’ for the Rainbow logo looks more elegant and is actually easier to read. The font used to recreate ‘Rising’ is Adobe Jenson Pro, condensed to fit the space used on the album cover.
This classic Rainbow logo went on to be used on the 1977 live album ‘Rainbow On Stage’, 1978’s ‘Long Live Rock ‘n’ Roll’, the label design for 1979’s ‘Down To Earth’ (even though a completely different style was used for the cover) complete with the ‘Rising’ clenched fist, various merchandise items over the next few years, before making a comeback on the album cover for the live compilation album ‘Finyl Vinyl’ and then various greatest hits and other live album releases.