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This was written by Eric Clapton and George Harrison. Harrison, who is listed on the album as "L'Angelo Misterioso," also played rhythm guitar on this, since Cream had only one guitarist: Clapton.
The title has nothing to do with the song. Clapton saw Harrison's notes for this, and misread "Bridge" as "Badge." He thought this is what Harrison named the song, so they used it for the title.
The lyrics are not intended to make sense. Many of them were taken from drunken conversations Harrison had with Ringo Starr.
Cream recorded this a week after they played their last shows: 2 sold out performances at Royal Albert Hall in England. It was one of 3 studio recordings on their last album. The rest of it was filled with live cuts.
Cream had broken up by the time this was released. Clapton was already working with his new group, Blind Faith.
This is one of the shortest Cream songs. They were known for their long, improvised jams. The Wheels Of Fire live album, for example, contains only 4 songs.
This is one of the few Cream songs that Eric Clapton sang lead on, as Jack Bruce usually handled vocals. Also, this is the only Cream song to include 5 people: in addition to Clapton, Bruce, Baker and Harrison, Felix Pappalardi played the piano and Mellotron. Pappalardi was the producer of 3 of Cream's 4 albums (Disreali Gears, Wheels Of Fire, and Goodbye) and contributed by playing a wide variety of instruments on those albums. (thanks, Geoff - Lake Arrowhead, CA)
Clapton ran his guitar through a Leslie speaker cabinet to create a swirling sound. The Leslie Cabinet contained a rotating paddle and was designed for organs, but many musicians tried it with guitars. Jimmy Page used the technique on "Good Times, Bad Times."
The song titles were written on tombstones inside the album, leaving little doubt that it was their last.
Clapton had played on Harrison's album Wonderwall
the previous year, and on The Beatles' "While My Guitar Gently Weeps
," which was released the same month as this.