I was figuring out how to play the chords of The Phantom of the Opera with my guitar. If the I-chord is eg. D minor, then when the song goes "the phantom of the opera is there", at that "there" the chord is, apparently, the rather strange but cool-sounding D-flat diminished (at least according to sources online).
I have never really learned the diminished chords on guitar, so I was trying to figure out how to play the Db dim. I knew from having studied it a bit that it's like Db minor, but with the fifth lowered to a fourth. Db minor would be first string free, second fret on second string, first fret on third string. But that last one would be the fifth from D, so we lower it one semitone, so the third string is also free.
Then I started thinking what the fourth string would be. Well, since E is in the chord, it would be the second fret. And indeed, it sounds like Db dim.
Then I suddenly realized... this finger pattern is actually awfully familiar. It's A7! Well, without the A on the fifth string, I suppose.
So I thought, what happens if I just play A7 instead of Db dim. It turns out it sounds pretty much exactly the same. Or at least same enough that you don't really hear the difference in the song.
This got me thinking: Wouldn't this work for any song in practice? Instead of playing a diminished chord, just play the 7 chord that's four semitones lower (eg. from Db to A)? At least on guitar that tends to be significantly easier.
(Although I suppose playing something like E7 instead of Ab dim might change the chord quite noticeably due to the highest note being an E, which doesn't belong in Ab dim...)
(Edit: I made a mistake above of calling the diminished fifth a "fourth". Shows how much I know about music theory... Still keeping it so that the responses below making the correction make sense.)