nice to see someone else who chooses accordion and ukulele as their weapons of mass-distraction.
Hey! I'm a ukulele/accordion guy too! Maybe we should create a group.
Anyhoo, to get back to the original question, here's the basic idea in a nutshell:
Chords are made up of notes, of course. Those notes have a certain "normal" order, starting with the root of the note. So a C chord has the notes C, E, and G. The C note is the root of the chord, and we use that letter in the name of the chord.
Here's the thing: The notes don't always have to be "in order". For example, you could take the C note and move it an octave higher. You'd get E, G, and C. The root of the chord is no longer the lowest note, but that's okay. It's still counts as a C chord.
As long as the individual notes that make up a particular chord are all being played somewhere, somehow, you can still call it by the same name.
Now take a look at the notes that are in your diminished chords. (By the way, what most ukulele players call a diminished chord is really a diminished
seventh chord, which has
four different notes. A true regular diminished chord just has three notes.)
Code:
Edim7 = E G Bb Db
Gdim7 = G Bb Db E
Bbdim7 = Bb Db E G
Dbdim7 = Db E G Bb
That's the cool thing about dim7 chords. They come in groups of four chords that all share the exact same notes. They're just in a different "normal" (starting with the root) order.
If you take one of them and put the notes in a different order, you'll get the "normal" version of another one. But since the order doesn't necessarily matter when you're naming a chord, this means that all four chords in each group can be justifiably called by any one of the four names.
...and it also means you can play them all with the same shape on your ukuele.
(Incidentally, there's a similar equivalency between major 6th chords and minor 7th chords. That's why a C6 is played the same as an Am7.)
JJ