Preemptive alert: If you dislike theoretical explanations, skip this post, and keep your whinging and wisecracks to yourself. If you'd like to learn some theory quickly, try this site:
http://www.musictheory.net/lessons
For some more help on deciphering chord names, see my previous post in another thread:
http://forum.ukuleleunderground.com/showthread.php?101568-G-g5-g7-g11#post1594382
Figuring out chords from their names can be a bit tricky. For instance, by default a 7 normally means a dominant (i.e. minor) 7th interval. But in "dim7", the 7th is a diminished 7th, i.e. a minor 7th which is lowered another half-step, which in the equal-tempered intonation system is equivalent to a major 6th interval. The 7th here is built a minor 3rd above an already diminished interval, the diminished 5th.
If, instead, you want a diminished triad with a dominant/minor 7th, you have what is called a "half-diminished" chord, spelled either
Xm7b5 or
Xø. It's called half-diminished because, measured from the root, the
dim7 chord has, in addition to a minor 3rd, two diminished intervals: the diminished 5th and the diminished 7th, whereas the
Xø chord only has one. The 7 in
Xm7b5 has its usual meaning (dominant 7th) because this spelling considers the base triad to be a minor triad rather than a diminished one: first you form the minor 7th chord (
Xm7),
then you diminish the 5th. And it normally functions as an altered dominant chord.
The diminished triad may also be spelled
X° or
Xo, though as with "dim" it's more common for this notation to mean the diminished 7th chord (and you'll also see
Xo7, the more proper spelling). To spell the diminished
triad unambiguously, most people write
Xmb5: a minor triad with the 5th diminished.
On the subject of notation, here's another anomaly: In standard notation, you'd write the chord with a diminished 7th, not a 6th, unless that would force you to use a triple-flat (never written). For example, here's the proper notes to write for the following chords:
C#dim7 = C# E G Bb (not A#)
Cdim7 = C Eb Gb Bbb (not A)
but
Cbdim7 = Cb Ebb Gbb Ab (not Bbbb)
That said, guitarists and ukists like to keep things simple, so you'll often see the simpler enharmonic equivalents (A instead of Bbb, and Bdim7 instead of Cbdim7).
The dim7 chord is quite useful because it creates harmonic disorientation and ambiguity: unlike dominant 7ths and minor 7ths, it can't be built naturally from diatonic scale notes. I think of it as a "roudabout" chord: you can get to it from almost any chord, and go to almost any other chord. Any note you choose is either in the chord or a half-step away (supporting voice leading).
Very frequently, though,
Xdim7 really functions as a rootless
Xb7b9. In other words, in a standard resolve-by-fifths progression like Dm7 - G7 - C, one might play play a dressier Dm7 -
G#dim7 - C, but really the 2nd chord would be G7b9 (and if a savvy bassist were playing along, he might play a G under your G#dim7). The second chord might also be notated as Ddim7 (keeping the same root as the preceding chord), Bdim7 (viewed as leading to C) or even Fdim7 (no rationale except that it plays the same notes), but none of these four dim7 spellings truly reflects what's happening harmonically. To see what I mean, try these three progressions:
Dm7 (5555) - G7 (4535) - C (5433)
Dm7 (5555) - G7b9 (0545) - C (5433)
Dm7 (5555) - G#dim7 (4545) - C (5433)
Then switch back and forth between the G7b9 and the G#dim7 (lifting and planting just your index finger). You're essentially playing the full five-note version of G7b9, 3rd-less the first time, rootless the second. (This sounds clearest on a linearly-tuned uke.)
I'm not saying the dim7 spellings are wrong, if the notator specifically wants the dim7 sound; it's sort of a choice between the mechanics and the meaning, the expression and the intent. Few uke players would understand, if they saw
X7b9, that they could well use
X#dim7 instead. But now you do, and how cool is that?: one easy shape for two entire sets of chords, and positioning is a piece of cake (for dim7, any note can be the root; for 7b9, any fret before can be the root).
