I have a piano at the house. Consequently, I mess around with theory a lot in my mind, because I have the optimal aparatus to do so.
I was thinking about relative minors (I started off playing a F$ minor chord, and then switched to an A Major chord, I like progressions like that, because it embodies that dominant seventh) and so I tried something a little different. Switching to the key of C, I took the relative minor (A) and decided to invert the two. Basically, what if I took C minor and A major? Does anythign work?
I tried switching between a C minor chord and an A major chord...and while it isn't orthodox, I kinda liked the sound. So, I compared the scales and noted that they only have two notes in common, compared to the usual 7 - D and G#.
Now, I noticed that those notes - D and G# - share an even interval. (Basically, the interval is the same whether you go up to the next note or down the the previous, not like the whole fifth/fourth thing. Get me?) This means that if I split the intervals again, I end up with - voila - two sets of diminsihed chords, namely Ddim and G#dim.
(It occurs to me that in the keys I'm talking about, G# should be Ab? Maybe? I don't remember hte circle of fifths offhand to remember which use sharps and which use flats. Anyway. Sorry.)
So I was wondering - is this the reason for the distinctive sound you get when switching beween a major and it's minor third interval minor scale? I figured there must be a correlation between the sound and the whole diminished thing. Oddly enough, a C minor chord fits with G#dim, along with an A major chord.
I was just wondering if any of you have thought about this before - this is the result of me listning to music, messing around with instruments, and thinking. Have at it.
-lunchmeat
The interval you've found, D to G# is called a tritone - it's three whole tones (or six half steps) between the notes. Since a chromatic scale has 12 half steps, or six whole steps, the tritone splits the octave exactly in half.
If you split a tritone in half, you get two intervals of three half steps each - minor third intervals. And two minor third intervals make a diminished triad. Adding another minor third to it gets you a fully-diminished seventh chord.
A fully-diminished seventh has four names: the tones D-F-Ab-Cb/B can be seen as Dº7, Fº7, Ab/G#º7 or Bº7; in each case the tones are identical. Because it's got so many names, it's especially useful for changing keys.
The keys of Cm and A don't really go together. But you can force them to go together by using the diminshed seventh. In a minor scale, the second degree (ii) naturally harmonizes to a diminished triad... in the key of Cm, this is Dº; in the key of A, it's Bº. By extending the diminished triads to a diminished seventh chord, you find the same exact set of notes - and you can use the diminished seventh can be used to 'pivot' between the two keys.
Let's say you go from Cm -> G#º -> Am. It's really two separate things, with enharmonic names:
Cm -> Dº (i -> ii in Cm)
Bº -> Am (ii -> i in Am)
That really doesn't have anything to do with the relationship between relative majors and minors though. The keys of C and Am are related because they both use the same basic notes, and the same key signature.
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Yeah, it doesn't relate to relative majors or minors, but that's the only thing I could think of to describe it, since I'm specifically using the minor third interval. Relative minors got me started on this in the first place.
I'd noticed that about the diminshed seventh - the intervals are the same between every note.
Tritones, eh? You learn somethign new every day...amazing stuff. I will try using the dim chord to start switching keys...we'll see how it goes!
-lunchmeat
You might also try the augmented. Not quite as vesatile, but an augmented triad has three names...
C-E-G# = C+, E+, Ab+
same principle - it's a pivot chord.
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