Here’s a bit of trivia that brings this full-circle, then. The Simpson’s theme song was composed by Danny Elfman, and I’ve seen in the past where he specifically mentioned Bartok as one of his classical influences.
Yes, Cage has used this kind of thing, too - but in a very different way to Bartok!
FWIW, you don’t have to mess around with these kinds of key signatures to find sections of music that go beyond the ‘standard’ keys. I think it’s in Schubert’s ninth symphony that a chain of fifths briefly reaches F flat major, before switching to sharps instead.
Bitonality and polytonality are concepts dating back to at least Mozart in classical music. Mozart used it facetiously in a piece called Ein musikalischer Spass. Others who have used it in the classical realm include Ives, Stravinsky, the aforementioned Cage, and plenty of others in the contemporary era of classical music. You will also find it creeping up in a lot of Eastern European folk music, which is, I suppose, where Bartok got a lot of his bitonality ideas from.
However, many bitonal and polytonal pieces are written out in a single key signature for ease of reading. It all depends on the preference of the composer or transcriber.
Lydian Dominant is actually a very common key for jazz soloing - it works nicely for almost all non-diatonic dominants, by providing an upward leading tone to the fifth and a downward to the sixth.
I use it quite frequently, and it works especially well in conjunction with the diminished scale (which nicely handles the upper extensions of a 7b9) to move around the neck (guitar) to get to other positions.
It’s the first non-modal scale I teach my students for handling outside changes in jazz soloing. (followed by the dim and whole tone scales)
[jazz geek]
Down with modal thinking!
[/jazz geek]
Of course, some Indian musicians might argue that there are hundreds of keys not represented by the typical Western music scale. 
Very true!
Back in school, I had a rather unconventional teacher for a few semesters. He was actually supposed to be my private instructor in guitar pedagogy, but we pretty much spent every class time discussing odd little minutiae of music - from performance to theory to various world traditions. I fondly remember all the lessons I was supposed to be studying some theory of teaching, and instead jammed with him on the sitar, or celtic harp, or samisen or somesuch instrument.
One of his favorite books - which I had for a long time, lost and now for the life of me can’t remember the title of - was a huge volume of all possible scales, ranging from four to thirteen tones, with every scale that had a name titled, and thousands more that were more or less mathematical permutations of the available tones.
It was pretty impressive - one of his favorite exercises was to assign me a scale or group of scales and then have me compose lines and pieces for that scale. And somehow manage to harmonize it, if I could. Infuriating at times, but really fun and good practice.
Still, it wasn’t as hard as when we got into Mick Goodrick’s theories, or when I dove into Ornette Coleman’s Harmolodics…
Ffftt. That’s nothing. Xenakis, a slightly-barmy but fantastic composer, outlined a mathematical model to calculate any scale, using any division of pitch, not necessarily repeating in each octave, and so on. The result? An infinite variety of scales.
Yeah, but I probably couldn’t have fit his book in my backpack, mr. smartypants.
There are a number of people who have written music in quarter tone “scales.” Sort of like playing music in the cracks of the keys.
And, poster K364 - are you, perhaps, a fan of the Symphonia Concertante?
As to what they are for…
The Major Keys are for the big things.
B-flat Major is the house. G Major is for the Car. F major is the store key.
The minor keys are for small things.
D minor is to the padlock on the shed.
A minor is a lonely miner.
F minor is the saddest of all keys
C sharp minor is the key to the suitcase you don’t use anymore.
Nobody knows the use for either E flat major or E flat minor. It might have been the key to my mom’s house and a filing cabinet or a locker at some bus station.
Oh, yes, and sixth-tone and eight-tone and …
Most of these pieces tend to be completely atonal, not having any central reference-point, so they’re no more using a particular scale, just a convenient and regular division of pitch.
Brilliant! Do you mind if I add this to a sheet I wrote earlier this week explaining relative major/minor keys?
I believe that E flat minor was used originally in England when a small child was run over by a steamroller and had to be slid under the door, as his mum was indisposed in the bathroom.
Well, damn, I guess I’m too late to this thread to add anything relevant.
Just one comment:
Where is the flatted 7th? To my ears, at least in the main theme, it’s just regular old lydian.
The second half of the main phrase/riff.
Depends on what you mean by “key.” I consider the concept of “key” to be one only useful when looking at Western music, and dictionaries seem to agree:
(for example, here’s Merriam-Webster’s take it: “key: A tonal system consisting of seven tones in fixed relationship to a tonic, having a characteristic key signature and being the structural foundation of the bulk of Western music; tonality.”)
Indian music has concepts of thats, ragas, and swaras underlying its musical structure and while these may be somewhat analogous to Western tradition, it’s really not that useful to think in traditional terms of key when it comes to non-Western music. The concept of key includes a major and minor distinction, something which does not exist in Indian music.
As for the Simpons theme, actually, you’re right. There is no dominant seventh in the main riff. I just listened to it, and the way it plays in my head is a little different than the actual recording; However, the dominant seventh harmony is heavily implied. If you “jam along” to the Simpsons chords, you’ll note that the major seventh sounds wrong, but the dominant seventh sounds right.
Also, right before the C - F# bass gives way to the B major chord, the leading chord before the B major is a C7, giving you the dominant seventh I hear so strongly implied. That tune changes tonal centers so many times…
You are correct. I meant that there is no such key as “A# major” although “a# minor” (using a lower-case a) does indeed exist. Sorry for the confusion.
At the risk of showing my ignorance and having all the “music weeds” snorting at me behind their snotty handkerchiefs, Chopin’s Nocturne in C-Sharp minor (1830), featured on Polanski’s The Pianist, is so beautiful, soulful and lyrical that something as mundane and tatty as an old suitcase (though invoking mystery - one element, I grant you, of the piece/performance) doesn’t do it justice, to my mind.