http://www.phy.mtu.edu/~suits/scales.html
...I had been wondering... the Just Scale is what makes sense. I first stumbled upon the frequencies of the equal tempered scale and was surprised to find it off from the obvious (1.2, 1.25, 1.333) Instead found this: http://www.phy.mtu.edu/~suits/notefreqs.html
which doesn't seem to work out at all. Results in 1, 1.06, 1.12, 1.19, 1.26!, 1.335?, 1.414, 1.498!, 1.59.....
I had made the assumption of a just scale.
But I had additionally wondered what would happen as one changed keys and normalized into the new key. So to go from C major to C# minor, would the ratios change?
Apparently so thus the existence of the equal tempered scale to keep things standable as you changed keys.
..clearly so actually. And it would sound relatively awful unless one had just become used to it. Which you can get used to playing stuff all out of tune, etc.
But how off would it otherwise sound?
And how would a scale like this sound?
1+1/16, 2/16, 3/16, 4/16, 5/16, 6/16, etc?
...I think I'd prefer to use a just scale tailored to whatever key I was in... Not sure how to easily manage that. (..and that's not well worded. But anyway...)
I suppose using a sampler and painstakingly putting each note in. Doing that to construct a number of alternative frequency sequences. Mostly would prefer something larger then the 12 tone scale. Really it's depressingly few notes, seems to me.
..why is there no 1.75, etc?
...to think further... Perhaps I'll attempt to construct a virtual instrument that combines a 16 tone and 20 tone scale. Or 16/10, or 8/10... I think the 16 tone scale I've in mind (1/16, 2/16, etc) would be too consonant. It would too much in agreement. Very pleasant sounding though. But it would be a bunch of people who basically all agree. 2 or 4, 8, 16 such a scale would be our rational minds. Our computer logic. Such a collection of notes would come more or less from the base two numbering system.
While, a 10 or 20 tone scale would come from our hands. Or our not entirely rational human bodies.
Then to combine the two into a 36 tone scale would be two competing and often discordant ideas. That of rational man, our conscious against our unconscious, our ancestry, that which we've evolved from which it is actually essential we hold on to, in order to be happy and find reason to continue existing.
Instead of always using the 12 tone scale (or the few others of nonwestern cultures) there is an infinite number of frequencies that an octave could hold. Of all the possibilities attempting to combine 1/16th, 2/16ths, etc with 1/20th, 2/20th etc seems like an idea to try...
The existing 12 tone just scale perhaps is already doing a far better job of presenting coherent competing ideas. Where by coherent I mean fractions of small whole integers. As opposed to everything being divided by 16 or 20 there is 6/5ths, 5/4ths, 4/3rds, 3/2nds. But, curious to reinvent the wheel some more. ..and actually all but 4/3rds is covered by 16 and 20...
