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I say: RATS!

🔗Herman Miller <hmiller@IO.COM>

3/15/2008 9:31:52 AM

What is a RAT? Depending on your preference, you could say that a RAT is a "regular abstract temperament", or perhaps a "regular abstract tuning". Substitute your own word beginning with T if you don't like either of these. The point is, it's regular, it's abstract, and the world of alternative tunings is full of them. Being named after a cute furry mammal is a bonus. You could even call it a "raw alternative tuning", a "really awful thing", or come up with your own acronym.

There are so many RATs that giving each one a personal name is a hopeless task. But there are a few special RATs that are easy to identify -- they divide the octave into steps of equal size, and represent the prime intervals (2/1, 3/1, 5/1, 7/1, etc.) in the most obvious way. So you can simply identify them by the number of steps in the octave: RAT-12, RAT-19, RAT-41, etc.*

(How does RAT-12 differ from 12-ET or 12-EDO? For one thing, the octave isn't necessarily exactly 1200.0 cents; it can be a tempered octave. Remember, RATs are "abstract". For another, RAT-12 always consistently represents 3/1 as 19 steps, 5/1 as 28 steps, 7/1 as 34 steps, 11/1 as 42 steps, 13/1 as 44 steps, and so on. That's what makes it "regular".)

*In some cases we need to refer to RATs that resemble these in some way, but have a different mapping of one or more prime intervals. For instance, 11/1 might be represented as 41 steps, or 13/1 as 45 steps, for a more accurate representation of 13/11 as 3 steps. Perhaps something like RAT-12b for a RAT that resembles RAT-12 but with the next-best approximation of 3/1, and so on ("a" representing 2/1, "b" for 3/1, "c" for 5/1, etc.) I'm open to suggestions.

These RATs are known for their prolific breeding, and any two of these RATs can get together to produce a new RAT. When RAT-12 got together with RAT-19, the result was a particular kind of meantone RAT. We'll name it RAT-12&19. It may appear identical to RAT-31&43 if you're only looking at 7-limit harmonic properties, but as you get to higher limits, the differences become more apparent. So there you have it, a naming scheme that covers practically all of the most interesting and productive RATs of the second generation (rank two).