ET genuses up to 100

Here are Euler genuses and rotated Euler genuses for the main
composite ets up to 100. I did not include the ones where one or the
other prime factor was not present, not because these are not
interesting but because they are MOS and we already know about them.
Some, such as 68 and 99, don't show up at all.

"Genus(3^a 5^b)" means all divisors of 3^a 5^b. "Ro" is the mapping
3-->10/3, 5-->16/3, and "rin" the mapping 3-->16/5, 5-->24/5. I think
the 3^11 5^5 for 72 is particularly interesting, and the number of
different ways of dealing with 84 is intriguing.

12: genus(3^3 5^2); ro(genus(3^3 5^2)); rin(genus(3^2 5^3))

15: genus(3^4 5^2); ro(genus(3^2 5^4)); rin(genus(3^2 5^4))

22: ro(genus(3^10 5)); rin(genus(3 5^10))

27: genus(3^8 5^2); rin(genus(3^2 5^8))

34: genus(3^16 5); ro(genus(3 5^16));

46: ro(genus(3^22 5); rin(genus(3 5^22))

50: genus(3 5^24); rin(genus(3^24 5))

58: genus(3^28 5); ro(genus(3 5^28))

72: genus(3^11 5^5); ro(genus(3^5 5^11))

80: genus(3 5^39); rin(genus(3^39 5))

81: ro(genus(3^26 5^2)); rin(genus(3^2 5^26))

84: genus(3^11 5^6); genus(3^2 5^27); ro(genus(3^6 5^11));
ro(genus(3^41 5)); rin(genus(3^27 5^2)); rin(genus(3 5^41))

87: genus(3^28 5^2); ro(genus(3^2 5^28))

94: genus(3 5^26); rin(genus(3^26 5))

>Here are Euler genuses and rotated Euler genuses for the main
>composite ets up to 100.

Why are Eurler genuses better than Fokker blocks for this
notational purpose?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Here are Euler genuses and rotated Euler genuses for the main
> >composite ets up to 100.
>
> Why are Eurler genuses better than Fokker blocks for this
> notational purpose?

They have neat edges. We can always find a corresponding Fokker block,
but in general they have ragged edges, and if you do this for cases
where n+1, n+2 or n+3 are the composites, you get holes nibbled out.
These, I think, would simply make neat, easily dealt with layouts for
programs like Musika. I'd rather deal with a 5x5 square for 22-et and
have three duplicate notes than with the somewhat ragged Fokker block
alternative for visual purposes.