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More epimorphic genera

🔗Gene Ward Smith <gwsmith@svpal.org>

8/28/2004 10:42:27 PM

Here is a list of n, n a 7-limit integer, for which genus(n) is
strictly epimorphic with the standard val, for n < 2^50. I give n, its
factorization, and the epimorph for genus(n). Note that for 12, we get
not only 675 (the Duodene) and 3^11 (Pythagorean), but also 525 and
50421. 3^6*7 = 5103 gives the 14-note genus(5103), which tempers in a
5/4, and 3^6*7^2, 3^11*7 (24 notes) and 3^11 * 7^2 (36 notes) are
epimorphic scales allowing 5120/5103 tempering. Genus(5^4 7^4), with
25 notes, gives plently of scope for 6144/6125 tempering; we have
(5^4 7^4)/6125 = 245, with six divisors.

3 3 <2 3|
5 5 <2 * 5|
7 7 <2 * * 5|
9 3^2 <3 5|
15 3 5 <4 6 9|
21 3 7 <4 6 * 11|
25 5^2 <3 * 7|
35 5 7 <4 * 10 11|
49 7^2 <3 * * 8|
75 3 5^2 <6 9 14|
81 3^4 <5 8|
125 5^3 <4 * 9|
147 3 7^2 <6 9 * 17|
175 5^2 7 <6 * 14 17|
225 3^2 5^2 <9 14 21|
343 7^3 <4 * * 11|
405 3^4 5 <10 16 23|
525 3 5^2 7 <12 19 28 34|
675 3^3 5^2 <12 19 28|
729 3^6 <7 11|
1225 5^2 7^2 <9 * 21 25|
1875 3 5^4 <10 15 23|
2401 7^4 <5 * * 14|
4725 3^3 5^2 7 <24 38 56 67|
5103 3^6 7 <14 22 * 39|
12005 5 7^4 <10 * 23 28|
15625 5^6 <7 * 16|
16807 7^5 <6 * * 17|
33075 3^3 5^2 7^2 <36 57 84 101|
35721 3^6 7^2 <21 33 * 59|
50421 3 7^5 <12 19 * 34|
60025 5^2 7^4 <15 * 35 42|
177147 3^11 <12 19|
234375 3 5^7 <16 24 37|
1240029 3^11 7 <24 38 * 67|
1500625 5^4 7^4 <25 * 58 70|
1953125 5^9 <10 * 23|
2941225 5^2 7^6 <21 * 49 59|
8680203 3^11 7^2 <36 57 * 101|
43046721 3^16 <17 27|
215233605 3^16 5 <34 54 79|
244140625 5^12 <13 * 30|
282475249 7^10 <11 * * 31|
847425747 3 7^10 <22 35 * 62|
30517578125 5^15 <16 * 37|
3814697265625 5^18 <19 * 44|
4747561509943 7^15 <16 * * 45|
14242684529829 3 7^15 <32 51 * 90|
22876792454961 3^28 <29 46|
114383962274805 3^28 5 <58 92 135|
476837158203125 5^21 <22 * 51|