A meantone genus pattern

For positive integers m, take |-7m 3 3m-2> and 81/80 to be commas,
getting <12m-5 19m-8 28m-12| = m<12 19 28| - <5 8 12| as a meantone val.
Now with genus(3^3 5^m) we have a single |-7m 3 3m-2> comma, and so we
have a genus picture of the meantone in question with one duplicate note.

7: genus(3^3 5), |-7 3 1>

19: genus(3^3 5^4), |-14 3 4>

31: genus(3^3 5^7), |-21 3 7>

43: genus(3^3 5^10), |28 -3 -10>

55: genus(3^3 5^13), |35 -3 -13>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

We have a similar kleismic pattern:

19: rin(genus(3^3 5^4), |-4 4 -1>

34: rin(genus(3^6 5^4)), |11 -4 -2>

49: rin(genus(3^9 5^4)), |18 -4 -5>

Since 15 is not as good for kleismic as 12 is for meantone, not as
interesting.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

Aside from the meantone and kleismic series, also worth mentioning
are:

50: ro(genus(3^16 5^2)), |15 14 -16>
53: ro(genus(3^5 5^8)), |9 -13 5>
74: ro(genus(3^24 5^2)), |22 22 -24>

50 and 74 are another meantone series.