Tenney-MOS

What is, or is not, a MOS of a rank-two temperament depends on the
tuning. There is a related concept which depends only on the abstract
temperament, which I propose to call a Tenney-MOS.

If you go both +n and -n generator steps in temperament T, reducing
each time by reducing to the period, then Tenney-reducing, iterating
until it stabilizes, and picking the smallest of the +n and -n
representative, you get what you might call the Tenney representative
for +-n generator steps. If for any n, the Tenney representative is
smaller than any previous Tenney representative, and if the val
resulting from solving for the commas and the Tenney representative is
un-contorted, we call n a Tenney-MOS.

For example, for septimal meantone 1, 2, 5, 7, 12, and 31 are Tenney-
MOS, with successive Tenney representatives 4/3, 9/8, 16/15, 21/20,
36/35, 49/48 and 1029/1024. If you Tenney reduce (1029/1024)^2 and
(1029/1024)^3 you get something smaller than 1029/1024, which would make
62 and 93 Tenney-MOS also without the condition that the corresponding
val must be un-contorted.