Malcolm Monochord Mutations

Consider the Malcolm Monochord/Just Chromatic scale

16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 16/9 15/8 2

This has step pattern LMLSLMLLSLML, where L is 16/15, M is 135/128, and S is 25/24. If we temper out 81/80, we merge S with M and we get twelve notes of meantone in the pattern LSLSLSLLSLSL, a MOS pattern. If we temper out 2048/2025, we get twelve notes of diaschismic, in the pattern LLLSLLLLSLLL, which isn't a MOS pattern but which is Paul's favored mode for this stuff. In between we find not only the monochord but marvel tempered versions of it. So maybe a good starting point for my quest would be a better understanding of non-MOS scale constructions like LLLSLLLLSLLL. How do you turn the crank and have things like that pop out in the same way LLLSLLLLLSLL pops out? When I was doing my own 22et stuff, I found it by tempering a 7-limit JI scale, which hardly seems the way to go. Paul, I think, tweaked the MOS but I don't really know.

genewardsmith wrote:
> Consider the Malcolm Monochord/Just Chromatic scale
> > 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 16/9 15/8 2
> > This has step pattern LMLSLMLLSLML, where L is 16/15, M is 135/128,
> and S is 25/24. If we temper out 81/80, we merge S with M and we get
> twelve notes of meantone in the pattern LSLSLSLLSLSL, a MOS pattern.
> If we temper out 2048/2025, we get twelve notes of diaschismic, in
> the pattern LLLSLLLLSLLL, which isn't a MOS pattern but which is
> Paul's favored mode for this stuff. In between we find not only the
> monochord but marvel tempered versions of it. So maybe a good
> starting point for my quest would be a better understanding of
> non-MOS scale constructions like LLLSLLLLSLLL. How do you turn the
> crank and have things like that pop out in the same way LLLSLLLLLSLL
> pops out? When I was doing my own 22et stuff, I found it by tempering
> a 7-limit JI scale, which hardly seems the way to go. Paul, I think,
> tweaked the MOS but I don't really know.

Interestingly, my favored mode of the lemba decatonic is also an asymmetrical one, SLSLSLLLSL (compare the symmetrical SLLSLSLLSL).