Mystery MOS

In-Reply-To: <200112100807.KAA134792@ius578.iil.intel.com>
Bob Valentine wrote:

> I have certainly been exploring MOS and MOS offspring so I'm
> interested in this topic. Recently I have been looking at
> mappings from one ed2 to another. For instance, this weekend
> I played with
>
> 31 : 4414414441
> 41 : 5525525552

That's the neutral third MOS. See
<http://x31eq.com/7plus3.htm>.

> which unfortunately doesn't have an analog in 19. I'm
> concentrating on 31 and 41 because although they have much
> of the same resources (perhaps too much) 31 approaches it
> them as a meantone and 41 as a quasi-pythagorean tuning.

No, 19 doesn't fit the pattern. Although 38 does.

But if you're talking about 31 and 41, that must be a re-mapping of
Miracle. In this case, as your generator is 3 secors, you're only getting
a third of the full Miracle temperament. Although everything's still
there if you take enharmonic equivalents in 31 or 41, the approximations
won't agree between them.

There's been a lot of fuss about Miracle the past year. My best starting
page is <http://x31eq.com/miracle.htm>.

> In Saturday improvisations I preferred 31, in part because
> the 5-(odd)-limit intervals are more palatable to me than the
> 3-(prime)-limit (more than compensating for the slightly
> bruised 3/2 and 4/3). I also preferred the more exagerated
> difference in step sizes (higher value of R).

Yes, the 5-limit approximations won't be consistent between 31 and 41 in
this mapping. The fifths will be 3:2 and the neutral thirds 11:9, which
also means 12:11 and 11:8 will match. The family that is consistent with
31-equal in the 5-limit includes 24= and 38=. Have you tried them? And
there's 17= for the more adventurous, with an approximation to 7:6.

Graham

> From: graham@microtonal.co.uk
> Subject: Mystery MOS
>
> Bob Valentine wrote:
>
> > I have certainly been exploring MOS and MOS offspring so I'm
> > interested in this topic. Recently I have been looking at
> > mappings from one ed2 to another. For instance, this weekend
> > I played with
> >
> > 31 : 4414414441
> > 41 : 5525525552
>
> That's the neutral third MOS. See
> <http://x31eq.com/7plus3.htm>.
>

yes i recognize that this is just the next branch down from
4545445. However, when you say "thats the neutral third MOS",
I feel it is ignoring the more pedestrian usage model that
becomes available at this point in that you have major and
minor triads, with the neutral third available as a third triad
type, or a neighbor tone, or a tension...

>
> Yes, the 5-limit approximations won't be consistent between 31 and 41 in
> this mapping. The fifths will be 3:2 and the neutral thirds 11:9, which
> also means 12:11 and 11:8 will match.

As per my reply to Paul, the "minor thirds" and "major thirds" line up
in a traditional notation. What changes is that the minor thirds are
~6/5 vs ~32/27 and ~5/4 vs ~81/64. The 11-limit stuff is all over the
place structurally between the systems, and pretty much in tune...

> The family that is consistent with
> 31-equal in the 5-limit includes 24= and 38=. Have you tried them? And
> there's 17= for the more adventurous, with an approximation to 7:6.
>

Now thats catching the point. The real idea here is the LLsLLsLLLs
structure. Mappings include

T-----L---s
17 2 1
24 3 1
31 4 1
38 5 1
45 6 1
27 3 2
41 5 2
55 7 2
etc...

I chose 31 because I like it and 41 because I'm thinking that
perhaps when I am reincarnated I'll need uniqueness at
the 9-limit. I should play around with a few of these given
that the R value turned out to be important in side-by-side
comparisons. 24 and 55 are interesting interpolations, 17 and
38 head for the deeper waters...

thanks

Bob Valentine

>
> Graham