Altered MOS

I�m wondering,how exactly do you define a altered MOS?The obvious cases are retaining the same number of small and large steps while changing the order,as in the altered diatonic scale C# D E F G A B or the LssLssL neutral third scale.

But what about alterations where the resulting scale no longer has two different step sizes?Such as the diatonic alterations C D E F G Ab B and its inversion C D E F G# A B.How are the MOS nature of these scales defined,and how does it apply to other generators like neutral,major or minor thirds?

Also,i have a new tune in 22-tet up on http://www.angelfire.com/mo/oljare/images/twisted.mid

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MATS �LJARE
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Mats wrote,

>I´m wondering,how exactly do you define a altered MOS?The obvious cases are

>retaining the same number of small and large steps while changing the
>order,as in the altered diatonic scale C# D E F G A B or the LssLssL
neutral
>third scale.

>But what about alterations where the resulting scale no longer has two
>different step sizes?Such as the diatonic alterations C D E F G Ab B and
its
>inversion C D E F G# A B.How are the MOS nature of these scales defined,and

>how does it apply to other generators like neutral,major or minor thirds?

Did you pick up that term from anything Wilson wrote? I don't know if he or
anyone else has proposed a definition of "altered MOS", but it might be akin
to the definition of "altered scales" (altered generalized-diatonic scales)
in my paper, http://www-math.cudenver.edu/~jstarret/22ALL.pdf.

Mats �ljare wrote,

<< I�m wondering,how exactly do you define a altered MOS?The obvious
cases are retaining the same number of small and large steps while
changing the order,as in the altered diatonic scale C# D E F G A B or
the LssLssL neutral third scale.>>

Hi Mats,

If you look at the full rotations of the two examples you gave you'll
see that both of these have three different interval sizes at two of
their scale degree's -- the 4th and 5th in the first example, and the
3rd and 6th in the second.

These are not MOS scales, but there are ways to do what it is that I
think you want to do here... try this Dave Keenan link out for
starters:

<http://www.uq.net.au/~zzdkeena/Music/2ChainOfFifthsTunings.htm>

<<But what about alterations where the resulting scale no longer has
two different step sizes?Such as the diatonic alterations C D E F G Ab
B and its inversion C D E F G# A B.How are the MOS nature of these
scales defined,and how does it apply to other generators like
neutral,major or minor thirds?>>

These scales would have the same 'problem' as the others. However, if
you were to use the two- to three-term conversion method that I've
posted about here in the recent past, a [3,4] index becomes a either a
[3,1,3] or a [3,3,1] index. And the [3,3,1] index has an interesting
two generator JI interpretation as:

125/108
\
\
\
25/18
\
\
\
5/3-----5/4
\ / \
\ / \
\ / \
1/1-----3/2
\
\
\
9/5

So the two generator chain is:

5/3, 5/3, 5/3, 972/625, 5/3, 5/3

And the resulting trivalent scale rotations are:

1/1 125/108 5/4 25/18 3/2 5/3 9/5 2/1
1/1 27/25 6/5 162/125 36/25 972/625 216/125 2/1
1/1 10/9 6/5 4/3 36/25 8/5 50/27 2/1
1/1 27/25 6/5 162/125 36/25 5/3 9/5 2/1
1/1 10/9 6/5 4/3 125/81 5/3 50/27 2/1
1/1 27/25 6/5 25/18 3/2 5/3 9/5 2/1
1/1 10/9 625/486 25/18 125/81 5/3 50/27 2/1

As far as a tempered interpretation goes, I think 19 or 26-tET would
house this far better than 12 as far as exploiting what's really
interesting about it... anyway, hope this helps.

--Dan Stearns