MODMOS's in 12-tET

I've read the xenwiki page on this, but just a few quick questions:
in 12-ET (with the ordinary diatonic scale as the albitonic scale), I want to get a complete list of MODMOS scale types.

1. Can I use E#, Fb, Cb, B#? I would imagine C,D,E,F,G,A,B must each
be used exactly once.

2. Obviously transpositions count as the same type, but will this
in itself eliminate all uses of 1)?

3. Hungarian is not RP, but does it have any other special characterisitics?

Thanks PGH

Paul - I have a half-finished, much longer reply to this that I'll
send shortly that involves a more complete understanding of the big
picture of this, as seen in terms of rank 2 periodicity blocks.
Perhaps you'll be able to then extend it to the set theory stuff that
you already know.

I think that what's going on is that academic set theory isn't
actually all that bad - it's just a very specific set theory for only
rank 1 scales that are subsets of 12-tet. Generalizing rank 1 set
theory to other ET's (like 19-ET) is simple enough; you just change
the size of the set and go from there. Generalizing it to rank 2 is I
think the gist of what we're doing, and it's much more mathematically
complicated (and I think useful).

Some quick responses in the meantime:

On Fri, Mar 18, 2011 at 2:47 PM, Paul <phjelmstad@msn.com> wrote:
>
> I've read the xenwiki page on this, but just a few quick questions:
> in 12-ET (with the ordinary diatonic scale as the albitonic scale), I want to get a complete list of MODMOS scale types.
>
> 1. Can I use E#, Fb, Cb, B#? I would imagine C,D,E,F,G,A,B must each
> be used exactly once.

You can use them, but if you use C# D# E# F# G# A# B# C# you haven't
really worked out a new scale. It's just the diatonic scale
transposed.

As for scales like C D E F G A B# C, I guess you can in 12-equal, but
it doesn't make much sense except for theoretically. On the other
hand, let's assume you're in 31-equal. Now E# and F are different, but
if you sharpen E, it won't be a part of the 12-note chromatic MOS
anymore. C D E# F G A B C is different from C D F F G A B C, whereas
in 12-equal they're the same. However, 31-equal's C D E# F G A B C
requires you to go up to the 19-note enharmonic MOS insofar as the
"chromatic pair" approach is going to be used (or it requires using a
chromatic MODMOS).

There is nothing wrong with this, but it's worth noting. The more
levels of MOS you have to go up, the more complex the resulting scalar
structure is going to be, as you now end up with something like a
chromatic triple instead of a chromatic pair. Time will tell if this
is truly important, but I think it is.

On the other hand, for something like porcupine[7], you actually DO
want to go up two levels of MOS, because porcupine[8] isn't a great
chromatic scale for porcupine[7]. It's more a "mega-albitonic" scale,
and porcupine[15] works better. So if your resulting MODMOS doesn't
fit into porcupine[8], but it does fit into porcupine[15], who cares?

It's just useful to harvest this data so that you can note it down as
a parameter for autogenerating this stuff. If you WANT to stick to a
certain scale as chromatic, make sure the resulting MODMOS fits within
that. That's all.

> 2. Obviously transpositions count as the same type, but will this
> in itself eliminate all uses of 1)?

What do you mean?

> 3. Hungarian is not RP, but does it have any other special characterisitics?

What do you mean RP? Which one was Hungarian, C D Eb F# G Ab B C?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Paul - I have a half-finished, much longer reply to this that I'll
> send shortly that involves a more complete understanding of the big
> picture of this, as seen in terms of rank 2 periodicity blocks.
> Perhaps you'll be able to then extend it to the set theory stuff that
> you already know.
>
> I think that what's going on is that academic set theory isn't
> actually all that bad - it's just a very specific set theory for only
> rank 1 scales that are subsets of 12-tet. Generalizing rank 1 set
> theory to other ET's (like 19-ET) is simple enough; you just change
> the size of the set and go from there. Generalizing it to rank 2 is I
> think the gist of what we're doing, and it's much more mathematically
> complicated (and I think useful).

Yes........
>
> Some quick responses in the meantime:
>
> On Fri, Mar 18, 2011 at 2:47 PM, Paul <phjelmstad@...> wrote:
> >
> > I've read the xenwiki page on this, but just a few quick questions:
> > in 12-ET (with the ordinary diatonic scale as the albitonic scale), I want to get a complete list of MODMOS scale types.
> >
> > 1. Can I use E#, Fb, Cb, B#? I would imagine C,D,E,F,G,A,B must each
> > be used exactly once.
>
> You can use them, but if you use C# D# E# F# G# A# B# C# you haven't
> really worked out a new scale. It's just the diatonic scale
> transposed.
>
> As for scales like C D E F G A B# C, I guess you can in 12-equal, but
> it doesn't make much sense except for theoretically. On the other
> hand, let's assume you're in 31-equal. Now E# and F are different, but
> if you sharpen E, it won't be a part of the 12-note chromatic MOS
> anymore. C D E# F G A B C is different from C D F F G A B C, whereas
> in 12-equal they're the same. However, 31-equal's C D E# F G A B C
> requires you to go up to the 19-note enharmonic MOS insofar as the
> "chromatic pair" approach is going to be used (or it requires using a
> chromatic MODMOS).
>
> There is nothing wrong with this, but it's worth noting. The more
> levels of MOS you have to go up, the more complex the resulting scalar
> structure is going to be, as you now end up with something like a
> chromatic triple instead of a chromatic pair. Time will tell if this
> is truly important, but I think it is.
>
> On the other hand, for something like porcupine[7], you actually DO
> want to go up two levels of MOS, because porcupine[8] isn't a great
> chromatic scale for porcupine[7]. It's more a "mega-albitonic" scale,
> and porcupine[15] works better. So if your resulting MODMOS doesn't
> fit into porcupine[8], but it does fit into porcupine[15], who cares?
>
> It's just useful to harvest this data so that you can note it down as
> a parameter for autogenerating this stuff. If you WANT to stick to a
> certain scale as chromatic, make sure the resulting MODMOS fits within
> that. That's all.

Yes........
>
> > 2. Obviously transpositions count as the same type, but will this
> > in itself eliminate all uses of 1)?
>
> What do you mean?

You answered it already, typically "having to add" E# probably means
the others are sharp too, so just a transposition of a common scale,
but I think there are a few exceptions.

> > 3. Hungarian is not RP, but does it have any other special characterisitics?
>
> What do you mean RP? Which one was Hungarian, C D Eb F# G Ab B C?

Sorry. Rothenberg-Proprietary (proper). Yes that's Hungarian.

Actually my main question should have been to see if there is a list
available, 12-tET only, with no enharmonic repeats (E# and F together)
of MODMOS.

I think I can write a simple computer program for this. I already
know that you can cover all hexachord types with simple accidentals
(except for 012345, This would require B#,C#,D,Eb,Fb...but then you are stuck with Gbb.)

I'll look at bit at porcupine....what do you mean jump to the "next level" of MODMOS?

PGH

> -Mike
>

--- In tuning-math@yahoogroups.com, "Paul" <phjelmstad@...> wrote:

> I think I can write a simple computer program for this. I already
> know that you can cover all hexachord types with simple accidentals
> (except for 012345, This would require B#,C#,D,Eb,Fb...but then you are stuck with Gbb.)

Twelve notes which can be either sharp, flat or neutral comes to 3^12 = 531441, so the computation can be done by brute force.

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning-math@yahoogroups.com, "Paul" <phjelmstad@> wrote:
>
> > I think I can write a simple computer program for this. I already
> > know that you can cover all hexachord types with simple accidentals
> > (except for 012345, This would require B#,C#,D,Eb,Fb...but then you are stuck with Gbb.)
>
> Twelve notes which can be either sharp, flat or neutral comes to 3^12 = 531441, so the computation can be done by brute force.

And of course that should be eleven notes, 3^11 = 177147.

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> > --- In tuning-math@yahoogroups.com, "Paul" <phjelmstad@> wrote:
> >
> > > I think I can write a simple computer program for this. I already
> > > know that you can cover all hexachord types with simple accidentals
> > > (except for 012345, This would require B#,C#,D,Eb,Fb...but then you are stuck with Gbb.)
> >
> > Twelve notes which can be either sharp, flat or neutral comes to 3^12 = 531441, so the computation can be done by brute force.
>
> And of course that should be eleven notes, 3^11 = 177147.

Don't you mean 3^7 notes? Actually I want to eliminate collisions, (enharmonics) and crossings (E# and Fb...) And then divide out any transpositions, also not caring about where the scale starts in the loop, of course, I was thinking about just looking at the step sizes, WWWHWWWW sort of thing might be fastest...am I missing something obvious?

PGH
>