Partial list of the MODMOS's of Porcupine[7]!

These are some of the most beautiful microtonal scales that I have
ever heard. It may be a good approach here to think tetrachordally, as
slamming together different tetrachords is a good way to generate
MODMOS's. I gave each MODMOS a number for reference. I don't claim
that this is the best way to index them, but it is useful nonetheless.

There were so many in 22-tet that I chose to not include any in which
the 1\22 step appears as an interval. If you do include these, you
start to get interesting options in which 7/6 and the like appear in
the scale. I also chose to ignore scales in which "3 3" never appears
- scales like This should be enough to get us started.

Modes where the 3/2 is unaltered, and in which 8:9:12 exists:
1: 4 3 3 3 3 3 3 - Porcupine[7] major
2: 4 2 4 3 3 3 3 - Porcupine[7] but with the 5/4 replaced with 6/5. In
this mode of the scale you still get the 8:9:11:12, but instead of a
major third you get a minor third. This one is @#&* awesome
3: 4 3 2 4 3 3 3 - Porcupine[7] but "ionian"ized! Take the major mode,
but replace the 11/8 with 4/3. This is one of my favorites
4: 4 2 3 4 3 3 3 - A combination of the above two near-MOS's. Take the
major mode and replace the 5/4 with 6/5, and ALSO replace the 11/8
with 4/3. This one is also badass.
5: 4 2 4 2 4 3 3 - Take the first Porcupine[7] near-MOS mentioned and
raise the ~11/6 by a diesis, thus changing it to a 15/8. Sounds a bit
like meantone melodic minor #4. Really neat.
6: 4 3 3 3 2 4 3 - Porcupine[7], but with the major sixth flattened a
diesis to become a minor sixth.
7: 4 2 4 3 2 4 3 - mix #6 with #2 - flatten 5/4 and 5/3 by a diesis
into 6/5 and 8/5.
8: 4 3 2 4 2 4 3 - mix #6 with #3 - this is kind of like a JI version
of mixolydian b6
9: 4 2 4 3 2 4 3 - mix #6 with #2
10: 4 2 3 4 2 4 3 - mix #6 with #4

Modes in which no 8:9:12 exists, and makes most sense if you view it
as one of the fifths getting flattened by a diesis:
7: 4 3 3 2 4 3 3 - This one is interesting. Take Porcupine[7] and
flatten the perfect fifth by a diesis. You end up with a somewhat
dissonant 655-cent "false fifth"
8: 4 3 2 3 4 3 3 - This one is like #6 combined with #3. Regular
porcupine but with a flat fifth and with the 11/8 turned into 4/3.
9: 4 2 3 3 4 3 3 - This one is like #6 combined with #4. Flatten the
fifth, the fourth, and the third.

There are just too many of these, so this should be enough to get
people started for now. One will clearly have to learn the pattern for
generating valid MODMOS's here instead of just memorizing them all by
rote.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> There were so many in 22-tet that I chose to not include any in which
> the 1\22 step appears as an interval.

Here are the proper 7-note scales, none of which comes with a 1\22 interval.

! prop22_7a.scl
Porcupine[7] strictly proper scale
! 3433333

! prop22_7b.scl
Strictly proper 7-note 22-et scale; Narada
! 4333342

! prop22_7c.scl
Strictly proper 7-note 22-et scale; Sarngadeva/Somantha
! 4333432

! prop22_7d.scl
Strictly proper 7-note 22-et scale; inverse prop22_7c
! 4333423

! prop22_7e.scl
Strictly proper 7-note 22-et scale; four fifths in circle
! 4324423

! prop22_7f.scl
Strictly proper 7-note 22-et scale; full circle of major/minor thirds
! 3424243

! prop22_7g.scl
Strictly proper 7-note 22-et scale; four major thirds in circle
! 3433432

! prop22_7h.scl
Strictly proper 7-note 22-et scale; quasi ascending melodic minor
! 3433423

! prop22_7i.scl
Strictly proper 7-note 22-et scale; inverse 22_7h
! 3243343

On Tue, Mar 22, 2011 at 1:55 AM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > There were so many in 22-tet that I chose to not include any in which
> > the 1\22 step appears as an interval.
>
> Here are the proper 7-note scales, none of which comes with a 1\22 interval.

All of the ones I pasted were proper, and there are a lot more where
they came from too - I truncated the list at 13 entries because the
list was too exhaustive. Is this supposed to be a complete list? Where
is 4 2 3 3 4 2 3?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > Here are the proper 7-note scales, none of which comes with a 1\22 interval.
>
> All of the ones I pasted were proper, and there are a lot more where
> they came from too - I truncated the list at 13 entries because the
> list was too exhaustive.

I didn't consider anything but strictly proper scales.

> Is this supposed to be a complete list?

It's from an old file of scale in Scala format which was supposed to be complete.

> Where
> is 4 2 3 3 4 2 3?

That's a scale of 21edo.

On Tue, Mar 22, 2011 at 3:13 AM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > Here are the proper 7-note scales, none of which comes with a 1\22 interval.
> >
> > All of the ones I pasted were proper, and there are a lot more where
> > they came from too - I truncated the list at 13 entries because the
> > list was too exhaustive.
>
> I didn't consider anything but strictly proper scales.

OK. I guess that in this case, only considering strictly proper scales
is equivalent to mostly looking at MODMOS's that are part of the
15-note chromatic scale, right? Because otherwise, if they were part
of the 22-note chromatic scale, we'd see some of the characteristic
tempering that causes them to be proper, not strictly proper.

I would suggest that we also consider proper scales as well. And being
as a lot of the scales we look at are actually improper to start with,
I'm not even sure where to begin. I think some kind of refinement of
Rothenberg propriety would be useful, as I think it's "almost there,"
but I'm not sure exactly what's wrong with it or how to fix it.

> > Where
> > is 4 2 3 3 4 2 3?
>
> That's a scale of 21edo.

I meant 4 3 3 3 2 4 3, sorry, and I see now that it is only proper,
not strictly proper.

-Mike