MOS and DE

Hi everyone!

How do moment-of-symmetry scales and distributionally even scales
differ? Is there any difference?

At least all MOS scales must be DE. Some DE scales are MOSes, aren't
they all?

Kalle

--- In tuning@y..., "Kalle Aho" <kalleaho@m...> wrote:
> Hi everyone!
>
> How do moment-of-symmetry scales and distributionally even scales
> differ? Is there any difference?

there is no difference, at least until you get to the problem of
interval of repetition vs. interval of equivalence. the academics
don't seem to distinguish the two, which is kind of silly, since for
example 12-equal has plenty of possibilities that repeat at an
interval smaller than the octave. i think the academics see those in
terms of a 3-tone universe, a 4-tone universe, etc. . . but when you
derive all these beasts from ji, as we've been doing on the tuning-
math list, this distinction begins to look awfully artificial.

> At least all MOS scales must be DE. Some DE scales are MOSes,
aren't
> they all?

yes.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41158.html#41166

wrote:
> --- In tuning@y..., "Kalle Aho" <kalleaho@m...> wrote:
> > Hi everyone!
> >
> > How do moment-of-symmetry scales and distributionally even scales
> > differ? Is there any difference?
>
> there is no difference, at least until you get to the problem of
> interval of repetition vs. interval of equivalence. the academics
> don't seem to distinguish the two, which is kind of silly, since
for
> example 12-equal has plenty of possibilities that repeat at an
> interval smaller than the octave. i think the academics see those
in
> terms of a 3-tone universe, a 4-tone universe, etc. . . but when
you
> derive all these beasts from ji, as we've been doing on the tuning-
> math list, this distinction begins to look awfully artificial.
>

***Hi Paul,

Would you mind please elaborating on this very briefly? I'm not
getting it, and it seems quite interesting... You're talking about
repeating *intervals??* How could those be equivalent? By
definition??

Thanks!

Joseph

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_41158.html#41166
>
> wrote:
> > --- In tuning@y..., "Kalle Aho" <kalleaho@m...> wrote:
> > > Hi everyone!
> > >
> > > How do moment-of-symmetry scales and distributionally even
scales
> > > differ? Is there any difference?
> >
> > there is no difference, at least until you get to the problem of
> > interval of repetition vs. interval of equivalence. the academics
> > don't seem to distinguish the two, which is kind of silly, since
> for
> > example 12-equal has plenty of possibilities that repeat at an
> > interval smaller than the octave. i think the academics see those
> in
> > terms of a 3-tone universe, a 4-tone universe, etc. . . but when
> you
> > derive all these beasts from ji, as we've been doing on the
tuning-
> > math list, this distinction begins to look awfully artificial.
> >
>
> ***Hi Paul,
>
> Would you mind please elaborating on this very briefly? I'm not
> getting it, and it seems quite interesting... You're talking about
> repeating *intervals??* How could those be equivalent? By
> definition??

for example, the diminished (octatonic) scale repeats at the minor
third. i think academic theorists would tend to think of this in
terms of the minor third being the *interval of equivalence* for this
scale, and the scale being ME, WF, DE, etc. with respect to
that "interval of equivalence". but on tuning-math, we call this
minor third merely an *interval of repetition* or *period*, while the
*interval of equivalence* continues to be the octave. the sub-octaval
repetition is merely the consequence of a particular comma (in this
case, 648:625) being tempered out . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41158.html#41195

>
> for example, the diminished (octatonic) scale repeats at the minor
> third. i think academic theorists would tend to think of this in
> terms of the minor third being the *interval of equivalence* for
this
> scale, and the scale being ME, WF, DE, etc. with respect to
> that "interval of equivalence". but on tuning-math, we call this
> minor third merely an *interval of repetition* or *period*, while
the
> *interval of equivalence* continues to be the octave. the sub-
octaval
> repetition is merely the consequence of a particular comma (in this
> case, 648:625) being tempered out . . .

***Well, I know they count *interval classes* for example, but I
don't know if they consider them "equivalent" in the way pitches from
the octave, with the same names, are considered "equivalent..." I
guess Chris Bailey could answer this question, since he's still
studying this stuff...

But what are the abbreviations, ME, WF, DE? They look like states...

Thanks!

Joseph

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_41158.html#41195
>
> >
> > for example, the diminished (octatonic) scale repeats at the
minor
> > third. i think academic theorists would tend to think of this in
> > terms of the minor third being the *interval of equivalence* for
> this
> > scale, and the scale being ME, WF, DE, etc. with respect to
> > that "interval of equivalence". but on tuning-math, we call this
> > minor third merely an *interval of repetition* or *period*, while
> the
> > *interval of equivalence* continues to be the octave. the sub-
> octaval
> > repetition is merely the consequence of a particular comma (in
this
> > case, 648:625) being tempered out . . .
>
> ***Well, I know they count *interval classes* for example, but I
> don't know if they consider them "equivalent" in the way pitches
from
> the octave, with the same names, are considered "equivalent..." I
> guess Chris Bailey could answer this question, since he's still
> studying this stuff...
>
> But what are the abbreviations, ME, WF, DE? They look like
states...

maximal evenness, well-formed, distributionally even . . . in
particular, the 'academics' i'm referring to are exponents
of "recent" scale theory, like clough, carey, clampitt, douthett,
etc. -- this is not the ic theory you're referring to above.