Yahoo Tuning Groups Ultimate Backup tuning Multi-MOS

In a remarkable instance of hell freezing over, I got Paul to propose
the name "Multi-MOS" for things like diminished[8]. He's willing to
accept that these things are MOS with respect to the period of
1/4-oct, and so that a full octave of them is just a string of
iterated MOS's, much like four octaves of the diatonic scale. He
proposed the name "Multi-MOS" for these things, which isn't the same
as proposing the name "MOS" for them, but it's a start, anyway.

I actually like this name a lot, because it's nice and compact and
easier to type than "fractional-octave period MOS" or whatever, which
is cumbersome and has been shown to contribute to things like
tendonitis and carpal tunnel syndrome.

As you might expect, we differ in whether Multi-MOS's are types of
MOS, or MOS's are types of Multi-MOS, or whether they're mutually
exclusive categories. Paul says he wants them to be mutually
exclusive. I, however, am indulging in my newfound love of
terminological pedantry to insist that any definition of scales like
diminished[8] as "not being MOS" is technically incorrect, because
even for these scales it's true that every generic interval comes in
two sizes except the "generic octave" (or period).

This is my definition of things:

1) Let the period p of a scale be the interval at which the scale repeats.
2) Let the equivalence interval e of an scale be the interval at which
pitch classes and note names repeat.
3) A scale is MOS if it has exactly two sizes of specific interval per
generic interval up to p.
4) A Multi-MOS scale is a scale that is MOS, and for which e/p = k for
k > 1 in N.

I think that this is a rather handy and simple way to define things.
However, this now creates an ambiguity between the term "MOS" (this
umbrella class of scales including Multi-MOS) and "MOS" (the name for
non-Multi-MOS). I suggest that in the rare cases when one needs a term
to stand for "MOS, but not Multi-MOS," that perhaps "Uni-MOS" might do
the trick.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Sat, Mar 3, 2012 at 4:15 PM, Mike Battaglia <battaglia01@...> wrote:
>
> As you might expect, we differ in whether Multi-MOS's are types of
> MOS, or MOS's are types of Multi-MOS, or whether they're mutually
> exclusive categories. Paul says he wants them to be mutually
> exclusive. I, however, am indulging in my newfound love of
> terminological pedantry to insist that any definition of scales like
> diminished[8] as "not being MOS" is technically incorrect, because
> even for these scales it's true that every generic interval comes in
> two sizes except the "generic octave" (or period).

Also, for the record, this is Paul's definition:

1) Let the period p of a scale be the interval at which the scale repeats.
2) Let the equivalence interval e of an scale be the interval at which
pitch classes and note names repeat.
3) A scale is MOS if it has exactly two sizes of specific interval per
generic interval up e.
4) A Multi-MOS scale is a scale that is MOS if it has exactly two
sizes of specific interval per generic interval up to p, and for which
e/p = k for
k > 1 in N.

Note that the change vs my definition is #3, where Paul defines a
scale as being MOS if it's got two sizes of specific interval per
generic interval up to e (mine was up to e).

This creates its own ambiguity, because then one has to ask what the
name of the entire umbrella class of scales that contains both MOS and
Multi-MOS is. I assume that "DE" is what Paul would suggest for this.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> I, however, am indulging in my newfound love of
> terminological pedantry to insist that any definition of scales like
> diminished[8] as "not being MOS" is technically incorrect, because
> even for these scales it's true that every generic interval comes in
> two sizes except the "generic octave" (or period).

I think you may have missed my objection, that step-size is only part of the picture. The construction of scales like diminished[8] or augmented[6] or blackwood[10] differs significantly from the construction of scales like meantone[7] or father[8], in that they require the additional step of stacking several "generic octaves" within the interval of equivalence. This additional step is never applied in any of Erv's writings, which as you noted never mention an "interval of equivalence" and typically treat the "generic octave" as an alternative interval of (at least notational) equivalence (if not perceptual equivalence).
For that reason, I still agree with Paul that we should distinguish between MOS scales and multi-MOS scales (great term, love it), as per your definition below, which is great:

> 1) Let the period p of a scale be the interval at which the scale repeats.
> 2) Let the equivalence interval e of an scale be the interval at which
> pitch classes and note names repeat.
> 3) A scale is MOS if it has exactly two sizes of specific interval per
> generic interval up to p.
> 4) A Multi-MOS scale is a scale that is MOS, and for which e/p = k for
> k > 1 in N.

> I think that this is a rather handy and simple way to define things.
> However, this now creates an ambiguity between the term "MOS" (this
> umbrella class of scales including Multi-MOS) and "MOS" (the name for
> non-Multi-MOS). I suggest that in the rare cases when one needs a term
> to stand for "MOS, but not Multi-MOS," that perhaps "Uni-MOS" might do
> the trick.

Sounds good.

-Igs

🔗cityoftheasleep <igliashon@...>

Also, a question: is it possible for the generic octave to exceed the interval of equivalence? And what of two octaves of meantone, 10L4s repeating every 4/1? MOS, multi-MOS, neither? It seems in this case 2/1 is both the generic octave (the period) and the interval of equivalence, but if we still want to say the scale repeats at 4/1, what does that make 4/1? It seems like this scale will satisfy all the criteria you layed out....

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > I, however, am indulging in my newfound love of
> > terminological pedantry to insist that any definition of scales like
> > diminished[8] as "not being MOS" is technically incorrect, because
> > even for these scales it's true that every generic interval comes in
> > two sizes except the "generic octave" (or period).
>
> I think you may have missed my objection, that step-size is only part of the picture. The construction of scales like diminished[8] or augmented[6] or blackwood[10] differs significantly from the construction of scales like meantone[7] or father[8], in that they require the additional step of stacking several "generic octaves" within the interval of equivalence. This additional step is never applied in any of Erv's writings, which as you noted never mention an "interval of equivalence" and typically treat the "generic octave" as an alternative interval of (at least notational) equivalence (if not perceptual equivalence).
> For that reason, I still agree with Paul that we should distinguish between MOS scales and multi-MOS scales (great term, love it), as per your definition below, which is great:
>
> > 1) Let the period p of a scale be the interval at which the scale repeats.
> > 2) Let the equivalence interval e of an scale be the interval at which
> > pitch classes and note names repeat.
> > 3) A scale is MOS if it has exactly two sizes of specific interval per
> > generic interval up to p.
> > 4) A Multi-MOS scale is a scale that is MOS, and for which e/p = k for
> > k > 1 in N.
>
> > I think that this is a rather handy and simple way to define things.
> > However, this now creates an ambiguity between the term "MOS" (this
> > umbrella class of scales including Multi-MOS) and "MOS" (the name for
> > non-Multi-MOS). I suggest that in the rare cases when one needs a term
> > to stand for "MOS, but not Multi-MOS," that perhaps "Uni-MOS" might do
> > the trick.
>
> Sounds good.
>
> -Igs
>

🔗Mike Battaglia <battaglia01@...>

On Mon, Mar 5, 2012 at 11:00 AM, cityoftheasleep <igliashon@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I, however, am indulging in my newfound love of
> > terminological pedantry to insist that any definition of scales like
> > diminished[8] as "not being MOS" is technically incorrect, because
> > even for these scales it's true that every generic interval comes in
> > two sizes except the "generic octave" (or period).
>
> I think you may have missed my objection, that step-size is only part of
> the picture. The construction of scales like diminished[8] or augmented[6]
> or blackwood[10] differs significantly from the construction of scales like
> meantone[7] or father[8], in that they require the additional step of
> stacking several "generic octaves" within the interval of equivalence. This
> additional step is never applied in any of Erv's writings, which as you
> noted never mention an "interval of equivalence" and typically treat the
> "generic octave" as an alternative interval of (at least notational)
> equivalence (if not perceptual equivalence).

No, that's not true. See Erv Wilson's page on scales in 12-EDO with
13\12 and 19\12 as period, respectively:

http://anaphoria.com/13.pdf

He still uses 12-EDO notation and doesn't bother to define a new one
or anything like that for these new "generic octaves." He says that
when the octave occurs in these scales, it's like a "dynamic
dissonance." I don't think he pretends that 13\12 or 19\12 is an
interval at which pitch chromata repeat.

> Also, a question: is it possible for the generic octave to exceed the
> interval of equivalence?

See Erv Wilson's example above.

> And what of two octaves of meantone, 10L4s
> repeating every 4/1? MOS, multi-MOS, neither? It seems in this case 2/1 is
> both the generic octave (the period) and the interval of equivalence, but if
> we still want to say the scale repeats at 4/1, what does that make 4/1? It
> seems like this scale will satisfy all the criteria you layed out....

I view multi-MOS's as a type of MOS. In the special case where the
period is a whole number divisor of the equivalence interval, and
there's more than one period per equivalence interval, it's a
multi-MOS. I don't think that you can say that these scales aren't
also MOS in addition to being multi-MOS, since they are. They're MOS
with respect to their period, which is longhand for saying "they're
MOS."

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

There's no difference between an instrument tuned to a
multiMOS and one tuned to its underlying MOS. The difference
appears only in the notation of pitch classes. This is a
significant difference, which is Paul's point, so I'm willing
to go along with multiMOS. Now, can we please start fighting
about whether to put in that hyphen?

-Carl

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

> I view multi-MOS's as a type of MOS. In the special case where the
> period is a whole number divisor of the equivalence interval, and
> there's more than one period per equivalence interval, it's a
> multi-MOS. I don't think that you can say that these scales aren't
> also MOS in addition to being multi-MOS, since they are. They're MOS
> with respect to their period, which is longhand for saying "they're
> MOS."
>
> -Mike

🔗Mike Battaglia <battaglia01@...>

On Mon, Mar 5, 2012 at 3:25 PM, Carl Lumma <carl@...> wrote:
>
> There's no difference between an instrument tuned to a
> multiMOS and one tuned to its underlying MOS. The difference
> appears only in the notation of pitch classes. This is a
> significant difference, which is Paul's point, so I'm willing
> to go along with multiMOS. Now, can we please start fighting
> about whether to put in that hyphen?
>
> -Carl

See the thing about Erv Wilson using MOS's in 12-EDO with 19\12 as
period, in which he still uses the usual 12-EDO notation, and in which
octaves are "dynamic dissonances."

multiMOS vs multi-MOS vs MultiMOS vs Multi-MOS. Hmm....

-Mike

🔗cityoftheasleep <igliashon@...>

🔗Carl Lumma <carl@...>

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

> > There's no difference between an instrument tuned to a
> > multiMOS and one tuned to its underlying MOS. The difference
> > appears only in the notation of pitch classes. This is a
> > significant difference, which is Paul's point, so I'm willing
> > to go along with multiMOS. Now, can we please start fighting
> > about whether to put in that hyphen?

> See the thing about Erv Wilson using MOS's in 12-EDO with
> 19\12 as period, in which he still uses the usual 12-EDO
> notation, and in which octaves are "dynamic dissonances."

That notation isn't periodic at 19/12. The notation
Paul or I would used for diminished[8] is.

> multiMOS vs multi-MOS vs MultiMOS vs Multi-MOS. Hmm....

I vote for multiMOS. Fight!

-Carl

🔗Mike Battaglia <battaglia01@...>

On Mon, Mar 5, 2012 at 9:26 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > There's no difference between an instrument tuned to a
> > > multiMOS and one tuned to its underlying MOS. The difference
> > > appears only in the notation of pitch classes. This is a
> > > significant difference, which is Paul's point, so I'm willing
> > > to go along with multiMOS. Now, can we please start fighting
> > > about whether to put in that hyphen?
>
> > See the thing about Erv Wilson using MOS's in 12-EDO with
> > 19\12 as period, in which he still uses the usual 12-EDO
> > notation, and in which octaves are "dynamic dissonances."

OK, so what are you saying? That MULTIMOS's aren't a type of MOS? If
so, what do we call the whole umbrella category of scales? DE scales?

> That notation isn't periodic at 19/12. The notation
> Paul or I would used for diminished[8] is.
>
>
> > multiMOS vs multi-MOS vs MultiMOS vs Multi-MOS. Hmm....
>
> I vote for multiMOS. Fight!

Apple programmers love camel case...

-Mike

🔗Carl Lumma <carl@...>

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

> > > > There's no difference between an instrument tuned to a
> > > > multiMOS and one tuned to its underlying MOS. The difference
> > > > appears only in the notation of pitch classes. This is a
> > > > significant difference, which is Paul's point, so I'm willing
> > > > to go along with multiMOS.

> OK, so what are you saying? That MULTIMOS's aren't a type of MOS?
> If so, what do we call the whole umbrella category of scales? DE
> scales?

I'm saying I wouldn't have even been willing to compromise
on "multiMOS" if it weren't for this point about notation.
(As you may know, the point you made in your fb post is
exactly the point I've been making all along about Paul's
"DE" trip).

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Mar 6, 2012 at 2:51 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > > > There's no difference between an instrument tuned to a
> > > > > multiMOS and one tuned to its underlying MOS. The difference
> > > > > appears only in the notation of pitch classes. This is a
> > > > > significant difference, which is Paul's point, so I'm willing
> > > > > to go along with multiMOS.
>
> > OK, so what are you saying? That MULTIMOS's aren't a type of MOS?
> > If so, what do we call the whole umbrella category of scales? DE
> > scales?
>
> I'm saying I wouldn't have even been willing to compromise
> on "multiMOS" if it weren't for this point about notation.
> (As you may know, the point you made in your fb post is
> exactly the point I've been making all along about Paul's
> "DE" trip).

The only reason I liked the name multiMOS is that it's a useful
abbreviation for "fractional-octave period MOS."

If you disagree and want to now argue that they're different, I won't argue it
anymore. My question for you is, do you think that multiMOS scales are
a type of MOS scale, or something else? And, if something else, then
what is the generic name of scale that includes both MOS and multiMOS?
DE?

-Mike

🔗Carl Lumma <carl@...>

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

> The only reason I liked the name multiMOS is that it's a useful
> abbreviation for "fractional-octave period MOS."
>
> If you disagree and want to now argue that they're different,
> I won't argue it anymore. My question for you is, do you think
> that multiMOS scales are a type of MOS scale, or something else?
> And, if something else, then what is the generic name of scale
> that includes both MOS and multiMOS? DE?

Jesus, I don't even know myself anymore. I was trying to agree
with you! I promise to never do that again.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Mar 6, 2012 at 5:58 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The only reason I liked the name multiMOS is that it's a useful
> > abbreviation for "fractional-octave period MOS."
> >
> > If you disagree and want to now argue that they're different,
> > I won't argue it anymore. My question for you is, do you think
> > that multiMOS scales are a type of MOS scale, or something else?
> > And, if something else, then what is the generic name of scale
> > that includes both MOS and multiMOS? DE?
>
> Jesus, I don't even know myself anymore. I was trying to agree
> with you! I promise to never do that again.

Are you saying that multiMOS is a type of MOS, and that the umbrella
term for this entire class of scales is "MOS"?

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > I'm saying I wouldn't have even been willing to compromise
> > > on "multiMOS" if it weren't for this point about notation.
> >
> > When analyzing chords, you normally pay attention to octaves.
>
> ? The octaves are there either way, but chords are usually
> expressed in some notation, so... -Carl

There's more to it than notation; when I was analyzing dyadic chords for various temperaments up to octave equivalence I had to treat "multiMOS" differently.

🔗Mike Battaglia <battaglia01@...>

On Tue, Mar 6, 2012 at 8:29 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > > I'm saying I wouldn't have even been willing to compromise
> > > > on "multiMOS" if it weren't for this point about notation.
> > >
> > > When analyzing chords, you normally pay attention to octaves.
> >
> > ? The octaves are there either way, but chords are usually
> > expressed in some notation, so... -Carl
>
> There's more to it than notation; when I was analyzing dyadic chords for
> various temperaments up to octave equivalence I had to treat "multiMOS"
> differently.

Likewise when I was messing around with z-relations and interval
vectors. Torsion gets involved pretty quickly over there.

All I care about at this point is if I'm supposed to say that multiMOS
and MOS are both MOS, or if multiMOS and MOS are both DE.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

UniMOS and multiMOS scales are both types of MOS scales. UniMOS is where period = interval of equivalence, multiMOS is where period = fraction of interval of equivalence. MOS, as we're using it now, is basically synonymous with "rank-2 scale".

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Mar 6, 2012 at 2:51 PM, Carl Lumma <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > > > > There's no difference between an instrument tuned to a
> > > > > > multiMOS and one tuned to its underlying MOS. The difference
> > > > > > appears only in the notation of pitch classes. This is a
> > > > > > significant difference, which is Paul's point, so I'm willing
> > > > > > to go along with multiMOS.
> >
> > > OK, so what are you saying? That MULTIMOS's aren't a type of MOS?
> > > If so, what do we call the whole umbrella category of scales? DE
> > > scales?
> >
> > I'm saying I wouldn't have even been willing to compromise
> > on "multiMOS" if it weren't for this point about notation.
> > (As you may know, the point you made in your fb post is
> > exactly the point I've been making all along about Paul's
> > "DE" trip).
>
> The only reason I liked the name multiMOS is that it's a useful
> abbreviation for "fractional-octave period MOS."
>
> If you disagree and want to now argue that they're different, I won't argue it
> anymore. My question for you is, do you think that multiMOS scales are
> a type of MOS scale, or something else? And, if something else, then
> what is the generic name of scale that includes both MOS and multiMOS?
> DE?
>
> -Mike
>

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

Perhaps I don't understand what "rank-2" means. I thought it referred to scales with two generators.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> MODMOS's are rank-2 scales.
>
> -Mike
>
>
> On Wed, Mar 7, 2012 at 7:00 PM, cityoftheasleep <igliashon@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > > >MOS, as we're using it now, is basically synonymous with "rank-2 scale".
> > >
> > > Is not.
> > >
> >
> > How is it not?
> >
> > -Igs
>

🔗Mike Battaglia <battaglia01@...>

On Wed, Mar 7, 2012 at 7:25 PM, cityoftheasleep <igliashon@...>
wrote:
>
> Perhaps I don't understand what "rank-2" means. I thought it referred to
> scales with two generators.
>
> -Igs

MODMOS's have two generators. They just don't form a convex set in on
the rank-2 lattice. For instance, the diatonic scale is this shape on
the lattice

#######

whereas melodic minor is this

# ##### #

-Mike