Yahoo Tuning Groups Ultimate Backup tuning-math The three proper 9-note 12-et scales

>> Are you calculating stability, or just propriety? The former
>> is something to put on those extra lines you dislike.
>
>Just propriety so far. There are two kinds of stability, one by some
>character named Lumma, which seems to be more broadly applicable. You
>would have any idea how to calculate that, I suppose?

Did I send you "Notes on a combinational strategy for ennumeration
problems" by DR? Apparently it's how he was able to calculate
stability for all subscales of things like 31 with the computers
of the day.

There is also DR's "ideal measure" (pg. 356, last paragraph,
Model for Pattern Perception with Musical Applications Part 2).
It is the portion of all subsets of a scale's rank-order matrix
which are strictly proper, and should be preferred to regular
stability if it's tractable.

Lumma stability, as I defined it in an unpublished paper circa
2000, is the portion of the octave not more than singly covered
by scale degrees, if that makes any sense (I could attempt a
more precise definition if not). There's also Lumma propriety,
which is the portion of the octave not covered at all. In Scala,
the latter is called "Lumma stability" and the 1 - the former
is called the "impropriety factor" (only displayed for improper
scales). How's that for confusing?

Whatever you call them, I think my two proposals have a lot of
promise (they're much easier to compute, for one), but to be
honest I haven't looked at the values to see how they behave
with respect to scales I'm familiar with.

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:

> Did I send you "Notes on a combinational strategy for ennumeration
> problems" by DR?

It rings no bells.

> There is also DR's "ideal measure" (pg. 356, last paragraph,
> Model for Pattern Perception with Musical Applications Part 2).
> It is the portion of all subsets of a scale's rank-order matrix
> which are strictly proper, and should be preferred to regular
> stability if it's tractable.

It might be worth coding up.

> Lumma stability, as I defined it in an unpublished paper circa
> 2000, is the portion of the octave not more than singly covered
> by scale degrees, if that makes any sense (I could attempt a
> more precise definition if not). There's also Lumma propriety,
> which is the portion of the octave not covered at all. In Scala,
> the latter is called "Lumma stability" and the 1 - the former
> is called the "impropriety factor" (only displayed for improper
> scales). How's that for confusing?

Pretty bad. If I write them up for my web page on quasiperidic scales,
what do I call them? Lumma propriety, I take it, means you remove
everything in the interval defined by members of a class, for proper
scales. Correct? Stability is where you remove everything in intervals
which also contain a class interval in their interior?

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:

I get that what you define as Lumma stability above is what Scala
computes as "impropriety factor" when the scale is improper. What you
define as Lumma propriety is 1 - (Scala Lumma stability) when the
scale is proper, but that seems to be something else when the scale is
improper, and I don't know what. Both numbers can be defined for any
quasiperiodic (ie, Scala-type) scale, and I'd recommend that they
should be.

These are easy to compute, and I'd like to put definitions on my web
page. Howewver, we need an agreed-on definition first. I'd like to use
"Lumma stability" for what Scala calls Lumma stability for proper
scales, on the grounds that Scala is using it, and find out what the
heck it is computing for improper scales and call that something else,
so we need Manuel in here. The other is "impropriety factor". You
called that stability, which Manuel uses for propriety, and it is zero
for proper scales, so "impropriety factor" is OK, I guess, but "Lumma
impropriety" raises the question of why the switch from "propriety" to
"impropriety", which doesn't seem that logical. Calling 1 -
(impropriety factor) "Lumma propriety" might be the best plan.

So, my proposals are:

(1) "Lumma stability" is to be what Scala calles "Lumma stability" for
proper scales, and is negative for improper scales, being one minus
what you call "Lumma propriety" with the definition extended to
overlapping interval classes.

(2) "Lumma propriety" is to be 1 - (Scala impropriety factor) for
improper scales, and is 1 for proper scales.

🔗Carl Lumma <ekin@lumma.org>

>> Lumma stability, as I defined it in an unpublished paper circa
>> 2000, is the portion of the octave not more than singly covered
>> by scale degrees, if that makes any sense (I could attempt a
>> more precise definition if not). There's also Lumma propriety,
>> which is the portion of the octave not covered at all. In Scala,
>> the latter is called "Lumma stability" and the 1 - the former
>> is called the "impropriety factor" (only displayed for improper
>> scales). How's that for confusing?
>
>Pretty bad. If I write them up for my web page on quasiperidic
>scales, what do I call them?

Perhaps I should adopt Scala's usage. But I don't think I like
it. The thing analogous to Rothenberg stability is what I call
stability in my 2000 paper.
Maybe they should have new names, like clarity and turbidity
or something.

>Lumma propriety, I take it, means you remove
>everything in the interval defined by members of a class, for proper
>scales. Correct? Stability is where you remove everything in
>intervals which also contain a class interval in their interior?

I don't follow this. Let me try to be precise...

Sticking with the usage from the 2000 paper, let the 2nds-list
of a t-tone scale with equivalence interval E be an ordered
list (s_1 s_2 ... s_t) such that

t
Sigma s_x = E
x=1

(which corresponds to the 2nds of the scale, with all numbers
being log frequency distances). Now for each 0 <= n < t, the
largest and smallest sum

x+n (mod t)
Sigma s_x
x

for all 0 < x <= t are endpoints of a closed interval in the
interval (1, E).

Lumma stability is one minus the sum of the lengths of the
intersections of all pairs of these intervals.

Lumma propriety is one minus the length of the union of
these intervals.

Again, this is somewhat the opposite of Scala's implementation.
And please let me know if this makes sense; I'm obviously
not a mathematician.

-Carl

🔗Carl Lumma <ekin@lumma.org>

>> Lumma stability, as I defined it in an unpublished paper circa
>> 2000, is the portion of the octave not more than singly covered
>> by scale degrees, if that makes any sense (I could attempt a
>> more precise definition if not). There's also Lumma propriety,
>> which is the portion of the octave not covered at all. In Scala,
>> the latter is called "Lumma stability" and the 1 - the former
>> is called the "impropriety factor" (only displayed for improper
>> scales). How's that for confusing?
>
>I get that what you define as Lumma stability above is what Scala
>computes as "impropriety factor" when the scale is improper.

1 - Lumma stability above is, yes.

>What you define as Lumma propriety is 1 - (Scala Lumma stability)
>when the scale is proper,

I don't think there's a 1 - here. Scala Lumma stability and
Lumma propriety above are the same.

>These are easy to compute,

Much easier than Rothenberg's stuff.

>and I'd like to put definitions on my web
>page.

Great! See my previous mail. I should ask Manuel to change this.

>Howewver, we need an agreed-on definition first. I'd like to use
>"Lumma stability" for what Scala calls Lumma stability for proper
>scales, on the grounds that Scala is using it, and find out what the
>heck it is computing for improper scales and call that something else,
>so we need Manuel in here. The other is "impropriety factor". You
>called that stability, which Manuel uses for propriety, and it is zero
>for proper scales, so "impropriety factor"

If he had to hide something, it would have been better to show
the "impropriety factor" is zero for proper scales, and hide the
"Lumma stability" for improper ones (this is the least-meaningful
situation IMO). But why not display everything?

>So, my proposals are:
>
>(1) "Lumma stability" is to be what Scala calles "Lumma stability" for
>proper scales, and is negative for improper scales, being one minus
>what you call "Lumma propriety" with the definition extended to
>overlapping interval classes.
>
>(2) "Lumma propriety" is to be 1 - (Scala impropriety factor) for
>improper scales, and is 1 for proper scales.

I'd like to go back to my original usage, but I suppose it isn't
a huge issue either way.

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:

> >I get that what you define as Lumma stability above is what Scala
> >computes as "impropriety factor" when the scale is improper.
>
> 1 - Lumma stability above is, yes.

So are you saying I should call "1 - (Scala impropriety factor)" by
the name "Lumma stability"?

> >What you define as Lumma propriety is 1 - (Scala Lumma stability)
> >when the scale is proper,
>
> I don't think there's a 1 - here. Scala Lumma stability and
> Lumma propriety above are the same.

So again, are you saying I should make "Lumma stability" to be the
same as what Scala computes as "Lumma propriety", when the scale is
improper?

🔗Carl Lumma <ekin@lumma.org>

I wrote:
>I'd like to go back to my original usage, but I suppose it
>isn't a huge issue either way.

If things are going to stay the Scala way, then what I'd
like to see done is this:

="show data" for proper scales=
scale is proper / strictly proper
Rothenberg stability
Lumma stability ;; portion of octave not covered
Rothenberg efficiency

="show data" for improper scales=
scale is improper
Lumma impropriety factor ;; portion of octave > single covered
Rothenberg efficiency

This keeps things pretty much the same, but hides stability
for improper scales (that's more hiding, but it's a good way
to simplify the situation). It would also involve moving
the proper / not proper declaration down next to the related
values (instead of alone up above there).

-Carl

🔗Carl Lumma <ekin@lumma.org>

At 11:09 PM 6/13/2006, you wrote:
>--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
>> >I get that what you define as Lumma stability above is what Scala
>> >computes as "impropriety factor" when the scale is improper.
>>
>> 1 - Lumma stability above is, yes.
>
>So are you saying I should call "1 - (Scala impropriety factor)" by
>the name "Lumma stability"?

Yes.

>> >What you define as Lumma propriety is 1 - (Scala Lumma stability)
>> >when the scale is proper,
>>
>> I don't think there's a 1 - here. Scala Lumma stability and
>> Lumma propriety above are the same.
>
>So again, are you saying I should make "Lumma stability" to be the
>same as what Scala computes as "Lumma propriety", when the scale is
>improper?

No. See above for Lumma stability.

Lumma propriety is what Scala computes as Lumma stability.

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:

> Lumma propriety is what Scala computes as Lumma stability.

What I have now is that Lumma propriety is what Scala computes as
Lumma stability *for proper scales*. For improper scales, it computes
something else. Whatever that something else is, I think it should
have a different name than either Lumma propriety *or* Lumma
stability, since the same simple formula should be used for both
proper and improper scales in my opinion.

🔗Carl Lumma <ekin@lumma.org>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
> <manuel.op.de.coul@> wrote:
> >
> > What Scala computes is described in the tips file.
> > See Help:Tip:Browse All
> > Ctrl-F Lumma
>
> Thanks. What do you think should be done about nomenclature?

I think I'll rename Impropriety factor to Lumma impropriety, and not
change it to Lumma propriety, otherwise it's likely to be confused
with Lumma stability.
I can add "Lumma regularity" too, which will be equal to Stability -
Impropriety.

Manuel

🔗Carl Lumma <ekin@lumma.org>

>I can add "Lumma regularity" too, which will be equal to
>Stability - Impropriety.

Don't do that. The impropriety is a far more severe thing
than a lack of stability.

If you want, just do this:

/tuning-math/message/15125?var=0

It's the easiest.

Gene: if you read the Help:Tip!:Browse All:Ctrl+F Lumma
thing... it looks like you may have found a bug. It doesn't
claim to change its definition of Lumma stability for
improper scales.

Oh, and re. harmonic entropy in Scala:

>To see Erlich's harmonic entropy value for the pitches in a
>scale, do SET ATTRIBUTE ENTROPY. This gives the Farey series
>entropy for Farey order of 80.

This is showing the dyadic entropy for the notes of the
scale as if they were dyads above its first degree? Am I
correct that it doesn't support higher-adic entropy?

Thanks everyone,

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@...> wrote:

> I think I'll rename Impropriety factor to Lumma impropriety, and not
> change it to Lumma propriety, otherwise it's likely to be confused
> with Lumma stability.

Shouldn't you change "impropiety factor" to "Lumma instability",
change "Lumma stability" to "Lumma propriety", and then make "Lumma
regularity" be Propriety-Intability?

I'd really like to get this headache cleaned up one way or another.

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:

> Gene: if you read the Help:Tip!:Browse All:Ctrl+F Lumma
> thing... it looks like you may have found a bug. It doesn't
> claim to change its definition of Lumma stability for
> improper scales.

I've just found this (in the Scala home drectory) and it makes for
strange but interesting reading. Here is the first tip:

To find out what is a good scale size for a Pythagorean scale with a
certain given fifth (or generator), use the command CONVERGENTS. The
parameter to this command should be the ratio between the logarithmic
size of the generator and the octave. From the convergents given, the
denominator is the number of notes and the numerator the corresponding
degree of the generator. This can be calculated with CALCULATE. For
example for a major third generator insidehalf an octave do:
CALCULATE/NOOUT 5/4 div 600.0
CONVERGENTS $0
If one of the convergents is chosen, then the resulting scale will be
strictly proper and have Myhill's property. If a semi-convergent is
chosen (use CONVERGENTS/SEMI), then the resulting scale will at least
have Myhill's property and be distributional even.

Create the scale with command LINEARTEMP. Use SHOW DATA to test if the
scale is strictly proper.

Moritz DrÃ¶bisch pioneered this kind of analysis in the 1850s.

Is this saying Moritz DrÃ¶bisch invented the MOS? Is "Pythagorean
scale" for a MOS standard vocabularly somewhere, and if so, where? Who
first used continued fractions for scale analysis--DrÃ¶bisch?

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> >I can add "Lumma regularity" too, which will be equal to
> >Stability - Impropriety.
>
> Don't do that. The impropriety is a far more severe thing
> than a lack of stability.
>
> If you want, just do this:
>
> /tuning-math/message/15125?var=0
>
> It's the easiest.

Sorry, I meant to reply later but forgot. I don't see so much need for
not mentioning stability for improper scales. They will have a low
stability, but their relation is not so strong as between propriety
and impropriety factor.

> >To see Erlich's harmonic entropy value for the pitches in a
> >scale, do SET ATTRIBUTE ENTROPY. This gives the Farey series
> >entropy for Farey order of 80.
>
> This is showing the dyadic entropy for the notes of the
> scale as if they were dyads above its first degree? Am I
> correct that it doesn't support higher-adic entropy?

Both yes indeed.

Manuel

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@...> wrote:

> Sorry, I meant to reply later but forgot. I don't see so much need for
> not mentioning stability for improper scales. They will have a low
> stability, but their relation is not so strong as between propriety
> and impropriety factor.

My concern is not with that; I want to see that you and Carl agree on
defintions for Lumma stability and Lumma propriety.

🔗Carl Lumma <ekin@lumma.org>

>> Sorry, I meant to reply later but forgot. I don't see so much need for
>> not mentioning stability for improper scales. They will have a low
>> stability, but their relation is not so strong as between propriety
>> and impropriety factor.
>
>My concern is not with that; I want to see that you and Carl agree on
>defintions for Lumma stability and Lumma propriety.

They should either be both always displayed, or both be turned into
selectively-displayed "factors".

In the former case, since Rothenberg calls the number of violations of
propriety "stability", I think the amount of violation should be
Lumma stability. But ultimately, which is called which doesn't matter
much.

-Carl

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
> They should either be both always displayed, or both be turned into
> selectively-displayed "factors".

Ok.

> In the former case, since Rothenberg calls the number of violations of
> propriety "stability", I think the amount of violation should be
> Lumma stability. But ultimately, which is called which doesn't matter
> much.

So, I'd better keep the definition as it is. A change would let the
different Scala versions give different answers. And some releases
have long intervals between them.

Manuel

🔗Carl Lumma <ekin@lumma.org>

At 05:31 AM 6/23/2006, you wrote:
>--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>> They should either be both always displayed, or both be turned into
>> selectively-displayed "factors".
>
>Ok.

Great. Can the output look like this:

scale is proper / strictly proper
Rothenberg stability
Lumma stability factor ;; portion of octave not covered
Rothenberg efficiency

scale is improper
Lumma impropriety factor ;; portion of octave > single covered
Rothenberg efficiency

Pretty please?

-Carl

🔗monz <monz@tonalsoft.com>

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
> <manuel.op.de.coul@> wrote:
>
> > Sorry, I meant to reply later but forgot. I don't see so much need for
> > not mentioning stability for improper scales. They will have a low
> > stability, but their relation is not so strong as between propriety
> > and impropriety factor.
>
> My concern is not with that; I want to see that you and Carl agree on
> defintions for Lumma stability and Lumma propriety.

I haven't been following any of the tunings lists much
lately, but happened to see this. If there are any changes
or amendments to be made to my Tonalsoft definitions,
or if there need to be some new definitions, *please*
send me an email about it.

monz(AT)tonalsoft.com

http://tonalsoft.com/enc/p/proper.aspx
http://tonalsoft.com/enc/r/rothenberg-stability.aspx
http://tonalsoft.com/enc/l/lumma-impropriety.aspx
http://tonalsoft.com/enc/l/lumma-stability.aspx

Thanks.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Carl Lumma <ekin@lumma.org>

>I haven't been following any of the tunings lists much
>lately, but happened to see this. If there are any changes
>or amendments to be made to my Tonalsoft definitions,
>or if there need to be some new definitions, *please*
>send me an email about it.
>
>monz(AT)tonalsoft.com
>
>http://tonalsoft.com/enc/p/proper.aspx
>http://tonalsoft.com/enc/r/rothenberg-stability.aspx
>http://tonalsoft.com/enc/l/lumma-impropriety.aspx
>http://tonalsoft.com/enc/l/lumma-stability.aspx
>
>Thanks.
>
>
>-monz
>http://tonalsoft.com
>Tonescape microtonal music software

Thanks for popping in, monz. Let's wait to see what Manuel
does with the next release of Scala, then I'll go about updating
all my documents, and I'll send you that e-mail.

-Carl

🔗monz <monz@tonalsoft.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> >http://tonalsoft.com/enc/p/proper.aspx
> >http://tonalsoft.com/enc/r/rothenberg-stability.aspx
> >http://tonalsoft.com/enc/l/lumma-impropriety.aspx
> >http://tonalsoft.com/enc/l/lumma-stability.aspx
> >
>
> Thanks for popping in, monz. Let's wait to see what Manuel
> does with the next release of Scala, then I'll go about updating
> all my documents, and I'll send you that e-mail.
>
> -Carl

OK, cool. I'm kinda too busy right now to work on the
Encyclopedia pages anyway.

(I never mentioned ... i got hired to compose the score
for a short film. The editing has just been completed,
and i'll be getting the film soon so that i can assemble
my musical ideas into a proper soundtrack. Target date
for the premiere in LA is ~July 10. Of course the score
is microtonal.)

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Carl Lumma <ekin@lumma.org>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>Can the output look like this:
> scale is proper / strictly proper
> Rothenberg stability
> Lumma stability factor ;; portion of octave not covered
> Rothenberg efficiency

Sorry considering this took some time. I moved these things together
but will not add the extra comments. For someone who doesn't know the
definition yet it's too short and vague, so those who are interested
must look it up anyway. What I'll do is make the definitions of the
properties given by show data more easily accessible.

Manuel