RE: CS (?)

[Erlich]
>Carl, I take it you've never looked at Erv Wilson's CS scales. Please refer
>to Kraig's Wilson Archives.

No, I haven't, and I was unable to find any mention of them on the Wilson
archives. But here's Kraig's original statement...

[Grady]
>The term is applied to "variations" of an MOS where each interval is
>allowed to vary in size but the overall chain remains the same.

So you can see where I was coming from when I said...

[Lumma]
>Paul, perhaps there is still confusion on what CS means. From Kraig's most
>recent post, I took it to refer to MOS's that don't change as the generator
>size does, ie all 2-tone chains are MOS, the 7-tone chain of fifths is a CS
>of the 12, 19, and 31 tone chains of fifths...

Which led you to say...

[Erlich]
>However, the concept you mistakenly took CS to mean is interesting. Can
you >explain further?

Not much. As you know from XH3, Wilson is interested in what the mapping
of harmony to the linear series means in music. He told me that he wants
to compose music in which the scale's mapping to the linear series is held
constant, but the size of the generator changes, so that the mapping of the
harmonies move over the scale degrees as the music evolves. He believes
this sort of thing is at work in free-pitched ensemble performance, and, on
a larger scale, in the evolution of musical languages. I believe Marcus
Hobbs has tried, or will soon try, to do demos of this with Kyma.

-C.

Carl!
there is no direct mention of constant structures in the Archives, only
some scales that fit. I don't know of any paper on the subject by him and
considering his work at the moment i don't foresee him backing up to write one!

Carl Lumma wrote:

> From: Carl Lumma <clumma@nni.com>
>
> [Erlich]
> >Carl, I take it you've never looked at Erv Wilson's CS scales. Please refer
> >to Kraig's Wilson Archives.
>
> No, I haven't, and I was unable to find any mention of them on the Wilson
> archives. But here's Kraig's original statement...
>
> .

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

Hi everybody!

The confusion and near lunacy found occasionally on this list, appears to
me, to be empirical evidence of a constant structure.

All the best, George

Kraig Grady wrote,

>Carl!
> there is no direct mention of constant structures in the Archives,

Kraig, you should know your own archives better than this! The third page of
http://www.anaphoria.com/trans22.html is entitled "22-tone constant scale
structure" and gives three 22-tone CS scales. The first is none other than
the classic 5-limit sruti scale that I recently derived from the Fokker
periodicity block formalism. I may be able to do the same for the other two.

>only
>some scales that fit.

Please educate Carl and me on which those are. We are having severe
communication difficulties!

>I don't know of any paper on the subject by him and
>considering his work at the moment i don't foresee him backing up to write
one!

That's too bad. So we're in your hands as far as the definition (though we
can always point out contradictions).

-Paul the tuning geek

I was aware of examples. it was definition that is lacking. Also in relation to
corsets, it is the reciprocal corsets that Erv seems to enjoy most. Like the
1-3-5/subharmonic 7-9-11!

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Kraig Grady wrote,
>
> >Carl!
> > there is no direct mention of constant structures in the Archives,
>
> Kraig, you should know your own archives better than this! The third page of
> http://www.anaphoria.com/trans22.html is entitled "22-tone constant scale
> structure" and gives three 22-tone CS scales. The first is none other than
> the classic 5-limit sruti scale that I recently derived from the Fokker
> periodicity block formalism. I may be able to do the same for the other two.
>
> >only
> >some scales that fit.
>
> Please educate Carl and me on which those are. We are having severe
> communication difficulties!
>
> >I don't know of any paper on the subject by him and
> >considering his work at the moment i don't foresee him backing up to write
> one!
>
> That's too bad. So we're in your hands as far as the definition (though we
> can always point out contradictions).
>
> -Paul the tuning geek
>
> > You do not need web access to participate. You may subscribe through
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-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

Kraig wrote,

> >Carl!
> > there is no direct mention of constant structures in the Archives,
> >only
> >some scales that fit.

I wrote,

> Please educate Carl and me on which those are. We are having severe
> communication difficulties!

Kraig did not respond to this request. For example, Kraig, didn't you once
make the point that 2nd order MOS scales, like C E F G B, are CS scales?
That would be an example for Carl of a clearly improper CS scale.

Paul!
I don't know if this is right. but it is a constant structure in relation
to the generator (4th) is always subtended by the same number of tones. I
think that Erv might object to calling this a CS. I will ask.

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Kraig wrote,
>
> > >Carl!
> > > there is no direct mention of constant structures in the Archives,
> > >only
> > >some scales that fit.
>
> I wrote,
>
> > Please educate Carl and me on which those are. We are having severe
> > communication difficulties!
>
> Kraig did not respond to this request. For example, Kraig, didn't you once
> make the point that 2nd order MOS scales, like C E F G B, are CS scales?
> That would be an example for Carl of a clearly improper CS scale.
>
> > You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@onelist.com - subscribe to the tuning list.
> tuning-unsubscribe@onelist.com - unsubscribe from the tuning list.
> tuning-digest@onelist.com - switch your subscription to digest mode.
> tuning-normal@onelist.com - switch your subscription to normal mode.

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

>> Please educate Carl and me on which those are. We are having severe
>> communication difficulties!
>
>Kraig did not respond to this request. For example, Kraig, didn't you once
>make the point that 2nd order MOS scales, like C E F G B, are CS scales?
>That would be an example for Carl of a clearly improper CS scale.

Paul, I already admitted that strict propriety is not required for your
definition of CS. But, if even one interval appears in more than one mode,
strict propriety is required, and I say again: the fact that no interval
appears in more than one mode will _far overshadow_ the fact that every
interval is only represented by one scale degree, to the point where the
latter loses all musical impact.

And, after looking at the three 22-tone scales, I still think that my
definition of CS is correct. You use the term as a property of a scale;
"such and such is a CS scale." But Wilson's paper is titled "22-tone
Constant Structure" singular. Referring to the 12-tone MOS-like structure
in each of the three scales (I think, I haven't had a chance to look at the
scales rigorously).

-C.

I wrote,

>>Kraig did not respond to this request. For example, Kraig, didn't you once
>>make the point that 2nd order MOS scales, like C E F G B, are CS scales?
>>That would be an example for Carl of a clearly improper CS scale.

Carl wrote,

>Paul, I already admitted that strict propriety is not required for your
>definition of CS. But, if even one interval appears in more than one mode,
>strict propriety is required,

Hardly! C E F G B is a CS according to an old post by Kraig (which he is now
unsure of), since C-E and G-B are each one step and since G-C, B-E, and C-F
are all 2 steps. "My definition of CS" was just what Kraig told me, which,
even when modified to require at least one or two intervals to appear more
than once in the scale, still does not imply strict propriety.

I don't know why you keep bringing up modes in this context -- all modes
have the same intervals.

>And, after looking at the three 22-tone scales, I still think that my
>definition of CS is correct.

Please explain your definition again; we can have Kraig ask Erv what he
thinks.

>You use the term as a property of a scale;
>"such and such is a CS scale."

Again, got that from Kraig. Search the archives (the Mills ones might prove
more fruitful).

>But Wilson's paper is titled "22-tone
>Constant Structure" singular. Referring to the 12-tone MOS-like structure
>in each of the three scales (I think, I haven't had a chance to look at the
>scales rigorously).

Please explain.

Carl wrote,

>But, if even one interval appears in more than one mode,
>strict propriety is required,

I wrote,

>C-E and G-B are each one step and since G-C, B-E, and C-F are all 2 steps.

I forgot to mention, B-C and E-F are each one step.

Carl Lumma wrote:

>
> And, after looking at the three 22-tone scales, I still think that my
> definition of CS is correct. You use the term as a property of a scale;
> "such and such is a CS scale." But Wilson's paper is titled "22-tone
> Constant Structure" singular.

I think it could and maybe should be plural. maybe he is referring to constant
structure as a verb! I will check

> Referring to the 12-tone MOS-like structure
> in each of the three scales (I think, I haven't had a chance to look at the
> scales rigorously).

intuitively I would assume there might be 22, 12 tone MOS-like structures all
that might be CS. I can't check right now

>
>
> -C.
>

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

"Paul H. Erlich" wrote:

>
>
> Hardly! C E F G B is a CS according to an old post by Kraig (which he is now
> unsure of), since C-E and G-B are each one step and since G-C, B-E, and C-F
> are all 2 steps. "My definition of CS" was just what Kraig told me, which,
> even when modified to require at least one or two intervals to appear more
> than once in the scale, still does not imply strict propriety.

my reluctance is the interval e-g which is two steps which is smaller than the
C-E and G-B one steps. the MOS sequence would be g-c-f-b-e. I guess this is ok
as the e-g is over the disjunction. I guess I would call it a CS

>
>
> I don't know why you keep bringing up modes in this context -- all modes
> have the same intervals.
>
> >And, after looking at the three 22-tone scales, I still think that my
> >definition of CS is correct.
>
> Please explain your definition again; we can have Kraig ask Erv what he
> thinks.
>
> >You use the term as a property of a scale;
> >"such and such is a CS scale."
>
> Again, got that from Kraig. Search the archives (the Mills ones might prove
> more fruitful).
>
> >But Wilson's paper is titled "22-tone
> >Constant Structure" singular. Referring to the 12-tone MOS-like structure
> >in each of the three scales (I think, I haven't had a chance to look at the
> >scales rigorously).

I answered this in the other post but i want to make sure that Carl does no
think that these 12 tone subsets are the basis of these being referred to as
Constant Structure. They are thought of as based on a 22 tone MOS.

>
>
> Please explain.
>
>

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

>Hardly! C E F G B is a CS according to an old post by Kraig (which he is now
>unsure of), since C-E and G-B are each one step and since G-C, B-E, and C-F
>are all 2 steps. "My definition of CS" was just what Kraig told me, which,
>even when modified to require at least one or two intervals to appear more
>than once in the scale, still does not imply strict propriety.

I thought you understood CS to mean that every acoustic interval was
represented by only one scale size. The above scale doesn't meet this
criterion, since 600 cents is both a 2nd and a 3rd.

>I don't know why you keep bringing up modes in this context -- all modes
>have the same intervals.

I don't know what you mean. Here's the interval matrix:

......C E F G B
2nds 4 1 2 4 1
3rds 5 3 6 5 5
4ths 7 7 7 9 6
5ths 11 8 11 10 8
6ths 12 12 12 12 12

The interval 11 appears only twice in the scale, both times as a 5th. If
it appeared as a 5th and anything else, it would remove strict propriety.

>Please explain your definition again; we can have Kraig ask Erv what he
>thinks.

I really don't know. I thought I had traced back to the original post from
Kraig on this, but it sounds like I didn't. But in the interest of
clearing this up for all concerned, I will make a stab:

"A list of integers representing the cardinalities of nested MOS's is a
Constant Structure of all scales that can support the entire nest. The
larger the numbers, and the more of them, the fewer the number of scales in
the Constant Structure (tho the number of scales is always infinite if you
assume infinite tuning precision)."

Carl

>>Hardly! C E F G B is a CS according to an old post by Kraig (which he is
now
>>unsure of), since C-E and G-B are each one step and since G-C, B-E, and
C-F
>>are all 2 steps. "My definition of CS" was just what Kraig told me, which,
>>even when modified to require at least one or two intervals to appear more
>>than once in the scale, still does not imply strict propriety.

>I thought you understood CS to mean that every acoustic interval was
>represented by only one scale size.

I do.

>The above scale doesn't meet this
>criterion, since 600 cents is both a 2nd and a 3rd.

Why are you assuming 12-tET? Try 1/1 5/4 4/3 3/2 15/8, or Pythagorean, or
meantone.

>>I don't know why you keep bringing up modes in this context -- all modes
>>have the same intervals.

>I don't know what you mean. Here's the interval matrix:

>......C E F G B
>2nds 4 1 2 4 1
>3rds 5 3 6 5 5
>4ths 7 7 7 9 6
>5ths 11 8 11 10 8
>6ths 12 12 12 12 12

>The interval 11 appears only twice in the scale, both times as a 5th. If
>it appeared as a 5th and anything else, it would remove strict propriety.

That's all fine, but still has nothing to do with modes. All 25 intervals in
your table appear in all modes. Intervals are not always contructed up from
the tonic!!!

>"A list of integers representing the cardinalities of nested MOS's is a
>Constant Structure of all scales that can support the entire nest. The
>larger the numbers, and the more of them, the fewer the number of scales in
>the Constant Structure (tho the number of scales is always infinite if you
>assume infinite tuning precision)."

Whoa, that's far out! Clearly not related to what we're arguing strict
propriety may or may not be implied by, right?