Re: constant structures

Paul!
First of all, the term has no relevance or misapplied to such objects. If
the same intervals did occur within such a random generation the chances are
it would not be subtended by an equal number of steps. Therefore I would say
it is not a constant structure. 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. I believe it would be safe to say that all constant structures have
intervals that are repeated. Also only over the disjuctions does one scale
step possibly transcend the size of one of its neighbors. At least that is
what has been noticed so far!

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> >>>How exactly are you defining "constant structures" here?
> >
> >>I got this from Kraig Grady who got it from Erv Wilson. It means that any
> >>specific interval will always be subtended by the same number of steps.
>
> >This requires strict propriety.
>
> No, it doesn't. For example, a scale of randomly chosen pitches from the
> continuum (say, by throwing darts on a dartboard) will be a constant
> structures scale, since every specific interval appears only once and is
> therefore always subtended by the same number of steps. Such a scale
> probably won't be strictly proper, though.
>

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

Sorry for the misapplication, and you are right that

>If
>the same intervals did occur within such a random generation the chances
are
>it would not be subtended by an equal number of steps.

but there would be a zero probability of equal intervals occuring in the
random generation.

>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.

That certainly sounds like it could apply to a Fokker periodicity block.

>Also only over the disjuctions does one scale
>step possibly transcend the size of one of its neighbors.

Can you clarify that statement? Are you addressing the propriety issue?

Paul!
I don't know any thing about the Fokker periodicity block. I was not
able to open the papers you sent me before!

"Paul H. Erlich" wrote:

>
> >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.
>
> That certainly sounds like it could apply to a Fokker periodicity block.
>
> >Also only over the disjuctions does one scale
> >step possibly transcend the size of one of its neighbors.
>
> Can you clarify that statement? Are you addressing the propriety issue?
>
>

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

Kraig,

What were you not able to open?

Also, can you address this:

> >Also only over the disjuctions does one scale
> >step possibly transcend the size of one of its neighbors.
>
> Can you clarify that statement? Are you addressing the propriety issue?

-Paul

Paul!
You sent a pdf file awhile but back I have a problem with my adobe
acrobat. This is why I don't put the archive on it.
As you mentioned before the augmented 4th is larger than the Dim. 5 in
pythagorean. these occur over the disjunction in a chain of 5ths (seven
places) i was not address propriety which as a concept seems to have drifted
from my mind like feathers that are blown away when you shake them :)

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Kraig,
>
> What were you not able to open?
>
> Also, can you address this:
>
> > >Also only over the disjuctions does one scale
> > >step possibly transcend the size of one of its neighbors.
> >
> > Can you clarify that statement? Are you addressing the propriety issue?
>
> -Paul
>
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-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

>>>I got this from Kraig Grady who got it from Erv Wilson. It means that any
>>>specific interval will always be subtended by the same number of steps.
>>
>>This requires strict propriety.
>
>No, it doesn't. For example, a scale of randomly chosen pitches from the
>continuum (say, by throwing darts on a dartboard) will be a constant
>structures scale, since every specific interval appears only once and is
>therefore always subtended by the same number of steps.

True, but the musical value of saying "such and such interval is always
subtended by the same number of steps" is about nil unless the interval
appears in more than one mode.

>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 the term is more for use when comparing scales than for speaking of any
single scale? That would fit with what I understand of Erv's interests.

>Also only over the disjuctions does one scale step possibly transcend the
>size of one of its neighbors. At least that is what has been noticed so far!

Yes, and it's damn curious.

-C.

Kraig,

The only .pdf file I might have tried to send you was my paper. Do you have
Xenharmonikon 17? Then you have my paper. It doesn't cover Fokker. We've
gone over the Fokker stuff here on the list; check the archives or stay
tuned since it's bound to get explained again.

-Paul

Carl Lumma wrote,

>True, but the musical value of saying "such and such interval is always
>subtended by the same number of steps" is about nil unless the interval
>appears in more than one mode.

OK, but the point is, you will find many CS scales that are not strictly
proper.

>>True, but the musical value of saying "such and such interval is always
>>subtended by the same number of steps" is about nil unless the interval
>>appears in more than one mode.
>
>OK, but the point is, you will find many CS scales that are not strictly
>proper.

By the old (incorrect) definition of CS, yes.

>>>Also only over the disjuctions does one scale
>>>step possibly transcend the size of one of its neighbors.
>>
>>Can you clarify that statement? Are you addressing the propriety issue?
>
>As you mentioned before the augmented 4th is larger than the Dim. 5 in
>pythagorean. these occur over the disjunction in a chain of 5ths (seven
>places) i was not address propriety which as a concept seems to have drifted
>from my mind like feathers that are blown away when you shake them :)

BTW, Kraig, you may have forgotten what Rothenberg called it, but you are
addressing propriety here!

-C.