Fwd: The Carlos scales.

--- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:

The Alpha scale is very close to 200tet. The Beta scale is close to
94tet and the Gamma scale is close to 171tet. Knowing this gives a
broader perspective to Wendy Carlos's scales.

--- End forwarded message ---

robert thomas martin wrote:
> --- In MicroMadeEasy@yahoogroups.com, "robert thomas martin" > <robertthomasmartin@...> wrote:
> > The Alpha scale is very close to 200tet. The Beta scale is close to > 94tet and the Gamma scale is close to 171tet. Knowing this gives a > broader perspective to Wendy Carlos's scales.

Alpha has steps of 78.0 cents, with 4 steps to the minor third (312 cents), 5 steps to the major third (390 cents), and 9 steps to the perfect fifth (702 cents). 200-ET has a 318.0 cent minor third and a 384.0-cent major third.

Really, the key to the Alpha, Beta, and Gamma scales is how the scale steps are mapped to intervals:

Alpha Beta Gamma
minor third 4 steps 5 steps 9 steps
major third 5 steps 6 steps 11 steps
fifth 9 steps 11 steps 20 steps

see http://www.wendycarlos.com/resources/pitch.html

So these scales are early examples of what we're now calling "rank 1 temperaments". We can add an octave generator to find a related set of rank 2 temperaments:

[<1, 1, 2], <0, 9, 5]> (1199.212102, 77.943790) valentine
[<1, 1, 2], <0, 11, 6]> (1200.738886, 63.853384) sycamore
[<1, 1, 2], <0, 20, 11]> (1200.051352, 35.099252) (unnamed?)

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
>
> robert thomas martin wrote:
> > --- In MicroMadeEasy@yahoogroups.com, "robert thomas martin"
> > <robertthomasmartin@> wrote:
> >
> > The Alpha scale is very close to 200tet. The Beta scale is close
to
> > 94tet and the Gamma scale is close to 171tet. Knowing this gives
a
> > broader perspective to Wendy Carlos's scales.
>
> Alpha has steps of 78.0 cents, with 4 steps to the minor third (312
> cents), 5 steps to the major third (390 cents), and 9 steps to the
> perfect fifth (702 cents). 200-ET has a 318.0 cent minor third and
a
> 384.0-cent major third.
>
> Really, the key to the Alpha, Beta, and Gamma scales is how the
scale
> steps are mapped to intervals:
>
> Alpha Beta Gamma
> minor third 4 steps 5 steps 9 steps
> major third 5 steps 6 steps 11 steps
> fifth 9 steps 11 steps 20 steps
>
> see http://www.wendycarlos.com/resources/pitch.html
>
> So these scales are early examples of what we're now calling "rank
1
> temperaments". We can add an octave generator to find a related set
of
> rank 2 temperaments:
>
> [<1, 1, 2], <0, 9, 5]> (1199.212102, 77.943790) valentine
> [<1, 1, 2], <0, 11, 6]> (1200.738886, 63.853384) sycamore
> [<1, 1, 2], <0, 20, 11]> (1200.051352, 35.099252) (unnamed?)
>
From Robert. 200tet has many 3rds including 312 and 390cents.

robert thomas martin wrote:
> From Robert. 200tet has many 3rds including 312 and 390cents.

And your point in stating the very obvious is what, exactly? 1200-ET has even more thirds. You're not going to understand Alpha if you try to compare it to some huge ET. It's what you get when you divide the perfect fifth into 9 equal parts. If you start with an exact 3/2 fifth, that gives you steps of about 77.995 cents. Hmm, isn't that really close to 240000tet?

And the sad thing is that this reply was so predictable. You should try tuning up some of these scales and doing something musical with them. You know, like ummm "make micro music" or something.

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
>
> robert thomas martin wrote:
> > From Robert. 200tet has many 3rds including 312 and 390cents.
>
> And your point in stating the very obvious is what, exactly? 1200-
ET has
> even more thirds. You're not going to understand Alpha if you try
to
> compare it to some huge ET. It's what you get when you divide the
> perfect fifth into 9 equal parts. If you start with an exact 3/2
fifth,
> that gives you steps of about 77.995 cents. Hmm, isn't that really
close
> to 240000tet?
>
> And the sad thing is that this reply was so predictable. You should
try
> tuning up some of these scales and doing something musical with
them.
> You know, like ummm "make micro music" or something.
>
From Robert. The Carlos scales as they stand in their original form
have been around for decades. I have recast them in a more
interesting mold so that people can interpret them in a different
light. But the appearance of your hostility is even more interesting.

--- In MakeMicroMusic@yahoogroups.com, "robert thomas martin" You should
> try
> > tuning up some of these scales and doing something musical with
> them.
> > You know, like ummm "make micro music" or something.
> >
> From Robert. The Carlos scales as they stand in their original form
> have been around for decades. I have recast them in a more
> interesting mold so that people can interpret them in a different
> light. But the appearance of your hostility is even more interesting.

"Interesting" how? when? to whom? to what end? Adjectives alone say
nothing!

I am interested in the metaphor of mold-casting = scale-making. I am
going to chew on it.

--- In MakeMicroMusic@yahoogroups.com, "Jacob"
<tricesimoprimalist@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "robert thomas martin" You
should
> > try
> > > tuning up some of these scales and doing something musical with
> > them.
> > > You know, like ummm "make micro music" or something.
> > >
> > From Robert. The Carlos scales as they stand in their original
form
> > have been around for decades. I have recast them in a more
> > interesting mold so that people can interpret them in a different
> > light. But the appearance of your hostility is even more
interesting.
>
> "Interesting" how? when? to whom? to what end? Adjectives alone say
> nothing!
>
> I am interested in the metaphor of mold-casting = scale-making. I am
> going to chew on it.
>
From Robert. The Alpha scale divides the 5th into 9 equal parts.
The 5th of 702cents=6x9x13cents. It should then be reasonable enough
to divide the 5th into either 6 or 13 parts (at least from an
experimental point of view). It then naturally follows that we end up
with three stacked scales using 117, 78 and 54cents. The actual
multiples of 702 are 2x3x3x3x13 so there are other possible ways to
divide the 5th of 702cents (approximated). I mention this merely to
show how the Carlos methodology can be expanded in a way that some
people might find interesting. Others may not.

I have always thought of constant structures as such- if you approach it with the idea that you you have a set number of notes that you fill with a set of intervals/ratios. It goes with keyboard mapping also.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Jacob wrote:
>
> --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>, "robert thomas martin" You > should
> > try
> > > tuning up some of these scales and doing something musical with
> > them.
> > > You know, like ummm "make micro music" or something.
> > >
> > From Robert. The Carlos scales as they stand in their original form
> > have been around for decades. I have recast them in a more
> > interesting mold so that people can interpret them in a different
> > light. But the appearance of your hostility is even more interesting.
>
> "Interesting" how? when? to whom? to what end? Adjectives alone say
> nothing!
>
> I am interested in the metaphor of mold-casting = scale-making. I am
> going to chew on it.
>
>

And what about the milioctave? Milan
> From Robert. The Alpha scale divides the 5th into 9 equal parts. > The 5th of 702cents=6x9x13cents. It should then be reasonable enough > to divide the 5th into either 6 or 13 parts (at least from an > experimental point of view). It then naturally follows that we end up > with three stacked scales using 117, 78 and 54cents. The actual > multiples of 702 are 2x3x3x3x13 so there are other possible ways to > divide the 5th of 702cents (approximated). I mention this merely to > show how the Carlos methodology can be expanded in a way that some > people might find interesting. Others may not.

--- In MakeMicroMusic@yahoogroups.com, aum <aum@...> wrote:
>
> And what about the milioctave? Milan
> > From Robert. The Alpha scale divides the 5th into 9 equal parts.
> > The 5th of 702cents=6x9x13cents. It should then be reasonable
enough
> > to divide the 5th into either 6 or 13 parts (at least from an
> > experimental point of view). It then naturally follows that we end
up
> > with three stacked scales using 117, 78 and 54cents. The actual
> > multiples of 702 are 2x3x3x3x13 so there are other possible ways to
> > divide the 5th of 702cents (approximated). I mention this merely to
> > show how the Carlos methodology can be expanded in a way that some
> > people might find interesting. Others may not.
>
From Robert. I don't work with millioctaves but if you are willing
to agree that a 5th is about 585 millioctaves then the possible
multiples are 3x3x5x13=585 unless I am mistaken about how millioctaves
are determined.

--- In MakeMicroMusic@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, aum <aum@> wrote:
> >
> > And what about the milioctave? Milan
> > > From Robert. The Alpha scale divides the 5th into 9 equal
parts.
> > > The 5th of 702cents=6x9x13cents. It should then be reasonable
> enough
> > > to divide the 5th into either 6 or 13 parts (at least from an
> > > experimental point of view). It then naturally follows that we
end
> up
> > > with three stacked scales using 117, 78 and 54cents. The actual
> > > multiples of 702 are 2x3x3x3x13 so there are other possible
ways to
> > > divide the 5th of 702cents (approximated). I mention this
merely to
> > > show how the Carlos methodology can be expanded in a way that
some
> > > people might find interesting. Others may not.
> >
> From Robert. I don't work with millioctaves but if you are
willing
> to agree that a 5th is about 585 millioctaves then the possible
> multiples are 3x3x5x13=585 unless I am mistaken about how
millioctaves
> are determined.
>
More from Robert. If the 5th is taken to be 700cents then the
multiples are 2x2x5x5x7=700cents which can produce some interesting
intervals.

Yes, if the 5th is taken to have any size (using some hypothetical units), we can get many different multiples... Many possibilities...
But the connection with the Carlos methodology is not clear to me.
Milan
> More from Robert. If the 5th is taken to be 700cents then the > multiples are 2x2x5x5x7=700cents which can produce some interesting > intervals.

--- In MakeMicroMusic@yahoogroups.com, aum <aum@...> wrote:
>
> Yes, if the 5th is taken to have any size (using some hypothetical
> units), we can get many different multiples... Many possibilities...
> But the connection with the Carlos methodology is not clear to me.
> Milan
> > More from Robert. If the 5th is taken to be 700cents then the
> > multiples are 2x2x5x5x7=700cents which can produce some interesting
> > intervals.
>
From Robert. I only have a book which explains the Carlos scales.
Perhaps someone else can supply some links on the internet. There is a
graph involved.

At 06:26 PM 6/3/2008, you wrote:
>--- In MakeMicroMusic@yahoogroups.com, aum <aum@...> wrote:
>>
>> Yes, if the 5th is taken to have any size (using some hypothetical
>> units), we can get many different multiples... Many possibilities...
>> But the connection with the Carlos methodology is not clear to me.
>> Milan
>> > More from Robert. If the 5th is taken to be 700cents then the
>> > multiples are 2x2x5x5x7=700cents which can produce some interesting
>> > intervals.
>>
> From Robert. I only have a book which explains the Carlos scales.
>Perhaps someone else can supply some links on the internet. There is a
>graph involved.

I believe the link to Carlos' own article on the subject was
already supplied either here or on the tuning list. So far
your posts, Robert, have nothing in common with her approach.
She used an algorithm to find the best non-octave divisions
in terms of approximations to JI. You're just rattling off
tables of cents. For some reason nobody else seems to have
mentioned recently that this mailing list is expressly not for
posting tables of cents.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> At 06:26 PM 6/3/2008, you wrote:
> >--- In MakeMicroMusic@yahoogroups.com, aum <aum@> wrote:
> >>
> >> Yes, if the 5th is taken to have any size (using some
hypothetical
> >> units), we can get many different multiples... Many
possibilities...
> >> But the connection with the Carlos methodology is not clear to
me.
> >> Milan
> >> > More from Robert. If the 5th is taken to be 700cents
then the
> >> > multiples are 2x2x5x5x7=700cents which can produce some
interesting
> >> > intervals.
> >>
> > From Robert. I only have a book which explains the Carlos
scales.
> >Perhaps someone else can supply some links on the internet. There
is a
> >graph involved.
>
> I believe the link to Carlos' own article on the subject was
> already supplied either here or on the tuning list. So far
> your posts, Robert, have nothing in common with her approach.
> She used an algorithm to find the best non-octave divisions
> in terms of approximations to JI. You're just rattling off
> tables of cents. For some reason nobody else seems to have
> mentioned recently that this mailing list is expressly not for
> posting tables of cents.
>
> -Carl
>
From Robert. Perhaps this mailing list is evolving as it goes
along. So is the link here or not? If so is someone able to supply it?

>From Robert. Perhaps this mailing list is evolving as it goes
>along. So is the link here or not? If so is someone able to supply it?

I googled for carlos alpha and this is the first result:

http://www.wendycarlos.com/resources/pitch.html

Are you unable to do so?

-Carl

robert thomas martin wrote:
> --- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...> > wrote:
>> robert thomas martin wrote:
>>> From Robert. 200tet has many 3rds including 312 and 390cents.
>> And your point in stating the very obvious is what, exactly? 1200-
> ET has >> even more thirds. You're not going to understand Alpha if you try > to >> compare it to some huge ET. It's what you get when you divide the >> perfect fifth into 9 equal parts. If you start with an exact 3/2 > fifth, >> that gives you steps of about 77.995 cents. Hmm, isn't that really > close >> to 240000tet?
>>
>> And the sad thing is that this reply was so predictable. You should > try >> tuning up some of these scales and doing something musical with > them. >> You know, like ummm "make micro music" or something.
>>
> From Robert. The Carlos scales as they stand in their original form > have been around for decades. I have recast them in a more > interesting mold so that people can interpret them in a different > light. But the appearance of your hostility is even more interesting. Hostility? I'm trying to be patient. Really. You're not making it easy. You've not shown any interest when anyone tries to help you understand things. Now go back and read the page on the wendycarlos site until you understand what it's saying.

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
>
> robert thomas martin wrote:
> > --- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@>
> > wrote:
> >> robert thomas martin wrote:
> >>> From Robert. 200tet has many 3rds including 312 and 390cents.
> >> And your point in stating the very obvious is what, exactly?
1200-
> > ET has
> >> even more thirds. You're not going to understand Alpha if you
try
> > to
> >> compare it to some huge ET. It's what you get when you divide
the
> >> perfect fifth into 9 equal parts. If you start with an exact 3/2
> > fifth,
> >> that gives you steps of about 77.995 cents. Hmm, isn't that
really
> > close
> >> to 240000tet?
> >>
> >> And the sad thing is that this reply was so predictable. You
should
> > try
> >> tuning up some of these scales and doing something musical with
> > them.
> >> You know, like ummm "make micro music" or something.
> >>
> > From Robert. The Carlos scales as they stand in their original
form
> > have been around for decades. I have recast them in a more
> > interesting mold so that people can interpret them in a different
> > light. But the appearance of your hostility is even more
interesting.
>
> Hostility? I'm trying to be patient. Really. You're not making it
easy.
> You've not shown any interest when anyone tries to help you
understand
> things. Now go back and read the page on the wendycarlos site until
you
> understand what it's saying.
>
From Robert. The Carlos scales are not sacred objects and are open
to interpretation and manipulation by anyone who cares to go to the
trouble. Your bullying tactics are becoming tiresome.

> > ...You're just rattling off
> > tables of cents. For some reason nobody else seems to have
> > mentioned recently that this mailing list is expressly not for
> > posting tables of cents.
> > -Carl
> >
> ...
> From Robert. Perhaps this mailing list is evolving as it goes
> along.

Evolution in some ways is fine, but. I have been wondering why people are
starting to post tables of cents here, with no coherent explanation. This
is a forum about making music. I think the tables of cents belong over in
the tuning or tuning math lists...

Rick

--- In MakeMicroMusic@yahoogroups.com, Rick McGowan <rick@...> wrote:
>
> > > ...You're just rattling off
> > > tables of cents. For some reason nobody else seems to have
> > > mentioned recently that this mailing list is expressly not for
> > > posting tables of cents.
> > > -Carl
> > >
> > ...
> > From Robert. Perhaps this mailing list is evolving as it goes
> > along.
>
> Evolution in some ways is fine, but. I have been wondering why
people are
> starting to post tables of cents here, with no coherent
explanation. This
> is a forum about making music. I think the tables of cents belong
over in
> the tuning or tuning math lists...
>
> Rick
>
From Rattling Off: Please feel free to delete the offending list.

robert thomas martin wrote:

> From Robert. The Carlos scales are not sacred objects and are open > to interpretation and manipulation by anyone who cares to go to the > trouble. Your bullying tactics are becoming tiresome.

My "bullying tactics". That's a first. Your personal attacks are becoming tiresome. Could there be a reason you seem to be attracting unfavorable replies to your messages? No, of course not, it's everyone else who must be wrong.

Interpretation is one thing. There are certainly lots of different ways of understanding and using a scale like the Alpha, Beta, and Gamma scales. I gave a bit of my own interpretation when I represented these scales as early representatives of the "rank one temperament" group. But the best way to evaluate a scale or a tuning is to make music with it. Otherwise it's just a list of numbers. Whatever pleases the ear, as Debussy is quoted as having said. :-)

Unfortunately, my only example of Carlos Alpha music that I've written is an early version of what ended up as Mizarian Porcupine Overture. The unfortunate thing about this is that I only have it in RealAudio format. (At the time the RealAudio player wasn't as annoying as it turned out to be later on.)

ftp://ftp.io.com/pub/usr/hmiller/ra-archive/alpha.ra