TOP Pelogic

So what is TOP Pelogic again??

Could somebody run that by me in a way that I could possibly
understand??

Thanks!

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> So what is TOP Pelogic again??

It's the tuning used for both "Mysterious Mush" (where it also
determines the inharmonic partials of the timbre) and its "Just"
complement (a misnomer, since the tuning was not Just Intonation, but
the timbres there were periodic, so that the tuning results in much
worse beating).

> Could somebody run that by me in a way that I could possibly
> understand??
>
> Thanks!
>
> JP

TOP Pelogic is a tuning system with an interval of repetition of
1206.55 cents, and a generator of 522.52 (or 685.03 = 1206.55 -
522.52) cents. The interval of repetition is supposed to approximate
the 2:1 ratio, the generator is supposed to approximate 4:3 (or 3:2
if you use the larger inversion), and a chain of *four* generators
(mod the interval of repetition), 327.02 cents, is supposed to
approximate 6:5 (unlike meantone where four generators gets you to
5:4).

Since you wanted them included in Monz's dictionary, I assume you
understand horagrams, right?

Here are the horagrams for TOP Meantone and TOP Miracle, both of
which would probably make a lot of sense to you:

/tuning/files/Erlich/meantone.gif

/tuning/files/miracle.gif

In the same form, here's TOP Pelogic:

/tuning/files/Erlich/pelogic.gif

Is this helping?

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_52666.html#52698

> TOP Pelogic is a tuning system with an interval of repetition of
> 1206.55 cents, and a generator of 522.52 (or 685.03 = 1206.55 -
> 522.52) cents. The interval of repetition is supposed to
approximate
> the 2:1 ratio, the generator is supposed to approximate 4:3 (or 3:2
> if you use the larger inversion), and a chain of *four* generators
> (mod the interval of repetition), 327.02 cents, is supposed to
> approximate 6:5 (unlike meantone where four generators gets you to
> 5:4).
>

***Oh! So this is the tunign with the slightly "stretched" octaves
and slightly "stretched" generator... Interesting. Well, it would
make sense than that if the timbre was not correspondingly stretched
it would beat more as a harmonic timbre. Thanks for helping to
clarify this; it's very interesting...

But what does the term "Pelogic" mean?? I guess it means it's
somewhat related to the tuning system Pelog... but how??

Thanks!

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_52666.html#52698
>
> > TOP Pelogic is a tuning system with an interval of repetition of
> > 1206.55 cents, and a generator of 522.52 (or 685.03 = 1206.55 -
> > 522.52) cents. The interval of repetition is supposed to
> approximate
> > the 2:1 ratio, the generator is supposed to approximate 4:3 (or
3:2
> > if you use the larger inversion), and a chain of *four*
generators
> > (mod the interval of repetition), 327.02 cents, is supposed to
> > approximate 6:5 (unlike meantone where four generators gets you
to
> > 5:4).
> >
>
> ***Oh! So this is the tunign with the slightly "stretched" octaves

Yes.

> and slightly "stretched" generator...

The generator is an extremely stretched fourth or *compressed* fifth.

> Interesting. Well, it would
> make sense than that if the timbre was not correspondingly
>stretched

And compressed in some places (the interval between the second and
third partials, being a fifth, is very compressed for example)

> But what does the term "Pelogic" mean?? I guess it means it's
> somewhat related to the tuning system Pelog... but how??

Some older theorists, as well as Easley Blackwood in his 23-equal
etude, have interpreted the Pelog tuning system and scale as the 7-
and 5-note MOSs arising from an extremely-stretched-fourth (or very-
compressed-fifth) generator. If you look at or listen to the
corresponding rings in the pelogic horagram, the resemblance to at
least some local variants of Pelog should be apparent.

But really, the interest in this temperament lies in the fact that,
like meantone, it "eats" a simple 5-limit interval. As you know,
meantone "eats" 81;80. Similarly, pelogic "eats" 135;128. It seems
that Gene and I have found two different ways of re-mapping intervals
so that 81;80 turns into 135;128, allowing a meantone piece to be
unambiguously converted into a pelogic piece. My method, which I
first described quite a while ago, is the easiest -- the meantone
generator is simply altered by a fraction of a semitone to become the
pelogic generator. The fascinating result is that all major triads
become (rough) minor triads, all minor triads become (rough) major
triads, and the diatonic scale turns into an approximation of the
Pelog tuning system -- but the notes remain in the same order. Gene's
method is more "warped" and alters the order of the notes, but major
triads get mapped to (rough) second-inversion major triads,
etc. . . . I asked Gene to elaborate but he has yet to respond.

Erv Wilson's notation and keyboard mapping on page 10 of
http://www.anaphoria.com/xen3a.PDF
is appropriate to pelogic and any similar system.

Herman Miller and others have created a lot of text and music around
these ideas; you seem to have been away from the list when this was
going on, though . . .

Best,
Paul

Maybe "pelogic" should really be called "mavila"?

See the first page of this Erv Wilson article:

http://www.anaphoria.com/meantone-mavila.PDF

Wilson seems to be using the equation

+4 = "5"

to express how meantone generators are chained to arrive at an
approximation of the 5th harmonic. His equation for mavila is

-3 = "5"

which would seem to correspond exactly, by analogy, to how we've
defined "pelogic".

The MOSs Wilson lists seem to support this hypothesis, agreeing as
they do with the rings of my horagrams until one is quite far from
the center. One wouldn't expect exact agreement since, as we know,
Wilson's "meta" paradigm is different from the TOP paradigm.

Unfortunately Wilson is far from explicit here. Kraig, are you
around? Can you shed some light? Also -- Herman take note.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > /tuning/topicId_52666.html#52698
> >
> > > TOP Pelogic is a tuning system with an interval of repetition
of
> > > 1206.55 cents, and a generator of 522.52 (or 685.03 = 1206.55 -
> > > 522.52) cents. The interval of repetition is supposed to
> > approximate
> > > the 2:1 ratio, the generator is supposed to approximate 4:3 (or
> 3:2
> > > if you use the larger inversion), and a chain of *four*
> generators
> > > (mod the interval of repetition), 327.02 cents, is supposed to
> > > approximate 6:5 (unlike meantone where four generators gets you
> to
> > > 5:4).
> > >
> >
> > ***Oh! So this is the tunign with the slightly "stretched" octaves
>
> Yes.
>
> > and slightly "stretched" generator...
>
> The generator is an extremely stretched fourth or *compressed*
fifth.
>
> > Interesting. Well, it would
> > make sense than that if the timbre was not correspondingly
> >stretched
>
> And compressed in some places (the interval between the second and
> third partials, being a fifth, is very compressed for example)
>
> > But what does the term "Pelogic" mean?? I guess it means it's
> > somewhat related to the tuning system Pelog... but how??
>
> Some older theorists, as well as Easley Blackwood in his 23-equal
> etude, have interpreted the Pelog tuning system and scale as the 7-
> and 5-note MOSs arising from an extremely-stretched-fourth (or very-
> compressed-fifth) generator. If you look at or listen to the
> corresponding rings in the pelogic horagram, the resemblance to at
> least some local variants of Pelog should be apparent.
>
> But really, the interest in this temperament lies in the fact that,
> like meantone, it "eats" a simple 5-limit interval. As you know,
> meantone "eats" 81;80. Similarly, pelogic "eats" 135;128. It seems
> that Gene and I have found two different ways of re-mapping
intervals
> so that 81;80 turns into 135;128, allowing a meantone piece to be
> unambiguously converted into a pelogic piece. My method, which I
> first described quite a while ago, is the easiest -- the meantone
> generator is simply altered by a fraction of a semitone to become
the
> pelogic generator. The fascinating result is that all major triads
> become (rough) minor triads, all minor triads become (rough) major
> triads, and the diatonic scale turns into an approximation of the
> Pelog tuning system -- but the notes remain in the same order.
Gene's
> method is more "warped" and alters the order of the notes, but
major
> triads get mapped to (rough) second-inversion major triads,
> etc. . . . I asked Gene to elaborate but he has yet to respond.
>
> Erv Wilson's notation and keyboard mapping on page 10 of
> http://www.anaphoria.com/xen3a.PDF
> is appropriate to pelogic and any similar system.
>
> Herman Miller and others have created a lot of text and music
around
> these ideas; you seem to have been away from the list when this was
> going on, though . . .
>
> Best,
> Paul

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> My method, which I
> first described quite a while ago, is the easiest -- the meantone
> generator is simply altered by a fraction of a semitone to become
the
> pelogic generator. The fascinating result is that all major triads
> become (rough) minor triads, all minor triads become (rough) major
> triads, and the diatonic scale turns into an approximation of the
> Pelog tuning system -- but the notes remain in the same order.

This seems to have been anticipated by Erv Wilson on page 6 of

http://www.anaphoria.com/meantone-mavila.PDF

What does the word "enantiodromia" mean? Apparently, the process when
a thing is replaced by its opposite.

http://phrontistery.50megs.com/e.html
http://home.mn.rr.com/wwftd/def.htm#enantiodromia

Was Wilson referring to the fact that major triads are converted into
minor triads here and vice versa? Or small steps into large steps and
vice versa? Or both?

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_52666.html#52723
>
> But really, the interest in this temperament lies in the fact that,
> like meantone, it "eats" a simple 5-limit interval. As you know,
> meantone "eats" 81;80. Similarly, pelogic "eats" 135;128. It seems
> that Gene and I have found two different ways of re-mapping
intervals
> so that 81;80 turns into 135;128, allowing a meantone piece to be
> unambiguously converted into a pelogic piece. My method, which I
> first described quite a while ago, is the easiest -- the meantone
> generator is simply altered by a fraction of a semitone to become
the
> pelogic generator. The fascinating result is that all major triads
> become (rough) minor triads, all minor triads become (rough) major
> triads, and the diatonic scale turns into an approximation of the
> Pelog tuning system -- but the notes remain in the same order.
Gene's
> method is more "warped" and alters the order of the notes, but
major
> triads get mapped to (rough) second-inversion major triads,
> etc. . . . I asked Gene to elaborate but he has yet to respond.
>

***So, essentially with TOP Pelogic, you've created a system where 5-
limit intervals are just (??) and the chromatic semitone is
maintained (??) Isn't that what 135;128 is all about??

And when do you use the ; rather than the : ? (just as a matter of
definitions...)

> Erv Wilson's notation and keyboard mapping on page 10 of
> http://www.anaphoria.com/xen3a.PDF
> is appropriate to pelogic and any similar system.
>
> Herman Miller and others have created a lot of text and music
around
> these ideas; you seem to have been away from the list when this was
> going on, though . . .
>

***I truly believe some of this took place *before* I joined the list
at the very end of 1999. Either that, or I haven't been paying
enough attention... :) [since I've actually read everything since
that time...]

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_52666.html#52723
> >
> > But really, the interest in this temperament lies in the fact
that,
> > like meantone, it "eats" a simple 5-limit interval. As you know,
> > meantone "eats" 81;80. Similarly, pelogic "eats" 135;128. It
seems
> > that Gene and I have found two different ways of re-mapping
> intervals
> > so that 81;80 turns into 135;128, allowing a meantone piece to be
> > unambiguously converted into a pelogic piece. My method, which I
> > first described quite a while ago, is the easiest -- the meantone
> > generator is simply altered by a fraction of a semitone to become
> the
> > pelogic generator. The fascinating result is that all major
triads
> > become (rough) minor triads, all minor triads become (rough)
major
> > triads, and the diatonic scale turns into an approximation of the
> > Pelog tuning system -- but the notes remain in the same order.
> Gene's
> > method is more "warped" and alters the order of the notes, but
> major
> > triads get mapped to (rough) second-inversion major triads,
> > etc. . . . I asked Gene to elaborate but he has yet to respond.
> >
>
> ***So, essentially with TOP Pelogic, you've created a system where
5-
> limit intervals are just (??)

No, their errors are larger, quite a bit larger than in meantone, so
certainly not just.

> and the chromatic semitone is
> maintained (??)

The chromatic semitone actually changes direction, so F# is *lower*
than F if you notate the chain of generators in the traditional way.

> Isn't that what 135;128 is all about??

What I'm saying is that, just as 81;80 *vanishes* in meantone, and
225;224, 1029;1024, and 2401;2400 all *vanish* in miracle, similarly
135;128 *vanishes* in this "pelogic" (or perhaps better, "mavila")
system. See below.

> And when do you use the ; rather than the : ? (just as a matter of
> definitions...)

We've occasionally used ";" instead of ":" when the tuning system is
tempered rather than just, to emphasize that the frequency ratio is
not simply the ratio of the two numbers, but rather a particular
temperament's representation of the interval. It's to be formed the
same way, through a chain of consonances, but the consonances are
tempered rather than just.

In JI, one can form 81:80 by going up three fifths and down a major
sixth plus an octave. In meantone, this same chain of consonances
lands you at the unison (i.e., exactly where you started). In JI, one
can form 135:128 by going up three fifths plus a major third and
going down two octaves. In pelogic/mavila, this same chain of
consonances lands you at the unison.

> > Erv Wilson's notation and keyboard mapping on page 10 of
> > http://www.anaphoria.com/xen3a.PDF
> > is appropriate to pelogic and any similar system.
> >
> > Herman Miller and others have created a lot of text and music
> around
> > these ideas; you seem to have been away from the list when this
was
> > going on, though . . .
> >
>
> ***I truly believe some of this took place *before* I joined the
list
> at the very end of 1999. Either that, or I haven't been paying
> enough attention... :) [since I've actually read everything since
> that time...]

Well, it's been *much* more recent than 1999.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Maybe "pelogic" should really be called "mavila"?
>
> See the first page of this Erv Wilson article:
>
> http://www.anaphoria.com/meantone-mavila.PDF
>
> Wilson seems to be using the equation
>
> +4 = "5"
>
> to express how meantone generators are chained to arrive at an
> approximation of the 5th harmonic. His equation for mavila is
>
> -3 = "5"
>
> which would seem to correspond exactly, by analogy, to how we've
> defined "pelogic".
>
> The MOSs Wilson lists seem to support this hypothesis, agreeing as
> they do with the rings of my horagrams until one is quite far from
> the center. One wouldn't expect exact agreement since, as we know,
> Wilson's "meta" paradigm is different from the TOP paradigm.
>
> Unfortunately Wilson is far from explicit here. Kraig, are you
> around? Can you shed some light? Also -- Herman take note.

I forwarded this to the SpecMus list and Kraig confirmed that I was
correct about what Erv meant with the above.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_52666.html#52757
>
> What I'm saying is that, just as 81;80 *vanishes* in meantone, and
> 225;224, 1029;1024, and 2401;2400 all *vanish* in miracle,
similarly
> 135;128 *vanishes* in this "pelogic" (or perhaps better, "mavila")
> system. >

***So, Paul, what would be the theoretical or audible advantages of
using TOP Pelogic??

TX!

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_52666.html#52934

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_52666.html#52757
> >
> > What I'm saying is that, just as 81;80 *vanishes* in meantone,
and
> > 225;224, 1029;1024, and 2401;2400 all *vanish* in miracle,
> similarly
> > 135;128 *vanishes* in this "pelogic" (or perhaps
better, "mavila")
> > system. >
>
> ***So, Paul, what would be the theoretical or audible advantages of
> using TOP Pelogic??
>
> TX!
>
> JP

***Paul answered this privately, by the way, but is involved in an
awsome microtonality writing project so will be away from the lists
for a bit! (Don't worry... he'll be baaaaaack...)

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_52666.html#52935

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> /tuning/topicId_52666.html#52934
>
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > /tuning/topicId_52666.html#52757
> > >
> > > What I'm saying is that, just as 81;80 *vanishes* in meantone,
> and
> > > 225;224, 1029;1024, and 2401;2400 all *vanish* in miracle,
> > similarly
> > > 135;128 *vanishes* in this "pelogic" (or perhaps
> better, "mavila")
> > > system. >
> >
> > ***So, Paul, what would be the theoretical or audible advantages
of
> > using TOP Pelogic??
> >
> > TX!
> >
> > JP
>
>
> ***Paul answered this privately, by the way, but is involved in an
> awsome microtonality writing project so will be away from the lists
> for a bit! (Don't worry... he'll be baaaaaack...)
>
> JP

***Next time I'll try to spell "awesome" right...

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_52666.html#52757
> >
> > What I'm saying is that, just as 81;80 *vanishes* in meantone,
and
> > 225;224, 1029;1024, and 2401;2400 all *vanish* in miracle,
> similarly
> > 135;128 *vanishes* in this "pelogic" (or perhaps
better, "mavila")
> > system. >
>
> ***So, Paul, what would be the theoretical or audible advantages of
> using TOP Pelogic??
>
> TX!
>
> JP

The TOP version of the temperament, in theory, minimizes the
maximum 'damage' any interval suffers from being mistuned relative to
JI. So it might be just the ticket if your hope is to best preserve
the traditional consonances, while exploiting the unusual topology
the temperament offers you.

In addition to all the cool things about Mavila (formerly 'Pelogic')
that I've posted about here recently, the TOP version (if you use,
say, the 9-note ring) has some really narrow intervals -- 31 cents!
In fact, if you notate 'conventionally', a *sharp* becomes 31 cents
*down*, and a *flat* becomes 31 cents *up*. Too subtle for some,
perhaps, but I know you've learned to love such tiny intervals,
Joseph ;)!

The temperament is one of my favorite resources and I know Kraig
likes it too, having used Erv Wilson's tuning of it -- Meta-Mavila --
on at least one of his CDs . . .

Did i ever mention that Mavila is a Chopi Village that i gave Erv the
measurements for?
just in case that detail went was not mentioned or not. Among the Chopis
, there tuning was considered the best, at least when Hugh Tracy was
Alive. Now all these ensembles i understand are non existent

wallyesterpaulrus wrote:

> The temperament is one of my favorite resources and I know Kraig
> likes it too, having used Erv Wilson's tuning of it -- Meta-Mavila --
> on at least one of his CDs . . .

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

> Did i ever mention that Mavila is a Chopi Village

Yes . . .

> that i gave Erv the
> measurements for?

Oh, I didn't know he got them from you.

> just in case that detail went was not mentioned or not. Among the
Chopis
> , there tuning was considered the best, at least when Hugh Tracy was
> Alive. Now all these ensembles i understand are non existent

Tragic.

Let's start a new one.