Yahoo Tuning Groups Ultimate Backup tuning refresh memory on "microtemperament" please

hi Joe,

From: "Joseph Pehrson" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, October 10, 2002 8:15 PM
Subject: [tuning] refresh memory on "microtemperament" please

> Hello Paul et al...
>
> Could somebody please refresh my memory regarding "microtemperament"
> as proposed by David Keenan??

hmmm ... i see that my Dictionary definition is really lacking
on this term, so i won't even give the link. IIRC, Dave gave me
a nice definition a while back but i didn't get the chance to
add it to the Dicionary. any help on this now would be appreciated.

> My impression was that it was a temperament designed to *facilitate*
> Just Intonation, specifically. Is that correct??
>
> So, in a way, it's what Margo was doing in her recent
> "tempered" just scale??
>
> The idea being, if I'm correct, that with microtemperament
> one actually arrives at *more* close to just intervals than
> in a pure just system?? Is that right?
>

a microtemperament is designed to *approximate* Just Intonation,
by providing intervals that are only very slightly deviant from
the JI ratios, and at the same time to maximize the number of
approximations that some imaginary "ideal" listener would find
recognizable as the JI ratio. each microtemperment interval
would be recognizable as two or more JI ratios.

unfortunately, i haven't had to the time to study either Margo's
or Pauline's scales, but would like to look deeper into both.

Pauline, i'd like to see a more lengthy summary of the mathematics
of your tuning -- specifically, what criteria did you use to arrive
at a particular value for a pitch or interval? is it fractions of
some comma, skhisma, etc.?

> However, this term would not be accepted at all by JI purists,
> correct, since they tend to see any *temperament* as definitionally
> *opposed* to the pureness of an "unadjusted" Just system... Right??

"unadjusted" Just system -- that's really a good one. thinking
about that can really twist your mind up. :)

anyway, Joe, in the sense you outline, you're correct that a
JI purist would be opposed to *any* temperament on "moral" grounds.

but on the other side of the coin, it's interesting to me to
consider an expanded type of JI itself as a sort of unequal
temperament. this is the approach i've used in many of my
JI pieces -- for example, _3 Plus 4_, downloadable from
the Tuning Punks page
http://artists.mp3s.com/artists/72/the_tuning_punks.html

and to my ears also Kraig Grady and Bill Wesley in much of
their JI work, and from what Kyle Gann wrote, seems to be what
David Beardsley has in mind as well.

🔗Gene Ward Smith <genewardsmith@juno.com>

--- In tuning@y..., "monz" <monz@a...> wrote:

> > Hello Paul et al...
> >
> > Could somebody please refresh my memory regarding "microtemperament"
> > as proposed by David Keenan??
>
>
> hmmm ... i see that my Dictionary definition is really lacking
> on this term, so i won't even give the link. IIRC, Dave gave me
> a nice definition a while back but i didn't get the chance to
> add it to the Dicionary. any help on this now would be appreciated.

For what it's worth, I reserve "microtemperament" for cases where the error is well under a cent, for instance Octoid or Hemififth, or the quintessential micro, Ennealimmal. Your milage may vary.

> a microtemperament is designed to *approximate* Just Intonation,
> by providing intervals that are only very slightly deviant from
> the JI ratios, and at the same time to maximize the number of
> approximations that some imaginary "ideal" listener would find
> recognizable as the JI ratio. each microtemperment interval
> would be recognizable as two or more JI ratios.

Eh? Why do you say that?

> > However, this term would not be accepted at all by JI purists,
> > correct, since they tend to see any *temperament* as definitionally
> > *opposed* to the pureness of an "unadjusted" Just system... Right??
>
>
> "unadjusted" Just system -- that's really a good one. thinking
> about that can really twist your mind up. :)
>
> anyway, Joe, in the sense you outline, you're correct that a
> JI purist would be opposed to *any* temperament on "moral" grounds.

What about the 19-tone scale I posted recently? It *can* be tuned in the 4375/4374 planar temperament, or in 1547-et, but it works nicely as an honest microtemperament even without any temperament. How do you categorize that one?

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@y..., "monz" <monz@a...> wrote:
>
> hi Joe,
>
>
>
> From: "Joseph Pehrson" <jpehrson@r...>
> To: <tuning@y...>
> Sent: Thursday, October 10, 2002 8:15 PM
> Subject: [tuning] refresh memory on "microtemperament" please
>
>
> > Hello Paul et al...
> >
> > Could somebody please refresh my memory
regarding "microtemperament"
> > as proposed by David Keenan??
>
>
> hmmm ... i see that my Dictionary definition is really lacking
> on this term, so i won't even give the link. IIRC, Dave gave me
> a nice definition a while back but i didn't get the chance to
> add it to the Dicionary. any help on this now would be appreciated.

a microtemperament is a temperament with really small deviations from
ji in the consonant intervals. dave keenan had some pretty detailed
criteria on how much error the temperament could impart to intervals
of each odd limit -- it would be best to ask him.

> > My impression was that it was a temperament designed to
*facilitate*
> > Just Intonation, specifically. Is that correct??
> >
> > So, in a way, it's what Margo was doing in her recent
> > "tempered" just scale??
> >
> > The idea being, if I'm correct, that with microtemperament
> > one actually arrives at *more* close to just intervals than
> > in a pure just system?? Is that right?

of course. this is true of temperaments in general.

i would substitute the word "intervals" for the word "approximations"
and the word "a" for the word "the" above.

> each microtemperment interval
> would be recognizable as two or more JI ratios.

huh? i don't see that at all.

> unfortunately, i haven't had to the time to study either Margo's
> or Pauline's scales, but would like to look deeper into both.

margo's scale used various complex ratios, rather than fixed
irrational numbers, to come up with the "compromise" intervals of the
temperament. this makes little audible difference, but conforms to an
old tradition of using only rational numbers. johnny reinhard showed
me that kirnberger II was in fact defined using only rational
numbers -- kirnberger split the syntonic comma in "half" using the
ratios 161:160 and 162:161, and each of the fifths D-A and A-E was
foreshortened from 3:2 by one of these "halves". so the entire tuning
could be expressed using only ratios, no irrational numbers. this is
indeed "just temperament" but certainly not "microtemperament" since
those two fifths were each off by a half a comma, 11 cents!

> Pauline, i'd like to see a more lengthy summary of the mathematics
> of your tuning -- specifically, what criteria did you use to arrive
> at a particular value for a pitch or interval? is it fractions of
> some comma, skhisma, etc.?

pauline has said she is not a mathie. but it seems her system is
nearly identical, in both measure and spirit, to the "classic"
microtemperament that dave keenan discussed quite a bit -- the 7-
limit planar temperament where 225:224 is tempered out. there are
_two_ independent tuning decisions to be made here (unlike the _one_
you have in a planar temperament such as meantone, schismic, etc.),
and, if you like, you can express both of them (the narrowing of the
3:2 and the narrowing of the 5:4) as fractions of the
225:224 "septimal kleisma". pauline herself does not seem concerned
with pinning things down much finer than 1 cent, and i can't say i
blame her.

which term? i don't see anything in your (joseph pehrson's)
terminology that could be controversial. you did say "close to just"
intervals -- you didn't say "just" intervals.

> but on the other side of the coin, it's interesting to me to
> consider an expanded type of JI itself as a sort of unequal
> temperament. this is the approach i've used in many of my
> JI pieces

> -- for example, _3 Plus 4_, downloadable from
> the Tuning Punks page
> http://artists.mp3s.com/artists/72/the_tuning_punks.html
>
> and to my ears also Kraig Grady and Bill Wesley in much of
> their JI work, and from what Kyle Gann wrote, seems to be what
> David Beardsley has in mind as well.

do you mean you're deliberately using the "wolves" of the ji scale,
since they're already rather mild? if not, what do you mean, monz?

p.s. i would call really, really mild wolves "puppies", so what gene
is talking about might be called a "basket of puppies" scale or
approach or whatever . . .

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Gene Ward Smith <genewardsmith@juno.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗David Beardsley <davidbeardsley@biink.com>

🔗monz <monz@attglobal.net>

----- Original Message -----
From: "David Beardsley" <davidbeardsley@biink.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, October 16, 2002 6:16 AM
Subject: Re: [tuning] refresh memory on "microtemperament" please

> ----- Original Message -----
> From: "monz" <monz@attglobal.net>
>
> >
> > but on the other side of the coin, it's interesting to me to
> > consider an expanded type of JI itself as a sort of unequal
> > temperament. this is the approach i've used in many of my
> > JI pieces -- for example, _3 Plus 4_, downloadable from
> > the Tuning Punks page
> > http://artists.mp3s.com/artists/72/the_tuning_punks.html
> >
> > and to my ears also Kraig Grady and Bill Wesley in much of
> > their JI work, and from what Kyle Gann wrote, seems to be what
> > David Beardsley has in mind as well.
>
> My approach has NOTHING to do with any kind of temperament.
>
>
> * David Beardsley
> * http://biink.com
> * http://mp3.com/davidbeardsley

hmmm ... OK, my bad. i really had something in mind along
the lines of my (admittedly somewhat unclear) ideas about "finity",
moreso than about temperament per so. sorry.

-monz

🔗David Beardsley <davidbeardsley@biink.com>

----- Original Message -----
From: "monz" <monz@attglobal.net>

> ----- Original Message -----
> From: "David Beardsley" <davidbeardsley@biink.com>

> > ----- Original Message -----
> > From: "monz" <monz@attglobal.net>
> >
> > > but on the other side of the coin, it's interesting to me to
> > > consider an expanded type of JI itself as a sort of unequal
> > > temperament. this is the approach i've used in many of my
> > > JI pieces -- for example, _3 Plus 4_, downloadable from
> > > the Tuning Punks page
> > > http://artists.mp3s.com/artists/72/the_tuning_punks.html
> > >
> > > and to my ears also Kraig Grady and Bill Wesley in much of
> > > their JI work, and from what Kyle Gann wrote, seems to be what
> > > David Beardsley has in mind as well.
> >
> > My approach has NOTHING to do with any kind of temperament.
>
> hmmm ... OK, my bad. i really had something in mind along
> the lines of my (admittedly somewhat unclear) ideas about "finity",
> moreso than about temperament per so. sorry.

The beats that Kyle heard were from microtones. The piece is named
Around D. Some really flat m9ths, some really sharp M7ths.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley