Re: [tuning] Re: are we rational or irrational [math question]

The Joes !
The use of any fractions qualifies as JI. The work of Augusto Navarro is one example of JI
use without the use of limits. In medieval Persia many ratio were chosen in scales not on the
basis of limits but on means in dividing larger intervals. This trend started in Greece (at
least). The limiting to JI to low number ratios (especially 5 limit) seems to be ignore this
history thus being nothing more than a enthno-chrono-centric viewpoint. The use of Limits
allow certain structural possibilities and it is these structures that make limits appealing.
Another common example is the 16-19-24 triad.

Monz wrote:

> In general, I think it's OK to equate 'just' with 'rational',
> but popular usage tends to keep 'just' limited to either 5-limit
> JI, or to higher-prime but otherwise low-integer JI (i.e., Partch).
> For that reason, I often use 'rational' to refer to rational
> tunings that are more complex than these.
>
> My 'just intonation' Dictionary entry refers to some of this.
>
> http://www.ixpres.com/interval/dict/just.htm
>
> Other opinions would be most welcome.

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

--- In tuning@egroups.com, Kraig Grady <kraiggrady@a...> wrote:

> The use of any fractions qualifies as JI. The work of Augusto
Navarro is one example of JI
> use without the use of limits.

Kraig,

Hello!

Could you provide some history and example scales from this theorist?
Sounds very interesting. I would like to learn more about the
historical theorists that have ventured beyond 11 and such.

Thanks,

Jacky

--- In tuning@egroups.com, Kraig Grady <kraiggrady@a...> wrote:
> http://www.egroups.com/message/tuning/12449
>
> The use of any fractions qualifies as JI. The work of Augusto
> Navarro is one example of JI use without the use of limits. In
> medieval Persia many ratio were chosen in scales not on the
> basis of limits but on means in dividing larger intervals. This
> trend started in Greece (at least). The limiting to JI to low
> number ratios (especially 5 limit) seems to be ignore this
> history thus being nothing more than a enthno-chrono-centric
> viewpoint. The use of Limits allow certain structural
> possibilities and it is these structures that make limits
> appealing.

Kraig!

Show me where it says that the Persians, Greeks and Novarro
called their systems 'just-intonation' and I'll make exceptions
in their, and any other documentable ethno-chrono-centric,
cases.

I suspect that you will be able to prove to me that Novarro called
his system 'just', so his case would be very exceptional. But
I really doubt that there's any evidence that the more ancient
cultures used the term.

Of course they understood the concept, but I'm saying here that
the term 'just-intonation' has historical usages dating from no
earlier than medieval times in Europe, that can be respected, by
choosing another more generic term, when what you're talking
about is the more generic case. I think that's rational...
(pun fully intended)

So otherwise my point still stands.

If I'm wrong, and exemplars can be given of other uses of the
term 'just intonation', I would love to be corrected. It would
add a lot more interesting historical info to the definitions.
Margo, can you be of any help on this?

Remember, I called my complex, large-scale tuning system
'JustMusic', so I'm not totally disagreeing with you. I'm
really 'just' nit-picking.
(pun not intended there, but oh well...)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Monz!
Better yet show me where those who came up with five limit tunings believe that they were
the inventors of "Just intonation". No! They understood that their work was an extension of
the tuning practices that had already gone on applied to a different set of circumstances.
Show me any historical reference where these tuning referred to as any term not synonymous
with Just intonation. If you look at Partch's book he refers to all these as Just intonation
scales, same with Lou Harrison. La Monte Young i believe with not object to his music being
referred to as Just intonation. All these individuals are using the term as it has been used
historically. To suggest that if I use the 37 harmonic that it is no longer Just intonation is
rather limited. Call up La Monte and tell him we doesn't use JI and He would probably wonder
what it is you are talking about.
There is no historical evidence that JI stops at 11 and 13. In fact if you want to be
so strict, we could say that 7 is the historical limit and all 7 limit music is not in Just
intonation.
outside of those on this list, I know of anywhere else where the definition is so restrictive.

Monz wrote:

> Kraig!
>
> Show me where it says that the Persians, Greeks and Novarro
> called their systems 'just-intonation' and I'll make exceptions
> in their, and any other documentable ethno-chrono-centric,
> cases.
>
> I suspect that you will be able to prove to me that Novarro called
> his system 'just', so his case would be very exceptional. But
> I really doubt that there's any evidence that the more ancient
> cultures used the term.
>
> Of course they understood the concept, but I'm saying here that
> the term 'just-intonation' has historical usages dating from no
> earlier than medieval times in Europe, that can be respected, by
> choosing another more generic term, when what you're talking
> about is the more generic case. I think that's rational...
> (pun fully intended)
>
> So otherwise my point still stands.
>
> If I'm wrong, and exemplars can be given of other uses of the
> term 'just intonation', I would love to be corrected. It would
> add a lot more interesting historical info to the definitions.
> Margo, can you be of any help on this?
>
> Remember, I called my complex, large-scale tuning system
> 'JustMusic', so I'm not totally disagreeing with you. I'm
> really 'just' nit-picking.
> (pun not intended there, but oh well...)
>
> -monz
> http://www.ixpres.com/interval/monzo/homepage.html
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Joseph!
of course! what else would it be called!

Joseph Pehrson wrote:

> Continuing this discussion just a little bit... it is true then that
> musicians like La Monte Young who use ratios comprised of very high
> integers believe they are composing in just intonation (??)

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

>>>>> "Kraig" == Kraig Grady <kraiggrady@anaphoria.com> writes:

Kraig> Joseph!
Kraig> of course! what else would it be called!

Kraig> Joseph Pehrson wrote:

>> Continuing this discussion just a little bit... it is true then that
>> musicians like La Monte Young who use ratios comprised of very high
>> integers believe they are composing in just intonation (??)

Recall the theorem that there is a rational approximation to any
non-rational with arbitrary accuracy, the rather suggests that within
the limits of hearing, everything is JI. Surely there is something
wrong here!

==John ffitch

>>>>> "Kraig" == Kraig Grady <kraiggrady@anaphoria.com> writes:

Kraig> Joseph!
Kraig> of course! what else would it be called!

Kraig> Joseph Pehrson wrote:

>> Continuing this discussion just a little bit... it is true then that
>> musicians like La Monte Young who use ratios comprised of very high
>> integers believe they are composing in just intonation (??)

Recall the theorem that there is a rational approximation to any
non-rational with arbitrary accuracy, the rather suggests that within
the limits of hearing, everything is JI. Surely there is something
wrong here!

==John ffitch

--- In tuning@egroups.com, J.P.FFITCH@M... wrote:

http://www.egroups.com/message/tuning/12962

> >>>>> "Kraig" == Kraig Grady <kraiggrady@a...> writes:
>
> Kraig> Joseph!
> Kraig> of course! what else would it be called!
>
> Kraig> Joseph Pehrson wrote:
>
> >> Continuing this discussion just a little bit... it is true then
that musicians like La Monte Young who use ratios comprised of very
high integers believe they are composing in just intonation (??)
>
> Recall the theorem that there is a rational approximation to any
> non-rational with arbitrary accuracy, the rather suggests that
within the limits of hearing, everything is JI. Surely there is
something wrong here!
>
> ==John ffitch

hEllO mR ffitch!

Well, that's exactly what I was thinking. However, Kraig Grady did
not feel similarly... in fact, he felt *SO* unsimilarly that he is
now off this list over this one point! He wants any rational
fractions called "Just Intonation' and I believe David Beardsley
agrees with this....

However, due to the approximations of these large fractions to
"irrational" numbers (actually, to my understanding, it is generally
the other way around..) some list members feel that this takes any
meaning from the term "Just Intonation."

Margo Schulter defined it thoroughly, back in

http://www.egroups.com/message/tuning/12459

Her posts, for me, seem the "intelligent final word" on this topic...
but the topic is, apparently, so incendiary that I prefer to have "no
opinion" and stand safely in the middle of the street....
_____________ ____ __ __ _ _
Joseph Pehrson

Joseph,

I think it is the method of pitch derivation that provides the best
and most accepted definition. If one uses Ratios to derive scale
pitches, then generally speaking - this is Just Intonation. Where one
might derive them using an irrational method - no matter how close
they come to Just, then it is still an irrational method of scale
construction.

I think more of the reason that we have the truly unfortunate loss of
Kraig Grady on this list has more to do with curt replies on this
topic - as it has been my perception that there is a seeming latent
hostility to JI practice on this list in general. It has been kind of
surprising to me to say the least. It is unfortunate that many want
to see this wonderful musical practice through the eyes and ears of
temperaments, and a 12 tET preconceptions of how a musical system
must behave. It's just not the same! As I've recently said - IMHO -
any tuning system has it's attributes, and it is foolhearty to
entertain the idea that any of them should act like the others do. It
is here that I would like to recommend that we all show mutual
respect for those that have musical paradigms different than our own.
Otherwise, we will probably see more turning away of vital
participants on this list. I mean how long is anyone going to do
something if it's not fun and mutually beneficial/respectful to all
involved? As I mentioned to another fellow lister today, I have made
an effort to hear and enjoy ALL of the music and musical concepts
that are put forth by our big happy family. In my mind we've all got
something to contribute - and is it really so all fired important to
always be right? Can't we agree to disagree on somethings, in order
to keep peace and show the much need respect for others that would
provide us with much needed unity here? I look at this as an
opportunity for a brotherhood and sisterhood of microtonal folks,
much more than an a forum for seeing who can win in a game of "one-
upmanship". Since it is my nature to forgive and forget, it is my
sincere hope that we can have Kraig to return to this list - we need
and benefit from everyone, no matter if they are Rational or
Earrational.

Sincerely,

Jacky Ligon

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
> > >>>>> "Kraig" == Kraig Grady <kraiggrady@a...> writes:
> >
> > Kraig> Joseph!
> > Kraig> of course! what else would it be called!
> >
> >
> > Recall the theorem that there is a rational approximation to any
> > non-rational with arbitrary accuracy, the rather suggests that
> within the limits of hearing, everything is JI. Surely there is
> something wrong here!
> >
> > ==John ffitch
>
> Well, that's exactly what I was thinking. However, Kraig Grady did
> not feel similarly... in fact, he felt *SO* unsimilarly that he is
> now off this list over this one point! He wants any rational
> fractions called "Just Intonation' and I believe David Beardsley
> agrees with this....
>
> However, due to the approximations of these large fractions to
> "irrational" numbers (actually, to my understanding, it is
generally
> the other way around..) some list members feel that this takes any
> meaning from the term "Just Intonation."
>
> Margo Schulter defined it thoroughly, back in
>
> http://www.egroups.com/message/tuning/12459
>
> Her posts, for me, seem the "intelligent final word" on this
topic...
> but the topic is, apparently, so incendiary that I prefer to
have "no
> opinion" and stand safely in the middle of the street....
> _____________ ____ __ __ _ _
> Joseph Pehrson

--- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...> wrote:
> Joseph,
>
> I think it is the method of pitch derivation that provides the best
> and most accepted definition. If one uses Ratios to derive scale
> pitches, then generally speaking - this is Just Intonation. Where
one might derive them using an irrational method - no matter how
close they come to Just, then it is still an irrational method of
scale construction.
>

Hi Jacky!

Well, this would certainly be a practical explanation, and surely one
definition... certainly description of *your own* work. Of course,
it is quite different from the definition that Margo Schulter gave
about having to have at least *SOME* really small integers in order
to get the Just Intonation "effect..." Some others seem to agree with
this. (Paul E. for example)

> I think more of the reason that we have the truly unfortunate loss
of Kraig Grady on this list has more to do with curt replies on this
> topic - as it has been my perception that there is a seeming latent
> hostility to JI practice on this list in general. It has been kind
of surprising to me to say the least.

Man, Jacky, I really don't want to get into this hotbed-morass... but
it might be claimed by some that there exist "Just Intonation
Extremists" out there... (sometimes "in here??") and what you're
seeing is a reaction to that.

Did I say that?? No I did not. See, I did not say that and you can
quote me... (not)

I can surely tell that you are quite "open minded" about tuning. I
am as well. My mind has been totally open...

___________ _____ __ _
Joseph Pehrson