Re: The Prime Series (for Jacky Ligon)

Hello, there, Jacky Ligon and everyone.

Congratulations on your prime ratio article, which I agree opens a
view of stars. As another exponent of rational intonation (RI) as a
very creative approach to tuning and music, I would like not only to
applaud your paper and some of the properties you are finding in large
integer ratios (prime and otherwise), but to address what may be some
possible misunderstandings about RI and its relationship to other
approaches, including traditional "low-integer" JI and various kinds
of irrational temperaments.

First, RI is not in my view intended as a substitute for intimate
familiarity with the intonational spectrum, but rather as one means of
exploring that spectrum. When I see that a given integer ratio is
slightly larger than 706 cents, I automatically as it were place it
somewhere between 17-tET and 39-tET, for example. The ratio takes on
meaning both from its integer associations, which might evoke various
complementary ratios in a tuning scheme, and from its place on the
spectrum.

Secondly, I would consider RI "valley/plateau-neutral": it may be used
either closely to approximate simple and discretely audible JI ratios,
or very intentionally to seek complex plateaus of a kind also sought
by devices such as the Noble Mediant; thank you, Jacky, for your
enthusiastic interest in this concept.

Third, I would certainly not consider RI a replacement for any other
kind of tuning system or philosophy, just another approach with a
potential for enriching our view of all the others. I find that pure
Pythagorean JI/RI, adaptive neo-Gothic JI for ratios of 2-3-7 of the
kind I'm discussing here, regular temperaments, well-temperaments, and
some very interesting RI systems (circulating or non-circulating) all
have their place.

Fourth, I would suggest that some of the "controversies" involving
large integer ratios are matters of conceptual as well as musical
taste, and that viewpoint here can differ. Personally, my enthusiasm
for ratios such as 14:11 or 13:11 or 32:27 or 81:64 does not depend on
their discreet audibility; they are a part of my musical tradition,
and I embrace them, without claiming any "superiority" to other
approaches and traditions.

Fifth, I find that RI is a fine art which can increase my familiarity
with simple as well as complex ratios, and help me to get to know the
spectrum better. Ratios can serve as names for interesting places and
reference points on the continuum of tunings and temperaments.

Sixth, I find that my encounters with RI can lead to a curious form of
"well-tuning" or maybe "fine-tuning" resembling a well-temperament in
seeking some scheme combining a near-even division of the octave with
some creative asymmetries -- and also, often, a number of audibly pure
JI ratios. It is kind of like doing JI and temperament at the same
time, and the kind of judgments required can test one's feel for both
approaches.

Seventh, I would urge that a pluralistic RI approach not be confused
with the kind of unfortunate viewpoint which takes a given number,
prime factor, or mathematical property, and presents it as the one
valid solution to tuning. If RI was presented as a solution "instead
of...," I would dissent; as a solution "in addition to...," I applaud
it.

To me, large integer ratios have a special poetry, and thank you,
Jacky, for your creative ideas in these and related areas, and
especially your championship of complex ratios and intervals as a very
important part of the art of music and intonation.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, Jacky Ligon and everyone.
>
> Congratulations on your prime ratio article, which I agree opens a
> view of stars. As another exponent of rational intonation (RI) as a
> very creative approach to tuning and music, I would like not only to
> applaud your paper and some of the properties you are finding in
large
> integer ratios (prime and otherwise), but to address what may be
some
> possible misunderstandings about RI and its relationship to other
> approaches, including traditional "low-integer" JI and various kinds
> of irrational temperaments.

Margo and others who have shown enthusiasm,

Thank you for your kind comments about this topic! What I have been
seeing, is that it is indeed very important to consider what we see
in the language of the higher primes - and especially the prime
series ratios. There are some very curious, and incredibly compelling
properties to be found here; those which reveal a kind of geometrical
relationship to all lower ratios. It provides yet another wonderful
and valid method of measurement of the pitch continuum.

Part of the fun for me, is that it seems to not be "in vogue", as
I've gotten the most positive responses about this from seasoned
RI/JI composers, such as yourself, and Kraig Grady.

(What's happened to that old "Prime Warrior" Joe Monzo? Worn from
battling alone perhaps?)

>
> First, RI is not in my view intended as a substitute for intimate
> familiarity with the intonational spectrum, but rather as one means
of
> exploring that spectrum. When I see that a given integer ratio is
> slightly larger than 706 cents, I automatically as it were place it
> somewhere between 17-tET and 39-tET, for example. The ratio takes on
> meaning both from its integer associations, which might evoke
various
> complementary ratios in a tuning scheme, and from its place on the
> spectrum.

As time goes on, I am experiencing a deepening appreciation of
looking at tuning systems from these many different methods of
measurement, and see value in all, with regard to the power it gives
one to communicate in the many "popular" tuning languages of today.

You will notice on this list, that we commonly compare intervals two
ways; either with low integer ratios, or equal temperaments. All that
I might humbly try to contribute, is to expand our view, with
the "short hand" to complexity, that is provided by the Prime Series
Ratios. I did not reveal its most elegant property in my paper.

>
> Secondly, I would consider RI "valley/plateau-neutral": it may be
used
> either closely to approximate simple and discretely audible JI
ratios,
> or very intentionally to seek complex plateaus of a kind also sought
> by devices such as the Noble Mediant; thank you, Jacky, for your
> enthusiastic interest in this concept.

Here I must thank first Paul Erlich for guiding me to the Noble
Mediant article, then you and Dave Keenan for opening a new world to
me. And also a new flower that has grown forth from Belgium: Peter
Mulkers. But I have also learned mightily from John Chalmers, Kraig
Grady and Erv Wilson's articles. (The wonders of the internet in
action!) I would site this as one of the most important things I've
learned from my interactions here, which has *huge* implications for
all future tuning efforts.

Peter Mulkers, along with Erv Wilson, are two folks that I'm aware
of, that have taken this to the greatest extremes, by methodically
mapping side-by-side the mediant spectrums.

>
> Third, I would certainly not consider RI a replacement for any other
> kind of tuning system or philosophy, just another approach with a
> potential for enriching our view of all the others. I find that pure
> Pythagorean JI/RI, adaptive neo-Gothic JI for ratios of 2-3-7 of the
> kind I'm discussing here, regular temperaments, well-temperaments,
and
> some very interesting RI systems (circulating or non-circulating)
all
> have their place.

This is brilliance in its purest unadulterated form! And I also find
value in understanding and making use of comparative analysis of
tunings. With all the means at our disposal to "puree" the octave,
each one gives us yet another valid way to measure the pitch
continuum. As we all know there are many ways to the same places,
and one must harness those best for your musical/theoretical
purposes.

>
> Fourth, I would suggest that some of the "controversies" involving
> large integer ratios are matters of conceptual as well as musical
> taste, and that viewpoint here can differ. Personally, my enthusiasm
> for ratios such as 14:11 or 13:11 or 32:27 or 81:64 does not depend
on
> their discreet audibility; they are a part of my musical tradition,
> and I embrace them, without claiming any "superiority" to other
> approaches and traditions.

I would agree here. It has been an important realization of late,
that our arcane ideas about the audibility of odd and prime limits,
and a preference for only the lower number ratios, actually can block
our view of the musical wonders which lie in the higher primes. There
are so many valid reasons why we can, and must go to higher primes,
and whether or not they will be possibly perceived as lower number
ratios or not, becomes a completely unusable reference point. We
should not worry at all, that with the inclusion of higher primes in
a tuning system, that they should always have "discreet audibility".
This is something that IMHO, represents a kind of
intellectual/musical paralysis to the RI/JI composer. When we leave
this old concept behind - freedom is what we find!

Concepts of "Odd and Prime Limits" are only good for *general*
descriptions at best, when we look to expand the RI palette. Whether
they are perceptible after a certain point, is irrelevant to me at
this point. No bold claims about odd and prime will be heard from my
quarter.

>
> Fifth, I find that RI is a fine art which can increase my
familiarity
> with simple as well as complex ratios, and help me to get to know
the
> spectrum better. Ratios can serve as names for interesting places
and
> reference points on the continuum of tunings and temperaments.

Absolutely!!! One atomic level observation here, is that higher
prime ratios always display a mathematical interconnectedness to the
lower and visa versa. And it just gives us another valid way to look
at things.

>
> Sixth, I find that my encounters with RI can lead to a curious form
of
> "well-tuning" or maybe "fine-tuning" resembling a well-temperament
in
> seeking some scheme combining a near-even division of the octave
with
> some creative asymmetries -- and also, often, a number of audibly
pure
> JI ratios. It is kind of like doing JI and temperament at the same
> time, and the kind of judgments required can test one's feel for
both
> approaches.

And to me, you have struck the mother-lode of gold, and reason of why
it is so crucial to embrace the spectrum of ratios outside the lower
primes.

>
> Seventh, I would urge that a pluralistic RI approach not be confused
> with the kind of unfortunate viewpoint which takes a given number,
> prime factor, or mathematical property, and presents it as the one
> valid solution to tuning. If RI was presented as a solution "instead
> of...," I would dissent; as a solution "in addition to...," I
applaud
> it.

Agreed! There are so many beautiful and meaningful ways to tune and
make music. This is the most important thing for me, as I enjoy
appreciating them all. I should point out that I'm not necessarily
fixated with ratio derived tunings alone - but may be about
microtonality in general. I have made music with many *popular* ETs,
but also "JI/RI", "NJNE", "Non-Octave JI", "Non-Octave Spectrum
Scales", BP, Constant Scales, MOS, etc - I actively seek to know what
these tunings *SOUND LIKE* so that I may best understand them and
make music with the properties found in each. I will never be
prepared to settle on just one thing, as I find it just way too
constraining for achieving greater levels of tuning comprehension - a
life's work.

>
> To me, large integer ratios have a special poetry, and thank you,
> Jacky, for your creative ideas in these and related areas, and
> especially your championship of complex ratios and intervals as a
very
> important part of the art of music and intonation.

As always, it is most refreshing to get the quality of positive input
from someone such as yourself, so eloquent in the language of the
ratios.

Thanks kindly,

Jacky Ligon