Happy Holidays, Pierre and Paul -- thank you!

Hello, there Paul and Pierre and everyone.

Please let me thank you both for your beautiful graphics, and comment
briefly both on your "pelog-style pentatonic" diagram with intervals
show as just ratios and in 36-tET, Pierre; and on your diagrams, Paul,
of harmonic entropy curves in margo2.gif and margo3.gif.

First, I'd like to emphasize that in describing my just pentatonic as
a "pelog-style" tuning, I was following my own very general or
"categorical" concept of pelog as "a pentatonic scale with semitones
and major thirds," something that might also apply to similar Japanese
scales. On looking at the Scala archives, and encountering Harrison's
near-identical tuning, I went with the Scala label, "pelog-style
pentatonic."

However, before complimenting you, Pierre, on your beautiful diagram,
I should agree with an important point you make, Paul, and which could
apply to many "adaptations" or "variations" on traditional tuning
systems of various cultures.

While I can't speak for Harrison or others who have taken the gamelan
form and adapted it to a range of intonational systems and cultural
settings, I can confirm that my quick survey of the Scala archives
indeed revealed no Javanese or Balinese pelog that I could find with
semitones narrower than 100 cents. I might consider something like 133
cents in 9-tET, or 36-tET for that matter, more typical.

Thus my own outlook, really shaped by a bit of listening to
traditional gamelan and Japanese music around the early 1970's, was
quite generic: "How about a `semitone/major third' kind of pentatonic
with ratios like 28:27, 7:6, and 9:7?" I'm not sure if Harrison took
the same kind of path, but that's how I got there.

Here I had some generic impression of a style of melody, which could
be applied to various kinds of intonational fabrics within certain
bounds of categorical perception. For example, I can take either 63
cents or 133 cents as a "semitone," and either 267 cents or 331 cents
as a kind of "minor third" or the like.

These categorical impressions may say at least as much about my own
cultural and musical background as about traditional gamelan or
Japanese intonation in what I call "semitone/major third" scales.

In contrast, Paul, you took the tradition of 22 srutis as followed in
the raga system of India, and related it to 22-tET or a 22-note
well-temperament for decatonic music. This should not be taken to draw
an equation between the 22-sruti system as practiced in India and your
style of decatonic and tetradic tonality.

Just as you would not attribute a style based on stable 4:5:6:7
tetrads to the Indian tradition, so I would not wish to imply that
progressions by contrary motion from 7:9:12 to 2:3:4, which my
"pelog-style" scale happens to support on the second degree, are
practiced in the Javanese or Balinese tradition.

Also, when I describe "Phrygian-like" or "Lydian-like" modes in my
scale, I am taking a medieval or Renaissance European perspective on
the melodic qualities of these modes (associated with larger diatonic
heptatonic sets), rather than a traditional pelog-oriented view (where
the full tuning actually has seven notes, as I understand, with five
of them forming what I hear as a "pentatonic scale").

Anyway, Pierre, I love your diagram: the different geometric shapes
showing what I might read as different modes for the just intervals,
and also the very engaging graphic of the 36-tET steps. Joe Pehrson,
if you're reading this, I'd say that this is one type of tuning where
36-tET gives a superb approximation, and along with the just tuning
and a couple of other tempered ones it's among my favorites.

Paul, while I might not have noted all the fine points distinguishing
margo2.gif from margo3.gif, maybe from a certain artistic point of
view these graphics reflect two different musical outlooks as well as
mathematical models.

In margo2.gif, the peaks and valleys look more nuanced or "gentle,"
with major and minor valleys more similarly proportioned; in
margo3.gif, a number of ratios are dramatically "deeper" in their
valleys than others.

Maybe I tend to lean more to the first approach, especially in a
neo-Gothic setting, approaching a bit nearer the second in a typical
Renaissance style in a harmonic timbre where meantone is the
historical norm.

Could it be that since the primary concords in neo-Gothic tend to be
1:1, 3:2, and 2:1 -- with 4:3 as the complement of 3:2 -- almost
everything else can be "nuanced" or "negotiable." Yes, I know you
might reply that evidently in 13-tET, 3:2 and 4:3 can also be
"nuanced" considerably <grin> -- although here the timbre might result
in a different curve, something interesting to study on the basis of
the actual timbres I use for this temperament.

Anyway, as a very friendly holiday present, I'd say that your diagrams
do show a lot of empathy for the way I tend to view things. However
they might reflect the likeliest models of harmonic entropy, which I
understand is an approach yet being developed, they might serve as a
most congenial map for my vision of the continuum.

Thank you both for your artistry, sharing of ideas, and generosity in
such a season among such a community.

Most appreciatively, with seasons tidings to all,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_31912.html#31912

>
> Anyway, Pierre, I love your diagram: the different geometric shapes
> showing what I might read as different modes for the just intervals,
> and also the very engaging graphic of the 36-tET steps. Joe Pehrson,
> if you're reading this, I'd say that this is one type of tuning
where
> 36-tET gives a superb approximation, and along with the just tuning
> and a couple of other tempered ones it's among my favorites.
>

Thank you very much for your reference to this, Margo, and Happy New
Year to you!

Anytime anything divides into 72, I'm bound to take notice of it
these days!

However, would somebody please mind translating Pierre's scale into
72-tET notation for me?

I would do it myself, but I happen to be "out of town" at the present
time... or at least that's as good an excuse as I can think of at the
moment...

Thanks again!

Joe Pehrson