source file: m1392.txt
Date: Wed, 22 Apr 1998 08:47:46 -0700

Subject: Re: TUNING digest 1391

From: csz@wco.com (Carter Scholz)

Dan,

Your thoughts on pelog make fascinating reading.  I hope to
read your whole article when you've finished revising it.
A few further thoughts:

>In the central Javanese palace instruments
>(cf the Gadja Mada study), this average is
>indeed around 665 cents. However, since so many modern
>instruments copy the RRI Solo tuning, with essentially
>a slendro kempyang ('fifth') of 721 cents, we may being
>witnessing one way in which a tuning trend develops.

That's interesting.  I didn't know that the RRI instruments
had become such a model.  I wonder why?  (Not just the power of
mass media, I hope.)

<Are you looking specifically for small-number ratios?
>No, but if someone does come up with a just solution
>(I lean toward the view that these tunings are kinds
>of 'well temperaments'), I would be _very_ interested
>in hearing it.

Dan Schmidt's pelog comes close.  It's a section of a harmonic
series from 8 (pelog 6) to 15 (pelog 5), omitting 13.  It violates
your condition (7), but if you lower pitch 2, I think it satisfies
them all:
1/1  16/15  6/5  7/5  3/2  8/5  9/5  2/1
(This tuning is tumbuk 6 with P4=S5, by the way.)

<To guarantee a functional pelog, I wonder if you
<might also need to constrain the 6-7 interval
<(already >80 cents, but usually a good deal
<larger), and possibly the 3-4 (usually at least
<twice as large as 4-5).
>These are already satisfied by setting 1-3 and 1-5.

I don't see this.  It appears to me that you could have an 80-cent
6-7 that satisfies all your conditions, and a 3-4 that equals 4-5.
E.g. (in cents): 0  100  300  500  700  850  930  1200
Am I missing something?

Carter