Reply to Jacky re: Pelog

--- In MakeMicroMusic@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
> --- In MakeMicroMusic@y..., "paulerlich" <paul@s...> wrote:
> > I hope to present a "tuning-math Pelog" musical example for you
> > relatively soon.
>
> Eargerly awaiting!
>
> JL
>
> P.S. Point me to some posts about this here tuning - sounds
> interesting. You know I loves some Pelog and Slendros.

Well, rather than force you to trudge through some rather technical
tuning-math posts, let me summarize the result in this way:

(NOTE: LARGE AMOUNT OF THEORY BELOW. PLEASE FORGIVE ME BUT I WOULD
REALLY LIKE TO COMMUNICATE THIS TO JACKY AND PERHAPS OTHERS WILL BE
INTERESTED)

Tuning in Western tonal music basically all comes down to eliminating
the interval 81:80. This alone unambiguously _defines_ meantone
tuning, implies the diatonic scale and Western notation. Similarly,
Pelog can be seen as being unambiguously defined by the elimination
of the 135:128. Just as Woolhouse in 1835 found that the optimal
meantone tuning has a generator of about 696 cents, similarly it can
be shown that the "optimal Pelog tuning" has a generator of about 677
cents. (If the octave is included in the optimization, an overall
stretch of 15 cents per octave can be implicated.) Retuning a
keyboard to a chain of 677 cent, instead of 700 cent, fifths, using
an open inharmonic timbre with a clear sense of pitch, and a non-
sustaining envelope, one can evoke a rather authentic Balinese
atmosphere by playing several simultaneous melodies in what look like
normal pentatonic scales like C-D-E-G-A and perhaps a few simple
modulations by fifths.

What happens when you generate a scale with 677 cent fifths?
Basically, you get "minor thirds" everywhere you expect to get "major
thirds", and vice versa! It sort of takes the usual Western
intervallic relationships and turns them upside-down.

It seems pretty clear to me that the details of the inharmonic timbre
are far less important for evoking the authentic Pelog effect. If a
timbre is used with too much energy in the lower overtones, though,
the 677-cent fifths will sound quite dissonant, unless the timbre is
made to match the tuning. But this does not result in an authentic-
sounding Balinese texture, by any means. The authentic Balinese sound
seems to cultivate beating, rather than trying to eliminate it. As
long as the timbres evoke a clear pitch without too much energy in
the lower overtones, my harmonic entropy model would seem to dictate
that 677 cents will be perceived as a 3:2 ratio, and thus act as a
strong interval in the music.

One may object that actual observed Pelog tunings seem to be chains
of fifths ranging from as low as 650 cents to as high as 700 cents,
rather than uniformly using fifths of 677 cents. Since the timbres
are rather "pastelized", as Margo puts it, such changes do not make
nearly as noticeable a difference as changes of this order of
magnitude would make with typical Western harmonic timbres. The
salient point though is, as long as the fifths _average_ about 677
cents, you will get "minor thirds" everywhere a Westerner expects to
get "major thirds", and vice versa. This feature is equivalent to the
statement that the elimination of the 135:128 _defines_ Pelog tuning,
just as the elimination of the 81:80 defines Western diatonic scales,
which are also found in varying (albeit with their lesser degree of
latitude due to the timbres) tunings historically and geographically.

The first person I know of to have observed that Pelog tuning seems
to be defined by the elimination of 135:128, just as Western tuning
has been defined by the elimination of 81:80, is Herman Miller. He
has made a great deal of very enjoyable music drawing inspiration
from various ethnic musics from around the world. It was most
heartening that, in our comprehensive investigation on tuning-math of
commas and the tunings they define, we found that the simplest 5-
limit tunings without exceedingly large errors were those defined by
the commas 81:80 and 135:128, respectively. When I saw that the
generator implied by the commatization of 135:128 was about 677
cents, I was immediately reminded of Herman Miller and his
Pelog "discovery".

Slendro may be understood as a temperament involving the primes 2, 3
and 7, instead of 2, 3 and 5. The defining comma could be said to be
1029:1024. As this interval is listed in Manuel's table as
the "Gamelan residue", this insight may at least partly be a rather
old one in the tuning literature. However, the tuning so defined has
rather small errors compared with JI, as opposed to Pelog's rather
large errors. Also I have much less listening experience with
authentic Slendro examples than with Pelog examples. Hence the
identification of Slendro with the 1029:1024-based temperament seems
much more speculative to me at this point, and I would not rule out
other explanations, such as a 3-limit tuning with 256:243 eliminated,
at this point.

--- In MakeMicroMusic@y..., "jacky_ligon" <jacky_ligon@y...> wrote:

> Paul,
>
> Looks neat! Don't get what you are saying about the 1215 cents wide
> octave though.

Well, this is sort of "optional" . . . everything else in my post
sort of assumed just octaves (what the Indonesians call "pleng"). But
it is quite possible to calculate the optimization allowing for the
octave to be tempered as well as all the other 5-limit
consonances . . . exactly how one does this can affect the results.

> Do you just make 1215 your IoE???

The generating fifth tends to get stretched too, brought closer to
just . . . so for example you could simply multiply all the cents
values of the "pleng" scale by 1.0125, and hence use a 1215-cent IoE.
There's certainly a lot of room for independently adjusting both
the "fifth" and the "octave" without greatly disturbing
the "optimality" of the tuning -- it's at a rather "wide" local
minimum.

> I'm a fan of Herman Miller's music. Is he still around in the
> internet tuning world? Haven't heard a thing out of him for a
while.
> Know if he's got any new tunes? Let's hear'em Herman - if you are
out
> there in internet land!
>
> Has anyone written any music with this here tuning yet? Lay it on
me!

Perhaps Herman has. I've done a lot of keyboard improvisation with
it, but my keyboard chops are positively rusty right now, and the
Ensoniq timbres are generally a little less than presentable. I set
the tuning up for my keyboardist collaborator Ara Sarkissian, using
Graham's MIDI Relay (just change the meantone fifth to 677 cents),
described to him the basic stylistic and scalar strategy, and pretty
soon a mind-bending modulatory masterwork was emerging. He's leaving
tomorrow for a few weeks in Lebanon (for a friend's wedding), but
when he returns, I'll make it a top priority to get something
recorded . . . there's a bit of a problem now with the decays of the
notes "bending" slightly . . . it seems Ara's Soundblaster card isn't
exactly liking what MIDI Relay is doing . . .