Two striking slendro tunings -- Scala archive

Hello, Mike and Keenan and all.

Some recent discussions about slendro and pelog led me to a
couple of "different" slendro tunings in the Scala archive which
may illustrate the range of variations in Javanese and Balinese
tunings. Of course, this may be of special interest to those
looking for slendro subsets in larger tuning systems, regular or
otherwise.

As you discussed, Keenan, one familiar model of slendro is a kind
of rather subtly irregular variation on 5-ED2 where each
three-step interval -- or 3d5 as George Secor might say -- can
serve as a "~3/2" for free transposibility. Many slendro tunings
in Bali, and maybe especially in Java accounting to one source,
do agree more or less with this kind of model.

Bill Alves, for example, in an outstanding article on JI gamelan
variations from his perspective as a composer, notes that his
septimal slendro with steps of 1/1-8/7-4/3-14/9-16/9-2/1 had a
tone at 9/8, narrower than any step in one survey of slendro
tunings he had seen (minimum 214 cents). And he noted that in
these tunings, "few steps were as large as a 7/6."

<http://www2.hmc.edu/~alves/pleng.html>

Alves found that an Indonesian gamelan maker named Suhirdjan took
no special note of "the greater variation in step size in my
tuning" with its 7/6 and 9/8 steps, but did find the tuning
unusual in being _pleng_, i.e. with "beatless octaves."

One term for the kind of slendro where variations are subtle
might be "equable pentatonic." However, a quick survey of
Indonesian slendro tunings listed in the Scala archive shows that
some of these tunings can be more equable than others.

In one Javanese book on gamelan music translated into English, I
recall a statement indicating that the "each three-step interval
a ~3/2" concept may be open to exceptions, or at least
qualifications.

To put this discussion in more of a Balinese or Javanese
perspective, we'll find a simple concept very helpful:
_kempyung_.

The term _kempyung_ often refers to an interval of three scale
steps or, as we might say, Secor's 3d5 -- counting inclusively,
we could call it a "pentatonic fourth." From the Indonesian book
in translation I recall that _kempyung_ was defined as
theoretically 3/2, but in practice often varying somewhat from
this. And the structure of slendro was explained as in theory
something like 5-ED2, but in practice again varying somewhat,
with a helpful sampling of tunings in cents offered to give some
sense of this variation. (At times, _kempyung_ can also refer to
a consonance of 2d5, or, in European terms, a "fourth.")

And in the often intricate counterpoint of gamelan, kempyung,
along with the octave, is the principal consonance and point of
repose, a meeting place for the often divergent melodic lines of
the texture.

Now the comment that may be especially relevant here is that in
practice, not every location necessarily has a good expression of
kempyung -- that is, as we might say, not every three-step
interval in slendro will be perceived as "~3/2."

Here's one Scala tuning to illustrate this point:

! slendro10.scl
!
Low gender from Singaraja (banjar Lod Peken), Bali, 1/1=172 Hz, McPhee, 1966
5
!
261.10972
465.01972
698.59664
991.68081
2/1

Here on the ~3/2 step we have a "kempyung" at around 762.5 cents,
close to 14/9, and likely perceived as something other than a
"3/2" type. Also, if we take the reported 2/1 step as accurate,
then we have an upper tone at 208.3 cents, or around 44/39. But
additionally there's the 261-465 cent step, a just 9/8 of the
kind that Bill Alves was concerned might not be so idiomatic!

Before sharing an emulation of this slendro that I found in the
MET-24 tuning, I should note a traditional view that it is, at
least, bad etiquette deliberately to copy the tuning of a
specific gamelan -- indeed, once a prohibited practice in regard
to court ensembles, for example. So I consider a bit of
divergence a plus: the ideal is that each gamelan should have its
own distinct sound.

! met24-slendro10-var_C.scl
!
Variation on slendro10.scl
5
!
264.84375
472.26563
704.29688
992.57813
2/1

Note how this tuning system bends things a bit toward the kind of
septimal JI that Alves and Lou Harrison, Jacques Dudon, and
others have explored. The tuning is also very much like Erv
Wilson's 1-3-7-9 hexany, except that we have a 39/22 or 16/9 in
place of 7/4 (leaving out the 9/8 step of the hexany).

Here's another slendro tuning from the Scala archive which might
be considered even more colorful in its contrasts:

! slendrob1.scl
!
Gamelan miring of Musadikrama, desa Katur, Bajanegara. 1/1=434 Hz
5
!
279.363 cents
531.624 cents
777.408 cents
1039.179 cents
2/1

The instances of kempyung vary in size over a range of more than
100 cents, from 668.4 to 777.4 cents! And the intervals at 759.8
and 777.4 cents might well illustrate that remark in the
collection of translated Indonesian writings that nor every instance
of kempyung will necessarily have what we might call a ~3/2
quality.

Also, the step leading up to the octave is only around 161 cents,
something we might more likely expect to find in an equable
heptatonic tuning of the kind common in Thailand and also in
Africa, for example in the famed music of the Chopi people, with
the meta-Mavila and assorted Mavila temperament schemes an
attempt to capture some of the flavor of the original tunings.
The very wide 531.6-cent fourth is often characteristic of pelog.
(Both pelog and equable heptatonic systems have wide fourths,
which may lead to their confusion; as I learned myself on this
list, pelog does not resemble 7-ED2, a point also made in the
text of modenam.par, one of the files that comes with Scala.)

Of course, this may not be the most typical slendro, but it's one
that caught my attention. Here's an emulation -- again, with
variations that I welcome following the tradition of gamelan --
in MET-24:

! met24-slendrob1-var_Ebup.scl
!
Variation on slendrob1.scl
5
!
275.39063
540.23438
772.26563
1037.10938
2/1

To me, a step at 1037 or 1039 cents might suggest a Turkish Segah
or Vietnamese Sa Mac rather than a Javanese slendro (a bit of
Googling indicates, if I'm right, that Bajanegara is in Java).
However, gamelan offers an immense variety!

Best,

Margo

Thanks for this interesting post, Margo.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
> Alves found that an Indonesian gamelan maker named Suhirdjan took
> no special note of "the greater variation in step size in my
> tuning" with its 7/6 and 9/8 steps, but did find the tuning
> unusual in being _pleng_, i.e. with "beatless octaves."

Yes, this definitely would be unusual.

> To put this discussion in more of a Balinese or Javanese
> perspective, we'll find a simple concept very helpful:
> _kempyung_.
>
> The term _kempyung_ often refers to an interval of three scale
> steps or, as we might say, Secor's 3d5 -- counting inclusively,
> we could call it a "pentatonic fourth." From the Indonesian book
> in translation I recall that _kempyung_ was defined as
> theoretically 3/2, but in practice often varying somewhat from
> this. And the structure of slendro was explained as in theory
> something like 5-ED2, but in practice again varying somewhat,
> with a helpful sampling of tunings in cents offered to give some
> sense of this variation. (At times, _kempyung_ can also refer to
> a consonance of 2d5, or, in European terms, a "fourth.")

There must be an interesting linguistic issue here. In Gamelan Sekar Jaya we always refer to this harmonization as "empat" or "ngempat", simply meaning "4" or "doing the 4ths thing". I have actually heard a word like "empyung" or "kempyung" used a couple of times, but never to refer to "empat" intervals - always to other unusual simultaneous intervals such as 2d5, or in jegog music, any simultaneous pair other than the single one that's common in jegog (tones 1 and 4).

> And in the often intricate counterpoint of gamelan, kempyung,
> along with the octave, is the principal consonance and point of
> repose, a meeting place for the often divergent melodic lines of
> the texture.

Most definitely.

> Now the comment that may be especially relevant here is that in
> practice, not every location necessarily has a good expression of
> kempyung -- that is, as we might say, not every three-step
> interval in slendro will be perceived as "~3/2."
>
> Here's one Scala tuning to illustrate this point:
>
> ! slendro10.scl
> !
> Low gender from Singaraja (banjar Lod Peken), Bali, 1/1=172 Hz, McPhee, 1966
> 5
> !
> 261.10972
> 465.01972
> 698.59664
> 991.68081
> 2/1
>
>
> Here on the ~3/2 step we have a "kempyung" at around 762.5 cents,
> close to 14/9, and likely perceived as something other than a
> "3/2" type.

Are you sure about this? If I play around with this scale with my "gamelan ears" on, that empat interval definitely has a different "flavor" than the others, but it still sounds like the same kind of animal - a wide 3/2. Of course, if I ignore the context and play the 762.5-cent interval by itself, the trained microtonalist in me says "that's clearly 14/9", but that's how usual gamelan listeners would perceive it.

There is also a serious problem with this Scala file, and the way you obtained that 762.5 cent figure. The first four pitches look like converted data from that McPhee paper (with too many significant figures, I note), but the last pitch, the period of the scale, is simply given as "2/1", which obviously isn't a product of any empirical measurement. Depending on what the octaves of these instruments actually were, that empat interval could have been different by more than a few cents.

> Before sharing an emulation of this slendro that I found in the
> MET-24 tuning, I should note a traditional view that it is, at
> least, bad etiquette deliberately to copy the tuning of a
> specific gamelan -- indeed, once a prohibited practice in regard
> to court ensembles, for example. So I consider a bit of
> divergence a plus: the ideal is that each gamelan should have its
> own distinct sound.

That's very interesting about the prohibition.

> Here's another slendro tuning from the Scala archive which might
> be considered even more colorful in its contrasts:
>
> ! slendrob1.scl
> !
> Gamelan miring of Musadikrama, desa Katur, Bajanegara. 1/1=434 Hz
> 5
> !
> 279.363 cents
> 531.624 cents
> 777.408 cents
> 1039.179 cents
> 2/1
>
> The instances of kempyung vary in size over a range of more than
> 100 cents, from 668.4 to 777.4 cents! And the intervals at 759.8
> and 777.4 cents might well illustrate that remark in the
> collection of translated Indonesian writings that nor every instance
> of kempyung will necessarily have what we might call a ~3/2
> quality.

Okay, in this case I readily admit that (accepting the 2/1 octave as close enough) some of the empat intervals sound nothing like 3/2 at all. This is a pretty weird slendro, but I can't say I dislike it.

One interesting thing I note about this scale is that the notes 777.408, 2/1, 279.363, and 531.624, in that order, sound just like the jegog scale! The jegog scale is sometimes explained as deriving from pelog (though it's probably from an independent tradition), so it's pretty trippy to be able to add one note to it and have an acceptable slendro.

> Also, the step leading up to the octave is only around 161 cents,
> something we might more likely expect to find in an equable
> heptatonic tuning of the kind common in Thailand and also in
> Africa, for example in the famed music of the Chopi people, with
> the meta-Mavila and assorted Mavila temperament schemes an
> attempt to capture some of the flavor of the original tunings.
> The very wide 531.6-cent fourth is often characteristic of pelog.
> (Both pelog and equable heptatonic systems have wide fourths,
> which may lead to their confusion; as I learned myself on this
> list, pelog does not resemble 7-ED2, a point also made in the
> text of modenam.par, one of the files that comes with Scala.)

Again, you're basing a lot of this on the 161 cent figure, which could only be obtained be subtracting 1039.179 cents from 1200 cents, the latter of which is not a measurement at all, but something arbitrarily put into a Scala file.

If the octave were 1240 cents (which *might* be unreasonably wide even for a gamelan tuning, but not completely out of the question), then the narrow interval you're talking about would in fact be more like 200 cents, and not so remarkable after all. It all depends on what the octaves of this tuning actually were, and this Scala file gives us no information about that.

Unusual as your slendro tunings are, I don't think any of them stand up to my favorite example of "slendro" - the genggong scale!

The genggong is a unique Balinese Jew's harp, and like all Jew's harps the sound is produced by using the vocal cavity to single out harmonic overtones of the vibrating tongue by resonance. Since they're *harmonic* overtones, we know *exactly* what the slendro pitches have to be!

! genggong.scl
!
Genggong polos scale, harmonics 5 through 9
5
!
6/5
7/5
8/5
9/5
2/1

When some innovative Balinese person many centuries ago first carved a tongue out of a piece of palm rib and heard this, he thought to himself "Cool! It plays slendro!". This just goes to show how flexible the concept of "slendro" is.

Actually, the way genggong is traditionally played is even more fascinating, because there are two instruments, polos and sangsih, which have different fundamentals. So different overtone numbers are used to play "the same" pitches. I'm not 100% sure what the specific scheme is (different performers might even do it different ways), but I think it's something like this:

polos ... sangsih
5 low ding
6 dong
7 ~ 8 deng
8 ~ 9 dung
9 ~ 10 dang
12 high ding

Keenan

> Thanks for this interesting post, Margo.

And thank you, Keenan, for a most educational post with lots of
performer's insights from which I and doubtless others can learn!

>> Alves found that an Indonesian gamelan maker named Suhirdjan
>> took no special note of "the greater variation in step size
>> in my tuning" with its 7/6 and 9/8 steps, but did find the
>> tuning unusual in being _pleng_, i.e. with "beatless
>> octaves."

> Yes, this definitely would be unusual.

And your warning about how Scala files or other data compiled by
people who take a "2/1" step for granted can give misleading
results on lots of other intervals is really important!

[on _kempyung_ as a term for a concord of 3d5, or in European
terms a "fifth"]

> There must be an interesting linguistic issue here. In Gamelan
> Sekar Jaya we always refer to this harmonization as "empat" or
> "ngempat", simply meaning "4" or "doing the 4ths thing". I
> have actually heard a word like "empyung" or "kempyung" used a
> couple of times, but never to refer to "empat" intervals -
> always to other unusual simultaneous intervals such as 2d5, or
> in jegog music, any simultaneous pair other than the single
> one that's common in jegog (tones 1 and 4).

This is very interesting, and suggests inclusive counting of
intervals (i.e. empat as a "pentatonic fourth")! One source on
the Web says that basically the Balinese use _empat_ for the
"4ths thing," while the Javanese use _kempyung_. It makes sense
to me that people who normally speak of empat might use kempyung
with a more special meaning. As you say, a "linguistic issue."

>> And in the often intricate counterpoint of gamelan, kempyung,
>> along with the octave, is the principal consonance and point of
>> repose, a meeting place for the often divergent melodic lines of
>> the texture.

> Most definitely.

In this regard there's a certain parallelism with 12th-14th
century European music -- and all kinds of differences, of course!

> Here's one Scala tuning to illustrate this point:
>
> ! slendro10.scl
> !
> Low gender from Singaraja (banjar Lod Peken), Bali, 1/1=172 Hz, McPhee, 1966
> 5
> !
> 261.10972
> 465.01972
> 698.59664
> 991.68081
> 2/1
>
>
> Here on the ~3/2 step we have a "kempyung" at around 762.5 cents,
> close to 14/9, and likely perceived as something other than a
> "3/2" type.

> Are you sure about this? If I play around with this scale with
> my "gamelan ears" on, that empat interval definitely has a
> different "flavor" than the others, but it still sounds like
> the same kind of animal - a wide 3/2. Of course, if I ignore
> the context and play the 762.5-cent interval by itself, the
> trained microtonalist in me says "that's clearly 14/9", but
> that's how usual gamelan listeners would perceive it.

Touche! This is exactly to the point, and is an area where one
pair of "gamelan ears" can be worth a thousand not-so-informed
guesses. And this leads to an interesting train of thought.

Maybe slendro does generally have what we might call a
"circulating" nature (e.g. step with an acceptable empat or
kempyung, depending on the Indonesian terminology in use), but
with a lot wider range for a recognizable "4th" (=European "5th")
than those of us not-so-experienced or when wearing a
"microtonalist" hat might assume!

And a disclaimer: I haven't tried the experiment of how I might
hear a near-14/9 (maybe in one of the septimal slendro tunings of
Bill Alves) on an actual gamelan during a performance! Even my
gamelan-loving but not-so-trained ears might take it as another
instance of empat.

> There is also a serious problem with this Scala file, and the
> way you obtained that 762.5 cent figure. The first four
> pitches look like converted data from that McPhee paper (with
> too many significant figures, I note), but the last pitch, the
> period of the scale, is simply given as "2/1", which obviously
> isn't a product of any empirical measurement. Depending on
> what the octaves of these instruments actually were, that
> empat interval could have been different by more than a few
> cents.

Absolutely true! My mistake was running in default mode, "This is
the Scala archive, and SHOW /LINE INTERVALS can't miss!" But, to
put it mildly, the rule of SISO (Skewed In, Skewed Out) is
something not even Manuel Op de Coul can avoid.

>> Before sharing an emulation of this slendro that I found in
>> the MET-24 tuning, I should note a traditional view that it
>> is, at least, bad etiquette deliberately to copy the tuning
>> of a specific gamelan -- indeed, once a prohibited practice
>> in regard to court ensembles, for example. So I consider a
>> bit of divergence a plus: the ideal is that each gamelan
>> should have its > own distinct sound.

> That's very interesting about the prohibition.

Your post later on raises the question of whether something like
genggong might be an exception, to the degree that the harmonics
define the tuning -- although if the octave is other than pleng
(2/1), or the harmonics stretched or compressed a bit, that might
involve customization.

> ! slendrob1.scl
> !
> Gamelan miring of Musadikrama, desa Katur, Bajanegara. 1/1=434 Hz
> 5
> !
> 279.363 cents
> 531.624 cents
> 777.408 cents
> 1039.179 cents
> 2/1

> The instances of kempyung vary in size over a range of more than
> 100 cents, from 668.4 to 777.4 cents! And the intervals at 759.8
> and 777.4 cents might well illustrate that remark in the
> collection of translated Indonesian writings that nor every instance
> of kempyung will necessarily have what we might call a ~3/2
> quality.

> Okay, in this case I readily admit that (accepting the 2/1 octave as close
> enough) some of the empat intervals sound nothing like 3/2 at all. This is a
> pretty weird slendro, but I can't say I dislike it.

It did look to me like maybe the exception that proves the rule.

> One interesting thing I note about this scale is that the
> notes 777.408, 2/1, 279.363, and 531.624, in that order, sound
> just like the jegog scale! The jegog scale is sometimes
> explained as deriving from pelog (though it's probably from an
> independent tradition), so it's pretty trippy to be able to
> add one note to it and have an acceptable slendro.

So this could be a kind of creative hybrid form?

> Also, the step leading up to the octave is only around 161 cents,

> Again, you're basing a lot of this on the 161 cent figure,
> which could only be obtained be subtracting 1039.179 cents
> from 1200 cents, the latter of which is not a measurement at
> all, but something arbitrarily put into a Scala file. If the
> octave were 1240 cents (which *might* be unreasonably wide
> even for a gamelan tuning, but not completely out of the
> question), then the narrow interval you're talking about would
> in fact be more like 200 cents, and not so remarkable after
> all. It all depends on what the octaves of this tuning
> actually were, and this Scala file gives us no information
> about that.

Yes, that default "2/1" can affect a lot of things. From one
study I read, something getting close to 1240 cents would be
likeliest in an ensemble seeking to be "flashy" or a bit
ostentatious; but 1215-1225 seems common, and in my own
not-so-informed attempts at gamelan-like music I might go up to
around a septimal comma. And I agree that while the sample of
tunings Alves saw had all the steps for slendro rather larger
than 9:8, steps in that area wouldn't be so surprising.

An idea for Manuel, with the credit going to you: just as Scala's
modenam.par now has a disclaimer that pelog is not close to
7-ED2, how about a caution that "2/1" in gamelan tuning files
should not be taken to imply that a traditional Javanese or
Balinese ensemble is actually using pure or beatless octaves!
And that ignoring this point means that the accuracy of other
intervals may vary -- a lot! I knew the first part of the
warning, but needed someone (you) to point out the second part.

> Unusual as your slendro tunings are, I don't think any of them stand up to my
> favorite example of "slendro" - the genggong scale!

I agree!

> The genggong is a unique Balinese Jew's harp, and like all
> Jew's harps the sound is produced by using the vocal cavity to
> single out harmonic overtones of the vibrating tongue by
> resonance. Since they're *harmonic* overtones, we know
> *exactly* what the slendro pitches have to be!

Which, as I reflected above, means that the usual etiquette about
not copying the tuning of a traditional ensemble might not apply?

! genggong.scl
!
Genggong polos scale, harmonics 5 through 9
5
!
6/5
7/5
8/5
9/5
2/1

> When some innovative Balinese person many centuries ago first
> carved a tongue out of a piece of palm rib and heard this, he
> thought to himself "Cool! It plays slendro!". This just goes
> to show how flexible the concept of "slendro" is.

A great example indeed!

> Actually, the way genggong is traditionally played is even
> more fascinating, because there are two instruments, polos and
> sangsih, which have different fundamentals. So different
> overtone numbers are used to play "the same" pitches. I'm not
> 100% sure what the specific scheme is (different performers
> might even do it different ways), but I think it's something
> like this: polos ... sangsih

> 5 low ding
> 6 dong
> 7 ~ 8 deng
> 8 ~ 9 dung
> 9 ~ 10 dang
> 12 high ding

Thanks for a post which is really an education for a gamelan novice.

> Keenan

Best,

Margo

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
> This is very interesting, and suggests inclusive counting of
> intervals (i.e. empat as a "pentatonic fourth")! One source on
> the Web says that basically the Balinese use _empat_ for the
> "4ths thing," while the Javanese use _kempyung_. It makes sense
> to me that people who normally speak of empat might use kempyung
> with a more special meaning. As you say, a "linguistic issue."

I believe that.

> In this regard there's a certain parallelism with 12th-14th
> century European music -- and all kinds of differences, of course!

They're similar in that they both treat only 3-odd-limit intervals as perfect consonances.

I remember reading your website about medieval polyphony many years ago, and having my mind blown that a major triad was not always perceived as a consonance. (Then I listened to a lot of Perotin and stuff, and had my mind blown some more.) Before that I had speculated that perhaps 5-limit was sort of a natural cutoff for humans, and for that reason music treating 7-limit or higher harmonies as perfect consonances would never catch on. Now I know better!

> > One interesting thing I note about this scale is that the
> > notes 777.408, 2/1, 279.363, and 531.624, in that order, sound
> > just like the jegog scale! The jegog scale is sometimes
> > explained as deriving from pelog (though it's probably from an
> > independent tradition), so it's pretty trippy to be able to
> > add one note to it and have an acceptable slendro.
>
> So this could be a kind of creative hybrid form?

Possibly. Modern, virtuosic compositions for semarandana (7-tone) pelog ensembles often make use of the fact that some of the 5-note modes sound like slendro. A slendro-jegog hybrid might be amazing.

> An idea for Manuel, with the credit going to you: just as Scala's
> modenam.par now has a disclaimer that pelog is not close to
> 7-ED2, how about a caution that "2/1" in gamelan tuning files
> should not be taken to imply that a traditional Javanese or
> Balinese ensemble is actually using pure or beatless octaves!
> And that ignoring this point means that the accuracy of other
> intervals may vary -- a lot! I knew the first part of the
> warning, but needed someone (you) to point out the second part.

Sounds like a good idea.

> > The genggong is a unique Balinese Jew's harp, and like all
> > Jew's harps the sound is produced by using the vocal cavity to
> > single out harmonic overtones of the vibrating tongue by
> > resonance. Since they're *harmonic* overtones, we know
> > *exactly* what the slendro pitches have to be!
>
> Which, as I reflected above, means that the usual etiquette about
> not copying the tuning of a traditional ensemble might not apply?

Of course. It's impossible to tune the different notes of a genggong individually, because they're harmonic overtones. All genggong instruments, therefore, play exactly the same scale (the harmonic series) out of physical necessity. Only the fundamental frequencies are different.

In fact, (and this comes from what Deirdre Morgan told me when she came to lead a genggong workshop for GSJ), the fundamentals are not even tuned as a normal part of genggong manufacture. When it's the right season for palm ribs, a genggong maker simply cuts a bunch of them, and about 10% eventually become playable instruments (the rest being discarded as failed attempts). Of those, the fundamental frequencies have some random distribution, and you can simply choose ones that form good polos-sangsih pairs (or unisons, for different kinds of genggong music).

Keenan

BTW, if anyone wants to hear a good example of a traditional genggong duet, here's a Grooveshark link: http://grooveshark.com/artist/Genggong+Duet/823738

Keenan