Pelog vs Mavila and Slendro vs 5-tet

I'm pretty confused about "pelog" and "slendro," and how they relate
to regular mapping. Is my understanding of this correct?

- Slendro consists of 5 notes that are roughly equally spaced in the
octave, but are actually unequal. So it's a 5-WT or something.
- Since slendro is not 5-tet, the choice of mode used makes a
difference in the sound at the end, and slendro has 3 modes that it
uses often because of this.
- Mavila tempers out 135/128 and generates 2+5 scales.
- Pelog does the same thing, but has fifths that are actually flatter
than those of an optimal mavila, and 7-out-of-9 is often cited as a
decent "regularly-mapped" version of pelog.

Is the above right? If so, here are a few questions then:
- When the Pelog fifths are that flat, are they better characterized
as something from a different temperament, like perhaps bug
temperament?
- Or is it that this is still best viewed as just a nonoptimal mavila
temperament, and for whatever reason people liked it and gravitated to
it despite its being fairly dissonant?
- The "minor thirds" in 9-tet are almost perfect 7/6's. Is it perhaps
that pelog:mavila::superpyth:meantone?
- In addition, the 9-tet mavila scale is proper, but not strictly
proper. There is an ambiguity between the large second and the small
third. Has this feature been exploited much in pelogian music? Even if
the true pelogian scale doesn't work out to exactly 7 of 9-equal, I
would assume that from a Rothenbergian standpoint, the resultant scale
would be close enough to proper that mentally, the similarity between
the intervals would be noted.

Does anyone have enough experience with Gamelan music to speak to any
of these questions?

-Mike

It is correct to see Slendro as a 5-WT in my opinion, that will avoid 5-equal, as you well said.
As a general rule, notes # 1 and 3 in the notation indicate the smallest fourth of the scale, even if the fifth above 1 is larger than 3/2 (that's the case with the Surakarta tuning : so in traditional music, all modes can be used).
A short 4/3 would be the best idea, but I would think a septimal tone larger than 8/7 could be used as well as a secondary model of slendro generation.

Pelog is a little bit more complex, and I am interested as well in the temperaments it would refer to, and the difference made between "Pelogic" and "Mavila" ; it seems that the Mavila mapping can sometimes produce "Pelog" scales, which can be confusing.
Traditional Pelog tunings would quite rarely be in 9-equal I think (just like 5-equal for the slendro), so a 9-edo would even less be a "Mavila" tuning, if ever we want to differentiate the two.
My personal suggestion to differentiate average Pelog and Mavila tunings in practice : see if 3 fifths comes closer to 16/5, or 13/4...
- - - - - - -
Jacques

Mike wrote :

> I'm pretty confused about "pelog" and "slendro," and how they relate
> to regular mapping. Is my understanding of this correct?
>
> - Slendro consists of 5 notes that are roughly equally spaced in the
> octave, but are actually unequal. So it's a 5-WT or something.
> - Since slendro is not 5-tet, the choice of mode used makes a
> difference in the sound at the end, and slendro has 3 modes that it
> uses often because of this.
> - Mavila tempers out 135/128 and generates 2+5 scales.
> - Pelog does the same thing, but has fifths that are actually flatter
> than those of an optimal mavila, and 7-out-of-9 is often cited as a
> decent "regularly-mapped" version of pelog.
>
> Is the above right? If so, here are a few questions then:
> - When the Pelog fifths are that flat, are they better characterized
> as something from a different temperament, like perhaps bug
> temperament?
> - Or is it that this is still best viewed as just a nonoptimal mavila
> temperament, and for whatever reason people liked it and gravitated to
> it despite its being fairly dissonant?
> - The "minor thirds" in 9-tet are almost perfect 7/6's. Is it perhaps
> that pelog:mavila::superpyth:meantone?
> - In addition, the 9-tet mavila scale is proper, but not strictly
> proper. There is an ambiguity between the large second and the small
> third. Has this feature been exploited much in pelogian music? Even if
> the true pelogian scale doesn't work out to exactly 7 of 9-equal, I
> would assume that from a Rothenbergian standpoint, the resultant scale
> would be close enough to proper that mentally, the similarity between
> the intervals would be noted.
>
> Does anyone have enough experience with Gamelan music to speak to any
> of these questions?
>
> -Mike

On 1/14/2011 9:03 PM, Mike Battaglia wrote:
> I'm pretty confused about "pelog" and "slendro," and how they relate
> to regular mapping. Is my understanding of this correct?
>
> - Slendro consists of 5 notes that are roughly equally spaced in the
> octave, but are actually unequal. So it's a 5-WT or something.
> - Since slendro is not 5-tet, the choice of mode used makes a
> difference in the sound at the end, and slendro has 3 modes that it
> uses often because of this.
> - Mavila tempers out 135/128 and generates 2+5 scales.
> - Pelog does the same thing, but has fifths that are actually flatter
> than those of an optimal mavila, and 7-out-of-9 is often cited as a
> decent "regularly-mapped" version of pelog.
>
> Is the above right? If so, here are a few questions then:
> - When the Pelog fifths are that flat, are they better characterized
> as something from a different temperament, like perhaps bug
> temperament?
> - Or is it that this is still best viewed as just a nonoptimal mavila
> temperament, and for whatever reason people liked it and gravitated to
> it despite its being fairly dissonant?
> - The "minor thirds" in 9-tet are almost perfect 7/6's. Is it perhaps
> that pelog:mavila::superpyth:meantone?
> - In addition, the 9-tet mavila scale is proper, but not strictly
> proper. There is an ambiguity between the large second and the small
> third. Has this feature been exploited much in pelogian music? Even if
> the true pelogian scale doesn't work out to exactly 7 of 9-equal, I
> would assume that from a Rothenbergian standpoint, the resultant scale
> would be close enough to proper that mentally, the similarity between
> the intervals would be noted.
>
> Does anyone have enough experience with Gamelan music to speak to any
> of these questions?

There's not really anything you can identify as a "typical" pelog scale; each one is a little different from one place to another. They do tend to be uneven, and in my opinion bug temperament seems to have a better approximation of pelog scales than mavila or 9-ET. It's true that "pelogic" was what we used to call mavila, and it does have something of the flavor of pelog, but I don't think it would be heard as "the real thing" if you were to tune a gamelan to it.

Bug does have a good pelog approximation within its 9-note MOS scale, but there probably isn't any one regular tuning that stands out as a good version of pelog. Also keep in mind that not all 7 notes of pelog are equal; typically 5 of the 7 notes will be used most frequently, and the other 2 notes only occasionally. So even if some tuning of the 7-note pelog is proper, the typical 5-note subset won't be.

Does anyone have the impression when listening to gamelan
music that it approximates JI, such that regular mapping
would be appropriate? I went through my gamelan listening
phase years ago, when my ear wasn't as good, but personally
I never had such an impression... -Carl

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> Bug does have a good pelog approximation within its 9-note MOS scale,
> but there probably isn't any one regular tuning that stands out as a
> good version of pelog.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Does anyone have the impression when listening to gamelan
> music that it approximates JI, such that regular mapping
> would be appropriate? I went through my gamelan listening
> phase years ago, when my ear wasn't as good, but personally
> I never had such an impression... -Carl

Most Central Java slendro gamelan tunings, such as Jogyakarta and Surakarta show four 2nd intervals approximating 8/7, as well as three fouths approximating 21/16 (or 64/49). Pertinent regular mappings are not difficult to find and the Ethno collection / Indonesian folder has a few -c and eq-b of those :
joged-bumbung.scl
natte.scl
septimal_2.scl
septimal_3.scl
cometslendro1.scl
cometslendro2.scl
slendra.scl
myriadgerm.scl

plus a 7-limit JI global frame, compiling Lou Harrison's 5 main slendro models, recognized as correct Central Java tunings :
slendro_matrix.scl

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@> wrote:
> > Bug does have a good pelog approximation within its 9-note MOS scale,
> > but there probably isn't any one regular tuning that stands out as a
> > good version of pelog.

It's to the Indonesian gamelan masters to say. But what would be a "good version of pelog" anyway ?
And how would you call this :

! gulu-nem.scl
!
5 tones Pelog from a sequence of very low Gulu-nem fifths (about 5/9 of an octave)
12
!
1/1
1393/1284
1393/1284
2015/1712
2015/1712
2015/1712
473/321
473/321
4105/2568
4105/2568
4105/2568
2/1
! Gulu-nem -c recurrent sequence, x^3 - 2x = 1/4, Dudon 2007
! Generator is a "Gulu-nem" extremely low fifth of 670.5060969 c.

This message which is a couple of months old doesn't seem to have got a great deal of responses so I'll dare to throw "my 2 cents" in as well, although somewhat belatedly.

Mike wrote:

> - Slendro consists of 5 notes that are roughly equally spaced in the
> octave, but are actually unequal. So it's a 5-WT or something.

I think so.

> - Since slendro is not 5-tet, the choice of mode used makes a
> difference in the sound at the end,

Agreed.

> and slendro has 3 modes that it
> uses often because of this.

You've lost me here.

> - Mavila tempers out 135/128

Right.

> and generates 2+5 scales.

Sure.

> - Pelog does the same thing,

Did you mean the former or the latter? Personally, I would certainly wish that both were true but I've already heard some people claim that there are more than two one-step sizes alternating in a "pelog" octave. If this were the case, then the 135/128 tempering might be debatable as well, which, at least for my personal attitude, is a very "unsatisfactory" thing to know as I've been comparing pelog to mavila since I first knew about the "extreme" temperaments.

> but has fifths that are actually flatter
> than those of an optimal mavila,

How do you know?

> and 7-out-of-9 is often cited as a
> decent "regularly-mapped" version of pelog.

I'm afraid that this description using 9-equal was the primary source of the confusion that we're all now trying to sort out.

> Is the above right? If so, here are a few questions then:

Let's hope someone else knows better than we do and is willing to share.

> - When the Pelog fifths are that flat, are they better characterized
> as something from a different temperament, like perhaps bug
> temperament?
> - Or is it that this is still best viewed as just a nonoptimal mavila
> temperament, and for whatever reason people liked it and gravitated to
> it despite its being fairly dissonant?

I'm not sure if anyone has ever answered this question.
According to Manuel's scale archive, Eric Von Hornbostel used two descriptions of pelog. Interestingly enough, both of his versions used fourths of 522 cents but there was one great difference. The "type A" was a regular temperament which stacked 6 generators of 522 cents in the "ordinary" fashion, while the "type B" used generators of 261 cents and was essentially an 8-tone chain of "semi-fourths" with one left out (like using generator counts from -2 to 5 but excluding 4, for example).
Now the question is how old Hornbostel's ideas were and what motivated him to do it this way.

> - The "minor thirds" in 9-tet are almost perfect 7/6's. Is it perhaps
> that pelog:mavila::superpyth:meantone?

I'm a bit doubtful here.

> - In addition, the 9-tet mavila scale is proper, but not strictly
> proper. There is an ambiguity between the large second and the small
> third. Has this feature been exploited much in pelogian music? Even if
> the true pelogian scale doesn't work out to exactly 7 of 9-equal, I
> would assume that from a Rothenbergian standpoint, the resultant scale
> would be close enough to proper that mentally, the similarity between
> the intervals would be noted.

Together with the claim of unequal one-step intervals, this might be another idea suggesting something like bug rather than mavila. The obvious question then is, of course, what do we do when bug(7) results in a "non-pelogian" scale. And the quickest solution, undeniably, is to start with bug(8) and then remove one pitch.

BTW: Although it may sound strange and foolish, I've also, run across a description of pelog like an enhanced version of slendro, which, making even less sense than 9-equal, started with 10-equal and went something like "1 1 2 2 1 1 2". From the viewpoint of regular temperaments, this is something completely weird because the larger interval should not occur twice in a row if it occurs less times than the smaller one.

Anyway, some gamelan music (even in its "traditional form") uses scales which are audibly not regular temperaments but get close to something like "A-B-C-E-F-A" or "A-Bb-C-E-F-A". This would suggest a 3D understanding, which may also offer many "non-gamelan" options like making a 5-limit JI version or taking a mode of orwell allowing you to use the pitch exactly between B and Bb.

Whatever it is, I still like mavila more than all the other options. :-D

Petr