ETHNO EXTRAS: Zalzalian 12 (Pt. 7) Rotation 8

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Ethno Extras: Zalzalian 12 set
Part 7: Rotation 8
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Hello, all.

To provide a convenient "itinerary" for the Zalzalian 12 set, so that
people can keep track of where we've been and where we're going, I'll
place at the beginning of each part a summary of the rotations adapted
from Scala output. Part 1 included an introduction on Ethno Extras,
the O3 temperament, and Buzurg modes, and started our journey with
Rotation 0. Part 2 addressed Rotations 1-3; Part 3, Rotation 4;
Part 4, Rotation 5; Part 5, Rotation 6; and Part 6, Rotation 7.
We now come to Rotation 8.

Again, my warmest thanks to Jacques and Francois and all
participants in the Ethno2 contest for the inspiration they have
lent, and to Ozan Yarman, Shaahin Mohajeri, and George Secor, as
well as now to Jacques Dudon, for the very special knowledge and
wisdom they have shared in the exploration of these and other
modes.

Rotation 0: 1/1
0 138.3 207.4 264.8 345.7 472.3 680.9 704.3 842.6 969.1 1050.0 1176.6 2/1

Rotation 1: 138.3 (~13/12)
0 69.1 126.6 207.4 334.0 542.6 566.0 704.3 830.9 911.7 1038.3 1061.7 2/1

Rotation 2: 207.4 (~9/8 or ~44/39)
0 57.4 138.3 264.8 473.4 496.9 635.2 761.7 842.6 969.1 992.6 1130.9 2/1

Rotation 3: 264.8 (~7/6)
0 80.9 207.4 416.0 439.5 577.7 704.3 785.2 911.7 935.2 1073.4 1142.6 2/1

Rotation 4: 345.7 (~11/9)
0 126.6 335.2 358.6 496.9 623.4 704.3 830.9 854.3 992.6 1061.7 1119.1 2/1

Rotation 5: 472.3 (~21/16)
0 208.6 232.0 370.3 496.9 577.7 704.3 727.7 866.0 935.2 992.6 1073.4 2/1

Rotation 6: 680.9 (~77/52)
0 23.4 161.7 288.3 369.1 495.7 519.1 657.4 726.6 784.0 864.8 991.4 2/1

Rotation 7: 704.3 (~3/2)
0 138.3 264.8 345.7 472.3 495.7 634.0 703.1 760.5 841.4 968.0 1176.6 2/1

Rotation 8: 842.6 (~13/8)
0 126.6 207.4 334.0 357.4 495.7 564.8 622.3 703.1 829.7 1038.3 1061.7 2/1

Rotation 9: 969.1 (~7/4)
0 80.9 207.4 230.9 369.1 438.3 495.7 576.6 703.1 911.7 935.2 1073.4 2/1

Rotation 10: 1050.0 (~11/6)
0 126.6 150.0 288.3 357.4 414.8 495.7 622.3 830.9 854.3 992.6 1119.1 2/1

Rotation 11: 1176.6 (~77/39)
0 23.4 161.7 230.9 288.3 369.1 495.7 704.3 727.7 866.0 992.6 1073.4 2/1

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Rotation 8 (13/8): Buzurg redux and Maqam `Iraq variation -- plus Pelog
-----------------------------------------------------------------------

0 126.6 207.4 334.0 357.4 495.7 564.8 622.3 703.1 829.7 1038.3 1061.7 2/1

In this rotation we again come to a symmetrical Buzurg mode
approximating the medieval 1/1-14/13-16/13-4/3-56/39-3/2 Buzurg
pentachord of Safi al-Din al-Urmawi and Qutb al-Din al-Shirazi, plus a
symmetrical upper tetrachord of 3/2-21/13-24/13-2/1.

Buzurg pentachord Upper Buzurg
|----------------------------------|----------------------|
0 126.6 357.4 495.7 622.3 703.1 829.7 1061.7 1200.0
~1/1 14/13 16/13 4/3 56/39 3/2 21/13 24/13 2/1

Strictly speaking, the medieval term "Buzurg" refers to a pentachord,
so that Ozan Yarman has suggested that a tetrachord such as
1/1-14/13-16/13-4/3 might be called Hijaz-i Buzurg or "Hijaz of
Buzurg," since this variety of tetrachord in fact often favored as one
choice flavor of Turkish Hijaz.

More generally, the middle interval of the Hijaz genus in a Turkish
understanding may range from around 8:7 through intermediate
"hemifourth" sizes around 15:13 (248 cents) or so to the very common
region around 7:6 (267 cents) to rather larger minor thirds around
13:11 (289 cents) or 32:27 (294 cents). In the Turkish comma system,
these flavors would be described as 10, 11, 12, or 13 commas
respectively, with all of them seen as involving an "augmented" step
somewhat larger than a usual tone around 9:8 or 9 commas.

The Lebanese composer and theorist Amine Beyhom seems to adopt a
similar viewpoint when he describes a step in Turkish Hijaz at around
237 or 242 cents in a measured performance by Kudsi Erguner as a
"slightly augmented second." It is interesting to ask what kinds of
categorical perception may have operated in the world of Safi al-Din
and Qutb al-Din, but the aptness of their tunings for modelling some
patterns of modern Near Eastern performance on flexible-pitch
instruments suggests their continuing relevance in practice as well as
in theory.

In contrast to our first encounter with Buzurg at Rotation 4 (Part 3
of this series), our "Buzurg redux" here has fewer options for
alternative upper tetrachords, the one choice in evidence being the
lowering of the neutral seventh by a comma from 1061.7 cents (~24/13)
to 1038.3 (~51/28). This nuance, as we shall see, is central to some
possible variations on the Turkish Segah or Ferahnak in this rotation.

As with our first Buzurg at Rotation 4, here we have available a
convenient modulation to Rast on the 14/13 step of our Buzurg mode, a
Rast featured in our next rotation. Using Turkish names for the
perdeler or steps, we have:

Buzurg Buzurg-i Hijaz
|----------------------------------|----------------------|
0 126.6 357.4 495.7 622.3 703.1 829.7 1061.7 1200.0
~1/1 14/13 16/13 4/3 56/39 3/2 21/13 24/13 2/1
evdj rast sarp segah chargah hijaz neva sarp evdj
dugah huseyni -126.6 0.0 230.9 369.1 495.7 576.6 703.1 935.2 1073.4 1200.0 ~13/14 1/1 8/7 26/21 4/3 39/28 3/2 12/7 13/7 2/1
|---------------------------|.............|----------------------|
Septimal Rast tone Septimal Rast

Using the same set of notes as the Buzurg mode, but starting on its
14/13 step, we can arrive at a septimal form of Rast using a close
approximation of Safi al-Din's steps of 8/7, 14/13, and 13/12, but
with his order for the two upper steps reversed so as to produce a
fine large neutral third for a Turkish Rast at around 26/21 (or 99/80)
rather than Safi al-Din's 16/13 at 359 cents, rather low by Turkish
standards but characteristic of many Arab styles.

Having established the Turkish Rast, we could then also bring into
play the usual versions of the steps dugah and huseyni at around 207
and 912 cents (near 9/8 or 44/39, and 22/13), thus setting the stage
for a related maqam making the most of another step also used in our
Buzurg mode but not directly involved in the septimal Rast shown
above, although it is present in the diagram: the perde or step hijaz
at 576.6 cents, ready to serve as the fourth step of Maqam Penchgah.

In addition to Buzurg, we have available what might be described as a
very low variation on the Arab Maqam `Iraq, here in a basic but still
usable and beautiful form. Maqam `Iraq, as a member of the Arab Sikah
family of maqamat, shares the element knitting together this family:
a Sikah trichord above the final consisting of a typically smallish
neutral second plus a tone, thus defining the neutral third of this
trichord. The following diagram shows Arab note names:

"Bayyati"
Sikah (Huseyni) Rast
|--------------|-----------------------|----------------.......|
0.0 126.6 334.0 495.7 622.3 829.7 1038.3 1200.0 1326.6
~ 1/1 14/13 40/33 4/3 56/39 21/13 51/28 2/1 28/13
`iraq rast dukah sikah jaharkah nawa huseyni awj kirdan
|----------------------|
`Iraq

Maqam `Iraq shares the name of its 1/1 or final, the step `iraq, a
neutral second below the cardinal reference point of rast. The lower
Sikah trichrd, `iraq-rast-dukah, at 0-127-334 cents, is likely
somewhat lower than a typical Arab tuning, possibly something like
1/1-13/12-39/32 or 0-139-342 cents, for example. These steps are the
final, neutral second, and neutral third of `Iraq, and also the
neutral second below, final, and major second of Rast.

The middle tetrachord takes the general form called "Bayyati" in Arab
theory, with two neutral seconds plus an upper tone to complete the
fourth. However, a typical Arab Bayyati might be something like
1/1-13/12-13/11-4/3 or 13:12-12:11-44:39 (138.6-150.6-208.8 cents). Our actual tetrachord is instead of the Turkish Huseyni type at
0-161.7-288.3-495.7 cents, still fitting the Arab structure in its
most generic sense, but with a characteristically Ottoman shade of
intonation! Either in a usual Arab tuning or this less usual one, this
central tetrachord consists of the steps dukah-sikah-jaharkah-nawa,
the major second, neutral third, fourth, and fifth of Maqam Rast --
or, the neutral third, fourth, augmented fourth or tritone, and
neutral sixth of the step `iraq.

In theory, the upper jins or genus of `Iraq is often cited as a Rast
trichord nawa-huseyni-awj, the fifth, major sixth, and neutral seventh
of Rast. In terms of our 1/1 at `iraq, these are the neutral sixth,
neutral seventh, and octave, so that this trichord completes a modal
textbook octave for Maqam `Iraq on the 2/1 step, awj.

In practice, however this Rast trichord, here an Ottoman flavor of
Rast at 0-207.4-370.3 cents or around 1/1-44/39-26/21, tends to
function as a Rast tetrachord completed by the step kirdan at an
octave above rast, and here 127 cents above awj, with awj pulling up
to kirdan. Thus kirdan, a small neutral ninth above the final, serves
as an attractive focus for the ascending sayr of the maqam, which may
then descend back toward `iraq.

Additionally, some Arab theorists recognize an alternative `Iraq
tetrachord above the final of `Iraq, and taking the name of this
maqam, thus `iraq-rast-dukah-sikah. One might explore this tetrachord,
for example, after ascending to kirdan and then descending back into
the lower fourth above the final.

It will be noted that Maqam `Iraq has no perfect fifth above the
final; and in some Syrian versions, the fourth step above `iraq may be
at around 21/16 (more precisely, in theory, 21 commas, or about 475
cents in either Pythagorean intonation or 53-EDO). This Syrian
interpretation of `Iraq provides a fine example of how a maqam need
not have either a 4/3 or 3/2, although most have at least one of these
two steps -- not so surprisingly, given the tetrachordal or sometimes
pentachordal focus of much Near Eastern theory and practice.

We have available also a variant upon Turkish Segah which makes the
most of a subtle comma nuance:

Segah tone Hijaz-i Buzurg
|------------------------|.........|-----------------------|
0.0 126.6 334.0 495.7 703.1 829.7 1061.7 1200.0
~ 1/1 14/13 40/33 4/3 3/2 21/13 24/13 2/1
segah chargah neva hisar evdj gerdaniye sarp buzurg
muhayyer

The lower tetrachord is a usual Ottoman Segah of the low neutral or
Zalzalian flavor, with a neutral second and third around 14/13 and
40/33. The disjunct upper tetrachord on the 3/2 step differs in having
a central step at a near-just 8:7 rather than the 9:8 or 44:39 of the
lower tetrachord, thus approximately 3/2-21/13-24/13-2/1 or
14:13-8:7-13:12, the classic Buzurg of the 13th century (or, more
accurately, the lower tetrachord of a classic Buzurg pentachord).

Since, in Turkish practice, this "Buzurg tetrachord" is recognized as
one common form of Hijaz, the overall ascending seyir or melodic path
thus fits the general category of Segah as disjunct Segah-Hijaz,
albeit in a less typical way. Then, the descending seyir might be like
this:

Segah tone Segah
|------------------------|.........|-----------------------|
0.0 126.6 334.0 495.7 703.1 829.7 1038.3 1200.0
~ 1/1 14/13 40/33 4/3 3/2 21/13 51/28 2/1
segah chargah neva hisar evdj gerdaniye muhayyer buzurg

Here for the descent, we have two disjunct Segah tetrachords. In this
interpretation, the 1/1 is a small neutral third above perde rast,
which in turn is the final of the Maqam Rast we explored in Rotation 4
(Part 3) of this series.

However, another interpretation might also be possible which regards
these ascending and descending forms as instead a variation on the
related Maqam Ferahnak, with the 1/1 on perde evdj, a small neutral
second below the perde rast of the Rast coming up in our next
rotation, and already previewed in the discussion above of a
Buzurg-Rast modulation. Our scheme would thus be:

Ascending seyir

Segah tone Hijaz-i Buzurg
|------------------------|.........|-----------------------|
0.0 126.6 334.0 495.7 703.1 829.7 1061.7 1200.0
~ 1/1 14/13 40/33 4/3 3/2 21/13 24/13 2/1
arak rast dugah segah hijaz neva sarp evdj
huseyni

Descending seyir

Segah tone Segah
|------------------------|.........|-----------------------|
0.0 126.6 334.0 495.7 703.1 829.7 1038.3 1200.0
~ 1/1 14/13 40/33 4/3 3/2 21/13 51/28 2/1
arak rast dugah segah hijaz neva huseyni evdj

In the lower range above the final of this Ferahnak variant, two
modified forms discussed by Ozan Yarman are possible. The first,
ascending, uses a very curious type of pentachord which he also
suggests for Buzurg:

0.0 126.6 334.0 622.3 703.1
~ 1/1 14/13 40/33 63/44 3/2
arak rast dugah chargah hijaz
126.6 207.4 288.3 80.9
~ 14:13 9:8 13:11 22:21

As Ozan observes, based on far greater experience with the maqamat
than mine, this structure is quite distinctive.

The other variant is a "diminished Ferahnak pentachord" with a fifth
lowered by a diatonic semitone or limma, thus around 63/44 (or 56/39):

0.0 126.6 334.0 495.7 622.3
~ 1/1 14/13 40/33 4/3 63/44
arak rast dugah segah chargah
126.6 207.4 161.7 126.6
~ 14:13 9:8 56:51 14:13

While the first variant has an aseending nature, pulling up by a
regular diatonic semitone to the fifth (63/44-3/2), the second has a
descending feeling in which the 63/44 step pulls down to 4/3, inviting
motion from there through the lower tetrachord to the final.

By altering the 126.6-cent step of the first variant to 207.4 cents,
we can derive a mode whose lower fifth resembles a medieval Nirizi
pentachord as discussed by Owen Wright, with a lower tone plus a Hijaz
tetrachord; and an upper tetrachord of the Ottoman Segah variety:

Nirizi Segah
|-----------------------------------|-------------------------|
0.0 207.4 334.0 622.3 703.1 829.7 1038.3 1200.0 ~ 1/1 9/8 40/33 63/44 3/2 21/13 51/28 2/1
arak shuri dugah chargah hijaz neva huseyni evdj
|........|--------------------------|
tone Hijaz

In descending, the 63/44 step may be lowered to 4/3, giving a form of
Nihavend-i Hagar, that is a "supraminor" flavor of the Turkish Maqam
Nihavend dedicated to the Matriarch Hagar:

Nihavend tone Segah
|-------------------------|........|--------------------------|
0.0 207.4 334.0 495.7 703.1 829.7 1038.3 1200.0 ~ 1/1 9/8 40/33 4/3 3/2 21/13 51/28 2/1
arak shuri dugah segah hijaz neva huseyni evdj

While the ascending Nirizi-Segah form fulfills my understanding that a
mode in honor of Hagar should include some form of Hijaz in order to
recall her experience of exile in the desert, which some of the Hebrew
sages have taught is comparable to the ordeal of the Hebrew people
during the Exodus, we can enlarge upon this understanding by using
another ascending form also with an upper Hijaz-i Buzurg:

Nihavend tone Hijaz-i Buzurg
|-------------------------|........|--------------------------|
0.0 207.4 334.0 495.7 703.1 829.7 1061.7 1200.0 ~ 1/1 9/8 40/33 4/3 3/2 21/13 24/13 2/1
arak shuri dugah segah hijaz neva huseyni evdj

Here I should note, or indeed confess, that the perde or step names
may be a bit arbitrary, since they place the 1/1 of a variant on Maqam
Nihavend on perde arak, although the usual untransposed final for
Nihavend is perde rast. Thus it might be said that we have transposed
this maqam down by about a 14:13! This approach has the advantage of
keeping a more or less typical Ottoman Rast, and its final rast, as a
point of reference -- the Rast of our next rotation.

Our approach introduces some less familiar perde or step names such as
Shuri, at a diatonic semitone or limma (here around 22:21 or 81 cents)
above perde rast. While it would be possible to call our 1/1 perde
rast rather than perde arak, this would involve the disadvantage in a
Turkish or Arab context that we would have a step named rast but
unable to support a usual form of Maqam Rast with a largish neutral
third around 16/13 (359 cents) or 26/21 (370 cents), for example, as
opposed to the much lower 334 cents which is here the only neutral
third available. The name of perde arak (or Arab `iraq), in contrast,
creates the expectation of a smallish neutral third, with 334 cents
typical of a certain shade of Ottoman intonation, and something around
39/32 (342 cents) or 11/9 (347 cents) likely more typical of many Arab
styles.

In more of a Persian context, however, a step named "rast" might well
have only a smallish neutral third above it, since this kind of
structure is typical of Ibn Sina's mode he calls Mustaqam with a
tetrachord of 1/1-9/8-39/32-4/3 or 0-203.9-342.5-498.0 cents
(9:8-13:12-128:117). This style of step naming would fit a maqam
sharing the lower tetrachord of Nihavend-i Hagar, but placing
considerable emphasis on major sixth and minor seventh steps not in
evidence for this rotation. and called Mustaqim al-Hagar since the
lower tetrachord can be seen as a variation on Ibn Sina's with the
neutral third somewhat lower, here about 334 cents. The Zalzalian 12
set, unfortunately, does not have the right notes and intervals in the
right places to realize this maqam; but the Ethno Extras series will
include a dedicated 12-note tuning set for Mustaqim al-Hagar.

* * *

This rotation offers a fascinating form of pelog which, however, may
be as closely related to Vietnamese music as to certain currents in
gamelan music.

A pelog tuning set typically consists of seven notes, out of which can
be formed various five-note modes, as well as some other modes listed
in the Scala file modename.par which may involve four or even all
seven notes of the set.

My idea began with this five-note mode:

0.0 126.6 334.0 703.1 829.7 1200.0
~ 1/1 14/13 40/33 3/2 21/13 2/1
126.6 207.4 369.1 126.6 370.3
~ 14:13 44:39 26:21 14:13 26:21

The large neutral third steps had a melodic effect that had a "pelog"
feeling for me, although I suspect that some details of intonation
might be a bit overly "regular" to approach the subtleties of a
Javanese or Balinese ensenble.

Expanding to a seven-note tuning from which different pelog modes
could be drawn was not difficult:

0 1 2 3 4 5 6 7
0.0 126.6 334.0 495.7 703.1 829.7 1038.3 1200.0
~ 1/1 14/13 40/33 4/3 3/2 21/13 51/28 2/1
126.6 207.4 161.7 207.4 126.6 208.6 161.7
~ 14:13 44:39 56:51 9:8 14:13 44:39 56:51

Curiously, the complete 7-note set seems identical with a Near Eastern
mode consisting of two distinct Segah tetrachords in the Ottoman
manner. For pelog, however, we are typically selecting or motating
between modes most often consisting of five-note or pentatonic
subsets. To help in this process, note numbers from 0 to 7, following
the conventions of Scala, are placed above the notes in the last
diagram.

From this perspective, our original five-note mode consists of steps
0-1-2-4-5-7 or 0.0-126.6-334.0-703.1-829.7-1200.0. Using the style of
modename.par, we find it has a pattern of 1-1-2-1-2 steps, which that
file describes as "Patet Lima, Patet Nem, Jawar, Selisir."

Another mode known as "Patet Lima, Nem with Pelog" has a pattern of
1-2-1-1-2, using steps 0-1-3-4-5-7:

1 2 1 1 2
0 1 3 4 5 7
0.0 126.6 495.7 703.1 829.7 1200.0
~ 1/1 14/13 4/3 3/2 21/13 2/1

Interestingly, this mode could be seen as a variation on a Malaysian
pelog, pelog_mal.scl, in the Scala archive:

! pelog_mal.scl
!
Malaysian Pelog, Pierre Genest: Diff?rentes gammes encore en usage
5
!
13/12
4/3
3/2
13/8
2/1

Here, if the Malaysian steps are at or very close to the just ratios
given by Pierre Genest, the main difference apart from the mild
tempering of 4/3 and 3/2 would be the use of 14/13 and 21/13 in place
of 13/12 and 13/8.

This subtle distinction might avert a possible question of etiquette. In the tradition of gamelan, it has been considered impolite, and
sometimes indeed outright forbidden, deliberately to copy the _embat_
or distinctive intonational style of a given ensemble. Presumably this
caution might apply to a traditional ensemble in Malaysia as well as
Bali or Java, so that small but appreciable divergences are very
welcome.

The five-note mode called Pelog uses the pattern 2-1-1-2-1, and
invites a connection with a different musical culture:

2 1 1 2 1
0 2 3 4 6 7
0.0 334.0 495.7 703.1 1038.3 1200.0
~ 1/1 40/33 4/3 3/2 21/13 2/1

Here it might be said that there are two essentially symmetrical and
disjunct trichords of 334.0-161.7 cents or 335.2-161.7 cents, with a
central step close to 9:8, thus 0-2-3 and 4-6-7. The resulting Pelog
pentatonic is very similar to a five-note subset of a hexatonic tuning
used in Vietnam called Sa Mac Dan Tranh, tranh3.scl in the Scala
archive, Dan Tranh being the name of a traditional Vietnamese zither:

! tranh3.scl
!
Sa Mac Dan Tranh scale
6
!
17/14
4/3
3/2
38/21
51/28
2/1

Looking at this tuning raises for me a possible query as to whether
the specified 38/21 step might actually have been intended as 34/21, a
4:3 fourth above 17/14 and a 9:8 tone below 51/28. If so, then this
complete hexatonic Vietnamese scale would be closely approximated as a
subset of our 7-note pelog set. However, the Scala archive file
art_nam.scl, a 9-note "Artificial Nam System," also has a 38/21 step,
so it appears that the relevant subset of the Sa Mac Dan Tranh tuning
would be 1/1-17/14-4/3-3/2-51/28-2/1, very close to our Pelog mode
above.

The Sa Mac mode is characteristic of Northern Vietnam, and associated
with such emotions as nostalgia and melancholy. The topic of modal
ethos or affect in different world traditions is a fascinating one, as
is an exploration of the modal subsets and permutations found in pelog
or Vietnamese music or the maqam/dastgah traditions of the Near East.
The great variety of pentatonic pelog modes available within a 7-note
set is a special delight.

With many thanks,

Margo Schulter
mschulter@...