ETHNO EXTRAS: Zalzalian 12 (Pt. 2) Rotations 1-3

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Ethno Extras: Zalzalian 12 set
Part 2: Rotations 1-3
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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. Here we'll
address Rotations 1-3.

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 1 (13/12): A low Maqam Sikah and the Penchgah of Hagar
---------------------------------------------------------------

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

Our rotation to Scala step 1 at 138.3 cents or a virtually just
13/8 brings us into a realm offering two "alternative" modes a
bit different in their intonational shadings and details than a
typical Arab Maqam Sikah or Turkish Maqam Penchgah, to which they
are related in their general patterns of steps and _ajnas_ or
"genres" such as tetrachords (the Arabic plural of _jins_,
"genus").

Thus it may be better to regard these two modes, which I much
like, as variations on rather than representations of current
Near Eastern practice.

The first has the general pattern and invites the _sayr_ (the
melodic "path" or development) of Arab Makam Sikah, but an
intonational style more like that of one shading of historical
Ottoman practice. The following diagram shows the basic
"textbook" form of Makam Sikah with a lower Sikah trichord,
central Rast tetrachord, and upper Rast trichord. This last
trichord, which leads up to the final of Sikah or its octave,
sometimes takes an alternative form where the second note is
subtly raised by a comma, so that it may serve as a leading tone
pulling up by a smaller and more incisive step to the final.

Sikah Rast Rast
|----------|------------------|------------|
0 127 334 542 704 831 1038 1200
1/1 14/13 40/33 160/117 3/2 21/13 51/28 2/1
127 207 209 162 127 207 162

|------------|
Septimal Rast
831 1062 1200
21/13 24/13 2/1
231 138

One hallmark of an Ottoman style of intonation is the middle Rast
tetrachord of 209-162-127 cents with its contrast between the
large 162-cent and small 127-cent neutral second, respectively
near 11:10 and 14:13, and the bright middle or neutral third at
370 cents or a virtually just 26:21. A typical Arab Rast might be
represented in this temperament as 209-150-138 cents, with the
neutral third at around 16:13. Conversely, the opening Sikah
trichord of 127-207 cents has a small neutral second step and a
neutral third at 334 cents, notably lower than in another form
available in the O3 system with steps at a rounded 138-207 cents
(0-207-346 cents or ~1/1-9/8-11/9) more representative of a
typical Arab shading.

In the "regular" form of our Ottoman-like Arab Sikah with a small
127-cent Zalzalian step above the final and a large 162-cent step
below it, the step above may act, a la Cameron Bobro, as a
leading tone pulling _downward_ to the final, as in this
three-voice cadence where the lowest voice descends by the small
neutral step and each upper voice ascends by a large one.

1038 (51/28) 1200 (2/1)
542 (117/60) 704 (3/2)
127 (14/13) 0 (1/1)

Here the first sonority at 0-416-912 cents, e.g. 1/1-14/11-22/13,
has a regular major third and sixth which, as in 14th-century
European counterpoint, expand to the fifth and octave -- but via
Zalzalian melodic steps announcing a new style of polyphony which
nicely fits the melodic structure of the maqam.

One tendency of Maqam Sikah (and also the related but distinct
Turkish Maqam Segah, which we will also meet in this 12-note set)
is sometimes to raise the step below the final, so that it may
serve as a more incisive leading tone pulling up to the final. Here this step is subtly and gently raised by a comma from 1038
to 162 cents, with the upper Rast trichord now taking the form of
231-138 cents, or 0-231-359 cents -- around 1/1-8/7-16/13:

|------------|
Septimal Rast
831 1062 1200
21/13 24/13 2/1
231 138

Here the first step of the trichord is expanded from 207 to 231
cents, or from 9:8 or 44:39 to 8:7, while the second step or
upward leading tone to the final is subtly compressed from 162
to 138 cents, or in superparticular terms from 11/10 to 13/12.

A cadence combining this upward leading tone of 138 cents with
the downward one of 127 cents features a near-just 12:14:21
sonority with a septimal minor third and seventh (7:6 and 7:4):

831 21/13 704 3/2
127 14/13 704 3/2
-138 12/13 0 1/1

Makam Sikah takes its name from the Persian _segah_, referring to
the "third" step, as does the related but distinct Turkish Maqam
Segah. This "third" step defining the final of Sikah is that of
the closely related Maqam Rast, "the mother of all maqamat" and
the reference point for the maqam system, to which Maqam Sikah
may often pleasantly modulate. The following diagram shows how
Maqam Sikah and Maqam Rast in their basic "textbook" forms share
the same steps of the gamut, with Sikah having its final on the
step named "sikah," and Rast -- not so surprisingly! -- on the
step named "rast." This diagram shows Arabic forms for the names
of the steps, since we are hear addressing the Arab pattern for
Maqam Sikah, with Turkish forms to follow shortly. The steps and
intervals shown in the upper part of the diagram apply to Maqam
Sikah, and those in the lower part to Maqam Rast.

Rast Sikah Rast Rast
|-----------|-------------|-------------------|-----------------|
207 162 127 207 209 162 127 207 162
21/13 51/28 1/1 14/13 40/33 160/117 3/2 21/13 51/28 2/1
831 1038 0 127 334 542 704 831 1038 1200
rast dukah sikah jahargah nawa huseyni awj kirdan muhayyer buzruk
0 207 369 496 703 912 1073 1200 207 369
1/1 9/8 26/21 4/3 3/2 22/13 13/7 2/1 9/8 26/21
207 162 127 207 209 162 127 207 162
|-----------------|.......|--------------------|----------------...
Rast tone Rast Rast

The form of Rast on which we are here focusing, often regarded in
modern times as the "fundamental Arab scale," has two disjunct
Rast tetrachords with a tone followed by a larger and smaller
neutral second, and a middle tone around 9:8. Note how the
central Rast tetrachord of Maqam Sikah coincides with the upper
tetrachord of Maqam Rast.

When the step below the final of Sikah is raised by a comma in
order to serve as a more incisive upward leading tone, from
another perspective we have arrived at a septimal flavor or
variation on a Rast tetrachord. This leading tone, dukah
(i.e. the "second" step of Rast), is raised from around 9/8 to
8/7, with the final sikah as the third step of the tetrachord,
producing a pattern of a general kind described by Safi al-Din
with steps of 8:7, 13:12, and 14:13.

|-----------------------|
0 231 369 496
1/1 8/7 26/21 4/3
rast dukah sikah jahargah
21/13 24/13 1/1 14/13
231 138 127
8:7 13:12 14:13

As in Dudon's s-n-buzurg.scl, an advantage of having some steps a
comma apart is that we can choose between nuances like the
regular form of Rast or Sikah shown in the diagram above, or this
septimal variation with dukah at 8/7 rather than 9/8 above rast.

Our second mode which stands out this rotation also invites such
a comma nuance, as we shall see: an "alternative" form rather
different from anything I know in Near Eastern practice, although
closely related to it, which I call Penchgah al-Hagar or the
Penchgah of Hagar in honor of the Matriarch Hagar, whose journey
of exile and liberation in the desert with her son Ishmael is
seen in the Jewish tradition as like that of the later Exodus,
and likewise in the Islamic tradition as a germinal event.

Penchgah al-Hagar, while it takes its name from the Ottoman Maqam
Penchgah, has a radically different intonational flavor closely
related to that of Mustaqim al-Hagar, a form calling for a 4/3
step not present in this rotation, but which we will meet in
Rotation 8.

A usual Turkish Penchgah, which we will also shortly meet, calls
for a high neutral third around 26/21 in this tuning -- or, in a
common modern practice described by Ozan Yarman, a third at
around 5/4, so that 26/21 might be called a "low" Penchgah.

In contrast, Penchgah al-Hagar, like the related Mustaqim
al-Hagar, uses the _smallest_ Zalzalian or neutral intervals. Here is the basic form, with a notation added in which "T" shows
a tone and "J" a mujannab or "middle" step somewhere between a
usual semitone and usual tone, here a large or small neutral
second:

Penchgah Mustaqim
|----------------------------|---------------------|
0 207 334 542 704 912 1038 1200
1/1 9/8 40/33 160/117 3/2 22/13 51/28 2/1
207 127 207 162 207 127 162
T J T J T J J

Here it may be helpful to look first at the upper tetrachord of
Mustaqim with its T-J-J structure: like a Rast tetrachord in
having a tone followed by two neutral or middle second steps, but
distinct in flavor because here the _smaller_ neutral second
precedes the larger, 207-127-162 cents (or 0-207-334-496 cents).
This contrasts dramatically with a Rast tetrachord having the
same step sizes but a different order: 207-162-127 cents or
0-207-369-496 cents, the bright Turkish Rast we met in our
version of Maqam Sikah.

The lower Penchgah pentachord has a structure of T-J-T-J,
starting like the upper Mustaqim tetrachord with steps of 207-127
cents, but then interposing a tone, bringing us (as in Arab
Sikah) to a step at a "superfourth" or small tritone above the
final, here a notably narrow 542 cents, and followed by another
neutral second to complete a perfect fifth.

For me, the small neutral third of the lower pentachord invites a
consideration of Hagar's exile, while the upper tetrachord, which
also occurs as a tetrchord below the final and leading up to it,
may have a more joyful and even ecstatic quality, celebrating the
richness and depth of her spiritual journey.

In Mustaqim al-Hagar, as will be discussed, and also in Penchgah
al-Hagar, it is my custom at some point in the seyir to include a Hijaz tetrachord in some form, which traditionally is
associated with the vastness of the desert, and thus fitly
commemorates the Matriarch Hagar's ordeal of exile, or Exodus.
In the Turkish tradition, interestingly, one form of Hijaz is
much like our medieval Buzurg, with lower and upper steps around
14;13 or 13:12, and a middle step around 8:7. Happily our tuning
in this rotation supplies such a form:

Penchgah Hijaz (Buzurg)
|----------------------------|---------------------|
0 207 334 542 704 831 1062 1200
1/1 9/8 40/33 160/117 3/2 21/13 24/13 2/1
207 127 207 162 127 231 138
T J T J J A J

Here in addition to tone (T) and mujannab (J) steps, we have an
8:7 step identified more generically as an "augmented" step (A)
somwhat larger than a usual tone. This middle "augmented" step
is here what the Lebanese musician Amine Beyhom calls "slightly"
augmented at 8:7 or so, while in other forms of Hijaz it is
wider, for example at around 7:6 or 13:11.

Following the seyir or procedure for Penchgah al-Hagar, we may
alternate between this Hijaz/Buzurg form of the upper tetrachord
and the regular form at 127-207-162 cents, with a possible nuance
of sometimes ascending to the final with the higher 24/13 step
and then descending with the usual 51/28 step at a comma lower.

Using the lower form of this step at around 51/28, we can form a
characteristic cadence featuring a vertical large neutral or
submajor third at around 26:21.

542 160/117 704 3/2
207 9/8 0 1/1
-162 51/56 0 1/1

In this stately cadence, the outer voices ascend by 162-cent
steps, large enough to be heard almost as whole tones, while the
middle voice descends by a regular tone around 9:8 or 44:39.

Both our Makam Sikah with an Ottoman flavor of intonation, and
Penchgah al-Hagar, borrow some familiar Near Eastern patterns but
modify them to arrive at modes a bit off the "beaten track." They
should be used and enjoyed as variations on, rather than
exemplars of, usual Arab or Turkish maqam music.

-----------------------------------------------
Rotation 2 (44/39): A conjunct "Shur," sans 3/2
-----------------------------------------------

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

For someone trained in a classic medieval or Renaissance European
perspective, it is easy to come upon a scale rotation without a 3/2
and conclude that since no proper "modes" are available from such
a perspective, one might as well proceed to the next rotation. In
a Near Eastern tradition, however, beautiful modes are available
which do not use a perfect fifth above the final, so I shall
resolutely resist this classic European temptation and consider
each rotation.

So considered, this rotation offers the treasure of a variation
on Shur Dastgah with _conjunct_ Shur tetrachords actually
following a pattern often favored by the gushe-s or melodic themes
making up this dastgah or modal family, where the fifth is
lowered by about a third of a tone from its "textbook" position
at 3/2. Here is a symmetrical form of this pattern, very
interesting to explore as an independent mode, with a possible
Persian style of note spelling shown:

Shur Shur tone
|-------------------|------------------|.......|
0 138 265 497 635 762 993 1200
1/1 13/12 7/6 4/3 13/9 14/9 16/9 2/1
D Ep F G Ap Bb C D
138 127 232 138 127 231 207

The Persian koron sign (ASCII "p") shows the lowering of a note
by about a third of a tone, an amount that varies somewhat
depending on the context and the musician's taste. The conjunct
Shur tetrachords follow Ibn Sina's 11th-century description of a
tuning with steps of 13:12-14:13-8:7, here 12:13:14:16, with the
larger 13:12 neutral step placed below the smaller 14:13, and
then the wide 8:7 tone to complete the fourth.

This modal form might also represent a septimal form of the Arab
Maqam Bayyatayn, with two conjunct Bayyati tetrachords which,
like the Persian Shur tetrachord, have two neutral second steps
followed by a tone. While the Arab Bayyati family often favors a
minor third at around the Pythagorean 32/27 or 294 cents, as
reported by Scott Marcus of Egyptian practice, he notes that some
Arab musicians favor a distinctly lower minor third; if the
difference is sometimes around a comma, then 7/6 could represent
one shade of this interpretation.

One could also introduce as comma variations the 21/16 and 7/4
steps available in this rotation.

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Rotation 3 (7/6): A "mirror image" Slendro and Maqam Najdi
----------------------------------------------------------

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

Keeping in mind the gamelan aspects of this scale, we should note
the availability of a version in original position of Jacques
Dudon's M (or Mi) type of septimal slendro, the "Mirror Image"
variety with steps, here tempered, of 1/1-9/8-9/7-3/2-12/7-2/1,
or 9:8-8:7-7:6-8:7-7:6.

0 207 439 704 935 1200
1/1 9/8 9/7 3/2 12/7 2/1
207 232 265 231 265

This rotation makes possible a rather less familiar Arab maqam
sometimes called Najdi which, however, as Ozan Yarman has noted,
is really a close relative of the Turkish Penchgah mentioned and
promised earlier -- here featuring a characteristic Ottoman
flavor of intonation, although not the most commonly cited in
modern practice. In its most regular form, our Najdi is as
follows:

Najdi Rast
|-------------------------|-------------------|
0 207 416 578 704 912 1073 1200 1/1 9/8 14/11 88/63 3/2 22/13 13/7 2/1
207 209 162 127 207 162 127
T T J J T J J
|......|------------------|-------------------|
tone Rast Rast

From one perspective Najdi, like a Turkish Penchgah, consists of
a lower pentachord with a tritonic step (here 578 cents, around
88/63) pulling up to 3/2, and then an upper Rast tetrachord. In
another view, we may also analyze this maqam as a _lower_ tone
around 9/8 plus two conjunct upper Rast tetrachords of T J J
(here a characteristically Ottoman 209-162-127 cents).

A variation is also possible favoring a septimal flavor for the
two conjunct Rast tetrachords, with the "A" notation showing the
8/7 as Beyhom's "slightly" augmented major second:

Najdi Rast
|-------------------------|-------------------|
0 207 439 578 704 935 1073 1200 1/1 9/8 9/7 88/63 3/2 12/7 13/7 2/1
207 232 138 127 231 138 127
T A J J A J J
|......|------------------|-------------------|
tone Rast Rast

Either form offers a very attractive three-voice cadence with a
large 26/21 neutral third at 370 cents expanding to a fifth and a
large neutral sixth at 866 cents or around 33/20 expanding to an
octave:

1073 13/7 1200 2/1
578 88/63 704 3/2
207 9/8 0 1/1

Another version of this cadence has a near-14:17:21 sonority on
the step below the final resolving to a fifth on the final:

578 88/63 704 3/2
207 9/8 704 3/2
-127 13/7 0 1/1

(Conclusion of Part 2)

Best,

Margo Schulter
mschulter@...