LONG -- For Carl: On Near Eastern steps and intonations

Dear Carl,

Please let me apologize for my failure to do something at once
responsive to your questions and possibly helpful more generally
to others who may be interested in Near Eastern music and
intonation: to offer a basic explanation of concepts such as "the
17 steps or perdeler" of Turkish theory.

While in the Ethno Extras series I'm seeking to look in depth at
some tuning sets and modes, the level of detail is not
necessarily the ideally gentle introduction to this area. And
from a lack of gentle introductions, as Paul Erlich has been wont
to call them, many misunderstandings can follow otherwise
avoidable.

In seeking to address some of these basic questions, tentatively,
as a nonnative "student" of some of these styles at an early
state of learning, I seek to provide one starting point for
addressing some of the issues you raise.

The 17 steps or perdeler -- perde-s as I might write in English
to show that this is a plural of Turkish "perde" (Persian pardah)
meaning "pitch," "step," or also "fret -- are one avenue for
exploring some points which seem to me central to some of the
discussions on the list.

Different Near Eastern schools of theory diverge both as to the
number of these cardinal steps -- each of which may be subject to
many fine shadings -- and the general scheme for their placement.
Thus Arab theorists and modern systems of notation often use a
model of 24 positions per octave -- not necessarily equal in
spacing!

Turkish and Syrian musicians often use a system of 53 commas,
while Amine Beyhom suggests that if a simpler categorization is
desired, 17 steps rather than 24 may be preferable. He used the
24-not-necessarily-equal scheme for his thesis, but later
expressed a preference for 17 steps as a simplified reference.

--------------------------------------
1. A 17-step concept, variously shaded
--------------------------------------

Here I'll focus on two of the possible versions for a 17-note set
of steps actually found in a 24-note temperament I use, the O3
system. As we'll see, in a "17-perde" concept, while some of the
steps like 4/3 and 3/2 tend to be stable across a range of
implementations, the location and color of other steps is highly
negotiable. My purpose is not only to present a list of names,
but some musical explanations. While I can hardly escape from my
own foibles and idiosyncrasies, I will try to make some of them
clear.

It should be understood that circulation is not a given for Near
Eastern systems, even though some like a 53-note Pythagorean
tuning or 53-EDO do meet this criterion, not to speak of many
unequal temperaments which could be applied. Thus a typical
17-note Persian tar tuning exemplifies the 17 steps, although in
a slightly different way than the models I'll be presenting, but
is generally quite noncirculation. George Secor's 17-WT _could_
be used for a tar fretting, I'd guess, and might yield pleasant
results; but it is not how Iranian musicians generally tune, any
more than traditional gamelan ensembles generally follow the JI
ratios of Lou Harrison or Jacques Dudon (as beautiful as they
are, also).

As it happens, my own concept of the 17 steps is a "thirdtone"
concept: that is, each perde or step will generally represent
some category of major, minor, or Zalzalian (also neutral or
middle) interval spaced at some kind of "thirdtone" from an
adjacent basic perde, say an interval of around 55-85 cents.
There can also be two or more versions of the same basic perde,
say a usual major second or tone around 9/8, or a septimal tone at
around 8/7, with such comma distinctions common, and indeed both
desirable and inevitable, in a 24-note system such as mine.

Fine variations are especially typical for Zalzalian intervals.
In my 24-note system, for example, there are neutral thirds at
334.0/335.2, 345.7/346,9, 357.4/358.6, and 369.1/370.3 cents,
with sizes for each type varying by 1/1024 octave at different
locations.

In an Arab context, taking the step called rast as the 1/1 of the
gamut (shown by the note C in modern staff notation), I would
consider the 357-359 cent variety as the standard distance
between the perde-s or steps rast and sikah, the latter the
neutral third above rast.

In a Turkish context, while this placement might be acceptable, I
would consider the largest neutral third at 369-370 cents as more
distinctly characteristic, giving this third a submajor quality,
melodic as well as vertical in polyphonic contexts, which has a
distinctly "Ottoman" air.

Either choice will affect the placement of other perde-s, and may
sometimes call for the use of a step altered by a comma from its
"standard" position, as well shall see. As Ozan might observe,
the mandatory use of such a nonstandard position (e.g. 12/7
rather than 22/13 for a major sixth in a given maqam if one
wishes to have a major sixth at all) is much more apt to happen
in a 24-note system with a large number of neutral shadings than
in a 79-note system such as that for his qanun with yet more
shadings but far more steps!

----------------------------------------------
2. A set of perde-s for Maqam Rast, Arab style
----------------------------------------------

To get a feel for a set of 17 perde-s that comes out fairly
"standard," at least in terms of my standard, let's consider an
Arab flavor of Maqam Rast that might not be too far from the norm
in Egypt or Lebanon, and possibly somewhere between these local
practices, I'd guess, but with some quirks.

As is often the case, the name of a step will correspond to that
of a maqam where it is either the final or resting note, or else
another prominent note in the course of the sayr or "path" of
melodic development. Thus perde rast, the main reference point
for Arab and Turkish gamuts, is the final of Maqam Rast; while
perde huseyni, at a major sixth higher, plays a very prominent
role as the fifth of Maqam Huseyni, often appearing more
prominently than the final dugah (a major second above rast).

Note that I'm capitalizing the names of maqamat (and tetrachords
or other genera, which often share the names of maqamat), but
giving the perde names in lower case: thus "huseyni is the fifth
degree of Maqam Huseyni."

Arbitrarily, let's select G on my upper12-note keyboard, here
shown as G*, as the location of perde rast, thus corresponding to
a standard Arab notation of C. Our table of 17 perde-s will be as
follows, with the choice of steps meant to favor an accent on the
routine where possible, for example regular diatonic major and
minor steps. I use the Turkish names, with the Arabic names often
identical or very similar, but sometimes different. Thus the step
called beyati in the Turkish terminology, at a minor sixth above
rast, is called shuri in a common Arab usage.

Perde Category Cents from rast Arab/keyboard Step size

rast unison 0.0 C / G*
70.3
shuri min2 70.3 Db G#
80.9
zengule Zal2 151.2 Dd A
57.4
dugah Maj2 208.6 D A*
80.9
kurdi min3 289.5 Eb Bb*
69.1
segah Zal3 358.6 Ed B
57.4
buselik Maj3 416.0 E B*
80.9
chargah Perf4 496.9 F C*
69.1
hijaz small "TT" 566.0 F+ C#
80.9
sabah large "TT" 646.9 Gd D
57.4
neva Perf5 704.3 G D*
80.9
beyati min6 785.2 Ab Eb*
69.1
hisar Zal6 854.3 Ad E
57.4
huseyni Maj6 911.7 A E*
80.9
ajem min7 992.6 Bb F*
69.1
evdj Zal7 1061.7 Bd F#
57.4
mahur Maj7 1119.1 B F#*
80.9
gerdaniye Perf8 1200.0 C G*

My purpose here is to give a quick overview, not to explore all
the ramifications, like the comma shifts required for a number of
these steps as one seeks to tune different maqamat in an
appropriate fashion. While many of the perde-s map conveniently to major,
minor, or neutral categories, the steps at some kind of "tritone" above
Rast are not so easily describable. They may be similar to a regular
diminished fifth or augmented fourth in a given tuning system, or distinct,
as with a lower hijaz at around 11/8 or a high sabah around 16/11.
Further, the flavor of a step such as sabah, with the higher position of
646.9 cents (keyboard D) shown in the table, but 623.4 cents (C#*) equally
vital, may vary not only from maqam to maqam, but within a performance in a
given maqam.

Let us focus on Maqam Rast itself for the moment. Here there is
what I term a "basic" set of nine steps, including the lower Rast
tetrachord of rast-dugah-segah-chargah, plus the combined notes
of upper Rast tetrachords in conjunct or disjunct positions:

207.4 150.0 138.3
704.3 911.7 1061.7 1200.0
neva huseyni evdj gerdaniye
208.6 150.0 138.3
0.0 208.6 358.6 496.9
rast dugah segah chargah

207.4 150.0 138.3
496.9 704.3 854.3 992.6
chargah neva hisar ajem

To many Arab and Turkish musicians, although not all, one
defining characteristic of a usual Rast tetrachord is that the
larger neutral second precedes the smaller, here 150.0-138.3
cents. Yes, these specific step sizes happen to approximate
superparticular ratios, but the general point is that the first
is somewhat larger than the second. Here the difference is rather
subtle, not quite 12 cents, but enough to mean for me and many
Near Eastern musicians that reversing the order to 138.3-150.3
cents, and retaining the initial tone of the tetrachord, would
properly define a related but different maqam sometimes called in
Arab theory Rast Jadid or "New Rast," and which I call Mustaqim
because of its resemblance to a mode of that name described by
Ibn Sina in the early 11th century.

Using these nine steps, we can obtain three common variations on
Maqam Rast involving different flavors of the sixth degree
(neutral or major) and seventh degree (minor or neutral):

Disjunct Rast

Rast Rast
|----------------------| tone |---------------------|
208.6 150.0 138.3 207.4 207.4 150.0 138.3
0.0 208.6 358.6 496.9 704.3 911.7 1061.7 1200
rast dugah segah chargah neva huseyni evdj gerdaniye
G* A* B C* D* E* F# G*

Conjunct (Nairuz) Rast

Rast Rast
|----------------------|-------------------| tone |
208.6 150.0 138.3 207.4 150.0 138.3 207.4
0.0 208.6 358.6 496.9 704.3 854.3 992.6 1200
rast dugah segah chargah neva hisar ajem gerdaniye
G* A* B C* D* E F* G*

Suzdular (Ajemli Rast)

Rast Buselik
|----------------------| tone |---------------------|
208.6 150.0 138.3 207.4 207.4 80.9 138.3
0.0 208.6 358.6 496.9 704.3 911.7 992.6 1200
rast dugah segah chargah neva huseyni ajem gerdaniye
G* A* B C* D* E* F* G*

Disjunct Rast is the standard modern Arab or Turkish form, and
Conjunct or Nairuz Rast the standard medieval form as given by
al-Farabi (not yet under the name of "Rast"). These forms have
tones, larger neutral seconds, and smaller neutral seconds as
their only adjacent steps.

The third form known as Suzdular to some Arab theorists, and
"Ajemli Rast" in Turkish theory because of its use of the minor
seventh step ajem (a term which could also apply to the conjunct
form), has a semitone step between the major sixth degree huseyni
and the minor seventh degree ajem. The upper tetrachord with
tone-semitone-tone is known in Turkish theory as Buselik, and in
Arab theory often as Nahawand (which in Turkish terms tends to
suggest a different shade of intonation with a larger minor, or
possibly supraminor, third).

In practice, It is very common to use the neutral seventh step
evdj (Arabic awj) in ascending and the minor seventh step ajem
(Arabic `ajam) in descending, while maintaining the major sixth
degree huseyni; and the conjunct form with the neutral sixth
degree hisar is also common.

Note that in all these forms, the shared element of the lower or
"root" Rast tetrachord, with the steps rast-dugah-segah-chargah
(Arabic rast-dukah-sikah-jahargah), from the Persian "rast"
meaning "right, correct, standard" plus the words for the
"second," "third," and "fourth" steps. These counting names
underscore both the centrality of the step rast itself, and the
form of the Rast tetrachord as having pride of place in defining
the most "fundamental" steps of the gamut.

For a performer of maqam music, the term "Maqam Rast" embraces
not only the above variations on the maqam proper, but also the
set of common modulations. Let's quickly look at one of these, a
shift from Maqam Rast on perde rast to Maqam Sikah located, not
so surprisingly, on perde sikah (the same name as Persian or
Turkish Segah, but a different mode than the Persian dastgah or
Turkish maqam bearing this name and founded on this same
degree).

Maqam Sikah

Sikah Rast Rast
|---------------|------------------------|---------------|
138.3 207.4 207.4 150.0 138.3 208.6 150.0
0.0 138.3 345.7 553.1 703.1 841.4 1050.0 1200.0
segah chargah neva huseyni ajem gerdaniye muhayyer tiz_segah
B C* D* E* F# G* A* B

Note that while Maqam Rast has larger neutral intervals above its
final, for example the third rast-segah at 358.6 cents, the sixth
rast-hisar at 854.3 cents, and the seventh rast-evdj at 1061.7
cents, here smaller neutral intervals prevail in terms of the
final. Thus in the lower Sikah trichord we have a Zalzalian second
at 138.3 cents and a third at 345.7 cents; elsewhere we have a
sixth segah-gerdaniye at 841.4 cents and a seventh segah-muhayyer
at 1050.0 cents. A widely shared although not universal
understanding is that the neutral intervals above the final of
Rast are larger than those above the final of Sikah.

At the same time, there is a subtle contrast, because the middle
tetrachord of Maqam Sikah is none other than a usual Rast with
its prominent larger neutral third to compare with the smaller
size in the SIkah trichord. Here, as it happens, the difference
is not quite 13 cents, or a bit more than half a comma (compare
segah-neva with neva-ajem). The upper trichord, also described as
Rast, is typically completed by a step of 138.3 cents arriving at
the step tiz chargah at an octave above chargah. In effect, we
thus have an upper tetrachord (gerdaniye-tiz chargah) like the
root tetrachord of Maqam Rast transposed up an octave.

We might say generally that the narrower neutral intervals are in
the "lower central" range, and the wider ones in the "higher
central" range. The "central range" might be around 135-160 cents
for neutral seconds and 342-360 cents for neutral thirds. Here
the difference in shading is rather subtle.

Shifting to a more exuberantly Ottoman flavor of Rast, however,
may make these nuances more obvious.

-------------------------------------------------
2. A set of perde-s for Maqam Rast, Ottoman style
-------------------------------------------------

While a neutral third of around 357-359 cents might be acceptable
for a Turkish Rast, this would be a "low" Rast. To obtain a more
distinctively Ottoman flavor, we must place perde rast and thus
the whole system of perde-s at another keyboard location, with
the step F#* as one of my favorite choices, and one that cries
out for at least one extra step beyond the usual 17 simply to
navigate the different forms of Maqam Rast itself:

Perde Category Cents from rast Arab/keyboard Step size

rast unison 0.0 C / F#*
80.9
shuri min2 80.9 Db G*
70.3
zengule Zal2 151.2 Dd G#
57.4
dugah Maj2 208.6 D G#*
80.9
kurdi min3 289.5 Eb A*
80.9
segah Zal3 370.3 Ed Bb*
69.1
nishabur Maj3 439.5 E B
57.4
chargah Perf4 496.9 F B*
80.9
hijaz small "TT" 577.7 Gb C*
69.1
sabah large "TT" 646.9 Gd C#
57.4
neva Perf5 704.3 G C#*
80.9
beyati min6 785.2 Ab D*
80.9
hisar Zal6 866.0 Ad Eb*
69.1
sarp huseyni Maj6 935.2 A E
57.4
ajem min7 992.6 Bb E*
80.9
evdj Zal7 1073.4 Bd F*
69.1
mahurek Maj7 1142.6 B F#
57.4
gerdaniye Perf8 1200.0 C F#*

This position is ideal for the large neutral or submajor
intervals it provides, but has the complication that some usual
major intervals are available only in their septimal rather than
regular forms, a comma higher than in our Arab or low Turkish
Rast. In varieties of Rast using the septimal major sixth step
known in Ozan's Turkish naming as "sarp huseyni," a "steep"
version of the step huseyni, we will find a septimal version of
the major second step, "sarp dugah" at 232.0 cents (located at A
on the keyboard), useful at a perfect fifth below sarp huseyni.

Thus, with a choice between regular dugah or sarp dugah for the
second step, we can form Rast variants such as the following:

Disjunct Rast

Rast Rast
|-----------------------| tone |-------------------------|
232.0 138.3 126.6 207.4 230.9 138.3 126.6
0.0 232.0 370,3 496.9 704.3 935.2 1073.4 1200.0
rast sarp_dugah segah chargah neva sarp_huseyni evdj gerdaniye
F#* A Bb B* C#* E F* F#*

Conjunct (Nairuz) Rast

Rast Rast
|----------------------|-------------------| tone |
208.6 161.7 126.6 207.4 161.7 126.7 207.4
0.0 208.6 370.3 496.9 704.3 866.0 992.6 1200.0
rast dugah segah chargah neva hisar ajem gerdaniye
F#* G#* Bb* B* C#* Eb* E* F#*

Suzdular (Ajemli Rast)

Rast Buselik
|----------------------| tone |---------------------|
232.0 138.3 126.6 207.4 230.9 57.4 207.4
0.0 232.0 370.3 496.9 704.3 935.2 992.6 1200.0
rast sarp-dugah segah chargah neva huseyni ajem gerdaniye
F#* A Bb* B* C#* E E* F#*

Here the conjunct form is really the best place to start, because
it shows the contrast between large and small neutral seconds at
161.7 and 126.6 cents. This difference of a full 35 cents might
be described as that between submajor and supraminor. In all
versions, the large neutral thirds at 369.1 or 370.3 cents have a
submajor quality also, both in a purely melodic context or in
vertical situations where they very nicely expand to fifths with
a musical effect analogous to that of a similar progression with
a regular major third at 414.8 or 416.0 cents. Both flavors of
thirds, submajor or regular major, are rather complex, and so
make expansion to a fifth by stepwise expansion in contrary
motion a very effective resolution. While a 357-359 cent third
can also be used nicely in such progressions, the central neutral
flavor is rather different than submajor/major.

In the forms with septimal whole-tones, we have tetrachords with
a large tone near 8:7 plus two small neutral seconds at 138.3 and
126.6 cents. While the contrast between the latter two steps is
muted by comparison to 161.7/126.6 cents in the conjunct form,
there is still the subtle distinction that 138.3 cents is a
"small central neutral second," while 126.6 is more of a
"supraminor second" or "quasi-semitone."

In practice, one might use either form of the major second step
(dugah or sarp dugah) depending on the context in any of these
Rast variations, for example using the near-8/7 step in ascending
toward a near-12/7 major sixth, but the 9/8 step when descending
or more generally when focusing on the lower tetrachord.

To appreciate how the territory of neutral intervals in this
Turkish style of tuning for Rast differs from that of the Arab
style also sometimes used in Turkey, let us consider the Turkish
counterpart of the Arab Maqam Sikah, which likewise is built on
the third step of Maqam Rast, perde segah. While the structure of
Maqam Segah differs somewhat from the Arab Sikah, both maqamat
have perde segah (Arabic sikah) as their final, and have
trichords or tetrachords above this final highlighting the steps
segah-chargah-neva (Arabic sikah-jaharkah-nawa).

An interesting feature of Maqam Segah is that it has distinct
ascending and descending forms. It is common for maqamat to have
certain steps often inflected differently differently depending
on the direction or focus of motion, for example the seventh step
of Rast frequently taken as the neutral seventh evdj when rising
toward the octave, and as the minor seventh ajem in descending.
In Segah, however, the contrast is more dramatic, bringing into
play in descent a strikingly disjunct tetrachordal structure:

Maqam Segah ascending:

Segah Hijaz
|---------------------| tone |------------------------|
126.6 207.4 161.7 207.4 126.6 289.5 80.9
0.0 126.6 334.0 495.7 703.1 829.7 1119.1 1200.0
segah chargah neva hisar evdj gerdaniye sunbule tiz_segah
Bb* B* C#* Eb* F* F#* A* Bb*

Maqam Segah descending:

Segah Mahur
|---------------------| apot |-------------------------| limma |
126.6 207.4 161.7 126.6 207.4 208.6 80.9 80.9
0.0 126.6 334.0 495.7 622.3 829.7 1038.3 1119.1 1200.0
segah chargah neva hisar ajem gerdaniye muhayyer sunbule tiz_segah
Bb* B* C#* Eb* E* F#* G#* A* Bb*

In contrast to the large neutral or submajor third of our Turkish Rast at
369.1 or 370.3 cents, Maqam Segah features a small neutral or supraminor
third above the final at 334.0 cents (segah-neva). The lower tetrachord
also has a supraminor second (segah-chargah) above the final, followed by a
regular tone (chargah-neva) and then a large neutral or submajor second
from the small neutral third step to the fourth (neva-hisar).

In the ascending form, this lower Segah tetrachord is followed by a tone
and then an upper Hijaz tetrachord, a genus often having a lower neutral
second (here the same 126.6-cent size as in the lower tetrachord), some
kind of minor third, and then a semitone to complete the octave. The step
sizes in this realization are 126.6-289.5-80.9 cents.

The descending form of Segah, as analyzed by Ozan Yarman in his thesis and
elsewhere, presents a striking instance of disjunct tetrachords with
intervening intervals other than tones. From tiz segah, the octave of the
final, we first descend a regular limma or diatonic semitone to the step
sunbule, an octave plus a minor third above perde rast, and an octave above
rast's minor third step called kurdi. This is the one step in the basic
seyir, i.e. the "path" or melodic development of Maqam Segah (Arabic sayr),
not found in our three variations on Maqam Rast shown above.

From this sunbule step, we proceed to explore a tetrachord of which it is
the fourth: Mahur (often known in Arab theory as `Ajam) with the intervals
in ascending order of tone, tone, and semitone, here a regular
207.4-208.6-80.9 cents (ajem-gerdaniye-muhayyer-sunbule). We then encounter
another interesting interval serving to connect two disjunct tetrachords:
from the lowest step ajem of the Mahur tetrachord, we descend by an apotome
of 126.6 cents to hisar, the upper note of the root Segah tetrachord.

Thus while our more typically Arab shading of Maqam Rast and its companion
Maqam Sikah reflected a rather subtle contrast between intervals in the
higher and lower regions of the central neutral range, our Turkish
Rast/Segah pair shows a much more dramatic contrast of submajor/supraminor.
In a polyphonic setting, just as a submajor third at 369-370 cents will
expand to a fifth by stepwise contrary motion much like a major third, so a
supraminor third at 334 cents (or sometimes 335 cents in this tuning) can
contract to a unison much like a regular minor third at 288.3 or 289.5
cents.

The basic contrast, however, is itself a primary melodic phenomenon quite
apart from the possible modern element of polyphony. While a Turkish Rast
tetrachord in this tuning features a supraminor second of 126.6 cents
ascending from the submajor third to the fourth (e.g. segah-chargah), the
corresponding Segah tetrachord has a descending supraminor second to the
final (e.g. chargah-segah). In either maqam, the "quasi-semitonal" nature
of this step makes it distinct from a neutral second in the central range,
and yet more so from the large neutral or submajor second of Rast (in its
usual form with a tone around 9:8) and Segah at 161.7 cents.

In a Turkish context, the significant of this not inappreciable contrast is
heightened when we consider that Rast and Segah alike are often performed
in an interpretation approaching 5-limit major and minor intervals
(e.g. rast-segah near 5:4 and segah-neva near 6:5), of which the submajor
and supraminor shadings favored here may be seen as kindred variations.

Ozan Yarman has suggested that the rast-segah third may vary from around
27/22 (355 cents) to 5/4 (386 cents), with the sizes here of 369-370 cents
around the middle of this range. Whatever the fine points of flexible pitch
performance as measured in recent studies, they are clearly distinct from a
24-EDO model, since the favored range is distinctly higher than 350 cents.

---------------------------------
3. Some conclusions and questions
---------------------------------

As these examples show, maqam music can feature either subtle or dramatic
contrasts between sizes of neutral intervals.

A submajor/supraminor contrast on the order of 35 cents, as in our examples
of one flavor of Turkish tuning (with some of the fine details reflecting
my temperament rather than any traditional Near Eastern system), is aurally
obvious and quite distinct from a model such as 24-EDO or 17-EDO where
all neutral seconds and thirds have identical sizes. For those seeking
models among smaller EDO tunings, 29-EDO or 36-EDO would be much more to
the point.

A not quite so dramatic but still clearly significant distinction occurs
when tunings of neutral intervals closely approximate the 53-comma model
favored in Turkey and Syria, and sometimes borrowed by Arab theorists from
other regions who wish to describe the fine points of intonation in the
course of a maqam performance. For example, musicians following something
like this model might play a small neutral second at around 6 commas or 136
cents, and a large neutral second at 7 commas or 158 cents; and tune
neutral thirds at around 15 commas or 340 cents and 16 commas or 362
cents. These differences should be discernible and appreciable.

A more complex situation occurs in evaluating flexible pitch performances
where intervals usually remain in the central neutral range. Are we merely
hearing small variations around an essentially equal division of the fifth
into two neutral thirds, or of the minor third into two equal Zalzalian
seconds -- whether approximating 24-EDO, 17-EDO, or some other model? Or is
there some purposeful distinction, however subtle it may seem, especially
to the uninitiated or only partially initiated?

One much look at each case in context. For example, the Iranian master
Dariush Tala`i favors a tuning of a Shur tetrachord at 140-140-220 cents, a
division of a 280-cent minor third into two equal neutral seconds not too
far from 17-EDO (141-141-212 cents). This tuning resembles that reported by
Nelly Caron and Dariouche Safvate in 1966 at 136-140-224 cents, with the
slight difference between the neutral second steps possibly seen as an
inconsequential variation rather than a characteristic of this modal
family.

In contrast, Hormoz Farhat's preferred tuning of 135-160-200 cents makes a
very clear distinction between small and large neutral seconds, with the
smaller preceding the larger, a distinction which he observes in describing
and notating other dastgah-s (Persian plural dastgah-ha) or modal families
also.

With subtle distinctions such as those which may be found in some regions
of the Arab world where smaller and larger neutral intervals within the
central range vary by considerably less than a comma, but possibly in
meaningful patterns, close study is required.

For example, suppose we find that in a number of pieces in Maqam Rast and
Maqam Bayyati as performed in the Egyptian tradition, neutral second sizes
seem to vary within a range of around 135-155 cents. If we find further
that the interval dugah-segah (Arabic dukah-sikah) tends to have a size of
around 150-155 cents in Rast, where it leads from the major second to
neutral third above the final, but 135-145 cents in Bayyati, where it leads
from the final to the neutral second above, then there is evidently a
subtle but significant difference. The 150-138 cent or 138-150 cent
division available in my temperament provides an example of this kind of
subtle distinction.

In fact, Scott Marcus reports that traditional Egyptian performers so hold
that the step sikah (Turkish segah) should be lower in Bayyati than in
Rast, and suggests a range of around 135-140 cents. He does not mention in
the writings I have read any estimate for the size of dukah-sikah in Rast,
so my hypothetical guess of 150-155 cents is simply that. Systematic
measurements would place Marcus's observation in a broader and more fully
fleshed out context.

On the other hand, we might among some performers or performances encounter
a situation where a neutral second in Maqam Bayyati seems to hover "around
150 cents" -- or possibly "around 147 cents," the mean of 32/27 Pythagorean
semiditone or minor third at 294 cents which Marcus suggests may be about
the norm for many Egyptian performers -- with variations around this
pattern of two essentially equal steps. Or, with performers who like Ali
Jihad Racy prefer a minor third in Bayyati distinctly smaller than
Pythagorean, we might encounter a division like that suggested by Tala`i
for the often analogous Persian modal family of Shur at 140-140-220 cents.

We should not expect a general consensus among all Near Eastern performers,
even those in the same region sharing a similar tradition, on these
points. Thus sources in the Syrian tradition give the usual tuning for the
lower tetrachord of Maqam Bayyati as either 7-6-9 commas (Tawfiq al-Sabbagh
as reported by Ali Jihad Racy) or 6-7-9 commas (one source reporting the
practice of Aleppo). The former concept fits al-Sabbagh's 24-note gamut
based on the 53-comma system which at the usual location for Bayyati
accommodates only a 7-6-9 comma or 158-136-204 cent division, while the
latter may also fit the traditional Egyptian performers described by
Marcus. The Egyptian concept may, however, typically involve a more subtle
distinction than suggested by the 6-7-9 concept -- say, for example
something on the order of 140-154-204 cents if a 32/27 third or thereabouts
is favored.

In short, a balanced appraisal should assume neither that EDO models with
equal neutral seconds and/or thirds are the prevailing norm, nor that
precisely or approximately equal divisions are always anathema to
traditional performers. There is evidently a continuum ranging from
essentially equal divisions with small and unsystematic variations through
subtle but significant distinctions to routine differences on the order of
a comma or even more, as with our supraminor/submajor steps and intervals
differing by about 35 cents.

Marcus reports a perception among some Arab performers that sikah (or
Turkish segah), the third of Maqam Rast, tends to rise as one travels from
Egypt to Palestine or Lebanon, from there to Iraq, and finally to Turkey,
where it may actually shift from a neutral to a major third. The
perceptions of a Turkish musician such as Ozan Yarman support this
suggested pattern at least in part: around 360 cents, which might be deemed
an average or even somewhat bright Rast in much of the Arab world, is in
Turkey a "low" Rast, with 370 cents close to the likely historical Ottoman
norm, and somewhere close to 5/4 (Ozan has suggested 382 cents as one
pleasant spot) as a high Rast of the kind which Marcus's Arab musicians may
have found noteworthy.

The Lebanon composer and theorist Amine Beyhom likewise suggests that in
different traditions of maqam music, the placement of the step sikah (or
Turkish segah) may range from about 330 cents above rast (for a Bayyati in
the popular Lebanese style, where the primary reference might actually be a
placement about 130 cents above dukah, the major second step of Rast and
the final of Bayyati) to a comma below Pythagorean in a Turkish Rast
(i.e. 384-385 cents in a 53-comma model based on Pythagorean tuning or
53-EDO). Ozan Yarman similarly identifies a number of flavors of segah on
his 79-tone qanun ranging from around 332 to 392 cents.

In the study of how this range of 50 cents or more is actually used in
different regional and personal practices as they affect different maqamat,
almost everything remains to be done, despite some promising beginnings and
insights by adept performers and listeners who provide a fine
starting-point for further research.

With or without the use of superparticular or other rational ratios for
neutral intervals as reference points, we can take a pragmatic approach in
appreciating the great intonational diversity which actually obtains.

Most appreciatively,

Margo Schulter
mschulter@...