Yahoo Tuning Groups Ultimate Backup tuning Namo temperament

> Yesterday I noticed that the following scale by Ozan Yarman
> can reasonably be tempered in the {144/143, 243/242}
> teemperament, with however the drastic effect of reducing the
> number of notes from 10 to 8:

Hello, Gene!

Here I'm taking your temperament to be 99-EDO ennealimmal, or
something so close that the distinction is rather academic, at
least for our present purposes

! yarman_ushaq.scl
!
10-tone Ushaq/Huseyni by Ozan Yarman
10
!
13/12
12/11
32/27
4/3
3/2
128/81
13/8
18/11
16/9
2/1

My first comment is that while simply tempering our the 144/143
is something you certainly have the power to do here, another
approach which ennealimmal brilliantly supports is to use your
equal bisection of the near-13/11 third into two 145-cent steps
as _one_ of the alternatives. Let's consider the equal bisection
first. One historian, Walter Feldman if I'm correct, suggests
that a near-equal division of the 32/27 may have been favored in
Ottoman practice around 1700 or so in order to permit use of the
same fret for either a large or small neutral second -- a bit
like the desire in the 16th-century on the lute to use the same
fret for either a major or minor semitone, thus 12-EDO
approximations.

This tempers as

! ushaq99.scl
!
yarman_ushaq in 99ef tempering
8
!
145.45455
290.90909
496.96970
703.03030
787.87879
848.48485
993.93939
1200.00000

In fact, either this or 41-EDO has a division very close to
medieval rational option, 4608:4235:3888 (146.134-148.001 cents)
for dividing 32/27 into two near-equal parts. The trick back then
was simply to place a fret midway between the 256/243 and 9/8
frets, resulting in an arithmetic bisection of the apotome and an
almost geometrically equal division of 32/27. (Since 32/27 is
equal to a limma plus an apotome plus a limma, an equal neutral
second would be a limma plus half of an apotome.) Cris Forster
discusses this division in his _Musical Mathematics_.

However, what 99-EDO or thereabouts also lets us do is have
subtly unequal divisions of the kind that Ozan Yarman was seeking
here. We could have 133-158 cents for an unequal division of the
291-cent third with a distinction of around a comma, or a 133-145
division for a smaller 278-cent third that might be very
stylistic in some Turkish styles (as well as in the related modal
family of Persian Shur).

So neutral seconds at 133-145-157 cents, and minor thirds at
278 and 291 cents, would give lots of flexibility!

Also, Ozan Yarman meant this tuning to be used for either Makam
Ushaq or Makam Huseyni. While all Turkish performers do not agree
with this in theory or practice, there is at least in some
schools a tendency to play the second degree of Huseyni higher,
with 157 cents a reasonable choice in this gamut -- I'd say just
below or around 11/10 might be ideal, but 169.7 cents a bit high
(Ozan, at least, feels that something as large as 1/7 octave is
not so generally characteristic of maqam, so it's a fine line).

But your tuning very neatly supports either 133-145 or 145-145
for Ushaq, and 157-133 for Huseyni. Actually some measurement
I've seen suggest even 157-121 might not be unstylish for a
Turkish Huseyni, although 121 cents is more a large semitone (say
15/14) than a small neutral second (say 14/13). Given that a
Turkish "middle interval" may be as small as a Pythagorean
apotome or as large as a double limma -- from around 16/15 to
10/9, putting aside schismas -- 157-121 as an option wouldn't be
too surprising, and it's yet another choice in ennealimmal!

Also, there's another convention mentioned by Scott Marcus in
Egypt and shown by some Turkish measurements: in Turkish Ushaq,
the neutral second tends to be smaller than the neutral sixth; in
Huseyni, they may both tend to be high. Thus in Huseyni, you
might do 157-861 cents; in Ushaq, something like 145-861 or
even 133-861. A big advantage of ennealimmal is that you can
observe such nuances, and still have the choice of 145-291
in the lower tetrachord, for example, when you want it.

Additionally, there's an element of sheer melodic
expressiveness. Playing the neutral second step a bit higher when
ascending to the 4/3 step than when descending to the 1/1 (a
nuance noted by Ali Jihad Racy and reported by Scott Marcus), or
maybe vice versa (a possibility mentioned by Amine Beyhom), is a
mark of refinement that the highly refined ennealimmal can
support.

And for a really low Ushaq, let's not forget 133-133 with its
near-just 7/6! Ozan Yarman had one example of something this low,
but it's a nice variation on 14:13:12 or 12:13:14 with the
169/168 tempered out. I tend to observe the comma, but either is
quite valid and beautiful.

> A few hours later I noticed that this

! segah_rat.scl
!
Rationalized Arabic Seg?
7
!
9/8
11/9
4/3
3/2
27/16
11/6
2/1

One clarification: this looks like something other than Arabic
Sikah (the Arabic version of the Persian name Segah, the "third"
step or mode, etc.). It's a permutation of al-Farabi's
9:8-12:11-88:81 with the two upper steps reversed. One Arab
theorist has called this Rast Jadid or "New Rast," but Segah is
different -- more shortly.

> also makes sense in the same temperament:

! segah99.scl
!
segah_rat in 99ef tempering
7
!
206.06061
351.51515
496.96970
703.03030
909.09091
1054.54545
1200.00000

Yes, you could do it this way, using a literal hemififth, a bit
like 24-EDO or 41-EDO. But that 351-cent step, at least in a
Turkish context, has another neat and very idiomatic use for a
very clueful performance! Why note 206-364-497 cents for your
usual moderate Turkish Rast (with 364 cents close to a
theoretical 16 commas and also to one measured average), but 351
cents as a descending gesture when making a final cadence. I tend
to observe a full comma distinction (370 vs. 346 cents), but the
ideal might be a bit more subtle, and ennealimmal gives us that
more subtle option! You might also then want 1067 cents as well
as 1054 cents for a neutral seventh, etc.

And for a low Rast Jadid (or Persian modal form like Shekaste),
you might want 206-339-497. The main point is that with
ennealimmal, we have lots of these options!

But how about Segah, often known in Arabic as Sikah? Here's a
2-3-11 version based on a permutation of al-Farabi's Zalzalian
mode (zalzal.scl):

! segah-zalzalian.scl
!
Arabic Segah (or Sikah) based on zalzal.scl (step 5 = 1/1)
7
!
88/81
11/9
11/8
3/2
44/27
11/6
2/1

Note that Segah or Sikah means "third," and this is basically a
rotation of a disjunct Rast starting on the third step, or a
conjunct Rast like zalzal.scl starting on step 5 (the neutral
sixth degree). It divides into a Sikah (Segah) trichord
1/1-88/81-11/9; a Rast tetrachord 11/9-11/8-3/2-44/27; and a
Rast trichord 44/27-11/6-2/1 often tending to ascend to the
neutral second above the octave, the 176/81.

Here's a possible 99-EDO version using your 351-cent and 849-cent
intervals, for the most part, but adding something to help a
stylish performance: a slightly higher version of the neutral
seventh degree for approaching the 1/1 or 2/1 step of the mode.
So we can use 1055 cents as the regular step, but 1067 cents
for a cadential leading tone.

! arab_segah-99edo.scl
!
99-edo Arab Segah with extra slightly raised leading tone to final
8
!
145.45455
351.51515
557.57576
703.03030
848.48485
1054.54545
1066.66667
2/1

Here we could also substitute 133, 339, and 1042 cents for
145, 351, and 1054 cents, making 1067 cents a more decidedly
contrasting leading tone. With ennealimmal, a variety of shades
are available!

> Today I noticed that Robert "Inventor" Walker has a scale which also makes sense
> in this temperament:

! walker.scl
!
Robert Walker's 2.3.11.13 scale
7
!
12/11
11/9
4/3
3/2
13/8
11/6
2/1

> Robert noticed that you can temper by 144/143 and 243/242 himself. Do it and you
> get Namo[7]--a MOS of a temperament I had forgotten about, but which obviously
> keeps turning up.

I've seen things a bit like this in some of Jacques Dudon's
tunings like mohajira_r.scl where we have 59/48 and 11/6, with
this fifth narrow by 177/176; here we have 12/11 and 13/8 with
the fifth narrow by 144/143. Change the 12/11 step to 13/12, and
you have one routine JI version of Mohajira that George Secor
found also (1/1-13/12-11/9-4/3-3/2-13/8-11/6-2/1). This involves
a 352/351 distinction, which could be observed or tempered out.
And a precedent might be William Lyman Young's young-wt.scl, a
slightly different permutation of the same basic idea.

But my main point here is that ennealimmal lets us emulate some
of the comma or half-comma nuances of maqam tunings like Ozan
Yarman's 10-note set for Ushaq and Huseyni, as well as follow an
equal division of the minor third, with possible 17th-century
Ottoman precedents, if/when we're so inclined.

Happy New Year,

Margo

Namo temperament

🔗genewardsmith <genewardsmith@...>

🔗Margo Schulter <mschulter@...>

🔗Margo Schulter <mschulter@...>

🔗genewardsmith <genewardsmith@...>

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