Yahoo Tuning Groups Ultimate Backup tuning Mohajira sequences (was Jacky Ligon's scales)

Dear Margo,

Once more, thank you so much for this incredibly well-documented and
passionating answer.
I believe you should write a book (it would probably take several
volumes) on the subject of Middle-East scales, in which your
knowledge seems to have no end. I think it would be extremely useful
for many searchers, luthiers, and of course microtonal musicians.

The fundamental distinction you make between what I can now name
"Mustaqim" in its original form, and the (Arab) Rast tetrachords is
very essential indeed, as much as it suggests a potential "mirroring"
mutation between the two, that I've actually seen used with
delectation by many musicians. It is also highly symbolic that this
mirroring occurs through a comma of 144/143, that unites 11 and 13.

I laughed a lot when I read you writing about the "Maqam Mohajira" -
this would need first to be demonstrated through compositions by real
traditional musicians (if they ever get into it someday), and we are
far from that ! But I take it as a very kind and and enthusiastic
encouragement, and why not ! Are'nt Indian musicians creating new
ragas all the time, even if ragas are known "to come from the Gods",
and no one will dare to say the contrary ? (for my part as I always
say, between the Heavens and the Earth, scales are welcome ! :)
To your very complete analysis the only thing I may add from my
humble experimentations is an ensemble of migratory but coherent
versions of "Mohajira" tetrachords, that one may find in the series
described by the two main recurrent sequences issued from 9 and 13 :

36 : 39 : 44 : 48 ("Old Esfahan" ?)
44 : 48 : 54 : 59
48 : 52 : 59 : 64 (Dudon_b.scl)
54 : 59 : 66 : 72 (Dudon_a.scl)
59 : 64 : 72 : 78
66 : 72 : 81 : 88 (Medieval Iraq)
81 : 88 : 99 : 108 (al-Farabi/Rast)
88 : 96 : 108 : 117
96 : 104 : 117 : 128 (Ibn Sina/Mustaqim)
99 : 108 : 121 : 132 (meantone temperament)
117 : 128 : 143 : 156 (meantone temperament)
117 : 128 : 144 : 156 (Mustaqim reversed)

You have already mentionned some of them from the traditional
sources, and among the possible traditional issues you found, I got
especially interested like you in the "Old Esfahan" tetrachord and
its larger central tone of 209 cents. This is precisely the size of
44/39 and by coïncidence, it appears to be part of the first
tetrachord of my list, that gives a a realistic harmonic version of
this tetrachord.
If we extend it in the higher tetrachord by a Bayati, this gives
again a magnificent Mohajira heptatonic scale I used to call "Ibina"
who is perhaps among all of them, the one I used the most :
72 : 78 : 88 : 96 : 108 : 117 : 128 : 144
(1/1 13/12 11/9 4/3 3/2 13/8 16/9 2/1)
(the reference tone, for the classic mode J T J T J T J, shifted to
117...)
And its mode from 96 = Mustaqim...

This tetrachord list also shows the use of prime limit 59 that
completes the two other major ingredients (besides 3), 11 and 13.
In the Mohajira series "issued from 13" : 18 22 26 32 39 48 59 72
88, 59 appears to have a transition role between 11 and 13 in regard
of differential coherence, expressed by the neutral thirds difference
tones and equal-beating properties :
59 - 48 = 11
72 - 59 = 13
(or in the equal-beating form) :
11*22 - 4*59 = 9*22 - 4*48 = 3*(4*72 - 11*26) = 3*(4*59 - 9*26) = 6

While 24-EDO, 31-EDO then 55-EDO would be the three main cycling
attractors of the fractal generator, your mention of 44-EDO is also
interesting for 13 steps would amount to a quasi 27/22 ; however I
don't consider it to be typically representative of a Mohajira
sequence, as there are different models for generators past the half
of a pure fifth and around 27/22 one of them is "Zalarith" whose
sequence is 8x^2 - 9x = 1 and based on the -c of 12/11, but that's
another story, and already a few teapots away !...)

Anyway no one could write a better description of Mohajira and I have
nothing to add !
Thank you also very much for the musical tracks you gave, that wouldbe certainly inspiring to hear !

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Jacques

🔗Margo Schulter <mschulter@...>

> Dear Margo,

> Once more, thank you so much for this incredibly well-documented and
> passionating answer.

Dear Jacques,

Thank you for your patience in reading through my rather lengthy
discussion, and your creativity in this reply!

> I believe you should write a book (it would probably take several
> volumes) on the subject of Middle-East scales, in which your
> knowledge seems to have no end. I think it would be extremely
> useful for many searchers, luthiers, and of course microtonal
> musicians.

Of course, my knowledge is very "partial" in both senses that world
can have in English: it is very incomplete knowledge, and also
"partial" in the sense of being biased or skewed toward certain
patterns which attract me. However, I warmly agree that such a book,
or possibly several such studies by different authors (with the modal
systematics of Amine Beyhom as one important approach), would do much
to deepen our understanding of Middle Eastern traditions.

> The fundamental distinction you make between what I can now name
> "Mustaqim" in its original form, and the (Arab) Rast tetrachords is
> very essential indeed, as much as it suggests a potential
> "mirroring" mutation between the two, that I've actually seen used
> with delectation by many musicians. It is also highly symbolic that
> this mirroring occurs through a comma of 144/143, that unites 11
> and 13.

As an aside, I might mention that in Zephyr-24, a superset of Wilson's
1-3-7-9-11-13 eikosany, 144/143 is pervasive, often as a scale step
which I used as a gamelan comma in the short piece _For Erin_. See
<http://www.bestII.com/~mschulter/mmm9948_ForErin.txt>.

> I laughed a lot when I read you writing about the "Maqam Mohajira"
> - this would need first to be demonstrated through compositions by
> real traditional musicians (if they ever get into it someday), and
> we are far from that ! But I take it as a very kind and and
> enthusiastic encouragement, and why not ! Are'nt Indian musicians
> creating new ragas all the time, even if ragas are known "to come
> from the Gods", and no one will dare to say the contrary ? (for my
> part as I always say, between the Heavens and the Earth, scales are
> welcome ! :)

Yes, there is a certain humor in speaking of Mohajira as a "maqam" at
this point, but you rightly understand my spirit of "enthusiastic
encouragement!" And I do recall that in the Ottoman tradition, honors
were sometimes awarded to a musician who celebrated the divine gift of
music by coming upon some new and pleasing maqam.

Might in fact a "Maqam Mohajira" be known among traditional Arab
musicians by a name such as Sikah Baladi? Here is a site with examples
in a format which I do not yet have the capability of playing, but
which perhaps might give a sample of some intonations:

<http://www.maqamworld.com/maqamat/sikah.html#sikah-baladi>

> To your very complete analysis the only thing I may add from my
> humble experimentations is an ensemble of migratory but coherent
> versions of "Mohajira" tetrachords, that one may find in the series
> described by the two main recurrent sequences issued from 9 and 13 :

Thank you for a most illuminating catalogue which moves me in turn to
some healthy humility, especially in taking the opportunity to clarify
between the documented Persian understanding of the "Old Esfahan" and
my own interpretation in Zephyr-24, for example, where your ratios are
a natural choice, or in temperaments where the regular major second is
around a 44/39. I will address thisshortly, but would like to focus on
the beauties of your catalogue:

> 36 : 39 : 44 : 48 ("Old Esfahan" ?)
> 44 : 48 : 54 : 59
> 48 : 52 : 59 : 64 (Dudon_b.scl)
> 54 : 59 : 66 : 72 (Dudon_a.scl)
> 59 : 64 : 72 : 78
> 66 : 72 : 81 : 88 (Medieval Iraq)
> 81 : 88 : 99 : 108 (al-Farabi/Rast)
> 88 : 96 : 108 : 117
> 96 : 104 : 117 : 128 (Ibn Sina/Mustaqim)
> 99 : 108 : 121 : 132 (meantone temperament)
> 117 : 128 : 143 : 156 (meantone temperament)
> 117 : 128 : 144 : 156 (Mustaqim reversed)

A few quick points about some of the felicities here. First, I am
delighted how you draw on Safi al-Din al-Urmawi's 64:59:54:48 ratios
in a modern -c context; I have thought of his tetrachord as a nice
shading for Maqam Bayyati at 141-153-204 cents rather close to
52:48:44:39 at 139-150-209 cents (here the string ratios come to me
more easily). Scott Marcus says that in Egyptian practice the minor
third may be close to 32/27, with the lower step at around 135-145
cents, so it seems that Safi al-Din's tetrachord may fit well.

Also, as a lover of the 352/351 relationship, I am pleased to see how
we sometimes have a 44/39 tone, and sometimes a "justly tempered"
fourth at 117/88. I guess my favorite regular temperaments at around
704-705 cents strike a certain compromise between these situations.

Finally, I never before considered 144/143 in terms of meantone, but
indeed 143:128 is close to Zarlino's 2/7-comma temperament!

And I love this kind of systematic exploration of possibilities and
permutations,

> You have already mentionned some of them from the traditional
> sources, and among the possible traditional issues you found, I got
> especially interested like you in the "Old Esfahan" tetrachord and
> its larger central tone of 209 cents. This is precisely the size
> of 44/39 and by co?ncidence, it appears to be part of the first
> tetrachord of my list, that gives a a realistic harmonic version of
> this tetrachord.

As I should have emphasized, 132-209-154 cents is merely my tempered
tuning in one regular 24-note system I favor, with another offering a
closer approximation at 138-208-150 cents of what I agree is an ideal
just tuning for this interpretaton at 36:39:44:48. However, the modern
Persian discussions about the "Old Esfahan" (the only ones I know) are
much more general, the main idea being "small neutral second, tone,
large neutral second." From Farhat's fretting diagram one might think
in terms of something like 135-205-160 cents to fit this description
(e.g. G-Ap-Bp-C), although his chosen location at D-Ep-F>-G would
actually yield in his tuning a Buzurg at 135-225-135 cents.

Interestingly a central tone around 44/39 does seem to occur in a
measured performance by setar master Ahmad Ebadi as reported by Jean
During, with steps of about 140.7-209.7-140.7 cents. Whatever kind of
an Esfahan this is, I would, assuming these measurements are accurate,
call it one shading of the Mohajira we seek in traditional practice.

> If we extend it in the higher tetrachord by a Bayati, this gives
> again a magnificent Mohajira heptatonic scale I used to call
> "Ibina" who is perhaps among all of them, the one I used the most :

> 72 : 78 : 88 : 96 : 108 : 117 : 128 : 144
> (1/1 13/12 11/9 4/3 3/2 13/8 16/9 2/1)
> (the reference tone, for the classic mode J T J T J T J,
shifted to 117...)

> And its mode from 96 = Mustaqim...

That is indeed a magnificent scale and a wonderful connection to Ibn
Sina! Here is a tempered version in Peppermint, a 24-note tuning based
on Keenan Pepper's regular temperament at 704.096 cents (using two
12-note chains at 58.68 cents apart for some just 7/6 thirds), which
shades the 16/9 to something very close to a 39/22:

! pep_dudon_ibina_E.scl
!
Peppermint tempering of Dudon's Ibina: 72:78:88:96:108:117:128:144
7
!
138.20166
346.39287
495.90439
704.09561
842.29727
991.80879
2/1

> This tetrachord list also shows the use of prime limit 59 that
> completes the two other major ingredients (besides 3), 11 and 13.

Might 23 sometimes arise? I reflect here on 23:16 (628 cents, close to
the 56:39 in Buzurg) or 23:14 (a larger neutral sixth at 859 cents,
a tad wider than 64:39), for example.

> In the Mohajira series "issued from 13" : 18 22 26 32 39 48 59 72 88,
> 59 appears to have a transition role between 11 and 13 in
> regard of differential coherence, expressed by the neutral thirds
> difference tones and equal-beating properties :

> 59 - 48 = 11
> 72 - 59 = 13
> (or in the equal-beating form) :
> 11*22 - 4*59 = 9*22 - 4*48 = 3*(4*72 - 11*26) = 3*(4*59 - 9*26) = 6

Could this be another instance where "spectrum coherence," the
proximity of 64:59 to 13:12 and 59:54 to 12:11, somehow relates to
these -c connections?

Also, I notice that the differences in the series sum up lots of the
relevant prime factors or their multiples:

18 22 26 32 39 48 59 72 88
4 4 6 7 9 11 13 16

Indeed 4:6:7:9:11:13 is a hexad summing up the main harmonic factors
in lots of tuning systems I use! A small point is that each pair of
adjacent terms define the ratio of a neutral third -- except for 22:26
or 13:11, one of my favorite sizes for a regular minor third.

> While 24-EDO, 31-EDO then 55-EDO would be the three main cycling
> attractors of the fractal generator, your mention of 44-EDO is also
> interesting for 13 steps would amount to a quasi 27/22 ; however I
> don't consider it to be typically representative of a Mohajira
> sequence, as there are different models for generators past the
> half of a pure fifth and around 27/22 one of them is "Zalarith"
> whose sequence is 8x^2 - 9x = 1 and based on the -c of 12/11, but
> that's another story, and already a few teapots away !...)

Curiously, most of my experience has been with temperaments around
704-705 cents where a Mohajira mode or chain of generators involves
two unequal neutral thirds, for example 341-363 cents at 704.607
cents. Your Soria 17+2 versions, while far more intricate, do seem to
have a kindred spirit, as well as things like hemifourths that i miss
in such regular schemes. George Secor's 17-note well-temperament
(secor.scl in my dated version of the Scala archives) has a spectrum
of shadings really inviting Mohajira as a tetrachord, mode, or method
of subset generation.

> Anyway no one could write a better description of Mohajira and I
> have nothing to add !

Please let me say what a pleasure it is to be a part of your saga of
discovering, rediscovering, or helping us better to recognize the
beauty of Mohajira!

> Thank you also very much for the musical tracks you gave, that would
> be certainly inspiring to hear !

And you are immensely adding to my knowledge and appreciation of maqam
music both known and yet evolving. Mohajira is a most fertile theme,
as you have known for almost two decades and I am happily learning.

With many thanks,

Margo
mschulter@...

🔗genewardsmith <genewardsmith@...>

🔗Margo Schulter <mschulter@...>

Dear Jacques and all,

Please let me explain that although this article is prompted
by a new "10+1" or "un/decatonic" set I am exploring, I am
including it here because I have a question as to whether a
mode I came upon might have any interesting from a -c
perspective. My original idea was a 10-note gamelan set
where the notes for slendro would alternate with those for
a 5-note pelog, but I soon found myself making it 10+1 to
include a complete tempered version of Wilson's 1.3.7.9
hexany.

What I quickly realized was that the 10+1 version also
completed a couple of useful maqam/dastgah sets, and that
there were lots of Mohajira tetrachords to explore in
various modes, as well as some complete Mohajira modes.

After reading your recent post about the "Ibina" tuning of

72 78 88 96 108 117 128 144
1/1 13/12 11/9 4/3 3/2 13/8 16/9 2/1

I searched for an approximation in my 11-note set, but
could not find the right notes in the right places.
However, I did find this, which I might not have noticed
if I were using the full 24-note temperament from which
my subset comes, where I would likely have found what I
sought and looked no further:

0 132 341 474 705 837 969 1200
132 209 132 231 132 132 231

This turns out to be trivalent scale, with the tempering out
of the 169/168 (so usefully observed in your s-n-buzurg.scl
in the Ethno2 collection), so various just interpretations
are possible. Here is one seeking to keep mostly to your
ratios, with the fourth and seventh each a 64/63 lower:

8 13 9 18 12 12 24
96 104 117 126 144 156 168 192
1/1 13/12 39/32 21/16 3/2 13/8 7/4 2/1
0 139 342 471 702 841 969 1200
13:12 9:8 14:13 8:7 13:12 14:13 8:7
139 204 128 231 139 128 231

The upper tetrachord is one interpretation of Ibn Sina's
tetrachord of Bayyati or Shur, and the lower a kind of
Mohajira variation where we have two smallish neutral
seconds plus a central step of around 9:8 rather than
the 8:7 of Buzurg, thus arriving at 21:16 rather than 4:3.
Indeed, if we exchange the positions of the 9:8 and 8:7
steps in the lower pentachord, we should have a usual
Buzurg tetrachord plus a disjunct septimal Bayyati

The 21/16 might actually be a bit tame compared to
your s-n-buzurg.scl, and is part of Wilson's hexany,
which I take to be of the N or M type, or possibly
both:

48 54 56 63 72 84 96
1/1 9/8 7/6 21/16 3/2 7/4 2/1

Anyway, I'll go more into the 10+1 set in other
posts, but wanted to thank you both for the
inspiring example of your Ethno2 (which I still
need to review!), and your Ibina tuning which. led me to this septimal variant.

! eb24-moha-bayyati-septimal_Eb.scl
!
Lower Mohajira tetrachord with 21/16; upper Bayyati ~12:13:14:16
7
!
132.24835
341.46217
473.71052
704.60690
836.85526
969.10361
2/1

With many thanks,

Margo

🔗Margo Schulter <mschulter@...>

>> Also, as a lover of the 352/351 relationship, I am pleased to see
>> how we sometimes have a 44/39 tone, and sometimes a "justly
>> tempered" fourth at 117/88. I guess my favorite regular
>> temperaments at around 704-705 cents strike a certain compromise
>> between these situations.

> Those are your favorites? I'm a big fan of 46et myself, but I
> thought you preferred 17 or 34.

Dear Gene,

Thank you for asking this question at a time when I'm looking back on
the summer of 2000, ten years ago, when I first got involved with
temperaments in what I came to call the "704-cent neighborhood."
Here are my first impressions, with a notable absence of any
discussion of Near Eastern music, which I was only to start exploring
in 2001-2002 thanks to the inspired mentorship of George Secor and the
very experienced and encouraging hand of Can Akkoc as I took my first
steps into the world of the maqam.

<http://www.bestII.com/~mschulter/NeoGothic-Parts_1_and_2.txt>

Please let me clarify that while I look on my favorite 24-note open
systems as having a kinship to 17-EDO or related unequal tunings such
as George Secor's 17-WT and now Jacques Dudon's Soria 17+2 versions,
and while these 24-note systems use shades of temperament quite close
to 46-EDO, the 24-note approach has its own logic.

In the e-based temperament at 704.607 cents, we have a single chain of
24 notes, with fifths about 2.65 cents wide. In Peppermint, based on
Kennan Pepper's proposed "Noble Fifth" temperament, we have fifths at
704.096 cents, with two 12-note chains at 58.680 cents apart so as to
provide via this "artificial diesis" some pure 7:6 minor thirds. This
involves stretching G#-D#, the middle fifth of the 23-fifth chain, by
about 11 cents -- a nice size for gamelan, along with the
approximations of 21:16 and 32:21 available in both systems. However,
as Jacques has reminded me, gamelan really also wants some hemifourths
closer to 250 cents, one good reason for using other systems too!

While the e-based temperament grew out of a mathematical speculation
in the early summer of 2000, we might describe it practically as
in the region where 15 fifths up yield a near-pure 7:4; 11 fifths
up yield a near-pure 11:8; and, interestingly, 6 fifths up yield a
near-pure 23:16. In Peppermint, 7/6 is pure, and a division like
33:36:39:42:44 has an overall accuracy as great as I've seen in any
tempered system. While the e-based system has only two sizes of
Zalzalian or neutral intervals (e.g. 132 and 154 cents), and uses a
twice a "mean-apotome" of 132.25 cents to approximate 7:6, Peppermint
has sizes of 129, 138, 150, and 159 cents, thus observing the 169/168
comma between 14:13 and 13:12 with near-just accuracy.

By the way, in the late summer of 2000, I devised a 17-note
circulating temperament with 12 fifths at 704.377 cents, yielding some
just 14:11 major thirds. The next summer, I learned about George
Secor's 17-WT where he used 8 fifths of the same size back in 1978 --
a shading almost identical to 46-EDO.

With many thanks,

Margo
mschulter@...

🔗genewardsmith <genewardsmith@...>

🔗Jacques Dudon <fotosonix@...>

Margo wrote :

> Might in fact a "Maqam Mohajira" be known among traditional Arab
> musicians by a name such as Sikah Baladi? Here is a site with examples
> in a format which I do not yet have the capability of playing, but
> which perhaps might give a sample of some intonations:
>
> <http://www.maqamworld.com/maqamat/sikah.html#sikah-baladi>

I could hear them, curiously by using the free videoplayer for Mac VLC.
All are very fine pieces, by very fine artists, but don't have much to see with Mohajira.
They all have a rather major third and most of them seem related to Hijaz, with large variations.
Also they show a semitone under the tonic in their conclusions (just as the score shows, in fact).
Only the last one, Qasida Man Mithlukum , by the Muezzins of Alep, would be closer but rather to some type of Buzurg tetrachord.
So, Sikah Baladi would not be really representative of a Mohajira mode.
I found Mohajira very difficult to sing, compared to Bayati or Rast : it's like singing Bayati on the second degree and then Rast on the third degree, may be that's why it's so rare, I don't know.

> > To your very complete analysis the only thing I may add from my
> > humble experimentations is an ensemble of migratory but coherent
> > versions of "Mohajira" tetrachords, that one may find in the series
> > described by the two main recurrent sequences issued from 9 and 13 :
>
> Thank you for a most illuminating catalogue which moves me in turn to
> some healthy humility, especially in taking the opportunity to clarify
> between the documented Persian understanding of the "Old Esfahan" and
> my own interpretation in Zephyr-24, for example, where your ratios are
> a natural choice, or in temperaments where the regular major second is
> around a 44/39. I will address this shortly, but would like to > focus on
> the beauties of your catalogue:
>
> > 36 : 39 : 44 : 48 ("Old Esfahan" ?)
> > 44 : 48 : 54 : 59
> > 48 : 52 : 59 : 64 (Dudon_b.scl)
> > 54 : 59 : 66 : 72 (Dudon_a.scl)
> > 59 : 64 : 72 : 78
> > 66 : 72 : 81 : 88 (Medieval Iraq)
> > 81 : 88 : 99 : 108 (al-Farabi/Rast)
> > 88 : 96 : 108 : 117
> > 96 : 104 : 117 : 128 (Ibn Sina/Mustaqim)
> > 99 : 108 : 121 : 132 (meantone temperament)
> > 117 : 128 : 143 : 156 (meantone temperament)
> > 117 : 128 : 144 : 156 (Mustaqim reversed)
>
> A few quick points about some of the felicities here. First, I am
> delighted how you draw on Safi al-Din al-Urmawi's 64:59:54:48 ratios
> in a modern -c context;

Yes, I had heard of the use of that 59/48 too (thanks to you I can give a name to that tetrachord now, that I use in some of my -c Rast lower tetrachord versions, since 59 - 48 = 11) - one very good example among others of the use of differentially-coherent intervals in oriental music !

> I have thought of his tetrachord as a nice
> shading for Maqam Bayyati at 141-153-204 cents rather close to
> 52:48:44:39 at 139-150-209 cents (here the string ratios come to me
> more easily). Scott Marcus says that in Egyptian practice the minor
> third may be close to 32/27, with the lower step at around 135-145
> cents, so it seems that Safi al-Din's tetrachord may fit well.

Haha, I like that, nice Bayati indeed, in strings ratios ! I would go up to 19/16 myself, but I like 13/11, and 32/27 has good arguments.

> Also, as a lover of the 352/351 relationship,

So am I ... and if we take the divisors of both 352 and 351
and bring them to the same octave (I experimented that with all possible commas years ago !) we get :
96 : 104 : 117 : 128 : 144 : 156 : 176 : 192 = Mohajira ...

> I am pleased to see how
> we sometimes have a 44/39 tone, and sometimes a "justly tempered"
> fourth at 117/88. I guess my favorite regular temperaments at around
> 704-705 cents strike a certain compromise between these situations.

468 : 703 (=19*37) : 1056 could be a very good start...

> Finally, I never before considered 144/143 in terms of meantone, but
> indeed 143:128 is close to Zarlino's 2/7-comma temperament !

A western temperament with possible Middle-East connexions...

> And I love this kind of systematic exploration of possibilities and
> permutations,
>
> > You have already mentionned some of them from the traditional
> > sources, and among the possible traditional issues you found, I got
> > especially interested like you in the "Old Esfahan" tetrachord and
> > its larger central tone of 209 cents. This is precisely the size
> > of 44/39 and by coincidence, it appears to be part of the first
> > tetrachord of my list, that gives a a realistic harmonic version of
> > this tetrachord.
>
> As I should have emphasized, 132-209-154 cents is merely my tempered
> tuning in one regular 24-note system I favor, with another offering a
> closer approximation at 138-208-150 cents of what I agree is an ideal
> just tuning for this interpretaton at 36:39:44:48. However, the modern
> Persian discussions about the "Old Esfahan" (the only ones I know) are
> much more general, the main idea being "small neutral second, tone,
> large neutral second." From Farhat's fretting diagram one might think
> in terms of something like 135-205-160 cents to fit this description
> (e.g. G-Ap-Bp-C), although his chosen location at D-Ep-F>-G would
> actually yield in his tuning a Buzurg at 135-225-135 cents.
>
> Interestingly a central tone around 44/39 does seem to occur in a
> measured performance by setar master Ahmad Ebadi as reported by Jean
> During, with steps of about 140.7-209.7-140.7 cents.

Would it suggest something like a 143 : 132 : 117 : 108 (or reverse) ?

> Whatever kind of an Esfahan this is, I would, assuming these
> measurements are accurate, call it one shading of the Mohajira we seek
> in traditional practice.
>
> > If we extend it in the higher tetrachord by a Bayati, this gives
> > again a magnificent Mohajira heptatonic scale I used to call
> > "Ibina" who is perhaps among all of them, the one I used the most :
>
> > 72 : 78 : 88 : 96 : 108 : 117 : 128 : 144
> > (1/1 13/12 11/9 4/3 3/2 13/8 16/9 2/1)
> > (the reference tone, for the classic mode J T J T J T J,
> shifted to 117...)
>
> > And its mode from 96 = Mustaqim...
>
> That is indeed a magnificent scale and a wonderful connection to Ibn
> Sina! Here is a tempered version in Peppermint, a 24-note tuning based
> on Keenan Pepper's regular temperament at 704.096 cents (using two
> 12-note chains at 58.68 cents apart for some just 7/6 thirds), which
> shades the 16/9 to something very close to a 39/22:
>
> ! pep_dudon_ibina_E.scl
> !
> Peppermint tempering of Dudon's Ibina: 72:78:88:96:108:117:128:144
> 7
> !
> 138.20166
> 346.39287
> 495.90439
> 704.09561
> 842.29727
> 991.80879
> 2/1
>
> > This tetrachord list also shows the use of prime limit 59 that
> > completes the two other major ingredients (besides 3), 11 and 13.
>
> Might 23 sometimes arise? I reflect here on 23:16 (628 cents, close to
> the 56:39 in Buzurg) or 23:14 (a larger neutral sixth at 859 cents,
> a tad wider than 64:39), for example.

I don't recall 23 coming in these series except in 161 (=7*23) in the series from 13, another famous meantone between 144 and 180.

> > In the Mohajira series "issued from 13" : 18 22 26 32 39 48 59 72 > 88,
> > 59 appears to have a transition role between 11 and 13 in
> > regard of differential coherence, expressed by the neutral thirds
> > difference tones and equal-beating properties :
>
> > 59 - 48 = 11
> > 72 - 59 = 13
> > (or in the equal-beating form) :
> > 11*22 - 4*59 = 9*22 - 4*48 = 3*(4*72 - 11*26) = 3*(4*59 - 9*26) = 6
>
> Could this be another instance where "spectrum coherence," the
> proximity of 64:59 to 13:12 and 59:54 to 12:11, somehow relates to
> these -c connections?

There would be a relation whenever a generating sequence would pass by these intervals. And this is the case, as they are part of the same tetrachords and issued from the same series.

> Also, I notice that the differences in the series sum up lots of the
> relevant prime factors or their multiples:
>
> 18 22 26 32 39 48 59 72 88
> 4 4 6 7 9 11 13 16

That's precisely what the -c algorithm of this sequence is based on :
m^5 -m^4 = 1/2
(there are also many other algorithms that can apply for mohajira temperaments)

> Indeed 4:6:7:9:11:13 is a hexad summing up the main harmonic factors
> in lots of tuning systems I use! A small point is that each pair of
> adjacent terms define the ratio of a neutral third -- except for 22:26
> or 13:11, one of my favorite sizes for a regular minor third.

Convergent series always start from diverging intervals, that sometimes give interesting surprises.
The repetition of 18 : 22 in 72 : 88 is a lucky one !
I never used 7 in this series, but that's an idea, and it appears later in 161 and 441.

> > While 24-EDO, 31-EDO then 55-EDO would be the three main cycling
> > attractors of the fractal generator, your mention of 44-EDO is also
> > interesting for 13 steps would amount to a quasi 27/22 ; however I
> > don't consider it to be typically representative of a Mohajira
> > sequence, as there are different models for generators past the
> > half of a pure fifth and around 27/22 one of them is "Zalarith"
> > whose sequence is 8x^2 - 9x = 1 and based on the -c of 12/11, but
> > that's another story, and already a few teapots away !...)
>
> Curiously, most of my experience has been with temperaments around
> 704-705 cents where a Mohajira mode or chain of generators involves
> two unequal neutral thirds, for example 341-363 cents at 704.607
> cents. Your Soria 17+2 versions, while far more intricate, do seem to
> have a kindred spirit, as well as things like hemifourths that i miss
> in such regular schemes. George Secor's 17-note well-temperament
> (secor.scl in my dated version of the Scala archives) has a spectrum
> of shadings really inviting Mohajira as a tetrachord, mode, or method
> of subset generation.

To my point of view there is a big distance between Mohajira as a linear temperament, and those whose x^2 pass beyond 3/2, who enter into the Buzurg family, and I am seeing many different sequences in between.
I tried to have a look to George Secor's 17 tones WTs, but there are many and all written in cents, I would have to play them but I am pressed by time now.

> > Anyway no one could write a better description of Mohajira and I
> > have nothing to add !
>
> Please let me say what a pleasure it is to be a part of your saga of
> discovering, rediscovering, or helping us better to recognize the
> beauty of Mohajira!

You are welcome, and I thank you so much to bring your lights on these Middle East connexions !

- - - - - -
Jacques

🔗Margo Schulter <mschulter@...>

Gene wrote [on the e-based temperament at 704.607 cents]

> That sounds a great deal like 109-equal, and suggests adding that
> taking 25 fifths yields a nearly pure 8/5.

Yes, this temperament is very close to 109-EDO, and interestingly
Zarlino's 2/7-comma meantone at 695.810 cents, as I later realized, is
very close to a ratio of e between the whole tone and _chromatic_
semitone, and also to 119-EDO. In an equally tempered version, the
whole tone is 19 steps, the larger semitone 12 steps, and the smaller
semitone 7 steps.

Here's an article I wrote a few weeks ago but haven't yet posted on
the intervals generated by the first 17 fifths that are my main focus
in using the tuning, and also the remote intervals present in a
24-note set or which would be in a larger set. We could explain the
385-cent major third from 25 fifths down as the usual 363-cent
diminished third plus a 17-comma of 22 cents; the usual 418-cent major
third less a 29-comma of 33 cents; or the remote 396-cent major third
from 21 fifths up or three apotomes -- apotomata for the classically
correct -- less a 46-comma.

<http://www.bestII.com/~mschulter/e-based_and_17_tentative.txt>

>> By the way, in the late summer of 2000, I devised a 17-note
>> circulating temperament with 12 fifths at 704.377 cents, yielding some
>> just 14:11 major thirds.

> You can do that sort of thing in 12 notes also, though George thinks
> that's going a bit too far.

While I can't speak for George, I was doing and advocating this sort
of thing in the late summer of 2000, when I observed that a regular
12-note chain at 704.377 cents is a fine tuning in itself, as well as
a basis for one type of 17-note circle.

</tuning/topicId_12284.html#12284>

What happens with this 12-note tuning, an almost identical
12-of-46-EDO, or Peppermint or e-based or anything in the general
neighborhood is a fine 21st-century variation on an Eb-G# Halberstadt
organ for 13th-14th century European styles, plus a few nice Near
Eastern tetrachords and octave species to whet ones appetite for
neutral intervals in more positions, if one is so inclined. While I
found Arab music very pleasant to listen to, back in 2000 I hadn't yet
delved into maqam and dastgah music: George helped make it happen.

Best,

Margo
mschulter@...

🔗Margo Schulter <mschulter@...>

Dear Jacques,

>> <[105]http://www.maqamworld.com/maqamat/sikah.html#sikah-baladi>

> I could hear them, curiously by using the free videoplayer for Mac VLC.

Please let me clarify that these files are Real Audio, if I'm correct,
and likely routinely supported on lots of systems; I'm using a
text-based LINUX where so far I've been accustomed to wav, mp3, and
ogg, but will try to install a player that I found for this format.

> All are very fine pieces, by very fine artists, but don't have much
> to see with Mohajira.

> They all have a rather major third and most of them seem related to
> Hijaz, with large variations. Also they show a semitone under the
> tonic in their conclusions (just as the score shows, in fact). Only
> the last one, Qasida [106]Man Mithlukum , by the Muezzins of Alep,
> would be closer but rather to some type of Buzurg tetrachord.

This is the kind of information that is very helpful! It might be
possible to have the middle interval of Hijaz contracted so that it's
closer to 8:7 than a usual 7:6 or larger and at the same time have a
major third: indeed Dariush Talai's tuning for Chahargah (like Hijaz
in the dastgah system) is 140-240-120 cents, or 140-380-500 cents,
with a 380-cent third of the kind that Ozan much likes also. The taste
for a Buzurg flavor in Syria might tie in with the Turkish acceptance
of Buzurg or the like as one interpretation of Hijaz.

> So, Sikah Baladi would not be really representative of a Mohajira
> mode.

Based on your observations, I'd much agree. What caught my attention
was the description and notation on the Maqamworld page, which I'm
looking at in a PDF version, giving a tuning like this, with an ASCII
koron "p" showing a half-flat and a sori ">" for a half-sharp, and the
signs for the quarternote step notation as in the original:

G Ap Bp C D Ep F> G
3/4 1 3/4 1 3/4 1 3/4

As often can happen, it seems that at least the musical samples on the
site may generally not fit this model.

> I found Mohajira very difficult to sing, compared to Bayati or Rast:
> it's like singing Bayati on the second degree and then Rast on the
> third degree, may be that's why it's so rare, I don't know.

Your question about Arab practice leads to a very interesting point:
the distinctive or "root" trichord for a maqam of J T or "3 4" in the
modern 24-step notation is very common, and indeed the defining jins
or genre of the Sikah family, also the name of this trichord.

Certainly one could describe this trichord (or the complete Mohajira
tetrachord) as having a neutral second above the lowest note, like
Bayyati; and then a neutral third, like Rast, e.g. C Dp Ep (F).
Depending on how one places these steps for Bayyati and Rast, this
concept leads to many shadings of Mohajira, and also of Buzurg if one
favors a notably low neutral second for Bayati and high neutral third
for Rast, e.g. a rounded 0-130-360-(495) cents.

In modern Arab theory, there is another approach for explaining and
finding a Sikah trichord. This involves what is sometimes called the
"Arab fundamental scale" of disjunct Rast, with note names sometimes
reflecting their order in this scheme, with each step either a tone or
a Zalzalian or neutral second, with D-Ep and A-Bp often understood to
be larger than Ep-F or Bp-C, with JL and Js showing these larger and
smaller neutral steps:

T JL Js T T JL Js
C D Ep F G A Bp C
rast dukah sikah jaharkah nawa huseyni awj kirdan

Here dukah, sikah, and jahargah are Arabic forms of the Persian names
for the "second," "third," and "fourth" notes. As Ozan would point
out, the Persian or Turkish versions of these names are a bit
different: thus in Turkish, dugah-segah-chargah; and in Persian,
dogah-segah-chahargah.

Now the Sikah trichord: we get it in this approach by starting on the
step sikah, and singing or playing Ep-F-G, or sikah-jaharkah-nawa. We
have J-T, or in a widespread understanding more specifically Js-T.

In other words, starting on the third step (literally "sikah") of
Rast, and singing Ep-F-G, gives the trichord above the final that is
the nucleus of the Sikah family of maqamat.

The flagship maqam of this family, not so surprisingly, is Maqam
Sikah, whose elementary "textbook" form can be found simply by
starting at the sikah step and playing or singing the resulting octave
species within the "fundamental scale" of Rast:

Sikah Rast Rast
|------------|----------------|------------|
Ep F G A Bp C D Ep
Js T T JL Js T JL
|-----------------------|------------------|
Sikah `Iraq

Note that in a usual modern division of this maqam, the lower Sikah
trichord Ep-F-G is followed by a middle tetrachord of Rast G-C and
then an upper Rast trichord C-D-Ep. It is also possible, however, to
divide it into a lower Sikah pentachord plus an upper `Iraq
tetrachord, the latter a form of Mohajira.

To explain the name `Iraq, we should note that this tetrachord found
within the fundamental Rast scale starts on Bp, the step a smaller
neutral second below rast or C and often leading up to it -- known as
awj in the octave above rast, but `iraq an octave lower.

In the usual trichord-tetrachord-trichord division, and in practice, a
lot of the emphasis is placed on Rast tetrachords. Thus Mohajira as a
distinct jins or genre may not be so evident, but it isn't because of
any problem with the J T or Sikah trichord.

This leads us to Maqam `Iraq, a close relative of Maqam Sikah and a
frequent modulation when within it.

Arab theorists sometimes point out that we can derive this maqam by
rotation if we start on the seventh step of Rast -- awj, which is
known an octave lower, or a neutral second below rast, as `iraq, the
final of this maqam bearing its name. Thus:

Sikah Bayyati Rast
|------------|----------------|-----------|
Bp C D Ep F G A Bp
Js T JL Js T T JL
|------------------|----------------------|
`Iraq Sikah

Again, the usual division is trichord-tetrachord-trichord, here with
the lower Sikah trichord as in Maqam Sikah; a middle Bayyati
tetrachord; and again an upper Rast trichord. You may notice that the
structure is rather like that of Segah Dastgah. In fact, the lower
tetrachord is recognized in theory as `Iraq, or in our terms a form of
Mohajira; but the usual division often emphasizes other ajnas (genres,
the Arabic plural of jins). Certain authors like Selim Helou (also
transliterated Salim al-Hilu) of Lebanon do consider the `Iraq
tetrachord as an optional jins in this maqam.

Some authors also note that when one ascends beyond the octave and
then descends, Bp or awj (at an octave above the final) may be lowered
to Bb or `ajam, thus permitting a tetrachord called Busalik on G,
G-A-Bb-C-(D). This inflection may fit with a pattern in Maqam Bayyati
and Shur Dastgah alike where a neutral third is favored below the
final but often a minor sixth above it.

Here is a sketch which may illustrate some of these points and
options:

<http://www.bestII.com/~mschulter/Iraq_sample.mp3>

Other maqamat in the Sikah family such as Huzam include a Hijaz
tetrachord. raising the question of its tuning, which I find can vary
greatly given both the different interpretations possible for this
genre and the exigencies of various transpositions. However, the above
examples may give some idea of how common the Sikah trichord is,
however prevalent or otherwise the `Iraq (or Mohajira) tetrachord that
results from adding to this a perfect fourth. which in my view may
sometimes be narrowed by a comma, at around 21:16, as may be seen
above Scala step 8 (~4/3) in either version of your Soria-17+2.

You offer many other fascinating things in your reply, including one
of the most even and accurate rational divisions of 14:11 into a chain
of four "justly tempered" fifths that I've seen, 703/468 at 704.419
cents! I'll address these topics in another reply, but couldn't
conclude this article without admiring that ratio.

Most appreciatively,

Margo Schulter
mschulter@...

🔗Jacques Dudon <fotosonix@...>

Dear Margo,

Your explanation of the the Sikah trichord in relation to Arab Rast makes perfect sense.
I need to be in search of interpretations of Sikah and Irak maqamat but it is clear that these would be the best tracks for Mohajira sequences in possible traditional usages.
Among other possibles,
- a compilation of Rast with Sikah but in place of the second tetrachord,
- or Irak in first tetrachord > Bayati in second tetrachord,
- or else a succession of three Sikah trichords,
would be good receipes but I have no idea if they would be of common practice.

Thanks for the Irak sample and all these complements !
- - - - - - - -
Jacques

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Dear Jacques,
>
> >> <[105]http://www.maqamworld.com/maqamat/sikah.html#sikah-baladi>
>
> > I could hear them, curiously by using the free videoplayer for Mac VLC.
>
> Please let me clarify that these files are Real Audio, if I'm correct,
> and likely routinely supported on lots of systems; I'm using a
> text-based LINUX where so far I've been accustomed to wav, mp3, and
> ogg, but will try to install a player that I found for this format.
>
> > All are very fine pieces, by very fine artists, but don't have much
> > to see with Mohajira.
>
> > They all have a rather major third and most of them seem related to
> > Hijaz, with large variations. Also they show a semitone under the
> > tonic in their conclusions (just as the score shows, in fact). Only
> > the last one, Qasida [106]Man Mithlukum , by the Muezzins of Alep,
> > would be closer but rather to some type of Buzurg tetrachord.
>
> This is the kind of information that is very helpful! It might be
> possible to have the middle interval of Hijaz contracted so that it's
> closer to 8:7 than a usual 7:6 or larger and at the same time have a
> major third: indeed Dariush Talai's tuning for Chahargah (like Hijaz
> in the dastgah system) is 140-240-120 cents, or 140-380-500 cents,
> with a 380-cent third of the kind that Ozan much likes also. The taste
> for a Buzurg flavor in Syria might tie in with the Turkish acceptance
> of Buzurg or the like as one interpretation of Hijaz.
>
> > So, Sikah Baladi would not be really representative of a Mohajira
> > mode.
>
> Based on your observations, I'd much agree. What caught my attention
> was the description and notation on the Maqamworld page, which I'm
> looking at in a PDF version, giving a tuning like this, with an ASCII
> koron "p" showing a half-flat and a sori ">" for a half-sharp, and the
> signs for the quarternote step notation as in the original:
>
> G Ap Bp C D Ep F> G
> 3/4 1 3/4 1 3/4 1 3/4
>
> As often can happen, it seems that at least the musical samples on the
> site may generally not fit this model.
>
> > I found Mohajira very difficult to sing, compared to Bayati or Rast:
> > it's like singing Bayati on the second degree and then Rast on the
> > third degree, may be that's why it's so rare, I don't know.
>
> Your question about Arab practice leads to a very interesting point:
> the distinctive or "root" trichord for a maqam of J T or "3 4" in the
> modern 24-step notation is very common, and indeed the defining jins
> or genre of the Sikah family, also the name of this trichord.
>
> Certainly one could describe this trichord (or the complete Mohajira
> tetrachord) as having a neutral second above the lowest note, like
> Bayyati; and then a neutral third, like Rast, e.g. C Dp Ep (F).
> Depending on how one places these steps for Bayyati and Rast, this
> concept leads to many shadings of Mohajira, and also of Buzurg if one
> favors a notably low neutral second for Bayati and high neutral third
> for Rast, e.g. a rounded 0-130-360-(495) cents.
>
> In modern Arab theory, there is another approach for explaining and
> finding a Sikah trichord. This involves what is sometimes called the
> "Arab fundamental scale" of disjunct Rast, with note names sometimes
> reflecting their order in this scheme, with each step either a tone or
> a Zalzalian or neutral second, with D-Ep and A-Bp often understood to
> be larger than Ep-F or Bp-C, with JL and Js showing these larger and
> smaller neutral steps:
>
> T JL Js T T JL Js
> C D Ep F G A Bp C
> rast dukah sikah jaharkah nawa huseyni awj kirdan
>
> Here dukah, sikah, and jahargah are Arabic forms of the Persian names
> for the "second," "third," and "fourth" notes. As Ozan would point
> out, the Persian or Turkish versions of these names are a bit
> different: thus in Turkish, dugah-segah-chargah; and in Persian,
> dogah-segah-chahargah.
>
> Now the Sikah trichord: we get it in this approach by starting on the
> step sikah, and singing or playing Ep-F-G, or sikah-jaharkah-nawa. We
> have J-T, or in a widespread understanding more specifically Js-T.
>
> In other words, starting on the third step (literally "sikah") of
> Rast, and singing Ep-F-G, gives the trichord above the final that is
> the nucleus of the Sikah family of maqamat.
>
> The flagship maqam of this family, not so surprisingly, is Maqam
> Sikah, whose elementary "textbook" form can be found simply by
> starting at the sikah step and playing or singing the resulting octave
> species within the "fundamental scale" of Rast:
>
> Sikah Rast Rast
> |------------|----------------|------------|
> Ep F G A Bp C D Ep
> Js T T JL Js T JL
> |-----------------------|------------------|
> Sikah `Iraq
>
> Note that in a usual modern division of this maqam, the lower Sikah
> trichord Ep-F-G is followed by a middle tetrachord of Rast G-C and
> then an upper Rast trichord C-D-Ep. It is also possible, however, to
> divide it into a lower Sikah pentachord plus an upper `Iraq
> tetrachord, the latter a form of Mohajira.
>
> To explain the name `Iraq, we should note that this tetrachord found
> within the fundamental Rast scale starts on Bp, the step a smaller
> neutral second below rast or C and often leading up to it -- known as
> awj in the octave above rast, but `iraq an octave lower.
>
> In the usual trichord-tetrachord-trichord division, and in practice, a
> lot of the emphasis is placed on Rast tetrachords. Thus Mohajira as a
> distinct jins or genre may not be so evident, but it isn't because of
> any problem with the J T or Sikah trichord.
>
> This leads us to Maqam `Iraq, a close relative of Maqam Sikah and a
> frequent modulation when within it.
>
> Arab theorists sometimes point out that we can derive this maqam by
> rotation if we start on the seventh step of Rast -- awj, which is
> known an octave lower, or a neutral second below rast, as `iraq, the
> final of this maqam bearing its name. Thus:
>
> Sikah Bayyati Rast
> |------------|----------------|-----------|
> Bp C D Ep F G A Bp
> Js T JL Js T T JL
> |------------------|----------------------|
> `Iraq Sikah
>
> Again, the usual division is trichord-tetrachord-trichord, here with
> the lower Sikah trichord as in Maqam Sikah; a middle Bayyati
> tetrachord; and again an upper Rast trichord. You may notice that the
> structure is rather like that of Segah Dastgah. In fact, the lower
> tetrachord is recognized in theory as `Iraq, or in our terms a form of
> Mohajira; but the usual division often emphasizes other ajnas (genres,
> the Arabic plural of jins). Certain authors like Selim Helou (also
> transliterated Salim al-Hilu) of Lebanon do consider the `Iraq
> tetrachord as an optional jins in this maqam.
>
> Some authors also note that when one ascends beyond the octave and
> then descends, Bp or awj (at an octave above the final) may be lowered
> to Bb or `ajam, thus permitting a tetrachord called Busalik on G,
> G-A-Bb-C-(D). This inflection may fit with a pattern in Maqam Bayyati
> and Shur Dastgah alike where a neutral third is favored below the
> final but often a minor sixth above it.
>
> Here is a sketch which may illustrate some of these points and
> options:
>
> <http://www.bestII.com/~mschulter/Iraq_sample.mp3>
>
> Other maqamat in the Sikah family such as Huzam include a Hijaz
> tetrachord. raising the question of its tuning, which I find can vary
> greatly given both the different interpretations possible for this
> genre and the exigencies of various transpositions. However, the above
> examples may give some idea of how common the Sikah trichord is,
> however prevalent or otherwise the `Iraq (or Mohajira) tetrachord that
> results from adding to this a perfect fourth. which in my view may
> sometimes be narrowed by a comma, at around 21:16, as may be seen
> above Scala step 8 (~4/3) in either version of your Soria-17+2.
>
> You offer many other fascinating things in your reply, including one
> of the most even and accurate rational divisions of 14:11 into a chain
> of four "justly tempered" fifths that I've seen, 703/468 at 704.419
> cents! I'll address these topics in another reply, but couldn't
> conclude this article without admiring that ratio.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@...

🔗Margo Schulter <mschulter@...>

Re: Mohajira sequences (was Jacky Ligon's scales) [142]jacques.dudon

> Dear Margo,

> Your explanation of the the Sikah trichord in relation to Arab Rast
> makes perfect sense.

> I need to be in search of interpretations of Sikah and Irak maqamat
> but it is clear that these would be the best tracks for Mohajira
> sequences in possible traditional usages.

Dear Jacques,

Please let me add that one place to search for these things in Arab
music would be the maqam tradition of Iraq, where there seems to be
influence both from the Persian dastgah tradition and from Turkey. As I'll discuss below, and you've suggested before, J T J is in theory
and practice a principal tetrachord of Persian Segah Dastgah, so it
would be fitting if Maqam `Iraq as performed in modern Iraq were to
show a similar tendency, in view of the your _Sumer_ and the story of
Mohajira.

> Among other possibles,
> - a compilation of Rast with Sikah but in place of the second tetrachord,

Would I be right in interpreting this as follows?

Rast tone `Iraq
|----------------| |-------------|
C D Ep F G Ap Bp C

Here we could think of the second jins either as trichord Sikah or
tetrachord `Iraq.

> - or Irak in first tetrachord > Bayati in second tetrachord,

This is beautiful, and something I especially focused on after reading
your discussion about the Ibina sequence producing such a mode.

> - or else a succession of three Sikah trichords,

This I hadn't considered, but it would indeed give J T, J T, J T (J).

> would be good receipes but I have no idea if they would be of common practice.
> Thanks for the Irak sample and all these complements !

What I would add is that whatever we find out about Arab music, Segah
Dastgah does have J T J as its primary tetrachord according to such
theorists as Hormoz Farhat, and much of the music for this dastgah
bears this out in practice.

Thus Farhat writes: "The fourth above [the final, Ep in his diagram]
defines the minimal upper register of the mode, which, in relationship
to the finalis, establishes the Segah tetrachord." (Hormoz Farhat,
_The Dastgah Concept in Persian Music_, p. 51).

Jean During gives the tuning of one noted Iranian setar master, Haji
Aqa Mohammad Irani, taking the 1/1 as the step a neutral third below
the final as placed in much modern theory: C-D-Ep-F-G-Ap. Here the
tetrachord of interest would be 353-507.5-703.5-857.5 cents, or about
154.5-196-154 cents. For whatever reason, During evidently didn't
measure the seventh degree Bb.

! segah-haji_aqa.scl
!
Iranian Segah Dastgah on setar of Haji Aqa Mohammad Irani (Jean During)
6
!
211.50000
353.00000
507.50000
703.50000
857.50000
2/1

One source showing some melodies in Segah Dastgah is _The Vocal Radif
and Old Tasnifs According to the Version of Abdollah Davami, Collected
by Faramarz Payvar_. In this volume, Shur Dastgah typically has a
final of A with Bp as the only signature accidental, while Segah has
Bp and Ep with the final on Bp. a neutral second higher (in Farhat,
these finals are D for Shur and Ep for Segah). The emphasis on the
tetrachord Bp-C-D-Ep -- Segah (or Mohajira) -- looks very common.

An interesting touch in Abdollah Davami's version is that the fifth
degree F above the final Bp is often raised in ascent to the perfect
fifth F>, and then used in its uninflected form in descent, maybe a
bit like the fifth degree of Shur, which is treated as a moteqayyer or
variable note. While I have seen this in another radif where the
fourth below the final of Segah is likewise raised and made perfect,
it seems especially common in this collection.

This also raises some interesting questions of theory, for example the
possible connection of Segah to the third step of Ibn Sina's Mustaqim
and the clue which may be offered by traditional Persian note names,
but I am focusing on what appears to be your quite accurate suggestion
that Segah Dastgah may represent your Mohajira in practice.

As you have noted, describing Segah or any dastgah gets more
complicated because of the various gushe-ha or melodic themes
(singular gushe) which are included in the "modal suite," as one might
call it, making up a performance in a given dastgah. For example, some
of the gushe-ha making up Segah Dastgah follow the modal pattern of
Shur. However, I'd be interested in whether and how you feel the
colors of Mohajira in some relevant gusheh-ha of Segah.

> Jacques

With many thanks,

Margo

🔗Jacques Dudon <fotosonix@...>

On may 31th 2010 Margo wrote :

> > (Jacques) :
> > Dear Margo,
> > Your explanation of the the Sikah trichord in relation to Arab Rast
> > makes perfect sense.
> > I need to be in search of interpretations of Sikah and Irak maqamat
> > but it is clear that these would be the best tracks for Mohajira
> > sequences in possible traditional usages.
>
> Dear Jacques,
>
> Please let me add that one place to search for these things in Arab
> music would be the maqam tradition of Iraq, where there seems to be
> influence both from the Persian dastgah tradition and from Turkey.

Thanks for this pertinent suggestion.

> As I'll discuss below, and you've suggested before, J T J is in > theory
> and practice a principal tetrachord of Persian Segah Dastgah, so it
> would be fitting if Maqam `Iraq as performed in modern Iraq were to
> show a similar tendency, in view of the your _Sumer_ and the story of
> Mohajira.

That would make sense.

> > Among other possibles,
> > - a compilation of Rast with Sikah but in place of the second > tetrachord,
>
> Would I be right in interpreting this as follows?
>
> Rast tone `Iraq
> |----------------| |-------------|
> C D Ep F G Ap Bp C
>
> Here we could think of the second jins either as trichord Sikah or
> tetrachord `Iraq.

Exactly.

> > - or Irak in first tetrachord > Bayati in second tetrachord,
>
> This is beautiful, and something I especially focused on after reading
> your discussion about the Ibina sequence producing such a mode.
>
> > - or else a succession of three Sikah trichords,
>
> This I hadn't considered, but it would indeed give J T, J T, J T (J).

The most fractal solution but very probably much less traditional !

> > would be good receipes but I have no idea if they would be of > common practice.
> > Thanks for the Irak sample and all these complements !
>
> What I would add is that whatever we find out about Arab music, Segah
> Dastgah does have J T J as its primary tetrachord according to such
> theorists as Hormoz Farhat, and much of the music for this dastgah
> bears this out in practice.
>
> Thus Farhat writes: "The fourth above [the final, Ep in his diagram]
> defines the minimal upper register of the mode, which, in relationship
> to the finalis, establishes the Segah tetrachord." (Hormoz Farhat,
> _The Dastgah Concept in Persian Music_, p. 51).
>
> Jean During gives the tuning of one noted Iranian setar master, Haji
> Aqa Mohammad Irani, taking the 1/1 as the step a neutral third below
> the final as placed in much modern theory: C-D-Ep-F-G-Ap. Here the
> tetrachord of interest would be 353-507.5-703.5-857.5 cents, or about
> 154.5-196-154 cents. For whatever reason, During evidently didn't
> measure the seventh degree Bb.
>
> ! segah-haji_aqa.scl
> !
> Iranian Segah Dastgah on setar of Haji Aqa Mohammad Irani (Jean > During)
> 6
> !
> 211.50000
> 353.00000
> 507.50000
> 703.50000
> 857.50000
> 2/1

Nice scale, very close to some of the tunings you favor isn't it ? when I find the time I will try to find a -c JI equivalent

> One source showing some melodies in Segah Dastgah is _The Vocal Radif
> and Old Tasnifs According to the Version of Abdollah Davami, Collected
> by Faramarz Payvar_. In this volume, Shur Dastgah typically has a
> final of A with Bp as the only signature accidental, while Segah has
> Bp and Ep with the final on Bp. a neutral second higher (in Farhat,
> these finals are D for Shur and Ep for Segah). The emphasis on the
> tetrachord Bp-C-D-Ep -- Segah (or Mohajira) -- looks very common.
>
> An interesting touch in Abdollah Davami's version is that the fifth
> degree F above the final Bp is often raised in ascent to the perfect
> fifth F>, and then used in its uninflected form in descent, maybe a
> bit like the fifth degree of Shur, which is treated as a moteqayyer or
> variable note. While I have seen this in another radif where the
> fourth below the final of Segah is likewise raised and made perfect,
> it seems especially common in this collection.
>
> This also raises some interesting questions of theory, for example the
> possible connection of Segah to the third step of Ibn Sina's Mustaqim
> and the clue which may be offered by traditional Persian note names,
> but I am focusing on what appears to be your quite accurate suggestion
> that Segah Dastgah may represent your Mohajira in practice.
>
> As you have noted, describing Segah or any dastgah gets more
> complicated because of the various gushe-ha or melodic themes
> (singular gushe) which are included in the "modal suite," as one might
> call it, making up a performance in a given dastgah. For example, some
> of the gushe-ha making up Segah Dastgah follow the modal pattern of
> Shur. However, I'd be interested in whether and how you feel the
> colors of Mohajira in some relevant gusheh-ha of Segah.
>
>>
> With many thanks,
>
> Margo

*I* should rather thank you for these passionating investigations !
Unfortunately I am giving a concert in Italy this WE and I can't get into it right now.
I will try later on to explain how I came, from what I understand by hearing, to a different model for Segah than a ordinary Mohajira sequence.
It is clear that the 1st tetrachord of Persian Segah does not differ from a "Mohajira" tetrachord ; but since the rest of the scale slightly differs (and uses to my point of view a different - and very interesting model), and because Segah, on the contrary to Arabic tetrachords combinations, is a full 7 tones scale,in respect for that masterpiece of the Persian tradition I don't feel encline to cut it in pieces, and for these reasons I would not use it as a perfect example of Mohajira.
One very important feature in order to compare any Mohajira with traditional scales is the differential coherence of the neutral thirds. There are two different ways for a neutral third to be -c in a chain of neutral third, that determines two radically different types of them :
1) in the smaller type (typically 11/9), Ep - C = Bb/16 or 11 - 9 = 2 = one full tone under the 1st note ;
2) in the larger type (typically 59/48 or 16/13), Ep - C = Bp/16 or 59 -48 = 11 = one neutral second under the 1st note.
That is why JI versions of Mohajira series, that often alternate these two types, are among the best solutions.
Now if we consider what seventh (Bb or Bp) occurs in the context of such scales, this gives serious indications of pertinent -c models, which are those I recommend, as you understood.
The problem is that when you ask to an Arabian musician what seventh would be pertinent in the context of a trichord like Sikah, or any tetrachord, he thinks the question inappropriate. I believe myself, and like indians do in the raga context, that some "non-played" notes can have an importance. Even if not played, a second tetrachord, naturally suggested by the voice or instrument's 3rd harmonics, is another example of "non-played"contextual importance.
In Vietnamese music, in various blues scales, etc. quartertones generated by the smaller type of neutral third often occur in contexts where a full tone under the 1st note is found.
etc...
- - - - - - -
Jacques