Yahoo Tuning Groups Ultimate Backup tuning Steps or perdeler in 704.607-cent tuning

Hello, Ozan and all.

Much inspired by your discussions of the 79-MOS and Ozan24, and by our
recent dialogues, I have decided to post a table of the perdeler or
steps in the 704.607-cent regular temperament that has been the
subject of some of my recent articles. Here this tuning is given as
realized in 1024-EDO, a standard for some synthesizers, where the
average size of the 23 fifths is about 704.603 cents.

For purposes of symmetry and good fit, I have placed Rast at G# on the
lower keyboard, although in practice this might not be the most
convenient location using the two 12-note keyboards assumed here. On a
Bosanquet or similar generalized keyboard, I suspect that it might be
an ideal arrangement for many purposes.

This table shows the distance from Rast of each note or perde in
cents, and also as an approximate JI ratio. Additionally, the closest
equivalents or approximations in the 79-MOS are shown by specifying
the number of 79-MOS steps, or yarmans, and sizes in cents.

A 79-MOS step or yarman is generally equal to about 2/3 of a Holdrian
comma (1/53 octave, 22.6415 cents), or 15.0943 cents, or two steps of
159-EDO -- with very slight variations to permit just tunings of steps
at 4/3 (perde chargah) and 3/2 (perde neva), for example. In order to
achieve a just fifth and octave, the 46th of the 79 steps is enlarged
to a full Holdrian comma, or something varying only minutely from it.
This single enlarged step has 3/2 or neva as its upper note or perde.

Incidentally, the Turkish term _perde_ or "note, pitch" (plural
perdeler) might possibly be related, I might guess, to the Persian
_pardeh_, which can have a similar meaning and more specifically
signify the "fret" of an instrument.

In naming the perdeler, I have tried to be guided both by Arab and
Turkish practice, and specifically by some of your conventions as they
might apply to a system with fewer alternatives than the 79-MOS. When
in doubt, I have taken the forms of Maqam Rast (as realized in this
temperament) as normative: that is, in placing segah and evc or evdj
(Arab awj) at 363 and 1068 cents, and hisar at 859 cents for the sixth
degree of Ajemli or Nirz Rast.

An interesting feature is that perde buselik is at an almost just
14/11, or about 18.5 Holdrian commas, sometimes suggested as a
preferred location by certain Near Eastern theorists.

_____________________________________________________________________
---------------------------------------------------------------------
Steps or Perdeler in e-based temperament (1024-EDO version)
with a comparison to 79-MOS tuning of Ozan Yarman
_____________________________________________________________________
---------------------------------------------------------------------
Step# Note Cents Approx JI Perde Approx 79-MOS
---------------------------------------------------------------------
0 G# 0.000 1/1 Rast 0 0.000
---------------------------------------------------------------------
1 G#* 55.078 32/31 Nerm Shuri 4 60.369
---------------------------------------------------------------------
2 A 77.344 23/22 Shuri 5 75.461
---------------------------------------------------------------------
3 A* 132.422 68/63 Nerm Zengule 9 135.830
---------------------------------------------------------------------
4 Bb 154.687 59/54 Zengule 10 150.923
---------------------------------------------------------------------
5 A# 209.766 44/39 Dugah 14 211.292
---------------------------------------------------------------------
6 B 285.937 33/28 Kurdi 19 286.753
---------------------------------------------------------------------
7 B* 341.016 28/23 Dik Kurdi or 22 332.030
Nerm Segah 23 347.122
---------------------------------------------------------------------
8 C 363.281 21/17 Segah 24 362.215
---------------------------------------------------------------------
9 B# 418.359 14/11 Buselik 28 422.584
---------------------------------------------------------------------
10 C# 495.703 4/3 Chargah 33 498.045
---------------------------------------------------------------------
11 C#* 550.781 11/8 Nerm Hijaz 37 558.414
---------------------------------------------------------------------
12 D 573.047 39/28 Hijaz 38 573.506
---------------------------------------------------------------------
13 D* 628.125 23/16 Saba 42 633.875
---------------------------------------------------------------------
14 Eb 649.219 16/11 Dik Saba 43 648.968
---------------------------------------------------------------------
15 D# 704.297 3/2 Neva 46 701.955
---------------------------------------------------------------------
16 E 781.641 11/7 Beyati 51 777.416
---------------------------------------------------------------------
17 E* 836.719 34/21 Nerm Hisar 55 837.785
---------------------------------------------------------------------
18 F 858.984 23/14 Hisar 56 852,878
57 867.970
---------------------------------------------------------------------
19 E# 914.062 56/33 Huseyni 60 913.247
---------------------------------------------------------------------
20 F# 991.406 39/22 Ajem 65 988.679
---------------------------------------------------------------------
21 F#* 1046.484 108/59 Nerm Evdj 69 1049.077
---------------------------------------------------------------------
22 G 1067.578 63/34 Evdj 70 1064.170
---------------------------------------------------------------------
23 G* 1122.656 44/23 Mahur 74 1124.539
---------------------------------------------------------------------
24 G# 1200.000 2/1 Gerdaniye 79 1200.000
_____________________________________________________________________
---------------------------------------------------------------------

It may also be helpful to list the most frequent steps and
accidental modifications with sizes of up to a minor third, with some
forms having two slightly different sizes in 1024-EDO:

______________________________________________________________________
----------------------------------------------------------------------
Description Example Cents Approx 79-MOS
----------------------------------------------------------------------
diesis (~32:31) C-C* 55.078 4 60.369
----------------------------------------------------------------------
limma (~23:22) F#-G 76.172 5 75.461
C#-D 77.344
----------------------------------------------------------------------
apotome (~68:63) D-D# 131.250 9 135.830
C-C# 132.422
----------------------------------------------------------------------
diminished 3rd (~59:54) C#-Eb 153.516 10 150.923
D#-F 154.687
----------------------------------------------------------------------
regular tone (~44:39) A-B 208.594 14 212.292
C-D 209.766
----------------------------------------------------------------------
large tone (~8:7) E*-G 230.859 15 226.384
B*-D 232.031
----------------------------------------------------------------------
small minor 3rd (~7:6) Bb-C* 263.672 18 271.661
C-D* 264.844
----------------------------------------------------------------------
regular minor 3rd (~33:28) C-Eb 285.937 19 286.753
287.109
______________________________________________________________________
----------------------------------------------------------------------

A pleasant feature of this tuning is the subtle distinction of about
21-22 cents, or not quite a Holdrian comma, between small and large
neutral seconds at around 132/154 cents -- and likewise other neutral
categories at 341/363, 837/859, and 1046/1068 cents. At certain
locations, one can thus distinguish from the same final or tonic
different shadings typical of certain maqamat.

For example, taking C# as our final, we can play either an Arab
Bayyati where the smaller neutral second is preferred above the final
but a wider neutral sixth is favored as an alternative inflection to
the usual minor sixth; or a Turkish Huseyni where the larger neutral
second might be placed before the smaller in the lower tetrachord:

Maqam Bayyati (Arab interpretation)

859
Bb
C# D* E F# G# A B C#
0 132 286 496 704 782 990 1200
132 154 210 208 77 208 210

Maqam Huseyni

C# Eb E F# G# Bb B C#
0 154 286 496 704 859 990 1200

Such a modulation is rather subtle, if both forms are used in a single
piece, since both maqamat might be regarded to belong to the same
_fasila_ or "family" in an Arab view, sharing a lower tetrachord with
two middle or neutral seconds plus an upper tone to complete the
fourth. Of course, the most important difference is in the seyir or
typical melodic development for each, with Huseyni emphasizing the
fifth degree (perde huseyni when the final is on perde dugah, its
regular location), and Arab Bayyati often emphasizing other degrees
such as the fourth (viewed as the lowest note of a tetrachord called
Buselik in Turkish theory but Nahawand in the Arab usage, F#-G#-A-B).

In other situations, this small difference of a comma may distinguish
maqamat varying more dramatically from each other in some other tuning
systems, but here by only a fine and discreet nuance:

Maqam Rast (Acemli or Nirz Rast flavor)

Rast Rast tone
|-----------------|----------------|....|
F# G# Bb B C# Eb E F#
0 208 363 495 704 858 990 1200
208 155 132 210 154 132 210

Maqam Nihavend (supraminor flavor)

Ascending

Nihavend tone Hijaz
|-----------------|......|-----------------|
F# G# A* B C# D* F F#
0 208 341 495 704 837 1068 1200
208 132 154 210 132 231 132

Descending

Nihavend tone Segah
|-----------------|......|-----------------|
F# G# A* B C# D* E* F#
0 208 341 495 704 837 1045 1200
208 132 154 210 132 208 155

To accentuate this point of very subtle distinctions, I have realized
the upper Hijaz tetrachord of the ascending form as C#-D*-F-F# or
0-132-363-496 cents (132-231-132 cents), although a more conventional
Hijaz at 0-132-418-496 cents or 132-286-77 cents would also be
possible. For the descending or Segah form of this tetrachord, I use
0-132-341-496 cents, or 132-208-155 cents. keeping a perfect fifth
between the third and seventh degrees of the maqam (at 341 and 1045
cents).

Here the supraminor third of Nihavend differs from the regular minor
third of Buselik by a diesis or about 55 cents (286 and 341 cents), as
does the submajor third of Rast from the regular major third of Mahur
(363 and 418 cents). However, the thirds of Nihavend and Rast differ
by only a comma (341 and 363 cents), the fine difference between
supraminor and submajor (or roughly 15 and 16 commas).

A technical note: in these examples I have tried to favor locations
where I can and do actually play the indicated maqamat using two
12-note keyboards. On a generalized keyboard, some other and possibly
more illustrative choices would be more practical, for example with
Huseyni and Arab Bayyati starting on perde dugah (A#, in the naming
system suggested above).

As suggested, the 79-MOS would have close equivalents for most of
these examples. A nice point is that while the style of intonation
would general suggest pure or wide (supra-Pythagorean) fifths,
sometimes narrow fifths (or wide fourths) could be used to advantage.
Thus for the final examples of Nihavend, the supraminor third at 341
cents could best be mapped to the smaller (and arguably yet better)
332.030 cents in the 79-MOS, with the supraminor sixth mapping to the
almost identical size of 837.785 cents. Between these degrees would be
a meantone fourth of some 505 cents, or about 1/3 Holdrian comma wide
-- thus showing the utility of such fourths even in a style which, in
the regular 704.607-cent tuning or 1024-EDO variation, is achieved
with consistently wide fifths or narrow fourths.

With many thanks,

Margo Schulter
mschulter@...

🔗Ozan Yarman <ozanyarman@...>

Hello Margo,

On Sep 2, 2008, at 11:29 AM, Margo Schulter wrote:

> Hello, Ozan and all.
>
> Much inspired by your discussions of the 79-MOS and Ozan24, and by our
> recent dialogues, I have decided to post a table of the perdeler or
> steps in the 704.607-cent regular temperament that has been the
> subject of some of my recent articles. Here this tuning is given as
> realized in 1024-EDO, a standard for some synthesizers, where the
> average size of the 23 fifths is about 704.603 cents.
>

That is a fine happenstance!

> For purposes of symmetry and good fit, I have placed Rast at G# on the
> lower keyboard, although in practice this might not be the most
> convenient location using the two 12-note keyboards assumed here. On a
> Bosanquet or similar generalized keyboard, I suspect that it might be
> an ideal arrangement for many purposes.
>
> This table shows the distance from Rast of each note or perde in
> cents, and also as an approximate JI ratio. Additionally, the closest
> equivalents or approximations in the 79-MOS are shown by specifying
> the number of 79-MOS steps, or yarmans, and sizes in cents.
>
> A 79-MOS step or yarman is generally equal to about 2/3 of a Holdrian
> comma (1/53 octave, 22.6415 cents), or 15.0943 cents, or two steps of
> 159-EDO -- with very slight variations to permit just tunings of steps
> at 4/3 (perde chargah) and 3/2 (perde neva), for example. In order to
> achieve a just fifth and octave, the 46th of the 79 steps is enlarged
> to a full Holdrian comma, or something varying only minutely from it.
> This single enlarged step has 3/2 or neva as its upper note or perde.
>
> Incidentally, the Turkish term _perde_ or "note, pitch" (plural
> perdeler) might possibly be related, I might guess, to the Persian
> _pardeh_, which can have a similar meaning and more specifically
> signify the "fret" of an instrument.
>

But we use perde not just for note or pitch, but also to indicate frets in Turkiye. The usage is the same for all Middle Eastern nations.

> In naming the perdeler, I have tried to be guided both by Arab and
> Turkish practice, and specifically by some of your conventions as they
> might apply to a system with fewer alternatives than the 79-MOS. When
> in doubt, I have taken the forms of Maqam Rast (as realized in this
> temperament) as normative: that is, in placing segah and evc or evdj
> (Arab awj) at 363 and 1068 cents, and hisar at 859 cents for the sixth
> degree of Ajemli or Nirz Rast.
>

Nirz Rast? Where does that name come from?

> An interesting feature is that perde buselik is at an almost just
> 14/11, or about 18.5 Holdrian commas, sometimes suggested as a
> preferred location by certain Near Eastern theorists.
>
>
> _____________________________________________________________________
> ---------------------------------------------------------------------
> Steps or Perdeler in e-based temperament (1024-EDO version)
> with a comparison to 79-MOS tuning of Ozan Yarman
> _____________________________________________________________________
> ---------------------------------------------------------------------
> Step# Note Cents Approx JI Perde Approx 79-MOS
> ---------------------------------------------------------------------
> 0 G# 0.000 1/1 Rast 0 0.000
> ---------------------------------------------------------------------
> 1 G#* 55.078 32/31 Nerm Shuri 4 60.369
> ---------------------------------------------------------------------
> 2 A 77.344 23/22 Shuri 5 75.461
> ---------------------------------------------------------------------
> 3 A* 132.422 68/63 Nerm Zengule 9 135.830
> ---------------------------------------------------------------------
> 4 Bb 154.687 59/54 Zengule 10 150.923
> ---------------------------------------------------------------------
> 5 A# 209.766 44/39 Dugah 14 211.292
> ---------------------------------------------------------------------
> 6 B 285.937 33/28 Kurdi 19 286.753
> ---------------------------------------------------------------------
> 7 B* 341.016 28/23 Dik Kurdi or 22 332.030
> Nerm Segah 23 347.122
> ---------------------------------------------------------------------
> 8 C 363.281 21/17 Segah 24 362.215
> ---------------------------------------------------------------------
> 9 B# 418.359 14/11 Buselik 28 422.584
> ---------------------------------------------------------------------
> 10 C# 495.703 4/3 Chargah 33 498.045
> ---------------------------------------------------------------------
> 11 C#* 550.781 11/8 Nerm Hijaz 37 558.414
> ---------------------------------------------------------------------
> 12 D 573.047 39/28 Hijaz 38 573.506
> ---------------------------------------------------------------------
> 13 D* 628.125 23/16 Saba 42 633.875
> ---------------------------------------------------------------------
> 14 Eb 649.219 16/11 Dik Saba 43 648.968
> ---------------------------------------------------------------------
> 15 D# 704.297 3/2 Neva 46 701.955
> ---------------------------------------------------------------------
> 16 E 781.641 11/7 Beyati 51 777.416
> ---------------------------------------------------------------------
> 17 E* 836.719 34/21 Nerm Hisar 55 837.785
> ---------------------------------------------------------------------
> 18 F 858.984 23/14 Hisar 56 852,878
> 57 867.970
> ---------------------------------------------------------------------
> 19 E# 914.062 56/33 Huseyni 60 913.247
> ---------------------------------------------------------------------
> 20 F# 991.406 39/22 Ajem 65 988.679
> ---------------------------------------------------------------------
> 21 F#* 1046.484 108/59 Nerm Evdj 69 1049.077
> ---------------------------------------------------------------------
> 22 G 1067.578 63/34 Evdj 70 1064.170
> ---------------------------------------------------------------------
> 23 G* 1122.656 44/23 Mahur 74 1124.539
> ---------------------------------------------------------------------
> 24 G# 1200.000 2/1 Gerdaniye 79 1200.000
> _____________________________________________________________________
> ---------------------------------------------------------------------
>
>

So far so good.

> It may also be helpful to list the most frequent steps and
> accidental modifications with sizes of up to a minor third, with some
> forms having two slightly different sizes in 1024-EDO:
>
> ______________________________________________________________________
> ----------------------------------------------------------------------
> Description Example Cents Approx 79-MOS
> ----------------------------------------------------------------------
> diesis (~32:31) C-C* 55.078 4 60.369
> ----------------------------------------------------------------------
> limma (~23:22) F#-G 76.172 5 75.461
> C#-D 77.344
> ----------------------------------------------------------------------
> apotome (~68:63) D-D# 131.250 9 135.830
> C-C# 132.422
> ----------------------------------------------------------------------
> diminished 3rd (~59:54) C#-Eb 153.516 10 150.923
> D#-F 154.687
> ----------------------------------------------------------------------
> regular tone (~44:39) A-B 208.594 14 212.292
> C-D 209.766
> ----------------------------------------------------------------------
> large tone (~8:7) E*-G 230.859 15 226.384
> B*-D 232.031
> ----------------------------------------------------------------------
> small minor 3rd (~7:6) Bb-C* 263.672 18 271.661
> C-D* 264.844
> ----------------------------------------------------------------------
> regular minor 3rd (~33:28) C-Eb 285.937 19 286.753
> 287.109
> ______________________________________________________________________
> ----------------------------------------------------------------------
>
> A pleasant feature of this tuning is the subtle distinction of about
> 21-22 cents, or not quite a Holdrian comma, between small and large
> neutral seconds at around 132/154 cents -- and likewise other neutral
> categories at 341/363, 837/859, and 1046/1068 cents. At certain
> locations, one can thus distinguish from the same final or tonic
> different shadings typical of certain maqamat.
>
> For example, taking C# as our final, we can play either an Arab
> Bayyati where the smaller neutral second is preferred above the final
> but a wider neutral sixth is favored as an alternative inflection to
> the usual minor sixth; or a Turkish Huseyni where the larger neutral
> second might be placed before the smaller in the lower tetrachord:
>
>
> Maqam Bayyati (Arab interpretation)
>
> 859
> Bb
> C# D* E F# G# A B C#
> 0 132 286 496 704 782 990 1200
> 132 154 210 208 77 208 210
>
>

The scale is also that of Ushshaq.

> Maqam Huseyni
>
> C# Eb E F# G# Bb B C#
> 0 154 286 496 704 859 990 1200
>
>

A marvelous rendition.

> Such a modulation is rather subtle, if both forms are used in a single
> piece, since both maqamat might be regarded to belong to the same
> _fasila_ or "family" in an Arab view, sharing a lower tetrachord with
> two middle or neutral seconds plus an upper tone to complete the
> fourth. Of course, the most important difference is in the seyir or
> typical melodic development for each, with Huseyni emphasizing the
> fifth degree (perde huseyni when the final is on perde dugah, its
> regular location), and Arab Bayyati often emphasizing other degrees
> such as the fourth (viewed as the lowest note of a tetrachord called
> Buselik in Turkish theory but Nahawand in the Arab usage, F#-G#-A-B).
>

Very good!

> In other situations, this small difference of a comma may distinguish
> maqamat varying more dramatically from each other in some other tuning
> systems, but here by only a fine and discreet nuance:
>
>
> Maqam Rast (Acemli or Nirz Rast flavor)
>
> Rast Rast tone
> |-----------------|----------------|....|
> F# G# Bb B C# Eb E F#
> 0 208 363 495 704 858 990 1200
> 208 155 132 210 154 132 210
>
>

This is a fine Ajemli Rast. But I hear the term Nirz Rast for the first time.

> Maqam Nihavend (supraminor flavor)
>
> Ascending
>
> Nihavend tone Hijaz
> |-----------------|......|-----------------|
> F# G# A* B C# D* F F#
> 0 208 341 495 704 837 1068 1200
> 208 132 154 210 132 231 132
>
>
> Descending
>
> Nihavend tone Segah
> |-----------------|......|-----------------|
> F# G# A* B C# D* E* F#
> 0 208 341 495 704 837 1045 1200
> 208 132 154 210 132 208 155
>

An acceptable Nihavend, save for E*, which I believe should be 9/8 lower from F#.

>
> To accentuate this point of very subtle distinctions, I have realized
> the upper Hijaz tetrachord of the ascending form as C#-D*-F-F# or
> 0-132-363-496 cents (132-231-132 cents), although a more conventional
> Hijaz at 0-132-418-496 cents or 132-286-77 cents would also be
> possible. For the descending or Segah form of this tetrachord, I use
> 0-132-341-496 cents, or 132-208-155 cents. keeping a perfect fifth
> between the third and seventh degrees of the maqam (at 341 and 1045
> cents).
>

155 cents is not appropriate as an interval between E* and F# for the descending scale of Nihavend I'm afraid.

> Here the supraminor third of Nihavend differs from the regular minor
> third of Buselik by a diesis or about 55 cents (286 and 341 cents), as
> does the submajor third of Rast from the regular major third of Mahur
> (363 and 418 cents). However, the thirds of Nihavend and Rast differ
> by only a comma (341 and 363 cents), the fine difference between
> supraminor and submajor (or roughly 15 and 16 commas).
>

This is very much agreeable.

> A technical note: in these examples I have tried to favor locations
> where I can and do actually play the indicated maqamat using two
> 12-note keyboards. On a generalized keyboard, some other and possibly
> more illustrative choices would be more practical, for example with
> Huseyni and Arab Bayyati starting on perde dugah (A#, in the naming
> system suggested above).
>
> As suggested, the 79-MOS would have close equivalents for most of
> these examples. A nice point is that while the style of intonation
> would general suggest pure or wide (supra-Pythagorean) fifths,
> sometimes narrow fifths (or wide fourths) could be used to advantage.
> Thus for the final examples of Nihavend, the supraminor third at 341
> cents could best be mapped to the smaller (and arguably yet better)
> 332.030 cents in the 79-MOS, with the supraminor sixth mapping to the
> almost identical size of 837.785 cents. Between these degrees would be
> a meantone fourth of some 505 cents, or about 1/3 Holdrian comma wide
> -- thus showing the utility of such fourths even in a style which, in
> the regular 704.607-cent tuning or 1024-EDO variation, is achieved
> with consistently wide fifths or narrow fourths.
>

Splendid.

> With many thanks,
>
> Margo Schulter
> mschulter@...
>

Oz.

🔗Margo Schulter <mschulter@...>

> Hello Margo,

Hello Ozan. Please let me apologize for the length of my last reply,
and try to keep this one a bit more concise. I am very happy that your
advice has guided me to a nice solution of the Nihavend question.

On Sep 2, 2008, at 11:29 AM, Margo Schulter wrote:

>> Hello, Ozan and all.

>> Much inspired by your discussions of the 79-MOS and Ozan24, and by
>> our recent dialogues, I have decided to post a table of the
>> perdeler or steps in the 704.607-cent regular temperament that has
>> been the subject of some of my recent articles. Here this tuning is
>> given as realized in 1024-EDO, a standard for some synthesizers,
>> where the average size of the 23 fifths is about 704.603 cents.

> That is a fine happenstance!

Yes, I was pleasantly surprised that the fit should be so close. There
are 17 fifths at 704.297 cents, and 6 fifths at 705.469 cents. The
wider fifths are at Eb-Bb, G-D, and B-F# on each keyboard.

>> Incidentally, the Turkish term _perde_ or "note, pitch" (plural
>> perdeler) might possibly be related, I might guess, to the Persian
>> _pardeh_, which can have a similar meaning and more specifically
>> signify the "fret" of an instrument.

> But we use perde not just for note or pitch, but also to indicate
> frets in Turkiye. The usage is the same for all Middle Eastern nations.

Thank you for educating me on this: maybe, like the origins of some of
the maqamat, it might be an interesting question what language this
term originated in. In reading Arab theory in English, so far, I'm not
sure if I've seen any related term: but perde and pardeh seem common.

>> In naming the perdeler, I have tried to be guided both by Arab and
>> Turkish practice, and specifically by some of your conventions as
>> they might apply to a system with fewer alternatives than the
>> 79-MOS. When in doubt, I have taken the forms of Maqam Rast (as
>> realized in this temperament) as normative: that is, in placing
>> segah and evc or evdj (Arab awj) at 363 and 1068 cents, and hisar
>> at 859 cents for the sixth degree of Ajemli or Nirz Rast.

> Nirz Rast? Where does that name come from?

Evidently the name Nirz Rast in Arab theory is another term for a
maqam also called Nairuz, an Arabic version of the name for the Iranic
New Year festival, with Nirz shortened from Nairuz. I also sometimes
call it Zalzalian Rast; Ajemli Rast is very descriptive. In commas, I
think of this as approximately 976|976|9, with the two conjuct Rast
tetrachords. Of course, there are various ajnas to be found, and some
Arab theorists may view it, for example, as disjunct Rast plus what is
called Bayyati (i.e. Ushshaq), 976-9-769, although I would say that
the upper 769 might be more like Huseyni than like the Arab version of
Ushshaq or "Bayyati," which 679 would better express.

> An interesting feature is that perde buselik is at an almost just
> 14/11, or about 18.5 Holdrian commas, sometimes suggested as a
> preferred location by certain Near Eastern theorists.
>

[Excerpt from my table of perdeler or steps, which I've trimmed]

> ---------------------------------------------------------------------
> 8 C 363.281 21/17 Segah 24 362.215
> ---------------------------------------------------------------------
> 18 F 858.984 23/14 Hisar 56 852,878
> 57 867.970
> ---------------------------------------------------------------------

> So far so good.

Our discussions since I made this table, however, raise one point,
since 859 cents is the perfect fourth of segah at 363 cents, might it
better be named dik hisar ("steep Hisar"), and 837 cents be considered
simply hisar? You suggested that dik hisar would be the right name in
Maqam Segah, at least.

> Maqam Bayyati (Arab interpretation)
>
> 859
> Bb
> C# D* E F# G# A B C#
> 0 132 286 496 704 782 990 1200
> 132 154 210 208 77 208 210

> The scale is also that of Ushshaq.

Yes, I would understand either Ushshaq as known in Turkey or what is
known in the Arab world as Bayyati to be 679|949|9 or the like, with
conjunct tetrachords of Ushshaq and Buselik (the latter known in Arab
theory as Nahawand -- in contrast to Turkish Nihavend at 958 or the
like, if I am right).

>> Maqam Huseyni
>>
>> C# Eb E F# G# Bb B C#
>> 0 154 286 496 704 859 990 1200

> A marvelous rendition.

Thank you! I love this maqam with the larger neutral second, and can
understand the advantages of making these intonational flavors a part
of theory as well as practice.

> Maqam Rast (Acemli or Nirz Rast flavor)
>
> Rast Rast tone
> |-----------------|----------------|....|
> F# G# Bb B C# Eb E F#
> 0 208 363 495 704 858 990 1200
> 208 155 132 210 154 132 210

> This is a fine Ajemli Rast. But I hear the term Nirz Rast for the
> first time.

Thank you for your feedback: as I suggested in another message, this
may be a bit like learning a language, and having the good fortune to
have a teacher who is not only an excellent native speaker, but a
leading scholar of its syntax and grammar!

There is a good question how widespread the term Nirz Rast is in the
Arab world: I have seen it, for example, in a dissertation by Scott
Marcus on _Arab Music Theory in the Modern Period_, where Yusuf Shawqi
(1964) is one source for this name. Some other sources of Arab theory
prefer Nairuz, for example <http://www.maqamworld.com/maqamat/rast.html>.
Interestingly, d'Erlanger has two spellings, Nairuz or Niriz, with the
latter close to Nirz. While al-Sabbagh, as cited by Marcus, calls the
maqam simmply Nirz, some others have Nirz Rast.

> An acceptable Nihavend, save for E*, which I believe should be 9/8
> lower from F#.

Ah, this is easily corrected, and the upper tetrachord might now, if I
am correct, be called Ushshaq -- if this is fitting for this maqam:

Descending

Nihavend tone Ushshaq
|-----------------|......|-----------------|
F# G# A* B C# D* E F#
0 208 341 495 704 837 991 1200
208 132 154 210 132 155 209

[...]

> 155 cents is not appropriate as an interval between E* and F# for
> the descending scale of Nihavend I'm afraid.

Here I may have made my mistake through a desire to have a perfect
fifth between the third and seventh degrees (A*-E*); but now I
understand that the seventh degree in the descending form should be a
9:8 below the octave of the final or tonic, with a perfect fourth
between the fourth and seventh degrees. Thus, in a supraminor flavor,
something like 967-9-679, but with the smaller neutral second at 132
cents a tad smaller than 6 full commas.

>> Here the supraminor third of Nihavend differs from the regular
>> minor third of Buselik by a diesis or about 55 cents (286 and 341
>> cents), as does the submajor third of Rast from the regular major
>> third of Mahur (363 and 418 cents). However, the thirds of Nihavend
>> and Rast differ by only a comma (341 and 363 cents), the fine
>> difference between supraminor and submajor (or roughly 15 and 16
>> commas).

> This is very much agreeable.

Again, your guidance is welcome, and the rule of a descending version
with the seventh degree at 16/9 nicely resolves my uncertainty.

> Oz.

With many thanks,

Margo

🔗Margo Schulter <mschulter@...>

Dear Tom and All,

> 13/11 * 14/11 = 3/2 * 364/363
> 19/15 * 19/16 = 3/2 * 361/360
> 13/11 * 19/15 = 3/2 * 494/495
> ...what can be made of this pseudo-tempering? 13/11 certainly looks
> like it should be quite recognizable as a minor 3rd...
> ~~~T~~~

Please let me enthusiastically respond by noting that since the year
2000, I would consider JI and tempered neomedieval systems centering
around the ratios of 3/2, 14/11, and 13/11 to be a great part of what
I'm about both in practice and in advocacy here on the Tuning List and
elsewhere.

In JI, this indeed is a fine example of "pseudo-tempering" or
"tempering by ratio," as with this neomedieval diatonic from the Scala
scale archive that offers a kind of modern variation on 13th-14th
century Pythagorean tuning in Europe:

! schulter_diat7.scl
!
Diatonic scale, symmetrical tetrachords based on 14/11 and 13/11 triads
7
!
44/39
14/11
4/3
3/2
22/13
21/11
2/1

While having some fifths at a pure 3:2, and others "virtually"
tempered at 182:181 or 364:363 (4.76 cents) wide, and 176:117 or
352:351 (4.93 cents wide) can be a stimulating contrast akin to that
of a 12-note well-temperament, for some purposes a regular temperament
where all fifths are about 2-3 cents impure might have a smoother
effect arguably more analogous to that of medieval European
Pythagorean tuning. This happens in such temperaments as Peppermint
(704.096 cents) and the e-based tuning (704.607 cents).

By a happy arrangement, extended JI systems or regular temperaments
featuring these ratios -- say in 17 or 24 notes -- also offer a rich
assortment of neutral intervals, and often septimal intervals also,
congenial for example to a range of Near Eastern melodic patterns and
modes -- the Arab/Kurdish/Turkish maqamat or modes, and the Persian
system of modal families or dastgah-ha.

These systems are designed as accentuated modern variations on
medieval Pythagorean tuning, where active and unstable thirds are the
norm, and are _not_ intended for use where a meantone aesthetic
applies.

Although not originally and specifically designed for a neomedieval
style, George Secor's 17-note well-temperament of early 1978 very
nicely supports this kind of stylistic setting: major thirds range
from a just 14:11 (417.508 cents) to around 428.882 cents as the best
approximation of 9:7 (435.084 cents), with the 8 more remote fifths
tempered at 704.377 cents to produce some pure 14:11 thirds and 11:7
minor sixths. Again, this system masterfully designed to situate
ratios of primes 2-3-7-11-13 in the best position for sonorities like
7:9:11:13 is meant to open a universe of sound radically distinct from
that of meantone based on ideal ratios for thirds of 5:4 and 6:5.

! secor17w.scl
!
George Secor's well temperament, fifths at (1936:49)^(1/9) and (56:11)^(1/4)
17
!
66.741199
144.856244
214.440905
278.338643
353.610226
428.881810
492.779548
562.364208
640.479253
707.220452
771.118190
849.233235
921.661357
985.559095
1057.987217
1136.102262
2/1

However, some forms of modified meantone in a 12-note circle feature
similar intervals in remote transpositions, with the nearer part of
the circle meant for standard 16th-century idioms (say Bb-G#), and the
remote regions for a neomedieval style like that of the 13th-14th
centuries.

Interestingly, if the fifths F-C# are tuned in 1/4-comma, and the
other four are made equally wide (about 4.89 cents) to close the
circle, then some intervals of 289.735, 417.108, and 706.843 cents
result -- very closely approximating JI sizes of 13:11, 14:11, and
182:181, the "pseudo-tempering" you describe above. A 417-cent major
third is at once ideal for neomedieval styles, and a colorful
diminished fourth in a meantone context, with spellings aptly varied
to reflect these contexts. Thus Ab-C-F to Gb-Db-Gb would be a very
effective neomedieval cadence, while E-G#-C would make a fine
Renaissance or Manneristic sonority with an upper diminished fourth --
with Ab/G#-C at 417 cents.

! schulter_qcmqd8_4.scl
!
F-C# in 1/4-comma meantone, other 5ths ~4.888 cents wide or (2048/2025)^(1/4)
12
!
76.04900
193.15686
289.73529
5/4
503.42157
579.47057
696.57843
782.89214
889.73529
996.57843
1082.89214
2/1

With many thanks,

Margo Schulter
mschulter@...

🔗Margo Schulter <mschulter@...>

---------------------------------------------------
Homage to Ozan Yarman:
Clarifying Maqam Chargah
----------------------------------------------------

Yesterday it was my great pleasure to have a copy of your dissertation
on Turkish music printed for me at my local University Library, thus
overcoming software problems I have been experiencing at home with the
processing of certain PDF files. What a pleasure it now is to have
this document conveniently at hand, and to begin studying and
absorbing its many facets.

As one method of celebrating this occasion, I have decided to seek
clarification on a point raised in one of your recent messages, with
due apologies if you have already discussed this point in some
previous postings here, or possibly in other writings or forums.

You mentioned that Maqam Chargah has been presented in some recent
Turkish theory as what might be described as simply a transposition of
the ascending form of Maqam Mahur from perde rast to chargah. as
opposed to the "original" tradition to which you remain true. Here I
would like to venture a guess as to two forms that tradition might
take, and warmly invite your response -- having been alerted by a jins
or genus Chargah mentioned at page 121 of your dissertation in
connection with Maqam Saba that my initial impression might not be the
correct one.

That first impression was that Maqam Chargah in Turkiye, like Maqam
Jahargah in the Arab world (the spelling variation reflecting a
difference of phonology between the Persian and Arabic languages),
involves disjunct Mahur and Rast tetrachords, as would accord with
al-Sabbagh's suggested tuning for this maqam, as reported by Ali Jihad
Racy, of around 9-9-4-9-9-7-6 commas. Here is my interpretation in a
regular 24-note temperament at 704.607 cents, available as it happens
within a single 12-MOS keyboard:

Mahur Rast
|-------------------------| T |-------------------------|
T T B T T Jk Js
209 209 77 209 209 154 132
E F# G# A B C# Eb E
0 209 418 495 705 914 1068 1200
chargah neva huseyni ajem gerdaniye muhayyer tiz tiz
segah chargah

In the above notation, I have borrowed some signs from medieval and
modern Near Eastern theory to show the intervals of a _tanini_ or
whole tone at 209 cents (T); a larger mujenneb (Jk) and smaller
mujenneb (Js), middle or neutral seconds at 154 and 132 cents; and a
_bakiye_ or usual limma at 77 cents (B). These tempered sizes
correspond to al-Sabbagh's approximate steps based on Pythagorean
tuning or 53-EDO of 9, 7, 6, and 4 commas respectively (around 204,
158, 136, and 90 cents).

However, your Chargah tetrachord alerted me to a rather different
possibility: a connection to the Persian Dastgah-e Chahargah, which
features tetrachords generally like those termed Hijaz in Arab and
Turkish theory. Your tetrachord occurring in a descending form of Saba
as one side of the complex _terkib_ or composite maqam is as follows:

|---------------------------------|
1/1 15/14 195/154 75/56
0 119 409 506
15/14 13/11 55/52
119 289 97

This looks much more like a relative of Persian Chahargah than of the
Mahur-Rast type of Maqam Jahargah that al-Sabbagh describes and I much
relish. Intuitively I might describe this as 16-38-13 steps of 159-EDO.
In your 79-MOS, as you note, it is steps 33-41-60-67 counting from
perde rast, or 8-19-7 steps.

You'll understand how I could easily picture a Turkish school like AEU
seeking to have "maqamat without quartertones" taking Maqam Chargah or
Jahargah in the common Arab understanding, and seeking to "Mahurize"
the upper tetrachord as 9-9-4 rather than 9-7-6. However, I am curious
whether your jins of Chargah as used in the descending portion of the
seyir for Maqam Saba could be a clue that the relevant version of
Maqam Chargah could instead involve this tetrachord.

WIth many thanks,

Margo Schulter
mschulter@...

🔗Margo Schulter <mschulter@...>

Dear Mario and All,

Please let me say that as a participant on this list, I feel a
responsibility to help promote an atmosphere of hospitality and good
humor. As someone who has for some years sought out tuning
"discoveries" which are often rediscoveries, I see this as a common
situation for any earnest devotee of the arts and scientists.

First of all, a tuning of 12 notes with 11 pure fifths is most worthy,
and its established history does not make it any less so. Welcoming a
"teaching moment," I would observe that this is an ideal tuning for
three and more centuries of European music, and an important side of
Near Eastern music also, although many more than 12 fifths are
required in order to obtain the middle or neutral intervals so vital
to this style.

To emphasize the virtues of the tuning you have described and answer
Brad's question at the same time: tuning a chain of 11 pure fifths
from Eb to G# appears to be a widespread practice of the 14th
century. It nicely fits the transcendent keyboard music of the
Robertsbridge Codex, as Mark Lindley has noted, and I would be
delighted to use the Eb-G# tuning for a wide range of music from
Perotin (and earlier) to Machaut.

Around 1400 or so, a tuning in which some of the customary sharps (F#,
C#, G#) are actually tuned as flats by pure fifths down or fourths up
from Eb. One popular choice is Gb-B; as Lindley notes, some pieces of
this area seem mostly to avoid the fifth B-F#, and theorists note that
this fifth is not available on current keyboards.

One reason Brad might not have discussed these famous tunings is that
they really pertain to medieval European music, not to his main era of
the 18th century. There's a general lesson to be learned here: a
tuning useful for one purpose may be quite unfitting for another.

For example, a few days ago, someone posted a question here about a
mathematical tuning relationship with which I am intimately familiar,
relying on it in a number of my favorite tunings. Eagerly I addressed
his question of what could be made of this pattern. Reading his
further clarification, however, I knew in a moment that we were
addressing radically different styles, with his perceptive
mathematical observation nicely serving my musical purposes rather
than his.

Mario, I am especially concerned that humor should serve to build
friendship and solidarity among us who participate here. George Secor,
a great musician and artist of tuning design, was playfully noting
that indeed you were following in the footsteps of Pythagoras, and of
many world musical traditions which use a tuning of pure fifths and
fourths as at least one important ingredient of their musics. We might
at once smile together at a mutual recognition that your discovery was
in fact a rediscovery, and take the occasion to wonder at the great
music which has been written and might be written with this system.

I conclude by noting that while 12 notes tuned in pure fifths
(producing 11 of these pure intervals) are ideal for much medieval
European music, a chain of 53 notes in such pure fifths will, in
effect, form a delightful circle, with one fifth made narrow by about
3.62 cents in order to obtain a pure octave and complete the circle.
Such a circle would be delightfully rich, and some generalized
keyboards now available could gracefully support it.

What we mostly find on the Tuning List is that different people have
different stylistic purposes, inviting different tunings, so that no
one is definitive or exclusive in its virtues.

A virtue of special importance, however, may be a mutual tempering
process by which we affirm each other's enthusiasm even while sharing
information that may lend a fuller perspective -- so that the mirror
of music or _Speculum musicae_, as Jacob of Liege or Jacob de Montibus
titled his great treatise, is often a place at once of delight and
laughter as we listen and gaze within.

With many thanks,

Margo Schulter
mschulter@...

🔗Ozan Yarman <ozanyarman@...>

Hi Margo!

On Sep 13, 2008, at 4:22 AM, Margo Schulter wrote:

>> Hello Margo,
>
> Hello Ozan. Please let me apologize for the length of my last reply,
> and try to keep this one a bit more concise. I am very happy that your
> advice has guided me to a nice solution of the Nihavend question.
>

I, on my part, apologize for my short attention span during this season. Fasting for the duration of Ramadan takes its toll on me. Still, I am happy to see that my brain is not totally dysfunctional! [grin]

> On Sep 2, 2008, at 11:29 AM, Margo Schulter wrote:
>
>>> Hello, Ozan and all.
>
>>> Much inspired by your discussions of the 79-MOS and Ozan24, and by
>>> our recent dialogues, I have decided to post a table of the
>>> perdeler or steps in the 704.607-cent regular temperament that has
>>> been the subject of some of my recent articles. Here this tuning is
>>> given as realized in 1024-EDO, a standard for some synthesizers,
>>> where the average size of the 23 fifths is about 704.603 cents.
>
>> That is a fine happenstance!
>
> Yes, I was pleasantly surprised that the fit should be so close. There
> are 17 fifths at 704.297 cents, and 6 fifths at 705.469 cents. The
> wider fifths are at Eb-Bb, G-D, and B-F# on each keyboard.
>
>>> Incidentally, the Turkish term _perde_ or "note, pitch" (plural
>>> perdeler) might possibly be related, I might guess, to the Persian
>>> _pardeh_, which can have a similar meaning and more specifically
>>> signify the "fret" of an instrument.
>
>> But we use perde not just for note or pitch, but also to indicate
>> frets in Turkiye. The usage is the same for all Middle Eastern >> nations.
>
> Thank you for educating me on this: maybe, like the origins of some of
> the maqamat, it might be an interesting question what language this
> term originated in. In reading Arab theory in English, so far, I'm not
> sure if I've seen any related term: but perde and pardeh seem common.
>

They are one and the same. The word originates in Persian as far as I know.

>>> In naming the perdeler, I have tried to be guided both by Arab and
>>> Turkish practice, and specifically by some of your conventions as
>>> they might apply to a system with fewer alternatives than the
>>> 79-MOS. When in doubt, I have taken the forms of Maqam Rast (as
>>> realized in this temperament) as normative: that is, in placing
>>> segah and evc or evdj (Arab awj) at 363 and 1068 cents, and hisar
>>> at 859 cents for the sixth degree of Ajemli or Nirz Rast.
>
>
>> Nirz Rast? Where does that name come from?
>
> Evidently the name Nirz Rast in Arab theory is another term for a
> maqam also called Nairuz, an Arabic version of the name for the Iranic
> New Year festival, with Nirz shortened from Nairuz. I also sometimes
> call it Zalzalian Rast; Ajemli Rast is very descriptive. In commas, I
> think of this as approximately 976|976|9, with the two conjuct Rast
> tetrachords. Of course, there are various ajnas to be found, and some
> Arab theorists may view it, for example, as disjunct Rast plus what is
> called Bayyati (i.e. Ushshaq), 976-9-769, although I would say that
> the upper 769 might be more like Huseyni than like the Arab version of
> Ushshaq or "Bayyati," which 679 would better express.
>

For those who did not follow the previous posts, let me clarify that ajnas are the plural of jins, which stands for genus and signifies the divisions of the tetrachord in medieval Islamic music theory. Since the late 19th Century, the term is applied to the divisions of pentachords too. I had at one point thought that ajnas could only be considered divisions of the tetrachord, but it occurred to me maqams such as Penchgah, Nihavend, Huseyni, Saba and even Huzzam require pentachords to explain their scales in a wholesome manner.

As for Nawruz, Abdulbaki Nasir Dede gives a detailed description which I interpret as follows:

1. An ascending-descending Nihavend pentachord from perde neva to muhayyer, G-A-Bb-c-d
2. A Mahur tetrachord from perde chargah to perde ajem, F-G-A-Bb
3. A possible Mahur tetrachord from perde ajem to perde sunbule, Bb-c-d-eb
4. Finalis on ajem, Bb

There are also Nawruz-i Ajem and Nawruz-i Sultani in Nasir Dede's treatise Tedkik u Tahkik. The latter is defined as a Nawruz-i Ajem that makes a Rast cadence. Nasir Dede says he gave the name himself as tribute to his patron Sultan Selim III. Nawruz-i Ajem, as the name implies, a Nawruz that concludes with Ajem. Ajem, according to Nasir Dede, is:

c-Bb-A-Ab-G-F-Ed-D

Accordingly, Nawruz-i Sultani becomes:

eb-d-c-Bb: Mahur on ajem
c-Bb-Ab-G-F: Nihavend on chargah
F-Ed-D-C: Rast on rast

Still, no sign of Huseini or Bayyati/Ushshaq on the upper conjunct pentachord.

>
>> An interesting feature is that perde buselik is at an almost just
>> 14/11, or about 18.5 Holdrian commas, sometimes suggested as a
>> preferred location by certain Near Eastern theorists.
>>
>
> [Excerpt from my table of perdeler or steps, which I've trimmed]
>
>> ---------------------------------------------------------------------
>> 8 C 363.281 21/17 Segah 24 362.215
>> ---------------------------------------------------------------------
>> 18 F 858.984 23/14 Hisar 56 852,878
>> 57 867.970
>> ---------------------------------------------------------------------
>
>> So far so good.
>
> Our discussions since I made this table, however, raise one point,
> since 859 cents is the perfect fourth of segah at 363 cents, might it
> better be named dik hisar ("steep Hisar"), and 837 cents be considered
> simply hisar? You suggested that dik hisar would be the right name in
> Maqam Segah, at least.
>

I have explained this in my previous post.

>> Maqam Bayyati (Arab interpretation)
>>
>> 859
>> Bb
>> C# D* E F# G# A B C#
>> 0 132 286 496 704 782 990 1200
>> 132 154 210 208 77 208 210
>
>> The scale is also that of Ushshaq.
>
> Yes, I would understand either Ushshaq as known in Turkey or what is
> known in the Arab world as Bayyati to be 679|949|9 or the like, with
> conjunct tetrachords of Ushshaq and Buselik (the latter known in Arab
> theory as Nahawand -- in contrast to Turkish Nihavend at 958 or the
> like, if I am right).

AEU theory considers Nihavend a transposition of Buselik.

>
>
>>> Maqam Huseyni
>>>
>>> C# Eb E F# G# Bb B C#
>>> 0 154 286 496 704 859 990 1200
>
>> A marvelous rendition.
>
> Thank you! I love this maqam with the larger neutral second, and can
> understand the advantages of making these intonational flavors a part
> of theory as well as practice.
>
>> Maqam Rast (Acemli or Nirz Rast flavor)
>>
>> Rast Rast tone
>> |-----------------|----------------|....|
>> F# G# Bb B C# Eb E F#
>> 0 208 363 495 704 858 990 1200
>> 208 155 132 210 154 132 210
>
>> This is a fine Ajemli Rast. But I hear the term Nirz Rast for the
>> first time.
>
> Thank you for your feedback: as I suggested in another message, this
> may be a bit like learning a language, and having the good fortune to
> have a teacher who is not only an excellent native speaker, but a
> leading scholar of its syntax and grammar!
>
> There is a good question how widespread the term Nirz Rast is in the
> Arab world: I have seen it, for example, in a dissertation by Scott
> Marcus on _Arab Music Theory in the Modern Period_, where Yusuf Shawqi
> (1964) is one source for this name. Some other sources of Arab theory
> prefer Nairuz, for example <http://www.maqamworld.com/maqamat/rast.html> >.
> Interestingly, d'Erlanger has two spellings, Nairuz or Niriz, with the
> latter close to Nirz. While al-Sabbagh, as cited by Marcus, calls the
> maqam simmply Nirz, some others have Nirz Rast.
>

That is a perversion. Nawruz can be likened to this modulation in Western music:

G minor => F Major => Bb Major => Eb Major => Bb Major.

>
>> Maqam Nihavend (supraminor flavor)
>>
>> Ascending
>>
>> Nihavend tone Hijaz
>> |-----------------|......|-----------------|
>> F# G# A* B C# D* F F#
>> 0 208 341 495 704 837 1068 1200
>> 208 132 154 210 132 231 132
>>
>>
>> Descending
>>
>> Nihavend tone Segah
>> |-----------------|......|-----------------|
>> F# G# A* B C# D* E* F#
>> 0 208 341 495 704 837 1045 1200
>> 208 132 154 210 132 208 155
>
>> An acceptable Nihavend, save for E*, which I believe should be 9/8
>> lower from F#.
>
> Ah, this is easily corrected, and the upper tetrachord might now, if I
> am correct, be called Ushshaq -- if this is fitting for this maqam:
>
> Descending
>
> Nihavend tone Ushshaq
> |-----------------|......|-----------------|
> F# G# A* B C# D* E F#
> 0 208 341 495 704 837 991 1200
> 208 132 154 210 132 155 209
>
> [...]

But I see that this is not acceptable. The third and sixth degrees must also be lowered by a diesis each. Nihavend and Buselik appear to be the same in your tuning.

>
>
>> 155 cents is not appropriate as an interval between E* and F# for
>> the descending scale of Nihavend I'm afraid.
>
> Here I may have made my mistake through a desire to have a perfect
> fifth between the third and seventh degrees (A*-E*); but now I
> understand that the seventh degree in the descending form should be a
> 9:8 below the octave of the final or tonic, with a perfect fourth
> between the fourth and seventh degrees. Thus, in a supraminor flavor,
> something like 967-9-679, but with the smaller neutral second at 132
> cents a tad smaller than 6 full commas.

On second thought, this rendition somewhat resembles Nihavend, though is not fully Nihavend!

>
>
>>> Here the supraminor third of Nihavend differs from the regular
>>> minor third of Buselik by a diesis or about 55 cents (286 and 341
>>> cents), as does the submajor third of Rast from the regular major
>>> third of Mahur (363 and 418 cents). However, the thirds of Nihavend
>>> and Rast differ by only a comma (341 and 363 cents), the fine
>>> difference between supraminor and submajor (or roughly 15 and 16
>>> commas).
>
>> This is very much agreeable.
>
> Again, your guidance is welcome, and the rule of a descending version
> with the seventh degree at 16/9 nicely resolves my uncertainty.
>
>> Oz.
>
> With many thanks,
>
> Margo
>
>

Cordially,
Oz.

🔗Ozan Yarman <ozanyarman@...>

O, Margo, you are very kind with your words. I am very pleased that you have obtained my thesis and found it useful. My responses are below:

On Sep 17, 2008, at 10:23 AM, Margo Schulter wrote:

>
>
> ---------------------------------------------------
> Homage to Ozan Yarman:
> Clarifying Maqam Chargah
> ----------------------------------------------------
>
> Yesterday it was my great pleasure to have a copy of your dissertation
> on Turkish music printed for me at my local University Library, thus
> overcoming software problems I have been experiencing at home with the
> processing of certain PDF files. What a pleasure it now is to have
> this document conveniently at hand, and to begin studying and
> absorbing its many facets.
>

It is gratifying to know that my work is acknowledged as a source in international music theory circles.

> As one method of celebrating this occasion, I have decided to seek
> clarification on a point raised in one of your recent messages, with
> due apologies if you have already discussed this point in some
> previous postings here, or possibly in other writings or forums.
>
> You mentioned that Maqam Chargah has been presented in some recent
> Turkish theory as what might be described as simply a transposition of
> the ascending form of Maqam Mahur from perde rast to chargah. as
> opposed to the "original" tradition to which you remain true. Here I
> would like to venture a guess as to two forms that tradition might
> take, and warmly invite your response -- having been alerted by a jins
> or genus Chargah mentioned at page 121 of your dissertation in
> connection with Maqam Saba that my initial impression might not be the
> correct one.
>
> That first impression was that Maqam Chargah in Turkiye, like Maqam
> Jahargah in the Arab world (the spelling variation reflecting a
> difference of phonology between the Persian and Arabic languages),
> involves disjunct Mahur and Rast tetrachords, as would accord with
> al-Sabbagh's suggested tuning for this maqam, as reported by Ali Jihad
> Racy, of around 9-9-4-9-9-7-6 commas. Here is my interpretation in a
> regular 24-note temperament at 704.607 cents, available as it happens
> within a single 12-MOS keyboard:
>
>
> Mahur Rast
> |-------------------------| T |-------------------------|
> T T B T T Jk Js
> 209 209 77 209 209 154 132
> E F# G# A B C# Eb E
> 0 209 418 495 705 914 1068 1200
> chargah neva huseyni ajem gerdaniye muhayyer tiz tiz
> segah chargah
>
> In the above notation, I have borrowed some signs from medieval and
> modern Near Eastern theory to show the intervals of a _tanini_ or
> whole tone at 209 cents (T); a larger mujenneb (Jk)

Mujannab-i kabir

> and smaller
> mujenneb (Js)

Mujannab-i sagir

> , middle or neutral seconds at 154 and 132 cents

As opposed to AEU 114 cents

> ; and a
> _bakiye_ or usual limma at 77 cents (B). These tempered sizes
> correspond to al-Sabbagh's approximate steps based on Pythagorean
> tuning or 53-EDO of 9, 7, 6, and 4 commas respectively (around 204,
> 158, 136, and 90 cents).
>

Suphi Ezgi writes about discussing with Saadettin Arel about the whole matter of using perde evdj instead of mahur in maqam Chargah. He nonchalantly confesses to their having decided to replace evdj with mahur because it did not agree with their conceptions of a main scale composed of natural, unaccidented notes!

> However, your Chargah tetrachord alerted me to a rather different
> possibility: a connection to the Persian Dastgah-e Chahargah, which
> features tetrachords generally like those termed Hijaz in Arab and
> Turkish theory. Your tetrachord occurring in a descending form of Saba
> as one side of the complex _terkib_ or composite maqam is as follows:
>
>
> |---------------------------------|
> 1/1 15/14 195/154 75/56
> 0 119 409 506
> 15/14 13/11 55/52
> 119 289 97
>
> This looks much more like a relative of Persian Chahargah than of the
> Mahur-Rast type of Maqam Jahargah that al-Sabbagh describes and I much
> relish.

Indeed so. But this is only half the picture just as it was the case with Arabs. This elusive maqam has been split in two by vast geographic distances into what you have described above. The correct Chargah, in my opinion, is the UNION of Turkish, Arabic and Persian traditions (except AEU of course!).

> Intuitively I might describe this as 16-38-13 steps of 159-EDO.
> In your 79-MOS, as you note, it is steps 33-41-60-67 counting from
> perde rast, or 8-19-7 steps.
>
> You'll understand how I could easily picture a Turkish school like AEU
> seeking to have "maqamat without quartertones" taking Maqam Chargah or
> Jahargah in the common Arab understanding, and seeking to "Mahurize"
> the upper tetrachord as 9-9-4 rather than 9-7-6.

That is precisely what seems to have happened. Even the 9-8-5 comma rendition offended Ezgi and Arel that they deemed it necessary to "Mahurize", that is to say, twist and contort Chargah to their whims.

> However, I am curious
> whether your jins of Chargah as used in the descending portion of the
> seyir for Maqam Saba could be a clue that the relevant version of
> Maqam Chargah could instead involve this tetrachord.
>

I do believe, just as Nasir Dede describes, that Chargah is a Saba with a finalis on chargah, comprising, moreover, a modulation that involves the alteration of the second degree of the Chargah genus to yield Mahur, and the second degree of the Hijaz genus, to yield Rast.

Though, I admit that, in a hurry to finish my dissertation, I have not remarked about the inclination of Gb and Eb in (F Gb A Bb C Db E F) to rise even higher than specified. Fortunately, A future 79MOS2deg159tET theory has room for that and more.

> WIth many thanks,
>
> Margo Schulter
> mschulter@...
>
>

Cordially,
Oz.

🔗Ozan Yarman <ozanyarman@...>

🔗Aaron Krister Johnson <aaron@...>

Hey Ozan and Margo,

This seems like an interesting discussion between you two, but I must
admit my utter ignorance of most of these Arabic names and theory.

Perhaps a glossary of Arabic and Persian musical terms put up in the
files section for tuning listers would help? Or it might go up on
Jacob Barton's xentonality wiki pages? (Or some links other than maqam
world, which is a world, and I would prefer a small village)

Of course, yes I could google stuff, but I thought it might be
interesting to hear an executive summary from someone with a tuning
list perspective who is intimate with all of this.

And/or maybe a ultra-concise guide/summary to this theory?

At least for me, I'm only half following this, and I'm mostly able due
to the help of some cents lists.

-A.

P.S. I've greatly enjoyed listening to some Turkish music from
turkishmusicportal.org in recent weeks. Thanks for the tip, Ozan.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> Hi Margo!
>
> On Sep 13, 2008, at 4:22 AM, Margo Schulter wrote:
>
> >> Hello Margo,
> >
> > Hello Ozan. Please let me apologize for the length of my last reply,
> > and try to keep this one a bit more concise. I am very happy that your
> > advice has guided me to a nice solution of the Nihavend question.
> >
>
>
> I, on my part, apologize for my short attention span during this
> season. Fasting for the duration of Ramadan takes its toll on me.
> Still, I am happy to see that my brain is not totally dysfunctional!
> [grin]
>
>
> > On Sep 2, 2008, at 11:29 AM, Margo Schulter wrote:
> >
> >>> Hello, Ozan and all.
> >
> >>> Much inspired by your discussions of the 79-MOS and Ozan24, and by
> >>> our recent dialogues, I have decided to post a table of the
> >>> perdeler or steps in the 704.607-cent regular temperament that has
> >>> been the subject of some of my recent articles. Here this tuning is
> >>> given as realized in 1024-EDO, a standard for some synthesizers,
> >>> where the average size of the 23 fifths is about 704.603 cents.
> >
> >> That is a fine happenstance!
> >
> > Yes, I was pleasantly surprised that the fit should be so close. There
> > are 17 fifths at 704.297 cents, and 6 fifths at 705.469 cents. The
> > wider fifths are at Eb-Bb, G-D, and B-F# on each keyboard.
> >
> >>> Incidentally, the Turkish term _perde_ or "note, pitch" (plural
> >>> perdeler) might possibly be related, I might guess, to the Persian
> >>> _pardeh_, which can have a similar meaning and more specifically
> >>> signify the "fret" of an instrument.
> >
> >> But we use perde not just for note or pitch, but also to indicate
> >> frets in Turkiye. The usage is the same for all Middle Eastern
> >> nations.
> >
> > Thank you for educating me on this: maybe, like the origins of some of
> > the maqamat, it might be an interesting question what language this
> > term originated in. In reading Arab theory in English, so far, I'm not
> > sure if I've seen any related term: but perde and pardeh seem common.
> >
>
>
> They are one and the same. The word originates in Persian as far as I
> know.
>
>
> >>> In naming the perdeler, I have tried to be guided both by Arab and
> >>> Turkish practice, and specifically by some of your conventions as
> >>> they might apply to a system with fewer alternatives than the
> >>> 79-MOS. When in doubt, I have taken the forms of Maqam Rast (as
> >>> realized in this temperament) as normative: that is, in placing
> >>> segah and evc or evdj (Arab awj) at 363 and 1068 cents, and hisar
> >>> at 859 cents for the sixth degree of Ajemli or Nirz Rast.
> >
> >
> >> Nirz Rast? Where does that name come from?
> >
> > Evidently the name Nirz Rast in Arab theory is another term for a
> > maqam also called Nairuz, an Arabic version of the name for the Iranic
> > New Year festival, with Nirz shortened from Nairuz. I also sometimes
> > call it Zalzalian Rast; Ajemli Rast is very descriptive. In commas, I
> > think of this as approximately 976|976|9, with the two conjuct Rast
> > tetrachords. Of course, there are various ajnas to be found, and some
> > Arab theorists may view it, for example, as disjunct Rast plus what is
> > called Bayyati (i.e. Ushshaq), 976-9-769, although I would say that
> > the upper 769 might be more like Huseyni than like the Arab version of
> > Ushshaq or "Bayyati," which 679 would better express.
> >
>
>
> For those who did not follow the previous posts, let me clarify that
> ajnas are the plural of jins, which stands for genus and signifies the
> divisions of the tetrachord in medieval Islamic music theory. Since
> the late 19th Century, the term is applied to the divisions of
> pentachords too. I had at one point thought that ajnas could only be
> considered divisions of the tetrachord, but it occurred to me maqams
> such as Penchgah, Nihavend, Huseyni, Saba and even Huzzam require
> pentachords to explain their scales in a wholesome manner.
>
> As for Nawruz, Abdulbaki Nasir Dede gives a detailed description which
> I interpret as follows:
>
> 1. An ascending-descending Nihavend pentachord from perde neva to
> muhayyer, G-A-Bb-c-d
> 2. A Mahur tetrachord from perde chargah to perde ajem, F-G-A-Bb
> 3. A possible Mahur tetrachord from perde ajem to perde sunbule, Bb-c-
> d-eb
> 4. Finalis on ajem, Bb
>
> There are also Nawruz-i Ajem and Nawruz-i Sultani in Nasir Dede's
> treatise Tedkik u Tahkik. The latter is defined as a Nawruz-i Ajem
> that makes a Rast cadence. Nasir Dede says he gave the name himself as
> tribute to his patron Sultan Selim III. Nawruz-i Ajem, as the name
> implies, a Nawruz that concludes with Ajem. Ajem, according to Nasir
> Dede, is:
>
> c-Bb-A-Ab-G-F-Ed-D
>
> Accordingly, Nawruz-i Sultani becomes:
>
> eb-d-c-Bb: Mahur on ajem
> c-Bb-Ab-G-F: Nihavend on chargah
> F-Ed-D-C: Rast on rast
>
>
> Still, no sign of Huseini or Bayyati/Ushshaq on the upper conjunct
> pentachord.
>
>
> >
> >> An interesting feature is that perde buselik is at an almost just
> >> 14/11, or about 18.5 Holdrian commas, sometimes suggested as a
> >> preferred location by certain Near Eastern theorists.
> >>
> >
> > [Excerpt from my table of perdeler or steps, which I've trimmed]
> >
> >> ---------------------------------------------------------------------
> >> 8 C 363.281 21/17 Segah 24 362.215
> >> ---------------------------------------------------------------------
> >> 18 F 858.984 23/14 Hisar 56 852,878
> >> 57 867.970
> >> ---------------------------------------------------------------------
> >
> >> So far so good.
> >
> > Our discussions since I made this table, however, raise one point,
> > since 859 cents is the perfect fourth of segah at 363 cents, might it
> > better be named dik hisar ("steep Hisar"), and 837 cents be considered
> > simply hisar? You suggested that dik hisar would be the right name in
> > Maqam Segah, at least.
> >
>
>
> I have explained this in my previous post.
>
>
> >> Maqam Bayyati (Arab interpretation)
> >>
> >> 859
> >> Bb
> >> C# D* E F# G# A B C#
> >> 0 132 286 496 704 782 990 1200
> >> 132 154 210 208 77 208 210
> >
> >> The scale is also that of Ushshaq.
> >
> > Yes, I would understand either Ushshaq as known in Turkey or what is
> > known in the Arab world as Bayyati to be 679|949|9 or the like, with
> > conjunct tetrachords of Ushshaq and Buselik (the latter known in Arab
> > theory as Nahawand -- in contrast to Turkish Nihavend at 958 or the
> > like, if I am right).
>
>
> AEU theory considers Nihavend a transposition of Buselik.
>
> >
> >
> >>> Maqam Huseyni
> >>>
> >>> C# Eb E F# G# Bb B C#
> >>> 0 154 286 496 704 859 990 1200
> >
> >> A marvelous rendition.
> >
> > Thank you! I love this maqam with the larger neutral second, and can
> > understand the advantages of making these intonational flavors a part
> > of theory as well as practice.
> >
> >> Maqam Rast (Acemli or Nirz Rast flavor)
> >>
> >> Rast Rast tone
> >> |-----------------|----------------|....|
> >> F# G# Bb B C# Eb E F#
> >> 0 208 363 495 704 858 990 1200
> >> 208 155 132 210 154 132 210
> >
> >> This is a fine Ajemli Rast. But I hear the term Nirz Rast for the
> >> first time.
> >
> > Thank you for your feedback: as I suggested in another message, this
> > may be a bit like learning a language, and having the good fortune to
> > have a teacher who is not only an excellent native speaker, but a
> > leading scholar of its syntax and grammar!
> >
> > There is a good question how widespread the term Nirz Rast is in the
> > Arab world: I have seen it, for example, in a dissertation by Scott
> > Marcus on _Arab Music Theory in the Modern Period_, where Yusuf Shawqi
> > (1964) is one source for this name. Some other sources of Arab theory
> > prefer Nairuz, for example
<http://www.maqamworld.com/maqamat/rast.html
> > >.
> > Interestingly, d'Erlanger has two spellings, Nairuz or Niriz, with the
> > latter close to Nirz. While al-Sabbagh, as cited by Marcus, calls the
> > maqam simmply Nirz, some others have Nirz Rast.
> >
>
>
> That is a perversion. Nawruz can be likened to this modulation in
> Western music:
>
> G minor => F Major => Bb Major => Eb Major => Bb Major.
>
>
> >
> >> Maqam Nihavend (supraminor flavor)
> >>
> >> Ascending
> >>
> >> Nihavend tone Hijaz
> >> |-----------------|......|-----------------|
> >> F# G# A* B C# D* F F#
> >> 0 208 341 495 704 837 1068 1200
> >> 208 132 154 210 132 231 132
> >>
> >>
> >> Descending
> >>
> >> Nihavend tone Segah
> >> |-----------------|......|-----------------|
> >> F# G# A* B C# D* E* F#
> >> 0 208 341 495 704 837 1045 1200
> >> 208 132 154 210 132 208 155
> >
> >> An acceptable Nihavend, save for E*, which I believe should be 9/8
> >> lower from F#.
> >
> > Ah, this is easily corrected, and the upper tetrachord might now, if I
> > am correct, be called Ushshaq -- if this is fitting for this maqam:
> >
> > Descending
> >
> > Nihavend tone Ushshaq
> > |-----------------|......|-----------------|
> > F# G# A* B C# D* E F#
> > 0 208 341 495 704 837 991 1200
> > 208 132 154 210 132 155 209
> >
> > [...]
>
>
> But I see that this is not acceptable. The third and sixth degrees
> must also be lowered by a diesis each. Nihavend and Buselik appear to
> be the same in your tuning.
>
>
> >
> >
> >> 155 cents is not appropriate as an interval between E* and F# for
> >> the descending scale of Nihavend I'm afraid.
> >
> > Here I may have made my mistake through a desire to have a perfect
> > fifth between the third and seventh degrees (A*-E*); but now I
> > understand that the seventh degree in the descending form should be a
> > 9:8 below the octave of the final or tonic, with a perfect fourth
> > between the fourth and seventh degrees. Thus, in a supraminor flavor,
> > something like 967-9-679, but with the smaller neutral second at 132
> > cents a tad smaller than 6 full commas.
>
>
> On second thought, this rendition somewhat resembles Nihavend, though
> is not fully Nihavend!
>
>
> >
> >
> >>> Here the supraminor third of Nihavend differs from the regular
> >>> minor third of Buselik by a diesis or about 55 cents (286 and 341
> >>> cents), as does the submajor third of Rast from the regular major
> >>> third of Mahur (363 and 418 cents). However, the thirds of Nihavend
> >>> and Rast differ by only a comma (341 and 363 cents), the fine
> >>> difference between supraminor and submajor (or roughly 15 and 16
> >>> commas).
> >
> >> This is very much agreeable.
> >
> > Again, your guidance is welcome, and the rule of a descending version
> > with the seventh degree at 16/9 nicely resolves my uncertainty.
> >
> >> Oz.
> >
> > With many thanks,
> >
> > Margo
> >
> >
>
>
> Cordially,
> Oz.
>

🔗Margo Schulter <mschulter@...>

Dear Ozan,

Please forgive me for now being the one who needs to catch up with
your wonderful recent posts and responses -- and with much less reason
than you have for needing wisely and prudently to pace yourself,
although this may be the best policy even when circumstances do not so
obviously require it.

My mother and I were both very much entertained by your notes and
commentary on my sonnet: the "bombards" were especially fitting,
because one meaning of a bombard is a medieval or Renaissance European
instrument, related to the Near Eastern shawm if I am correct from
which it is derived, known for its penetrating sound. We were both
delighted, as I shall share more when responding to that post.

Also, you have given me the wonderful gift of that seyir in your
dissertation for Maqam Saba, which exquisitely fits my regular
tempered system if I put perde rast at C* on the upper keyboard! What
a beautiful maqam, noted both for its sadness and its mystical ecstasy
or _tarab_, if that is the term that Ali Jihad Racy uses. The lower
Saba pentachord of 1/1-12/11-13/11-9/7-3/2 from perde dugah, as it
maps to this system (D*-E-F*-G-A*), is so fitting, at least to my
curious ear. This, also, is another thread: my purpose here is just to
say how beautiful the music is that this maqam offers, with your seyir
indeed as an invaluable "road map" and the use of pentachords very
helpful, just as you noted in one your most recent replies.

> Why does Safiuddin Urmavi describe a 17-tone Pythagorean Abjad scale
> when, at the same time, mentioning tetrachordal divisions involving
> middle seconds (characterized by high-prime limit RI) and Ud finger
> positions as given below?

> FRET CENT RATIO
> A Mutlak 0 1/1
> B Mücenneb-i Sebbabe (zaid) 90 256/243
> C Half tanini (Mücenneb-i Sebbabe) 99 18/17
> C Mücenneb-i Sebbabe (Fars vusta) 145 162/149
> C Mücenneb-i Sebbabe (Zelzel vusta) 168 54/49
> D Sebbabe 204 9/8
> h Mücenneb-i (qadim) vusta 294 32/27
> V Fars vusta 303 81/68
> V Zelzel vusta 355 27/22
> Z Bınsır 408 81/64
> Hınsır 498 4/3

Now to your question about Safi al-Din al-Urmavi and the reason he
might write a great deal about middle or neutral intervals, and
discuss many tetrachords using them, but nevertheless favor a 17-note
Pythagorean MOS which, of course, yields other flavors but not these
neutral ones.

Maybe this question belongs with the three things, as I recall, that
even the wise King Salamon or Suleyman said were difficult to
understand. However, as someone much concerned with the theory of the
Mutazilah era although not familiar with the relevant writings in the
way that you are, I agree that it is a worthy question and one that
can be highly edifying, even if we mostly end up bombarding each other
with more and more friendly questions and arguments! Indeed, that
might be one of the best reasons for asking it.

Certainly, as you rightly emphasize in your dissertation, Safi al-Din,
and also modern writers such as al-Sabbagh who take a mostly
Pythagorean approach to tuning are hardly shy about discussing middle
or neutral intervals. Urmavi, of course, discusses these middle
intervals at great length and uses them in a variety of JI
tetrachords, but also recommends a Pythagorean 17-MOS which cannot
yield these flavors.

Although al-Sabbagh's 24-of-53-EDO tuning, with one break in the chain
of fifths, if I'm right, does yield a few neutral intervals for
maqamat like Rast, which he makes a point of emphasizing should be
tuned 976-9-976 rather than in equal quartertones, still, as Scott
Marcus notes, these intervals are not so ample. If I entered the
tuning correctly into Scala, then there is a chain of 22 fifths among
the 24 notes, so that the neutral flavors aren't that more prevalent
than in a simple chain of 23 fifths.

This dramatically contrasts with medieval tunings of Zalzal/al-Farabi
and Ibn Sina for instruments such as the `ud, where Zalzal's variously
placed wusta (27/22, 39/32, or whatever) signals that neutral flavors
are basic and central to the style -- as well as lots of tetrachords
in Urmavi and Qutb al-Din al-Shirazi. In modern times, of course,
contrasting with al-Sabbagh's 24-note system (a better example than
AEU, since special ideological considerations obviously don't apply to
a theorist quite eager to use the comma system to show how neutral
intervals should be tuned), we have Persian theorists such as Hormoz
Farhat, Dariush Anooshfar (see Scala archive, persian.scl and
persian-far.scl), and Dariush Tala`i who leave no doubt that neutral
intervals get priority in theory and practice.

Curiously, Farhat in his book on the dastgah system does document a
Persian theory seeking to explain tuning in terms of Pythagorean
intervals of a kind produced by 10 or fewer generators -- this means
regular and schismatic or 5-limit flavors, as opposed to the neutral
flavors noted by others. What we find in Farhat and others, based in
part on pragmatic surveys of how people actually fret and tune
instruments such as the tar with its 17 or so steps per octave, are
tunings with lots of Pythagorean and neutral flavors, and a few
5-limit flavors of the kind we might expect from chains of 7-10
generators at or quite close to 3:2.

If you want a few guesses as to possible factors, here they are:

(1) In a historical setting like that of the Mutazilah Era where
various primes may be used in JI tetrachords and systems,
including a delightful variety of neutral flavors, the main
constraining factor may be (as far as I know) the absence of
a theory of temperament, or more specifically of subtle
regular temperament or the like. If you prefer a regular
system of generators, your obvious choice in JI is
Pythagorean: and unless you go to a 29-MOS or larger,
neutral flavors will be absent (as in a 17-MOS) or rather
sparse (as in a regular or nearly-regular 24-note system,
e.g. al-Sabbagh or AEU). You have a choice of neutral
flavors, _or_ regularity (maybe especially attractive if you
seek a "systematic" approach) -- but not both at the same
time in a world without a theory of subtle temperament.

(2) Like al-Sabbagh, as interpreted by Marcus, a theorist might
feel that 5-limit flavors, or a free choice at lots of
places between these flavors and Pythagoran ones (e.g. Mahur
versus a 5-limit Rast, or Buselik vs. Nihavend) is more
important than neutral flavors. Of course, with a
Pythagorean 29-MOS or larger, there are enough intervals of
all these flavors that the question of priorities becomes
less urgent. Even with a full circle of 52 pure fifths plus
one fifth at 3,615 cents narrow, of course, the variety of
neutral flavors will be less than in the 79-MOS -- but that
little 53-comma adds at least a bit of variety beyond the
two sizes for each category (e.g. 6 or 7 commas for a middle
second) in 53-EDO. It's quite possible to devise a 24-note
Pythagorean system with _lots_ of neutral flavors, but not a
regular one: two 12-MOS chains at 3 commas apart will do it
just fine! That's another story, however.

Getting back to Urmavi and the 17-note system, maybe he
liked the elegant way that a Pythagorean 17-MOS could yield
_some_ of his favorite flavors, evidently including a
5-limit Rast much like that favored in Turkey today. The
17-MOS would be a neat theoretical model yielding some quite
beautiful tunings; and people could turn to his discussion
on middle intervals and tetrachords, and the tuning
practices involving neutral intervals which doubtless
prevailed, to enjoy what this 17-MOS didn't cover. I can
easily imagine someone looking at his theoretical 17-MOS
maqamat and intoning them so that 8192/6561 (~5/4) becomes
something like 27/22 or 21/17 or 26/21, etc. This kind of
thing is still happening today, as I know from reading Owen
Wright and "adapting" some tunings to a certain style of
temperament -- not to mention our conversations.

(3) Flexible-pitch performers aren't bound by fixed systems,
small or otherwise; and people tuning the `ud or tar or
whatever might tend to follow less "systematic" methods and
wind up with lots more neutral flavors, a la Zalzal, Ibn
Sina, etc. European theory has its "academic" tuning systems
also, which may tell us more about concepts and mathematical
tools than about prevalent tunings. Thus Ramos (1482) gives
a 5-limit JI tuning with a prominent Wolf fifth -- but also,
less often noted, describes a practical keyboard, as
chronicled by Mark Lindley, which seems very much in some
kind of meantone temperament (Ab-C#). In 1518, Henricus
Grammateus described a modification of Pythagorean tuning in
which accidentals divide a 9:8 tone into two equal semitones
(~101.955 cents or so) -- but by this point it is very
likely that some kind of meantone, regular or modified, was
the rule (as in Schlick, 1511, and Aaron, 1523).

This doesn't mean that we should ignore "academic" tunings,
or ignore what theorists say, especially when urged to do so
by people less familiar with a given style. Thus Urmavi's
17-MOS could point to a great interest in schismatic thirds
and related intervals (he mentions 5:4, 6:5, and 7:6 as
having a considerable degree of concord), as well as a taste
for regularity in getting an unbroken chain of fifths.
Likewise the 5-limit monochord of Ramos, as well as his
likely description of a meantone keyboard, signal a move
toward a 5-limit aesthetic and away from the earlier vibrant
tradition of the 13th-14th centuries based on the regular
intervals of Pythagorean tuning, and its accentuated
variations for flexible pitch performances (Marchettus).
The modified Pythagorean system of Grammateus reflects a
great interest in the art of temperament and irrational
geometric divisions, with systems for calculating 12-EDO on
the lute (taken as standard by around the middle of the
century), and ultimately 17th-century and later theory based
on logarithms, as descendants of this line of inquiry.

(4) Is it possible that different tunings might have been
preferred for different instruments, at least in widespread
practice and/or theory? In later 16th-century Europe, for
example, we often read that ensembles have tuning problems
because keyboards are customarily in meantone (say 1/5-1/3
comma, with varying tastes), lutes in 12-EDO, and singers
approximating 5-limit. While singers could adjust, the
harpsichord vs. lute issue might be more difficult. I'm not
sure if there's any analogy in the world of Islamic
Civilization around the late 13th century -- just a stray
thought. Or, might people have often shifted between
different tunings, or maybe had two or three `uds or the
like with different frettings, sort of like modern guitars
in 17-EDO or 19-EDO or 29-EDO or 31-EDO or whatever? If so,
maybe they could tune one instrument to Zalzal/al-Farabi or
the fine tuning of Urmavi you quote above: the "Persian"
neutral second at 162/149 would be quite close to the
smaller step of Zalzal/al-Farabi at 88:81 -- and another in
a Pythagorean 17-MOS or the like. On a flexible-pitch
instrument (maybe strings without frets?), you could take
both systems as models, and shift between them -- a wild
guess with any known basis? Could some instruments be
readily retuned to one system or another, like adjusting a
usual qanun to the maqam or family at use at a given time?

These are questions or points for discussion and argument, rather than
"solutions" to your question.

Of course, there can be variety of constraints in tuning, and some
decisions might be "overdetermined" in a way: for example, a medieval
theorist might prefer a Pythagorean 17-MOS both because of a love for
5-limit flavors and from a simple love for having pure and reliable
fifths at every position but one in the gamut. One might also prefer
it for regularity and the support for using usual diatonic intervals
(1-6 generators) in lots of locations -- as with Prosdocimus and
Ugolino in the early 15th century, who specifically want these usual
sizes in directed progressions such as cadences rather than the
schismatic sizes with major intervals a comma smaller and minor ones a
comma larger (another story).

Similarly, a modern theorist might like a system with lots of support
for a 5-limit version of Rast because of a special liking for that
tuning, or an understanding that it is very prevalent and should be
supported, or possibly also because of some ideological motivation to
avoid more neutral flavors -- at least on paper! If a system like the
79-MOS has pervasive support for neutral intervals also, we can
discount the last motivation!

Interestingly, as possibly with Urmavi and the Pythagorean 17-MOS, a
modern theorist might gravitate toward a 5-limit Rast as at least one
main option because of a logic like this -- just an example of how
people _might_ make decisions for various reasons in various eras:

(1) Rast is the principal maqam, and it should be very
easy to notate and play.

(2) This means, in 20th-21st century conditions, that
Rast should be defined by an unbroken chain of
fifths, permitting regular spellings (i.e. a diatonic
spelling of the basic disjunct form from rast to
gerdaniye or C-C without accidentals).

(3) However, they cannot all be Pythagorean fifths,
because then we would have Mahur rather than Rast!

(4) Further, if we assume that no fifth in the chain
should be tempered by more than 7 cents or so (around
1/3-comma, say a Holdrian comma in the 79-MOS or a
full 159-EDO), this sets a lower limit on the size of
the third, or the distance from rast to segah: no
more than around 4/3 comma or two yarmans smaller
than a Pythagorean 81/64, around 30 cents of
narrowing -- and thus something like 378 cents (a tad
less than the 379 cents of 19-EDO).

(5) Using a neutral flavor of Rast instead will involve
either breaking the chain of fifths (another option,
of course, in the 79-MOS), or else tempering fifths
at considerably more than 1/3-comma -- as in
something like 26-EDO submajor range around 26/21. If
we reasonably take around 1/3-comma as the limit of
tasteful tempering for these purposes, then 5-limit
indeed looks like the kind of Rast that fits a
"regular spellings with 1/3-comma or less of
tempering" agenda.

I'm mentioning the modern Rast question not as any close analogy to
Urmavi's possible reasons, but simply to suggest that there could be a
variety of such reasons, maybe largely left unwritten and not so easy
to discover some seven centuries later.

Yet your question is a call to a most noble and worthy endeavor or
struggle to learn whatever we can, and to exercise our gift of reason
in the great Mutazilah tradition.

WIth many thanks,

Margo

🔗Ozan Yarman <ozanyarman@...>

Hello Aaron!

Where to start, where to start? There is a glossary section at the back of my thesis, but I gather you need a concise summary of the terms we use in maqam music. Ok. Here are some common terms that you may store at the tuning list cellar:

maqam/pl. maqamat or makamlar: A scale or collection of scales (sometimes exceeding an octave) with specific intervallic relationships between their degrees (called perdeler). They are likened to modes, but may also be defined as "key" with an emphasis on modality instead of tonality.

terkib/ pl. terkibat: Composite maqam (such as Kurdilihijazkar, Ferahfeza) or maqam with a suffix maqam attached (such as Saba-Zemzeme, Muhayyer-Kurdi, Beyati-Araban). A terkib is an agglomerate of two or more maqams, embroidered in a composition such that they come in a repeating pattern or sequence. The usage of the term is obsolete today.

perde/pl. perdeler or perdeha: Tone or pitch used by a maqam usually corresponding to a degree of 53 logarithmically equal divisions of the octave. The naming of the perdeler does not necessarily repeat at the octave (for example: rast-gerdaniye, dugah-muhayyer, segah-tiz segah). Some perdes, such as segah or hijaz (saba), are not always stationary and flaunt wide microtonal inflections depending on the maqam. The frequencies of perdeler depends on the ahenk chosen.

qarar or duraq: Finalis or tonic of a maqam or terkib.

asma qarar: Equivalent to dominant or sub-dominant in Western music. Asma qarar may sometimes be the third or other degree of the maqam's principal scale.

gechki: Modulation to another maqam.

cheshni: Savour, or borrowing from another maqam which is usually compatible with the maqam performed.

shedd: Transposition. Shedd maqam is a transposed maqam or the segment of a maqam which is transposed over to a perde other than its original finalis.

basqi/pl. basqilar: Intonation. Correct execution of a pitch.

ijra: Performance by a maqam music ensemble.

edvar (pl. of devir): Scales not exceeding an octave (named Ushshaq, Neva, Ebuselik, Rast, Hijaz, Nawruz, etc...) and written in Abjad notation in Medieval Islamic music treatises (most famous are those by Safi al-din Urmavi and Abdulqadir Maragi) comprising 17 (Pythagorean) tones to the octave (up 4 fifths, down 12 fifth from tone of origin); the treatises themselves.

ika: Meter.

usul/pl. usuller: Rhythm with a simple or composite pattern of beats.

aralik/pl. araliklar: Interval.

ahenk: Diapason, reference pitch. There are, in theory, 12 possible ahenks, each corresponding to a specific size of ney reed. The most famous ahenks from which ijra is executed are Bolahenk (rast on D), Supurde (rast on C), Mustahsen (rast on B), Kiz (rast on A), Mansur (rast on G) and Shah (rast on F).

jins/pl. ajnas: Divisions of the tetrachord or pentachord.

beshli: The interval of a fifth or pentachord.

dortlu: The interval of a fourth or tetrachord.

Ask me and I will give more definitions.

Cordially,
Oz.

On Sep 18, 2008, at 6:14 PM, Aaron Krister Johnson wrote:

> Hey Ozan and Margo,
>
> This seems like an interesting discussion between you two, but I must
> admit my utter ignorance of most of these Arabic names and theory.
>
> Perhaps a glossary of Arabic and Persian musical terms put up in the
> files section for tuning listers would help? Or it might go up on
> Jacob Barton's xentonality wiki pages? (Or some links other than maqam
> world, which is a world, and I would prefer a small village)
>
> Of course, yes I could google stuff, but I thought it might be
> interesting to hear an executive summary from someone with a tuning
> list perspective who is intimate with all of this.
>
> And/or maybe a ultra-concise guide/summary to this theory?
>
> At least for me, I'm only half following this, and I'm mostly able due
> to the help of some cents lists.
>
> -A.
>
> P.S. I've greatly enjoyed listening to some Turkish music from
> turkishmusicportal.org in recent weeks. Thanks for the tip, Ozan.
>
> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> Hi Margo!
>>
>> On Sep 13, 2008, at 4:22 AM, Margo Schulter wrote:
>>
>>>> Hello Margo,
>>>
>>> Hello Ozan. Please let me apologize for the length of my last reply,
>>> and try to keep this one a bit more concise. I am very happy that >>> your
>>> advice has guided me to a nice solution of the Nihavend question.
>>>
>>
>>
>> I, on my part, apologize for my short attention span during this
>> season. Fasting for the duration of Ramadan takes its toll on me.
>> Still, I am happy to see that my brain is not totally dysfunctional!
>> [grin]
>>
>>
>>> On Sep 2, 2008, at 11:29 AM, Margo Schulter wrote:
>>>
>>>>> Hello, Ozan and all.
>>>
>>>>> Much inspired by your discussions of the 79-MOS and Ozan24, and by
>>>>> our recent dialogues, I have decided to post a table of the
>>>>> perdeler or steps in the 704.607-cent regular temperament that has
>>>>> been the subject of some of my recent articles. Here this tuning >>>>> is
>>>>> given as realized in 1024-EDO, a standard for some synthesizers,
>>>>> where the average size of the 23 fifths is about 704.603 cents.
>>>
>>>> That is a fine happenstance!
>>>
>>> Yes, I was pleasantly surprised that the fit should be so close. >>> There
>>> are 17 fifths at 704.297 cents, and 6 fifths at 705.469 cents. The
>>> wider fifths are at Eb-Bb, G-D, and B-F# on each keyboard.
>>>
>>>>> Incidentally, the Turkish term _perde_ or "note, pitch" (plural
>>>>> perdeler) might possibly be related, I might guess, to the Persian
>>>>> _pardeh_, which can have a similar meaning and more specifically
>>>>> signify the "fret" of an instrument.
>>>
>>>> But we use perde not just for note or pitch, but also to indicate
>>>> frets in Turkiye. The usage is the same for all Middle Eastern
>>>> nations.
>>>
>>> Thank you for educating me on this: maybe, like the origins of >>> some of
>>> the maqamat, it might be an interesting question what language this
>>> term originated in. In reading Arab theory in English, so far, I'm >>> not
>>> sure if I've seen any related term: but perde and pardeh seem >>> common.
>>>
>>
>>
>> They are one and the same. The word originates in Persian as far as I
>> know.
>>
>>
>>>>> In naming the perdeler, I have tried to be guided both by Arab and
>>>>> Turkish practice, and specifically by some of your conventions as
>>>>> they might apply to a system with fewer alternatives than the
>>>>> 79-MOS. When in doubt, I have taken the forms of Maqam Rast (as
>>>>> realized in this temperament) as normative: that is, in placing
>>>>> segah and evc or evdj (Arab awj) at 363 and 1068 cents, and hisar
>>>>> at 859 cents for the sixth degree of Ajemli or Nirz Rast.
>>>
>>>
>>>> Nirz Rast? Where does that name come from?
>>>
>>> Evidently the name Nirz Rast in Arab theory is another term for a
>>> maqam also called Nairuz, an Arabic version of the name for the >>> Iranic
>>> New Year festival, with Nirz shortened from Nairuz. I also sometimes
>>> call it Zalzalian Rast; Ajemli Rast is very descriptive. In >>> commas, I
>>> think of this as approximately 976|976|9, with the two conjuct Rast
>>> tetrachords. Of course, there are various ajnas to be found, and >>> some
>>> Arab theorists may view it, for example, as disjunct Rast plus >>> what is
>>> called Bayyati (i.e. Ushshaq), 976-9-769, although I would say that
>>> the upper 769 might be more like Huseyni than like the Arab >>> version of
>>> Ushshaq or "Bayyati," which 679 would better express.
>>>
>>
>>
>> For those who did not follow the previous posts, let me clarify that
>> ajnas are the plural of jins, which stands for genus and signifies >> the
>> divisions of the tetrachord in medieval Islamic music theory. Since
>> the late 19th Century, the term is applied to the divisions of
>> pentachords too. I had at one point thought that ajnas could only be
>> considered divisions of the tetrachord, but it occurred to me maqams
>> such as Penchgah, Nihavend, Huseyni, Saba and even Huzzam require
>> pentachords to explain their scales in a wholesome manner.
>>
>> As for Nawruz, Abdulbaki Nasir Dede gives a detailed description >> which
>> I interpret as follows:
>>
>> 1. An ascending-descending Nihavend pentachord from perde neva to
>> muhayyer, G-A-Bb-c-d
>> 2. A Mahur tetrachord from perde chargah to perde ajem, F-G-A-Bb
>> 3. A possible Mahur tetrachord from perde ajem to perde sunbule, Bb->> c-
>> d-eb
>> 4. Finalis on ajem, Bb
>>
>> There are also Nawruz-i Ajem and Nawruz-i Sultani in Nasir Dede's
>> treatise Tedkik u Tahkik. The latter is defined as a Nawruz-i Ajem
>> that makes a Rast cadence. Nasir Dede says he gave the name himself >> as
>> tribute to his patron Sultan Selim III. Nawruz-i Ajem, as the name
>> implies, a Nawruz that concludes with Ajem. Ajem, according to Nasir
>> Dede, is:
>>
>> c-Bb-A-Ab-G-F-Ed-D
>>
>> Accordingly, Nawruz-i Sultani becomes:
>>
>> eb-d-c-Bb: Mahur on ajem
>> c-Bb-Ab-G-F: Nihavend on chargah
>> F-Ed-D-C: Rast on rast
>>
>>
>> Still, no sign of Huseini or Bayyati/Ushshaq on the upper conjunct
>> pentachord.
>>
>>
>>>
>>>> An interesting feature is that perde buselik is at an almost just
>>>> 14/11, or about 18.5 Holdrian commas, sometimes suggested as a
>>>> preferred location by certain Near Eastern theorists.
>>>>
>>>
>>> [Excerpt from my table of perdeler or steps, which I've trimmed]
>>>
>>>> ---------------------------------------------------------------------
>>>> 8 C 363.281 21/17 Segah 24 362.215
>>>> ---------------------------------------------------------------------
>>>> 18 F 858.984 23/14 Hisar 56 852,878
>>>> 57 867.970
>>>> ---------------------------------------------------------------------
>>>
>>>> So far so good.
>>>
>>> Our discussions since I made this table, however, raise one point,
>>> since 859 cents is the perfect fourth of segah at 363 cents, might >>> it
>>> better be named dik hisar ("steep Hisar"), and 837 cents be >>> considered
>>> simply hisar? You suggested that dik hisar would be the right name >>> in
>>> Maqam Segah, at least.
>>>
>>
>>
>> I have explained this in my previous post.
>>
>>
>>>> Maqam Bayyati (Arab interpretation)
>>>>
>>>> 859
>>>> Bb
>>>> C# D* E F# G# A B C#
>>>> 0 132 286 496 704 782 990 1200
>>>> 132 154 210 208 77 208 210
>>>
>>>> The scale is also that of Ushshaq.
>>>
>>> Yes, I would understand either Ushshaq as known in Turkey or what is
>>> known in the Arab world as Bayyati to be 679|949|9 or the like, with
>>> conjunct tetrachords of Ushshaq and Buselik (the latter known in >>> Arab
>>> theory as Nahawand -- in contrast to Turkish Nihavend at 958 or the
>>> like, if I am right).
>>
>>
>> AEU theory considers Nihavend a transposition of Buselik.
>>
>>>
>>>
>>>>> Maqam Huseyni
>>>>>
>>>>> C# Eb E F# G# Bb B C#
>>>>> 0 154 286 496 704 859 990 1200
>>>
>>>> A marvelous rendition.
>>>
>>> Thank you! I love this maqam with the larger neutral second, and can
>>> understand the advantages of making these intonational flavors a >>> part
>>> of theory as well as practice.
>>>
>>>> Maqam Rast (Acemli or Nirz Rast flavor)
>>>>
>>>> Rast Rast tone
>>>> |-----------------|----------------|....|
>>>> F# G# Bb B C# Eb E F#
>>>> 0 208 363 495 704 858 990 1200
>>>> 208 155 132 210 154 132 210
>>>
>>>> This is a fine Ajemli Rast. But I hear the term Nirz Rast for the
>>>> first time.
>>>
>>> Thank you for your feedback: as I suggested in another message, this
>>> may be a bit like learning a language, and having the good fortune >>> to
>>> have a teacher who is not only an excellent native speaker, but a
>>> leading scholar of its syntax and grammar!
>>>
>>> There is a good question how widespread the term Nirz Rast is in the
>>> Arab world: I have seen it, for example, in a dissertation by Scott
>>> Marcus on _Arab Music Theory in the Modern Period_, where Yusuf >>> Shawqi
>>> (1964) is one source for this name. Some other sources of Arab >>> theory
>>> prefer Nairuz, for example
> <http://www.maqamworld.com/maqamat/rast.html
>>>> .
>>> Interestingly, d'Erlanger has two spellings, Nairuz or Niriz, with >>> the
>>> latter close to Nirz. While al-Sabbagh, as cited by Marcus, calls >>> the
>>> maqam simmply Nirz, some others have Nirz Rast.
>>>
>>
>>
>> That is a perversion. Nawruz can be likened to this modulation in
>> Western music:
>>
>> G minor => F Major => Bb Major => Eb Major => Bb Major.
>>
>>
>>>
>>>> Maqam Nihavend (supraminor flavor)
>>>>
>>>> Ascending
>>>>
>>>> Nihavend tone Hijaz
>>>> |-----------------|......|-----------------|
>>>> F# G# A* B C# D* F F#
>>>> 0 208 341 495 704 837 1068 1200
>>>> 208 132 154 210 132 231 132
>>>>
>>>>
>>>> Descending
>>>>
>>>> Nihavend tone Segah
>>>> |-----------------|......|-----------------|
>>>> F# G# A* B C# D* E* F#
>>>> 0 208 341 495 704 837 1045 1200
>>>> 208 132 154 210 132 208 155
>>>
>>>> An acceptable Nihavend, save for E*, which I believe should be 9/8
>>>> lower from F#.
>>>
>>> Ah, this is easily corrected, and the upper tetrachord might now, >>> if I
>>> am correct, be called Ushshaq -- if this is fitting for this maqam:
>>>
>>> Descending
>>>
>>> Nihavend tone Ushshaq
>>> |-----------------|......|-----------------|
>>> F# G# A* B C# D* E F#
>>> 0 208 341 495 704 837 991 1200
>>> 208 132 154 210 132 155 209
>>>
>>> [...]
>>
>>
>> But I see that this is not acceptable. The third and sixth degrees
>> must also be lowered by a diesis each. Nihavend and Buselik appear to
>> be the same in your tuning.
>>
>>
>>>
>>>
>>>> 155 cents is not appropriate as an interval between E* and F# for
>>>> the descending scale of Nihavend I'm afraid.
>>>
>>> Here I may have made my mistake through a desire to have a perfect
>>> fifth between the third and seventh degrees (A*-E*); but now I
>>> understand that the seventh degree in the descending form should >>> be a
>>> 9:8 below the octave of the final or tonic, with a perfect fourth
>>> between the fourth and seventh degrees. Thus, in a supraminor >>> flavor,
>>> something like 967-9-679, but with the smaller neutral second at 132
>>> cents a tad smaller than 6 full commas.
>>
>>
>> On second thought, this rendition somewhat resembles Nihavend, though
>> is not fully Nihavend!
>>
>>
>>>
>>>
>>>>> Here the supraminor third of Nihavend differs from the regular
>>>>> minor third of Buselik by a diesis or about 55 cents (286 and 341
>>>>> cents), as does the submajor third of Rast from the regular major
>>>>> third of Mahur (363 and 418 cents). However, the thirds of >>>>> Nihavend
>>>>> and Rast differ by only a comma (341 and 363 cents), the fine
>>>>> difference between supraminor and submajor (or roughly 15 and 16
>>>>> commas).
>>>
>>>> This is very much agreeable.
>>>
>>> Again, your guidance is welcome, and the rule of a descending >>> version
>>> with the seventh degree at 16/9 nicely resolves my uncertainty.
>>>
>>>> Oz.
>>>
>>> With many thanks,
>>>
>>> Margo
>>>
>>>
>>
>>
>> Cordially,
>> Oz.
>>
>
>
>
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🔗Ozan Yarman <ozanyarman@...>

Some more terms I forgot in my last post:

mujannab-i kebir or buyuk mujannnab: An interval of 65536:59049 in Yekta's and Arel-Ezgi-Uzdilek (AEU) theory.

mujannab-i sagir or koutchuk mujannab: An interval of 2187:2048 in Yekta's and Arel-Ezgi-Uzdilek (AEU) theory.

mujannab bolgesi: Mujannab zone (coined by Yalchin Tura). Defined by Urmavi as mujannabat, that denotes the half-tone to middle second region comprising 18:17, 162:149 and 54:49.

bakiye: An interval of 256:243 in Yekta's and Arel-Ezgi-Uzdilek (AEU) theory.

yeden or yeden ses: Leading tone.

Oz.

On Sep 18, 2008, at 6:14 PM, Aaron Krister Johnson wrote:

🔗Margo Schulter <mschulter@...>

Hello, Ozan, Aaron, and all.

As part of a longer letter or article, available in its full form at
<http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt>,
I have proposed a "middle-resolution" system for describing types of
intervals and steps used in Arab/Turkish/Kurdish maqam and Persian
dastgah music based on the familiar concept of 53 commas to an
octave.

The concept of nine commas to a regular 9:8 tone, and thus 53 to an
octave in Pythagorean intonation or the later 53-EDO, is a basic
element of Turkish and some Syrian theory, with recognition elsewhere
in the Arab world also. The scheme suggested here borrows extensively
from recent Turkish usage, while seeking to remedy such anomalies as
the frequent omission of neutral second steps because of ideological
factors, specifically a political dislike for associating the Turkish
heritage of maqam music with "Arab" and "Byzantine" systems featuring
the use of "quartertones." Your dissertation, Ozan, of course covers
all of this history and more in great detail, a fascinating education
for me and others who read it.

Aaron, and others who may be new to this, I should explain that Near
Eastern theory offers various degrees of "resolution" or specificity
in defining the types or sizes of intervals that are -- or in the
writer's view should be -- used in the intonation of a given
tetrachord, maqam, etc.

A "low resolution" system says basically: "This step is or should be a
tone, semitone, neutral second, or an "augmented step" or
"plus-second" often equal to some kind of minor third ranging from
septimal or slightly smaller up to around Pythagorean."

For example, consider a typical Arab form of a tetrachord or _jins_
(from the Greek _genus_) named Rast, also the name of a maqam or modal
complex drawing its basic steps from two of these tetrachords. Here's
a low-resolution notation for this variety of Rast using an
approximate quartertone system (common in 19th-21st century Arab
theory) or an approximate thirdtone system. Note that "d" represents a
half-flat symbol used to show an _approximate_ quartertone alteration,
but not necessarily one of precisely 50 cents as in 24-EDO!

C D Ed F
24: 0 4 7 10
4 3 3

17: 0 3 5 7
3 2 2

Describing Rast as 4-3-3 in the 24-step system or 3-2-2 in the 17-step
system is a very useful shorthand, but leaves open, for example, just
how the neutral third of the tetrachord should be placed, and which of
the two neutral second steps, the first or the second, should be
larger or smaller. These issues wouldn't come up in 17-EDO or 24-EDO,
where there is only one size of neutral second step -- but will come
in traditional performances of Near Eastern music, where there are
almost infinite shadings of these steps and playing "in tune" involves
an appreciation of this.

A 53-comma notation, or the letter notation of the Persian theorist
Hormoz Farhat, addresses these vital questions but still leaves lots
of room for "fine-tuning," or for the vagaries of different JI or
tempered systems. Here's a middle-level description of Rast in both
these systems:

53: C D Ed F
0 9 16 22
9 7 6

Farhat: M N n

Just as the 17-step and 24-step notations don't necessarily imply
using 17-EDO or 24-EDO, so the 53-step or 53-comma system doesn't
necessarily imply 53-EDO or Pythagorean: rather it provides a handy
numerical shorthand that can be adapted to various tuning systems, or
to flexible-pitch performance (often the main focus!). Farhat's system
uses letters to show a (M)ajor second, large (N)eutral or small
(n)eutral step, or (m)inor second step -- the last not used in Rast.

Read literally in 53-EDO terms, the 9-7-6 notation would call for
steps of 204-158-136 cents -- a very pleasant tuning, in fact, but
only one of many possibilities fitting the spirit of this or Farhat's
M-N-n notation.

The important point is that we are told not only that this version of
Rast has a lower tone plus two neutral seconds, but that the lower
neutral second is the larger one.

The 53-comma system is also very useful in distinguishing this flavor
of Rast, the usual one in Arab theory, with a different flavor known
in medieval and modern times, and the one taken as the standard model,
so to speak, in modern Turkey:

53: C D E F
0 9 17 22
9 8 5

This is a 5-limit flavor of Rast, as shown by the 53-comma notation.
Interestingly, as in your 79-MOS, Ozan, this tuning might actually be
realized by a single unbroken chain of fifths with at least some of
these generators tempered, as in a European meantone. What 9-8-5
notation shows us is the 5-limit pattern, in contrast to 9-7-6 with
its use of two neutral seconds and a largish neutral third rather than
a 5:4 major third.

A "high-resolution" notation, of course, could use cents; or JI
ratios; or steps smaller than a 53-comma, as with the 79-MOS, where
the usual unit is the yarman, equal to about 2/3 of a comma or about
15.09 cents. Indeed, thinking of yarmans as "just a tad larger than
15 cents" is a great shortcut for keeping track of them! That,
however, is another topic and another post.

Getting back to the 53-comma system, I should explain that the table
below isn't meant to cover all intervals, but those either likely to
be used as basic steps in maqam and dastgah music, or smaller than
these usual steps but important for measuring certain inflections or
differences in size: the comma itself, and the 2-comma category, which
could be called a demi-limma, half-limma, or medieval diaschisma (not
to be confused with another use of this last term for a smaller
interval of 2048:2025 or about 19.55 cents).

One general set of categories might invite a quick explanation: the
"augmented" step or "plus-second" ranging from a bit larger than 8:7
up through 15:13 (11 commas) and the 7:6 minor third (12 commas) up to
around a Pythagorean minor third (13 commas). This is the middle step
of a tetrachord type known as Hijaz, and also in the Persian tradition
as Chahargah (or Turkish Chargah). One tradition style of tuning for
Hijaz might be about as follows:

D Ed F# G
cents 0 140 408 498
140 268 90

53-commas 0 6 18 22
6 12 4

To show how the 53-comma system might be adapted to a temperament,
categories corresponding to the Pythagorean of 53-EDO ones are shown
for a regular temperament known as the "e-based" tuning since the
ratio between the regular tone and diatonic semitone or limma is equal
to Euler's e, around 2.71828 -- thus a fifth around 704.607 cents.
The categories often map reasonably well, although the chains of
generators are often different -- thus the Pythagorean or 53-EDO
12-comma at around 23 cents matches up with the e-based 17-comma at
around 22 cents.

----------------------------------------------------------------------
Middle-resolution categories based on 53-comma system
----------------------------------------------------------------------
53-EDO type commas cents symbol e-based type 53-commas cents
----------------------------------------------------------------------
12-comma 1 22.64 F 17-comma 0.96 21.68
......................................................................
demi-limma 2 45.28 D -------- ----- -----
......................................................................
reduced limma 3 67.92 E 12-diesis 2.44 55.28
----------------------------------------------------------------------
limma 4 90.57 B limma 3.40 76.97
----------------------------------------------------------------------
apotome 5 113.21 S limma + comma 4.36 98.65
......................................................................
small neut 2nd 6 135.85 Js apotome 5.84 132.25
......................................................................
large neut 2nd 7 158.49 Jk dim 3rd 6.80 153.93
......................................................................
dim 3rd 8 181.13 K reduced tone 8.28 187.53
----------------------------------------------------------------------
tone 9 203.77 T tone 9.24 209.21
......................................................................
large tone 10 226.42 T10 large tone 10.20 230.90
----------------------------------------------------------------------
hemifourth 11 249.06 A11 ---------- ----- ------
......................................................................
small min 3rd 12 271.70 A12 small min 3rd 11.68 264.50
......................................................................
min 3rd 13 294.34 A13 min 3rd 12.64 286.18
----------------------------------------------------------------------

Much more could be said about the history of some of these symbols in
recent Turkish theory, and I'd warmly invite you to add any helpful
details or corrections, Ozan or anyone else.

With many thanks,

Margo

🔗Margo Schulter <mschulter@...>

Dear Daniel Stearns and all,

Thank you for this fascinating document, and the
sobering reminding of the violence and genocide that took
place during the Second World War, tying in so tragically
with the musical history you are chronicling. One reaction
on my part is to think of Adriaan Fokker, who was fortunate
enough to survive that war and occupation of the Netherlands;
and his colleague in physics Lise Meitner, who left Germany
just in time (1938) -- thus saving her life, but very
possibly also contributing to the circumstances in which her
colleagues rather than she received the Nobel Prize for their
discovery as a team of nuclear fission.

Reading what I could understand by a crude process of looking for
Latin-related words or cognates -- the PDF file ran fine, by
the way -- showed a discussion of the 24-tone and 17-tone views
of Arab music, and also use of the ultimately medieval European
distinction between b (Bb) and h (B-natural) -- for example,
e-f, b-c, and a-b as diatonic semitones.

What I try to imagine is what these different currents of world
music might have seemed like to Haba in the interwar era, as we
now think of it -- the "postwar" era, of course, as it seemed
more optimistically at the time. It's fascinating that Haba cites
a study of an 11th-century manuscript from Montpellier (not to be
confused with the 13th-century collection of polyphony with which
I'm familiar) having signs which, it's been argued, might represent
microtonal inflections.

Of course, today, there are still many current of world music: and
I often wonder how my colleagues Ozan Yarman and Shaahin Mohaajeri
may view the diversity in which we all participate. My background
is mostly in medieval European music, a curious vantagepoint, but
no more nor less valid than any other.

As to 24-EDO, I do have some comments. In my view, it's a beautiful
tuning, but necessarily a limited one -- as any equal temperament
of around this size will necessarily be, since an EDO, from one
viewpoint, is a strategy for getting the smallest possible number
of interval sizes in a given tuning size <grin>.

From a "regional" point of view, 24-EDO might be said to have three
main categories or families of intervals, all useful, but, because
of the modest size plus EDO structure, not as varied as may be
required for some applications (hardly a unique "flaw"!).

Being able to describe in what I hope are reasonably objective terms
the types or regions of intervals offered by a given tuning system
seems to me a desirable goal for 21st-century theory. Let's quickly
consider 24-EDO from this point of view.

The regular 12-EDO intervals, as with that smaller tuning, may be
taken as a slightly "subdued" variation on 12-note Pythagorean
intonation of a kind standard in medieval Europe, or as a rather
inaccurate meantone temperament at the upper boundary of that tuning
style. If the goal is simply to make a 12-note Pythagorean system into
a circle, then in fact this is a fine solution, although the colors
are a bit diluted -- in contrast to the modern strategy of tempering
a comparable amount in the more "interesting" or wide direction for
neomedieval music today.

As has been mentioned, 24-EDO has an excellent family of intervals in
the central portion of the neutral range: thus 150 cents (12:11); 350
cents (11:9 or 27:22); 850 cents (44:27 or 18:11); and 1050 cents (11:6).
The main criticism here -- as with 17-EDO or 31-EDO -- is that we have
only neutral size for each category, e.g. only one neutral second.
In Near Eastern styles, the contrast between small and large neutral
intervals is often a vital one, one of the reasons why the "24-tone"
model of Arab music is simply that, a model, rather than a precise guide
to intonation. However, there's lots of beautiful music that can be made
with these 24-EDO neutral sizes -- and the related "superfourth" at
550 cents, very close to 11:8.

A big attraction of 24-EDO is the set of what I term interseptimal
intervals at 250, 450, 750, and 950 cents. These are one of the greatest
charms of the tuning, in my view: "interseptimal" refers to the fact
each of these ratios is located between landmark septimal ratios such
as 8:7 and 7:6 (231-250-267 cents); 9:7 and 21:16 (435-450-471 cents);
32:21 and 14:9 (729-750-765 cents); or 12:7 and 7:4 (933-950-969 cents).

These intervals are routine in Balinese or Javanese gamelan, for example,
but "revolutionary" from a conventional European perspective since they
seem about midway between two familiar categories such as "major second"
and "minor third." Indeed, following standard 14th-century European
counterpoint patterns, 950 cents can nicely serve as either a wide major
sixth expanding to an octave, or a narrow minor seventh contracting to a
fifth. It's an interesting question whether more "ebullient"
interpretations of the intonational precepts of Marchettus of Padua (1318)
may have produced intervals in this region -- but, in any event, a fine
harmonic resource for the 21st century.

The interseptimal intervals of 24-EDO could be compared to just ratios of
15:13 or 22:19 (250 cents); 22:17 or 13:10 (450 cents); 20:13 or 17:11
(750 cents); and 19:11 or 26:15 (950 cents).

A point to be emphasized is that from an historical European perspective,
both the neutral and interseptimal families of 24-EDO represent "the sound
of the new" -- although from a perspective of Near Eastern maqam/dastgah
music or the custom-tuned ensembles of gamelan, the tuning might rather
represent merely a quick sampler of the familiar, hopefully leading people
coming from a European perspective who are intrigued by these sounds to
look more deeply into these traditions where they have been in use for
many centuries.

On a "regional" approach to intervals and ratios, see also:

<http://www.bestII.com/~mschulter/IntervalSpectrumRegions.txt>

Again, Daniel, you're an ideal person to present this Haba material in
its fuller human and musical context -- thank you!

Thanks also to the others who have enriched this discussion. The mention
of 15th-century "atonality" is of great interest to me, and I am curious
to which pieces or style this label might apply (I am aware of hotly
debated attempts, as by Edward Lowinsky, to use this terminology in
a 16th-century or early 17th-century context, as with Gesualdo -- and
the strongly differing views of Richard Crocker and Carl Dahlhaus, for
example). Some of the very adventurous pieces such as Solage's _Fumeux
fume_ in the era of 1380-1400 or so, or Guillaume (if I'm correct)
Legrant in the following generation, are indeed "wayward," as one
anthology puts it -- but I'd say that elements of modality (in the free
polyphonic sense) and cadential direction still supply a feeling of a
"finalis."

Most appreciatively,

Margo

🔗Daniel Forro <dan.for@...>

Dear Margo Schulter,

thank you for your deep insight.

On 25 Sep 2008, at 11:35 AM, Margo Schulter wrote:
> Dear Daniel Stearns and all,
>
> Thank you for this fascinating document, and the
> sobering reminding of the violence and genocide that took
> place during the Second World War, tying in so tragically
> with the musical history you are chronicling. One reaction
> on my part is to think of Adriaan Fokker, who was fortunate
> enough to survive that war and occupation of the Netherlands;
> and his colleague in physics Lise Meitner, who left Germany
> just in time (1938) -- thus saving her life, but very
> possibly also contributing to the circumstances in which her
> colleagues rather than she received the Nobel Prize for their
> discovery as a team of nuclear fission.
>
> Reading what I could understand by a crude process of looking for
> Latin-related words or cognates -- the PDF file ran fine, by
> the way -- showed a discussion of the 24-tone and 17-tone views
> of Arab music, and also use of the ultimately medieval European
> distinction between b (Bb) and h (B-natural) -- for example,
> e-f, b-c, and a-b as diatonic semitones.
>
Czech music theory was in the past connected to German one, so Czech language uses the same system for names of tones, we distinct B and H - that's the reason I could compose easily few pieces on B-A-C-H :-)
We have as well -is endings for sharps, -es for flats, -isis for double sharps, -eses for double flats (with few exceptions), pronunciated as written:

Cis Dis Eis Fis Gis Ais His
Ces Des Es Fes Ges As Hes (or B pronunciated "be")
Cisis Disis Eisis Fisis Gisis Aisis Hisis
Ceses Deses Eses Feses Geses Asas Heses

I have heard that Dutch uses some hybrid of German and English system, as they have only B and use it with -is, -es endings for B sharp and B flat (Bis, Bes). Maybe somebody here who knows Dutch will confirm.
> What I try to imagine is what these different currents of world
> music might have seemed like to Haba in the interwar era, as we
> now think of it -- the "postwar" era, of course, as it seemed
> more optimistically at the time.
>
Yes, indeed, last decades world is more connected thanks to media, and recording technology of all kinds, and of course internet as not always trustful source of information. We can now listen, study and get scores to any music, one can find inspiration anywhere and connect everything with everything. Which I do as well in my music, prefering to make an organic synthesis, not just mix of styles. Open minded people like Haba are happy with such possibilities.
> It's fascinating that Haba cites
> a study of an 11th-century manuscript from Montpellier (not to be
> confused with the 13th-century collection of polyphony with which
> I'm familiar) having signs which, it's been argued, might represent
> microtonal inflections.
>
He mentioned it's considered to be quartertones.
But concerning microintervals he totally omitted Antonin Rejcha (1770-1836), until now underestimated great Czech composer, teacher and theoretician living mostly in Vienna and later in Paris. Rejcha mentioned in his theoretical works on music composition quartertones in old Greek music theory and practice and their compositional using in "modern" music, his ideas inspired J. F. Halevy who used quartertones in its incidental music to Promethee Enchaine (1849).
He didn't mentioned Czech acoustician and amateur microtonalist Josef Sumec (1867-1934), who worked with 612 EDO and created four microintervallic reed organs (2 with 24 EDO, one 36 EDO, one 60 EDO). Maybe he didn't liked him (very often a relation of professional to amateur, kind of jealousy or who knows - Sumec was very clever and very advanced, but not musician, and he was criticising Haba's theoretical works and his prefering of quartertones. I would say he was right, Haba should listen to him more.).
> Of course, today, there are still many current of world music: and
> I often wonder how my colleagues Ozan Yarman and Shaahin Mohaajeri
> may view the diversity in which we all participate. My background
> is mostly in medieval European music, a curious vantagepoint, but
> no more nor less valid than any other.
>
>
That's great, I love, study and have been performing medieval music for 25 years, especially Ars Subtilior from Yale university transcriptions from 50ies, in my arrangements for synthesizers (where is easy to setup different temperaments). It was a revelation for me to found this material. I'm not so much interested in tunings in this context, but fascinated by rhythmic complexity, polymodality, and all that manneurism (colored notation, way of writing music without score in modern sense, without barlines and time signatures...). Absolutely inspiring for contemporary composers. Usually I combine at concerts my experimental, polystylistic, computer, microintervallic or improvised music with medieval and Renaissance music (especially Venosa), and sometimes listeners wondered how such old music can sound like contemporary one. Not because my music sounds so old, but opposite :-)
> As to 24-EDO, I do have some comments. In my view, it's a beautiful
> tuning, but necessarily a limited one -- as any equal temperament
> of around this size will necessarily be, since an EDO, from one
> viewpoint, is a strategy for getting the smallest possible number
> of interval sizes in a given tuning size <grin>.
>
> From a "regional" point of view, 24-EDO might be said to have three
> main categories or families of intervals, all useful, but, because
> of the modest size plus EDO structure, not as varied as may be
> required for some applications (hardly a unique "flaw"!).
>
> Being able to describe in what I hope are reasonably objective terms
> the types or regions of intervals offered by a given tuning system
> seems to me a desirable goal for 21st-century theory. Let's quickly
> consider 24-EDO from this point of view.
>
> The regular 12-EDO intervals, as with that smaller tuning, may be
> taken as a slightly "subdued" variation on 12-note Pythagorean
> intonation of a kind standard in medieval Europe, or as a rather
> inaccurate meantone temperament at the upper boundary of that tuning
> style. If the goal is simply to make a 12-note Pythagorean system into
> a circle, then in fact this is a fine solution, although the colors
> are a bit diluted -- in contrast to the modern strategy of tempering
> a comparable amount in the more "interesting" or wide direction for
> neomedieval music today.
>
> As has been mentioned, 24-EDO has an excellent family of intervals in
> the central portion of the neutral range: thus 150 cents (12:11); 350
> cents (11:9 or 27:22); 850 cents (44:27 or 18:11); and 1050 cents > (11:6).
> The main criticism here -- as with 17-EDO or 31-EDO -- is that we have
> only neutral size for each category, e.g. only one neutral second.
> In Near Eastern styles, the contrast between small and large neutral
> intervals is often a vital one, one of the reasons why the "24-tone"
> model of Arab music is simply that, a model, rather than a precise > guide
> to intonation. However, there's lots of beautiful music that can be > made
> with these 24-EDO neutral sizes -- and the related "superfourth" at
> 550 cents, very close to 11:8.
>
> A big attraction of 24-EDO is the set of what I term interseptimal
> intervals at 250, 450, 750, and 950 cents. These are one of the > greatest
> charms of the tuning, in my view: "interseptimal" refers to the fact
> each of these ratios is located between landmark septimal ratios such
> as 8:7 and 7:6 (231-250-267 cents); 9:7 and 21:16 (435-450-471 cents);
> 32:21 and 14:9 (729-750-765 cents); or 12:7 and 7:4 (933-950-969 > cents).
>
> These intervals are routine in Balinese or Javanese gamelan, for > example,
> but "revolutionary" from a conventional European perspective since > they
> seem about midway between two familiar categories such as "major > second"
> and "minor third." Indeed, following standard 14th-century European
> counterpoint patterns, 950 cents can nicely serve as either a wide > major
> sixth expanding to an octave, or a narrow minor seventh contracting > to a
> fifth. It's an interesting question whether more "ebullient"
> interpretations of the intonational precepts of Marchettus of Padua > (1318)
> may have produced intervals in this region -- but, in any event, a > fine
> harmonic resource for the 21st century.
>
> The interseptimal intervals of 24-EDO could be compared to just > ratios of
> 15:13 or 22:19 (250 cents); 22:17 or 13:10 (450 cents); 20:13 or 17:11
> (750 cents); and 19:11 or 26:15 (950 cents).
>
> A point to be emphasized is that from an historical European > perspective,
> both the neutral and interseptimal families of 24-EDO represent > "the sound
> of the new" -- although from a perspective of Near Eastern maqam/> dastgah
> music or the custom-tuned ensembles of gamelan, the tuning might > rather
> represent merely a quick sampler of the familiar, hopefully leading > people
> coming from a European perspective who are intrigued by these > sounds to
> look more deeply into these traditions where they have been in use for
> many centuries.
>
> On a "regional" approach to intervals and ratios, see also:
>
> <http://www.bestII.com/~mschulter/IntervalSpectrumRegions.txt>
>
You have written here a brilliant analysis, but even after reading it somehow I didn't started to like 24 EDO... I used it in some of my microintervallic works, melodically just for making music different and more interesting, harmonically for neutral thirds, otherwise just as a sound effect, timbre in soundscapes, atmospheres...
> Again, Daniel, you're an ideal person to present this Haba material in
> its fuller human and musical context -- thank you!
>
If you mean my person, thank you for your appreciation. I would say I can help with getting and translating material from Czech or some other languages if somebody is really interested, if I'm interested as well, and find time for it. Or can try to get some records from my old country for analysis. Frankly said Haba somehow is not exactly my cup of green tea as a composer because of his quite traditional way of composition, there are much more interesting personalities in Czech music of 20th century, not necessarily working with microintervals. I will be happy to write sometimes about Moravian folklore, or anything about Czech music or some other (now I have a great opportunity to study more about Japanese music for example), as well about pop/jazz/rock, chords, harmony, or my own compositional using of microintervals... if there are some questions, answers could be found... I have many interests :-)
> Thanks also to the others who have enriched this discussion. The > mention
> of 15th-century "atonality" is of great interest to me, and I am > curious
> to which pieces or style this label might apply (I am aware of hotly
> debated attempts, as by Edward Lowinsky, to use this terminology in
> a 16th-century or early 17th-century context, as with Gesualdo -- and
> the strongly differing views of Richard Crocker and Carl Dahlhaus, for
> example).
>
Then we have same love again. I don't think we can call this atonality, but as a working term it's OK. Atonality came after tonality as its negation, early "atonality" should be called maybe more apropriate "primal chaos", from which later entropy of tonality came. What for me personally is interesting in this context is a chromaticism in European music from this early state until 12tone music... I collect scores of compositions using interesting chromatic progressions, be it melodically, polymelodically or harmonically. I'd like to write one day some work from this material.
And concerning tonality/atonality, it doesn't need to be antagonistic - it's possible to find a way how to combine it, which I have tried in many of my works. So I used for example different kinds of 12tone music, and result can sound quite tonal. Or tonal or modal melody is harmonized atonally...
> Some of the very adventurous pieces such as Solage's _Fumeux
> fume_ in the era of 1380-1400 or so,
>
Oh, my beloved piece, almost my "musical visitcard" as I perform it at the beginning of almost every my concert. Unbelievable work. There are discussions what that "fume" was in that rather enigmatic lyrics of this piece, as tobacco was still unknown those times in Europe. It's not totally excluded it could be canabis, hashish or so... Then no wonder that music is like it is, if it was inspired by drugs :-)

I would be happy to exchange from time to time some facts about this kind of music, you evidently know a lot about it. I would be grateful if you can indicate me some interesting material on the net, or scores, or direct me somewhere... Always hungry for new information. I will try to balance.
> or Guillaume (if I'm correct)
> Legrant in the following generation, are indeed "wayward," as one
> anthology puts it -- but I'd say that elements of modality (in the > free
> polyphonic sense) and cadential direction still supply a feeling of a
> "finalis."
>
> Most appreciatively,
>
> Margo
>
Have a nice day!

Daniel Forro

P.S.: A small part of my works of all kind is on <www.soundclick.com/forrotronics>, now about 400. Purely microintervallic works are:
Seven Microintervallic Studies
Euphony 1
Euphony 2
Musica per Piazza nel campo a Siena
Preludio metallico
Ecmelic Music
Harmonia Mundi

Microintervals were used partly in:
Moravian meditation
Syntphonies
Music for Erno Rubik
Crimson Space
The Wizard of Oz
Digital Music 01/87
Musica ex machina 01/88
Music to Vernisage
Drawn music - Music drawing
Cosmopolitan Music
Musica Ethnica 01/92
Fudoo Myoo e no inori
Music for Dyje
Concertino for synthesizers and drums
Orbis Fictus

More will come step by step.
Opinions, criticism, questions highly welcomed!

🔗Torsten Anders <torsten.anders@...>

🔗Daniel Forro <dan.for@...>

🔗Margo Schulter <mschulter@...>

Dear Daniel,

Thank you for a wonderful article, and a fascinating meeting between
us as musicians who seem in some ways to have had strikingly similar
formations and experiences. Such a dialogue is the greatest delight
and honor.

> Dear Margo Schulter,
> thank you for your deep insight.

And likewise!

> Czech music theory was in the past connected to German one, so Czech
> language uses the same system for names of tones, we distinct B and H
> - that's the reason I could compose easily few pieces on B-A-C-H :-)

Yes, and with the change of hexachords, so to speak. I am somehow
imagining it as a figure in a madrigal, and what Wert or Marenzio might
do with it. Or, a 14th-century progression occur to me; this is an
exercise for which I am long overdue! If I could compose something on
this figure and post it here, that might be fun.

> We have as well -is endings for sharps, -es for flats, -isis for
> double sharps, -eses for double flats (with few exceptions),
> pronunciated as written:
> Cis Dis Eis Fis Gis Ais His
> Ces Des Es Fes Ges As Hes (or B pronunciated "be")
> Cisis Disis Eisis Fisis Gisis Aisis Hisis
> Ceses Deses Eses Feses Geses Asas Heses
> I have heard that Dutch uses some hybrid of German and English
> system, as they have only B and use it with -is, -es endings for B
> sharp and B flat (Bis, Bes). Maybe somebody here who knows Dutch will
> confirm.

For some music, if the Dutch system is as you have heard, that might
raise the question of how "B#" (His) as used by the Prince of Venosa,
for example, would be identified, assuming that Bes is B and Bis is H
(a logical usage given the hexachord system with B-fa and B-mi, or
round and square B). Maybe Fokker's 31-note notation would give us a
practical answer if he uses this Dutch system to name the notes, and
his system is of course admirably suited to Venosa's music.

> Yes, indeed, last decades world is more connected thanks to media,
> and recording technology of all kinds, and of course internet as
> not always trustful source of information. We can now listen, study
> and get scores to any music, one can find inspiration anywhere and
> connect everything with everything. Which I do as well in my music,
> prefering to make an organic synthesis, not just mix of
> styles. Open minded people like Haba are happy with such
> possibilities.

The "connectivity" as some people call it is indeed incredible; and I
agree that some kind of organic synthesis should be a goal. George
Secor, who sometimes posts here, lent me great impetus in 2001-2002 to
seeking out coherent styles which indeed synthesize historical styles,
and in the process arrive at new possibilities, or as I might say in
the language of around 1600, new "rhetorical figures."

This could be a fascinating discussion: how one discovers "new rules,"
and integrates them into some kind of reasonably consistent style.

>> It's fascinating that Haba cites a study of an 11th-century
>> manuscript from Montpellier (not to be confused with the
>> 13th-century collection of polyphony with which I'm familiar)
>> having signs which, it's been argued, might represent microtonal
>> inflections.

> He mentioned it's considered to be quartertones.

> But concerning microintervals he totally omitted Antonin Rejcha
> (1770-1836), until now underestimated great Czech composer, teacher
> and theoretician living mostly in Vienna and later in Paris. Rejcha
> mentioned in his theoretical works on music composition
> quartertones in old Greek music theory and practice and their
> compositional using in "modern" music, his ideas inspired
> J. F. Halevy who used quartertones in its incidental music to
> Promethee Enchaine (1849). He didn't mentioned Czech acoustician
> and amateur microtonalist Josef Sumec (1867-1934), who worked with
> 612 EDO and created four microintervallic reed organs (2 with 24
> EDO, one 36 EDO, one 60 EDO).

This is a fascinating history. Rejcha interestingly represents around
the period when "modern" Arab music theory is said to have started,
with some Europeans reporting that either 17 thirdtones or 24
quartertones were taken as the model for describing the modes or
maqamat. I wonder if any of these Czech composers were acquainted with
the writings of Vicentino or Colonna. Halevy's use of quartertones
would be interesting to see, a side of the 19th century indeed not
often mentioned as far as I know, although this isn't the most
familiar era to me. Sometimes Sumac's 612-EDO model is discussed on
this list, with Gene Ward Smith as one who likes it.

> Maybe he didn't liked him (very often a relation of professional to
> amateur, kind of jealousy or who knows - Sumec was very clever and
> very advanced, but not musician, and he was criticising Haba's
> theoretical works and his prefering of quartertones. I would say he
> was right, Haba should listen to him more.).

Certainly I'd agree that precise quartertones of 1/24 octave are only
a very small part of a vast universe. For Renaissance music, either
31-EDO or a 31-note circle in 1/4-comma meantone (with one odd fifth
virtually just!) would be an ideal choice, for example.

> Of course, today, there are still many current of world music: and
> I often wonder how my colleagues Ozan Yarman and Shaahin Mohaajeri
> may view the diversity in which we all participate. My background
> is mostly in medieval European music, a curious vantagepoint, but
> no more nor less valid than any other.

> That's great, I love, study and have been performing medieval music
> for 25 years, especially Ars Subtilior from Yale university
> transcriptions from 50ies, in my arrangements for synthesizers
> (where is easy to setup different temperaments). It was a
> revelation for me to found this material. I'm not so much
> interested in tunings in this context, but fascinated by rhythmic
> complexity, polymodality, and all that manneurism (colored
> notation, way of writing music without score in modern sense,
> without barlines and time signatures...). Absolutely inspiring for
> contemporary composers. Usually I combine at concerts my
> experimental, polystylistic, computer, microintervallic or
> improvised music with medieval and Renaissance music (especially
> Venosa), and sometimes listeners wondered how such old music can
> sound like contemporary one. Not because my music sounds so old,
> but opposite :-)

When I was in college, the Ars Subtilior was one of my favorite eras
also, and I had Willi Apel's transcriptions. Around the early 1980's,
I recorded a few pieces using a monophonic synthesizer, one voice at a
time, counting my minims; one of the pieces was transcribed by Richard
Hoppin, and you nicely describe the nature of this music. If only I
could read the original notation! Some modern transcriptions such as
Apel's do use devices like irregular or alternative barlines in
different parts.

Back then, I really didn't much consider tuning, and certainly, as you
say, there are many other sides to this music. However, nowadays, I
sometimes find myself improvisating at the keyboard in this kind of
style -- likely not as sophisticated in it as you have become, I must
admit! -- in a regular temperament with fifths around 704 or 705
cents. I should hear your music, and maybe record something like this.

[Here, to save space, I'll refer readers to my discussion
of 24-EDO in my earlier post.]

> You have written here a brilliant analysis, but even after reading
> it somehow I didn't started to like 24 EDO... I used it in some of
> my microintervallic works, melodically just for making music
> different and more interesting, harmonically for neutral thirds,
> otherwise just as a sound effect, timbre in soundscapes,
> atmospheres...

That's more than fair enough: analysis can explain the resources of a
tuning, but tastes will vary much as before, I smile to reflect. Back
in the year 2000, I can remember an enchanting evening session of
improvising in 24-EDO; but it was indeed a momentary diversion from my
main agenda, which often concerned -- then as now -- tunings with
fifths wider than pure, and sometimes also meantone.

>> Again, Daniel, you're an ideal person to present this Haba material in
>> its fuller human and musical context -- thank you!

> If you mean my person, thank you for your appreciation.

Yes, and your knowledge of earlier and contemporary developments puts
Haba in a richer context. I might add that my comments could also
apply to Daniel Stearns and Daniel Wolf as well: but your focus on
medieval music gives us something in common that I find quite
remarkable after exploring this music for 40 years.

> I would say I can help with getting and translating material from
> Czech or some other languages if somebody is really interested, if
> I'm interested as well, and find time for it. Or can try to get
> some records from my old country for analysis. Frankly said Haba
> somehow is not exactly my cup of green tea as a composer because of
> his quite traditional way of composition, there are much more
> interesting personalities in Czech music of 20th century, not
> necessarily working with microintervals. I will be happy to write
> sometimes about Moravian folklore, or anything about Czech music or
> some other (now I have a great opportunity to study more about
> Japanese music for example), as well about pop/jazz/rock, chords,
> harmony, or my own compositional using of microintervals...

The Haba text posted in PDF format makes me very curious about earlier
Czech theory also, as well as about some of the other areas where
translations could be very valuable also. One person I am very
interested in is Peter Chelcicky, one of the greatest social
philosophers of all time, I would say, whose book on the three estates
might be very timely here in the U.S.A.

Your compositions and use of microintervals would very much interest
me: it is often intriguing how people can share a common background,
for example in the Ars Subtilior or the Manneristic style around 1600,
and then take that in various creative directions. One of my main
regrets is not having composed and recorded more, and your pieces may
lend some inspiration to me and others here also.

> if there are some questions, answers could be found... I have many
> interests :-)

This makes me think of a few records I have of Czech music, some of it
from the 15th and 16th centuries: the notes discuss how some of the
songs involve an element of social protest, which also comes up in
something like the Roman de Fauvel in the early Ars Nova.

[On "atonality" in 15th-16th century music]

> Then we have same love again. I don't think we can call this
> atonality, but as a working term it's OK. Atonality came after
> tonality as its negation, early "atonality" should be called maybe
> more apropriate "primal chaos", from which later entropy of
> tonality came. What for me personally is interesting in this
> context is a chromaticism in European music from this early state
> until 12tone music... I collect scores of compositions using
> interesting chromatic progressions, be it melodically,
> polymelodically or harmonically. I'd like to write one day some
> work from this material. And concerning tonality/atonality, it
> doesn't need to be antagonistic - it's possible to find a way how
> to combine it, which I have tried in many of my works.

"Primal chaos" is one possible phrase; maybe another is a kind of
"pleasant wandering," as with Pietro Aaron's remark in 1525 that some
composers approach the modes like a child playing a game called
_alleta_ or tag in which you can wander in almost any direction as
long as you eventually return to your "base."

Chromaticism is something that we've both been intrigued by, and it
seems to be that chromaticism may be especially effective in tuning
systems where there's a rather large diesis or difference between cis
and des, for example, say around 40-70 cents. This happens, of course,
in a useful Renaissance meantone at around 1/4-comma to 1/3-comma, or
with a fifth of 695-697 cents, say -- and again, with a "neomedieval"
fifth at around 703-706 cents.

The idea of an anthology of historical examples of chromaticism would
be a fine project! Of course, it would be a good idea to include
"enharmonicism" or "diesis-ism" also, as with Vicentino, or Venosa's
contrast of B# and C. Here's a piece of this kind from the Coimbra
Manuscript in Portugal, which one scholar has suggested might date
from the mid-16th century era of Vicentino, but sounds to me very much
like something written around 1600, or the epoch of Venosa and
Colonna:

<http://www.bestII.com/~mschulter/Coimbra48.mp3>
<http://www.bestII.com/~mschulter/Coimbra48.ps>

Here's a piece using some contrasting accidentals, also not as
adventurously as with the diesis steps in the Coimbra piece:

<http://www.bestii.com/~mschulter/IntradaFLydian.mp3>
<http://www.bestii.com/~mschulter/IntradaFLydian.pdf>

> So I used for example different kinds of 12tone music, and result
> can sound quite tonal. Or tonal or modal melody is harmonized
> atonally...

I'd love to learn more about some of your favorite historical examples
of chromaticism, or original pieces -- suspecting that the period
around 1600 might be a favorite for us both in this area.

The idea of harmonizing a modal melody, or carrying through a
contrapuntal idea, with a series of smooth and satisfying cadences or
other progressions which yet are "related only to each other" rather
than to any obvious modal procedure, might be one of the things you
are discussing -- and I'd like to explore it more also.

>> Some of the very adventurous pieces such as Solage's _Fumeux >
>> fume_ in the era of 1380-1400 or so,

> Oh, my beloved piece, almost my "musical visitcard" as I perform it
> at the beginning of almost every my concert. Unbelievable
> work. There are discussions what that "fume" was in that rather
> enigmatic lyrics of this piece, as tobacco was still unknown those
> times in Europe. It's not totally excluded it could be canabis,
> hashish or so... Then no wonder that music is like it is, if it was
> inspired by drugs :-)

Yes, there are various theories about "fume" and the "fumeurs" --
another view says that it could be like the English "letting off
steam" in a way -- or, better, indulging ones "humors," although the
drug theory was popular around 1970. I love Solage's _S'aincy estoit_,
and Senleches, and some of the "less complicated" pieces also. Anyway,
I would agree that _Fumeux fume_ is a _great_ musical visiting or
calling card.

> I would be happy to exchange from time to time some facts about
> this kind of music, you evidently know a lot about it. I would be
> grateful if you can indicate me some interesting material on the
> net, or scores, or direct me somewhere... Always hungry for new
> information. I will try to balance.

It would be a pleasure to exchange knowledge, and doubtless to learn a
great deal in the process. I should see what is available on the net;
there are some very nice MIDI files of 14th-century pieces, which
could be retuned with Scala, as well as some realizations of medieval
and Renaissance pieces by Aaron Johnson, who also has lots of his own.

At my website, I have some original pieces plus a few historical ones:

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

There's also a "Quick Tour"

<http://www.bestII.com/~mschulter/QuickTour.html>

with links to some theoretical material on medieval music at
<http://www.medieval.org/emfaq/>, a great site edited by Todd McComb of
the Medieval Music and Arts Foundation to which many people have
contributed.

> Have a nice day!
> Daniel Forro

> P.S.: A small part of my works of all kind is on
> <http://www.soundclick.com/forrotronics>, now about 400.

> Purely microintervallic works are:

> Seven Microintervallic Studies
> Euphony 1
> Euphony 2
> Musica per Piazza nel campo a Siena
> Preludio metallico
> Ecmelic Music
> Harmonia Mundi

> Microintervals were used partly in:
> Moravian meditation
> Syntphonies
> Music for Erno Rubik
> Crimson Space
> The Wizard of Oz
> Digital Music 01/87
> Musica ex machina 01/88
> Music to Vernisage
> Drawn music - Music drawing
> Cosmopolitan Music
> Musica Ethnica 01/92
> Fudoo Myoo e no inori
> Music for Dyje
> Concertino for synthesizers and drums
> Orbis Fictus

> More will come step by step.
> Opinions, criticism, questions highly welcomed!

These I look forward to hearing -- an impressive list, with the title
_Orbis Fictus_ especially intriguing; possible an "Invented World,"
rather as one "invents" notes outside of the Guidonian hand or regular
gamut. When I have heard some of this music, I may be able to ask more
and better questions.

With many thanks,

Margo
mschulter@...

🔗Ozan Yarman <ozanyarman@...>

Dear Margo,

Thank you for this well-prepared digest! Some points I would like to comment on are these:

1. Prosdocimus' version of 17-tone Pythagorean tuning does seem to differ from Safi al-Din's suggestion in terms of ratios as you emphasized and as given in http://tonalsoft.com/monzo/article/article.htm. I should have been more careful about that.

2. Safi al-Din's Rast utilizes 16/9 on the seventh degree, not 4096/2187. This is what we recognize as ajemli Rast. Notice also, that he does not ascribe to his scales the perde names we are familiar with today.

3. In part 2.2 G#-rast must be 496 cents, not 495. Also, you may consider exchanging places of perde saba with perde hijaz as I have done in my thesis. Otherwise, maqams Saba and Hijaz will not reflect quotidian practice.

4. Notice, that I lately deem ajemli Rast to require the conjunct union of Rast+Mahur tetrachords, not Rast+Rast as specified in my thesis. But either version will do fine depending on the performance tradition.

5. I admire the way you have so quickly adopted Turkish idioms on music theory!

6. Shirazi's Hijaz tetrachord is perfectly rendered, bravo! On second thought, you may like to keep the order of perdes saba and hijaz.

7. Not gevart, gevasht. Not buselek, buselik. Mind the Meva=Neva in part 3.

8. I like your approval of 79 MOS 2deg159tET and the way you help us picture it.

9. Carrying the chain of fifths to 29 notes sounds interesting. Maybe I should expand Yarman24 to accomodate 5 more pitches to reflect maqam intonation better.

10. Given my lack of knowledge on the particulars of Persian dastgah theory, I can only read your excursions with a smile on my face. :)

11. Do not be so hasty in disregarding Safi al-Din as a theorist favouring middle second flavours. For indeed, he defines Isfahan as JJJB = 13:12 x 14:13 x 15:14 x 16:15, Zirefkend-i Kutchek as 10:9 x 81:70 x 13:12 x 14:13, and Buzurg as 23:22 x 14:13 x 13:12 x 8:7 x 14:13 (no other than today's Huzzam) in his treatise "Risala al-Sharafiyyah". Why he constructs a 17-tone Pythagorean scale given these divisions of the pentachord, I am at a loss to explain. Maybe you can shed some light on the situation.

12. Check the spelling for common practoce in the conclusion part.

13. You might want to use a small t to define reduced tone, and assign K the status of a 22 cent comma.

Cordially,
Oz.

On Sep 23, 2008, at 10:06 AM, Margo Schulter wrote:

> Hello, Ozan, Aaron, and all.
>
> As part of a longer letter or article, available in its full form at
> <http://www.bestii.com/~mschulter/17-MOS-tunings_Letter-to-Ozan.txt>,
> I have proposed a "middle-resolution" system for describing types of
> intervals and steps used in Arab/Turkish/Kurdish maqam and Persian
> dastgah music based on the familiar concept of 53 commas to an
> octave.
>
> The concept of nine commas to a regular 9:8 tone, and thus 53 to an
> octave in Pythagorean intonation or the later 53-EDO, is a basic
> element of Turkish and some Syrian theory, with recognition elsewhere
> in the Arab world also. The scheme suggested here borrows extensively
> from recent Turkish usage, while seeking to remedy such anomalies as
> the frequent omission of neutral second steps because of ideological
> factors, specifically a political dislike for associating the Turkish
> heritage of maqam music with "Arab" and "Byzantine" systems featuring
> the use of "quartertones." Your dissertation, Ozan, of course covers
> all of this history and more in great detail, a fascinating education
> for me and others who read it.
>
> Aaron, and others who may be new to this, I should explain that Near
> Eastern theory offers various degrees of "resolution" or specificity
> in defining the types or sizes of intervals that are -- or in the
> writer's view should be -- used in the intonation of a given
> tetrachord, maqam, etc.
>
> A "low resolution" system says basically: "This step is or should be a
> tone, semitone, neutral second, or an "augmented step" or
> "plus-second" often equal to some kind of minor third ranging from
> septimal or slightly smaller up to around Pythagorean."
>
> For example, consider a typical Arab form of a tetrachord or _jins_
> (from the Greek _genus_) named Rast, also the name of a maqam or modal
> complex drawing its basic steps from two of these tetrachords. Here's
> a low-resolution notation for this variety of Rast using an
> approximate quartertone system (common in 19th-21st century Arab
> theory) or an approximate thirdtone system. Note that "d" represents a
> half-flat symbol used to show an _approximate_ quartertone alteration,
> but not necessarily one of precisely 50 cents as in 24-EDO!
>
> C D Ed F
> 24: 0 4 7 10
> 4 3 3
>
> 17: 0 3 5 7
> 3 2 2
>
> Describing Rast as 4-3-3 in the 24-step system or 3-2-2 in the 17-step
> system is a very useful shorthand, but leaves open, for example, just
> how the neutral third of the tetrachord should be placed, and which of
> the two neutral second steps, the first or the second, should be
> larger or smaller. These issues wouldn't come up in 17-EDO or 24-EDO,
> where there is only one size of neutral second step -- but will come
> in traditional performances of Near Eastern music, where there are
> almost infinite shadings of these steps and playing "in tune" involves
> an appreciation of this.
>
> A 53-comma notation, or the letter notation of the Persian theorist
> Hormoz Farhat, addresses these vital questions but still leaves lots
> of room for "fine-tuning," or for the vagaries of different JI or
> tempered systems. Here's a middle-level description of Rast in both
> these systems:
>
> 53: C D Ed F
> 0 9 16 22
> 9 7 6
>
> Farhat: M N n
>
>
> Just as the 17-step and 24-step notations don't necessarily imply
> using 17-EDO or 24-EDO, so the 53-step or 53-comma system doesn't
> necessarily imply 53-EDO or Pythagorean: rather it provides a handy
> numerical shorthand that can be adapted to various tuning systems, or
> to flexible-pitch performance (often the main focus!). Farhat's system
> uses letters to show a (M)ajor second, large (N)eutral or small
> (n)eutral step, or (m)inor second step -- the last not used in Rast.
>
> Read literally in 53-EDO terms, the 9-7-6 notation would call for
> steps of 204-158-136 cents -- a very pleasant tuning, in fact, but
> only one of many possibilities fitting the spirit of this or Farhat's
> M-N-n notation.
>
> The important point is that we are told not only that this version of
> Rast has a lower tone plus two neutral seconds, but that the lower
> neutral second is the larger one.
>
> The 53-comma system is also very useful in distinguishing this flavor
> of Rast, the usual one in Arab theory, with a different flavor known
> in medieval and modern times, and the one taken as the standard model,
> so to speak, in modern Turkey:
>
> 53: C D E F
> 0 9 17 22
> 9 8 5
>
> This is a 5-limit flavor of Rast, as shown by the 53-comma notation.
> Interestingly, as in your 79-MOS, Ozan, this tuning might actually be
> realized by a single unbroken chain of fifths with at least some of
> these generators tempered, as in a European meantone. What 9-8-5
> notation shows us is the 5-limit pattern, in contrast to 9-7-6 with
> its use of two neutral seconds and a largish neutral third rather than
> a 5:4 major third.
>
> A "high-resolution" notation, of course, could use cents; or JI
> ratios; or steps smaller than a 53-comma, as with the 79-MOS, where
> the usual unit is the yarman, equal to about 2/3 of a comma or about
> 15.09 cents. Indeed, thinking of yarmans as "just a tad larger than
> 15 cents" is a great shortcut for keeping track of them! That,
> however, is another topic and another post.
>
> Getting back to the 53-comma system, I should explain that the table
> below isn't meant to cover all intervals, but those either likely to
> be used as basic steps in maqam and dastgah music, or smaller than
> these usual steps but important for measuring certain inflections or
> differences in size: the comma itself, and the 2-comma category, which
> could be called a demi-limma, half-limma, or medieval diaschisma (not
> to be confused with another use of this last term for a smaller
> interval of 2048:2025 or about 19.55 cents).
>
> One general set of categories might invite a quick explanation: the
> "augmented" step or "plus-second" ranging from a bit larger than 8:7
> up through 15:13 (11 commas) and the 7:6 minor third (12 commas) up to
> around a Pythagorean minor third (13 commas). This is the middle step
> of a tetrachord type known as Hijaz, and also in the Persian tradition
> as Chahargah (or Turkish Chargah). One tradition style of tuning for
> Hijaz might be about as follows:
>
> D Ed F# G
> cents 0 140 408 498
> 140 268 90
>
> 53-commas 0 6 18 22
> 6 12 4
>
> To show how the 53-comma system might be adapted to a temperament,
> categories corresponding to the Pythagorean of 53-EDO ones are shown
> for a regular temperament known as the "e-based" tuning since the
> ratio between the regular tone and diatonic semitone or limma is equal
> to Euler's e, around 2.71828 -- thus a fifth around 704.607 cents.
> The categories often map reasonably well, although the chains of
> generators are often different -- thus the Pythagorean or 53-EDO
> 12-comma at around 23 cents matches up with the e-based 17-comma at
> around 22 cents.
>
>
> ----------------------------------------------------------------------
> Middle-resolution categories based on 53-comma system
> ----------------------------------------------------------------------
> 53-EDO type commas cents symbol e-based type 53-commas cents
> ----------------------------------------------------------------------
> 12-comma 1 22.64 F 17-comma 0.96 21.68
> ......................................................................
> demi-limma 2 45.28 D -------- ----- -----
> ......................................................................
> reduced limma 3 67.92 E 12-diesis 2.44 55.28
> ----------------------------------------------------------------------
> limma 4 90.57 B limma 3.40 76.97
> ----------------------------------------------------------------------
> apotome 5 113.21 S limma + comma 4.36 98.65
> ......................................................................
> small neut 2nd 6 135.85 Js apotome 5.84 132.25
> ......................................................................
> large neut 2nd 7 158.49 Jk dim 3rd 6.80 153.93
> ......................................................................
> dim 3rd 8 181.13 K reduced tone 8.28 187.53
> ----------------------------------------------------------------------
> tone 9 203.77 T tone 9.24 209.21
> ......................................................................
> large tone 10 226.42 T10 large tone 10.20 230.90
> ----------------------------------------------------------------------
> hemifourth 11 249.06 A11 ---------- ----- ------
> ......................................................................
> small min 3rd 12 271.70 A12 small min 3rd 11.68 264.50
> ......................................................................
> min 3rd 13 294.34 A13 min 3rd 12.64 286.18
> ----------------------------------------------------------------------
>
> Much more could be said about the history of some of these symbols in
> recent Turkish theory, and I'd warmly invite you to add any helpful
> details or corrections, Ozan or anyone else.
>
> With many thanks,
>
> Margo
>
>
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🔗Margo Schulter <mschulter@...>

> Dear Margo,

> Thank you for this well-prepared digest! Some points I would like to
> comment on are these:

Dear Yarman,

Thank you for your helpful corrections and notes, ranging from one
comical typographical error I'm amazed I didn't catch to a real
mistake about a perde name to a serious error of omission I definitely
will correct in a revised version of the longer letter, giving you
credit for prompting me to write a new section which needs to be
included.

Having such an attentive and informed reader is invaluable; and your
judgment may be helpful when I write the section which shouldn't have
been left out, as explained below.

> 1. Prosdocimus' version of 17-tone Pythagorean tuning does seem to
> differ from Safi al-Din's suggestion in terms of ratios as you
> emphasized and as given in
> [35]http://tonalsoft.com/monzo/article/article.htm . I should have
> been more careful about that.

What I might say is that knowing what could be called the polyphonic
seyir of 13th-14th century European pieces helps in understanding
Prosdocimus -- just as your familiarity with the maqamat in various
parts of the Near East helps you in appreciating the tunings of Safi
al-Din al-Urmavi. It should be emphasized, of course that the wealth
of middle or neutral steps in the Islamic tradition means a radically
richer system of maqamat or dastgah-ha than any scheme of classic
European modes or keys, although these too follow a kind of seyir.

> 2. Safi al-Din's Rast utilizes 16/9 on the seventh degree, not
> 4096/2187. This is what we recognize as ajemli Rast. Notice also,
> that he does not ascribe to his scales the perde names we are
> familiar with today.

This is a vital correction, as re-reading your colleague's article on
Urmavi also reminded me! In my revision, I will make this clear while
showing both the conjunct form of Urmavi (acemli Rast) and the
disjunct form.

> 3. In part 2.2 G#-rast must be 496 cents, not 495. Also, you may
> consider exchanging places of perde saba with perde hijaz as I have
> done in my thesis. Otherwise, maqams Saba and Hijaz will not reflect
> quotidian practice.

As to your first point, indeed my cents were inconsistent! Here I
think that 495 cents, following the "theoretically correct" rather
than 1024-EDO tuning, might be better for the sake of simplicity in
showing the 17-MOS structure. With the 79-MOS of 159-EDO -- or close
to it! -- you may have a special motivation to use precise rather than
regular 159-EDO values, in order to show the just 4:3 and 3:2 fourths
and fifths.

The saba/hijaz question is a bit unclear, as you note below.
Curiously, with this temperament, either the third step of Maqam Hijaz
or the fourth step of Maqam Sabah, starting from dugah, is typically
at around 56/39 or 16/11 from rast; 39/28 is very typical of Maqam
Penchgah (1/1-44/39-21/17-39/28-3/2 or 0-209-363-572-705 cents).
However, if we agree with a Turkish source you have cited that what I
call Buzurg-Hijaz or JTJ at 6-10-6 commas or 9-15-9 yarmans, then if
starting from perde dugah, we will indeed use perde hijaz as the third
step! That could be an argument for the modern ordering of these
names. What I should do in the revision is make the difference between
the old and new names clear, at least.

> 4. Notice, that I lately deem ajemli Rast to require the conjunct
> union of Rast+Mahur tetrachords, not Rast+Rast as specified in my
> thesis. But either version will do fine depending on the performance
> tradition.

Interesting! Both forms are familiar to me, and seem in Arab theory
recognized as variations on Rast, as a "family" defined mainly by the
lower tetrachord. Curiously, conjunct Rast|Mahur is known in Arab
theory as, of all things, Suz-i Dilara! Given a few hints you have
offered about the nature of that terkib, I suspect that this could be
one aspect of a complex set of inflections or modulations.

> 5. I admire the way you have so quickly adopted Turkish idioms on
> music theory!

Thank you -- of course, I have just begun to learn.

> 6. Shirazi's Hijaz tetrachord is perfectly rendered, bravo! On
> second thought, you may like to keep the order of perdes saba and
> hijaz.

It's an open question: apart from "Buzurg-Hijaz" or JTJ, it's true
that I tend to take Hijaz as 154-264-77 or 132-286-77 cents, which
could be 10-18-5 or 9-19-5 yarmans -- once again, the 79-MOS nicely
emulates another tuning system! Saba, a real beginner's delight for me
with the help of your writings, is another topic.

> 7. Not gevart, gevasht. Not buselek, buselik. Mind the Meva=Neva in
> part 3.

On gevart, that was my confusion of the name; buselek looks like a
typo (I would use buselik as a Turkish form and busalik in an Arab
spelling); and Meva could be a sign I had problems reading my font on
the computer screen! Thanks for catching them all. By the way, it's
interesting that Safi al-Din's Abusalik or B-T-T looks like modern
Kurdi. His Nawa (or Neva) or T-B-T is the modern Buselik.

> 8. I like your approval of 79 MOS 2deg159tET and the way you help us
> picture it.

It's lots of fun, and to be involved in a dlalogue with the designer
of such a system is a special delight.

> 9. Carrying the chain of fifths to 29 notes sounds
> interesting. Maybe I should expand Yarman24 to accomodate 5 more
> pitches to reflect maqam intonation better.

Your new Yarman29 is something I'll look at closely --
congratulations! With the 704.607-cent tuning, I do find the 24-note
version convenient for two standard keyboards, but the 29-MOS could be
a very attractive set.

> 10. Given my lack of knowledge on the particulars of Persian dastgah
> theory, I can only read your excursions with a smile on my face. :)

I wonder what Shaahin might say.

> 11. Do not be so hasty in disregarding Safi al-Din as a theorist
> favouring middle second flavours. For indeed, he defines Isfahan as
> JJJB = 13:12 x 14:13 x 15:14 x 16:15, Zirefkend-i Kutchek as 10:9 x
> 81:70 x 13:12 x 14:13, and Buzurg as 23:22 x 14:13 x 13:12 x 8:7 x
> 14:13 (no other than today's Huzzam) in his treatise "Risala al-
> Sharafiyyah". Why he constructs a 17-tone Pythagorean scale given
> these divisions of the pentachord, I am at a loss to explain. Maybe
> you can shed some light on the situation.

This is the critically important point I referred to at the beginning:
while it was certainly not my intention to disregard Safi al-Din's use
of middle intervals in any way, I realize that I indeed very seriously
erred in omitting these tetrachords and maqamat from my examples,
where they should have been included along with those of Ibn Sina and
Qutb al-Din al-Shirazi.

Actually I may have erred out of caution, or a desire not to get
things wrong, given how one sometimes finds different ratios from
different people for a given tuning of Safi al-Din. However, that is
not a complication limited to his tunings only <grin>, and I agree
that, having presented his 17-note tuning, I _must_, for the sake of
balance, include some of these beautiful neutral steps of his also!

Reading Dr. Fazli Arslan's paper again, and looking over your
examples, helps a great deal in this. As you note in another post,
your intervals for Buzurg here need to be read in the reverse
direction; or, in other words, are correct if read starting with the
shortest two strings or highest notes at 23:22.

A small point about Safi al-Din's Isfahan. While indeed he defines it
as 12:13:14:15:16 (Arslan, p. 11), it's curious that (ibid. p. 19) he
also defines it JJJB, which Arslan takes to mean that the last step is
a limma rather than an apotome (which at 2187:2048 or 113.685 cents
would, of course, be equivalent to 16:15). If JJJB indeed means an
upper limma step, then I could be tempted to try something like
13:12-14:13-12:11-22:21 (a tempered 0-132-264-418-495 cents). This
might involve an interesting seyir. However, if this is indeed a
stretch, I might be wiser to stick with a number of other fine
tetrachords and maqamat where such a "creative" reading isn't needed.

> 12. Check the spelling for common practoce in the conclusion part.

Ah, at first I took this to mean that I had again erred on the
spelling of some perde names -- but I see that "common practoce" is
itself the spelling that needs correction! That might help to explain
my perde meva!

> 13. You might want to use a small t to define reduced tone, and
> assign K the status of a 22 cent comma.

Actually something like T8, T(9), and T10 -- or Ts, T, Tk -- would
nicely fit the European theory of Jacobus of Liege in the era around
1300 that we're discussing; he evidently was in his youth when Urmavi
was writing his treatises. Jacobus discusses a regular tone at 9:8, or
a limma plus an apotome; a _tonus minor_ or small tone equal to two
limmas; and a _tonus maior_ or large tone equal to two apotomes.

An advantage of T8 or Ts is that, as I learned a few years ago, some
blind people or people with other visual disabilities on the Internet
use audio software for reading text which may problems distinguishing
"T" from "t" -- but T8 or Ts would avoid this problem.

Here the open question I might have is this: How strongly does "T" or
tanini carry the implication of a _full_ tone of at 9:8, 9 or 10 commas
rather than 8? Apart from that, talking about small, middle, and large
tones of 8-9-10 commas seems indeed very natural to me.

> Cordially,
> Oz.

With many thanks,

Margo