Some unqualified thoughts about maqam tunings, inspired by J.J Weiss

Argh, it seems I got infected by a kind of maqam virus, too... I apparently got it from writing the XenWiki page about Julien Weiss's tunings for qanun ( http://xenharmonic.wikispaces.comtuning+systems+for+qanun ). So I think I want to share some of the strange stuff that is haunting my head. There is one of Julien Weiss's various tuning systems that caught my attention - never heard how its sounds, I just liked the math. It goes as follows:

Take a basically pythagorean skeleton, i.e pythagorean whole tone (9/8, 204 cents), pythagorean minor second or limma (256/243, 90 cents) and its difference (2187/2048, apotome, 114 cents). Divide the apotome into 3 equal parts, which gives 38 cents, and add that to the limma, which gives 128 cents. And that is a close approximation for 14/13, a 2/3-tone, one of the various middle seconds that occur in maqams (AFAIK, at least).

Now the point is that Julien Weiss's complete systems encompass 105 tones per octave, which is good for the qanun but much too many notes for me... I just wonder if the ideas sketched above can be used (or maybe have already been used) for some kind of maqam temperament or something?
--
Hans Straub

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> Argh, it seems I got infected by a kind of maqam virus, too...

You may like to play around with

http://tarsos.0110.be

Be sure to report your results here if so!

-Carl

> Argh, it seems I got infected by a kind of maqam virus,
> too... I apparently got it from writing the XenWiki page about
> Julien Weiss's tunings for qanun
> <http://xenharmonic.wikispaces.com/tuning+systems+for+qanun>.

Dear Hans,

This is a great page! Jacques Dudon called my attention to some
of these tunings by Julien Jalaleddine Weiss.

A caution at the start: translating from his divisions of the
apotome (e.g 38-38-38 cents) to divisions of the tetrachord is
something I do below, and may or may not be clear. Please feel
free to ask questions, which may help me improve my presentation!

> So I think I want to share some of the strange stuff that is
> haunting my head. There is one of Julien Weiss's various tuning
> systems that caught my attention - never heard how its sounds,
> I just liked the math. It goes as follows:

> Take a basically pythagorean skeleton, i.e pythagorean whole
> tone (9/8, 204 cents), pythagorean minor second or limma
> (256/243, 90 cents) and its difference (2187/2048, apotome, 114
> cents). Divide the apotome into 3 equal parts, which gives 38
> cents, and add that to the limma, which gives 128 cents. And
> that is a close approximation for 14/13, a 2/3-tone, one of the
> various middle seconds that occur in maqams (AFAIK, at least).

This is quite correct: with 38-38-38 we have 90-128-166-204
cents. If 14/13 is just, then the steps within the tone for this
division would be 1/1-256/243-14/13-208/189-9/8.

Actually one could trace this type of division back to Ibn Sina
around a millennium ago (his dates are 980-1037) with a
tetrachord of 1/1-9/8-63/52-4/3 (0-204-332-498 cents), or
9:8-14:13-208:189 (steps of 204-128-166 cents). At 166 cents, the
208:189 is not quite a cent larger than a simpler 11:10.

A 2/3-tone around 14/13 or 128 cents might occur in a low Persian
Shur or Turkish Ushshaq, where J. J. Weiss's division of
128-166-204 would be fine.

In Lebanon, Amine Beyhom says that a "popular" or "folk" tuning
for the similar Maqam Bayyati favors a step around 130 cents, so
a 128-166-204 division would likely be right at home. It varies
with region and style: a classic Egyptian Bayyati might be more
like 140-154-204, for example, assuming a just 9/8 and 32/27.

And with Weiss's 38-38-38 division of the apotome, we can get not
only 128-166-204, but also 166-128-204 for a good Turkish Maqam
Huseyni. And with this tuning we also get 204-166-128, a great
classic Ottoman Rast with a 370-cent third (26/21), as Weiss
mentions in the notes for one of his albums.

Anyway, Weiss's 38-38-38 division is very useful!

> Now the point is that Julien Weiss's complete systems
> encompass 105 tones per octave, which is good for the qanun
> but much too many notes for me... I just wonder if the ideas
> sketched above can be used (or maybe have already been used)
> for some kind of maqam temperament or something?

Obviously with 17 or 24 notes per octave rather than 105, there
will be compromises, but I'd say his ideas have lots of potential
for temperaments and smaller systems generally also!

Actually, what happens is that I may get each of the neutral
sizes, or something reasonably close, _somewhere_ in a 24-note
system -- but not with lots of choices all over the place, as
with his 105-note qanun!

For example (Weiss's "First System", not all steps shown!):

[90]-125-138-150-166-[204]

And one of my tempered tunings:

[81]-125-139-150-163-[207]

The difference is that I need to move around the system to get
all of these, with at most two available at any one location:
maybe 125 and 150, or 139 and 163 -- but not all of them in way
lots of places, as on his qanun!

How things get warped or distorted a bit in tempered systems is
another topic I'd be glad to discuss, but Weiss's tunings are a
real dream come true!

> --
> Hans Straub

Best,

Margo