back to list

persian modes :RE: [tuning] Re: "Arabic mode"

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

6/12/2006 8:44:33 PM
Attachments

Hi

Although theories of farabi ( and not urmevi ) are a good basis for
persian music but we have different terms and trends:

Reference :
http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/radif.pdf

1- we have mayeh instead of jins and ajnas , although some
tetrachords and ..... in them are common. In Persian music we have 4
tetrachord ( or dang in Persian) which make 11 mayehs or jins.

2- The general structure of tetrachord is important and not using
5/4 or 390cent or 410 cent. Principally , pure consonance and beatless
harmony is not main problem in Persian music but melodic aesthetic.
Mystically , beating is somehow good for giving vibration and energy to
player.

3- Also , sounding of our instruments ( intervals , inharmonicity)
leads us not to consider pure sounding and intervals.

4- And another thing , for music
<http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/tar-tombak
.mp3> for tar and tombak and my orchestral music
<http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/orchestr.m
p3> , I didn't used only pure intervals but EDL-system in orchestral
music and a EDL-based tuninig in tar . what is the degree of dissonance
in them , although I know that all the condition to have a good
distinction are not available( good recording , ......).

Shaahin Mohaajeri

Tombak Player & Researcher , Microtonal Composer

My web site , click picture : <http://240edo.tripod.com/index.html>

My tombak musics in Rhythmweb: www.rhythmweb.com/gdg
<http://www.rhythmweb.com/gdg>

My articles in Harmonytalk:

- www.harmonytalk.com/archives/000296.html
<http://www.harmonytalk.com/archives/000296.html>

- www.harmonytalk.com/archives/000288.html
<http://www.harmonytalk.com/archives/000288.html>

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

My musics in Wikipedia, the free encyclopedia :

- A composition based on a folk melody of Shiraz region, in shur-dastgah
by Mohajeri Shahin <http://www.xenharmony.org/mp3/shaahin/shur.mp3>

- An experiment in Iranian homayun and chahargah modes by Mohajeri
Shahin <http://www.xenharmony.org/mp3/shaahin/homayun.mp3>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Cris Forster
Sent: Tuesday, June 13, 2006 6:38 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: "Arabic mode"

>...why not Al-Farabi's 27/22? And could 16/13 work?

Danny,

Despite all perpetuated half-truths (and I mean
*1/2-truth* quite literally) about what Safi Al-Din did
not accomplish, you are absolutely on the right
track.

Cris Forster, Music Director
www.chrysalis-foundation.org

🔗Cris Forster <cris.forster@comcast.net>

6/13/2006 8:30:27 AM

Mohajeri,

The works of Al-Kindi, Al-Farabi, Safi Al-Din, and
Al-Jurjani have very little to do with Persian music.

In contrast, the works of Ibn Sina have everything
to do with Persian music, especially the strategic
implementation of prime number 13.

All the intervals described by Hormoz Farhat on the
modern tar and setar can be played on Ibn Sina's
ud. This also applies to many modern dastgah.
This comes as no surprise, since Ibn Sina was born
and lived most of his life in Persia. Although all his
major musical and medical works were written in
Arabic, his later scientific treatises were written in
Persian.

Cris Forster, Music Director
www.chrysalis-foundation.org

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
> Hi
>
>
>
> Although theories of farabi ( and not urmevi ) are a good basis for
> persian music but we have different terms and trends:
>
> Reference :
>
http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/radif.pd
f
>
> 1- we have mayeh instead of jins and ajnas , although some
> tetrachords and ..... in them are common. In Persian music we have
4
> tetrachord ( or dang in Persian) which make 11 mayehs or jins.
>
> 2- The general structure of tetrachord is important and not
using
> 5/4 or 390cent or 410 cent. Principally , pure consonance and
beatless
> harmony is not main problem in Persian music but melodic aesthetic.
> Mystically , beating is somehow good for giving vibration and
energy to
> player.
>
> 3- Also , sounding of our instruments ( intervals ,
inharmonicity)
> leads us not to consider pure sounding and intervals.
>
> 4- And another thing , for music
> <http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/tar-
tombak
> .mp3> for tar and tombak and my orchestral music
>
<http://240edo.tripod.com/sitebuildercontent/sitebuilderfiles/orchest
r.m
> p3> , I didn't used only pure intervals but EDL-system in
orchestral
> music and a EDL-based tuninig in tar . what is the degree of
dissonance
> in them , although I know that all the condition to have a good
> distinction are not available( good recording , ......).
>
>
>
> Shaahin Mohaajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
> My web site , click picture :
<http://240edo.tripod.com/index.html>
>
> My tombak musics in Rhythmweb: www.rhythmweb.com/gdg
> <http://www.rhythmweb.com/gdg>
>
> My articles in Harmonytalk:
>
> - www.harmonytalk.com/archives/000296.html
> <http://www.harmonytalk.com/archives/000296.html>
>
> - www.harmonytalk.com/archives/000288.html
> <http://www.harmonytalk.com/archives/000288.html>
>
> My article in DrumDojo:
>
> www.drumdojo.com/world/persia/tonbak_acoustics.htm
> <http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>
>
> My musics in Wikipedia, the free encyclopedia :
>
> - A composition based on a folk melody of Shiraz region, in shur-
dastgah
> by Mohajeri Shahin
<http://www.xenharmony.org/mp3/shaahin/shur.mp3>
>
> - An experiment in Iranian homayun and chahargah modes by Mohajeri
> Shahin <http://www.xenharmony.org/mp3/shaahin/homayun.mp3>
>
> ________________________________
>
> From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On
Behalf
> Of Cris Forster
> Sent: Tuesday, June 13, 2006 6:38 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: "Arabic mode"
>
>
>
> >...why not Al-Farabi's 27/22? And could 16/13 work?
>
> Danny,
>
> Despite all perpetuated half-truths (and I mean
> *1/2-truth* quite literally) about what Safi Al-Din did
> not accomplish, you are absolutely on the right
> track.
>
> Cris Forster, Music Director
> www.chrysalis-foundation.org
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

6/13/2006 9:10:26 AM

Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled `Avicenna and his
catalogued books on music`, gives the following ratios of a 17-tone tuning
attributed to Ibn Sina:

1/1
273/256
13/12
9/8
32/27
39/32
81/64
4/3
91/64
13/9
3/2
128/81
13/8
27/16
16/9
91/48
152/67
2/1

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 13 Haziran 2006 Sal� 18:30
Subject: [tuning] Ibn Sina and Persian Music

> Mohajeri,
>
> The works of Al-Kindi, Al-Farabi, Safi Al-Din, and
> Al-Jurjani have very little to do with Persian music.
>
> In contrast, the works of Ibn Sina have everything
> to do with Persian music, especially the strategic
> implementation of prime number 13.
>
> All the intervals described by Hormoz Farhat on the
> modern tar and setar can be played on Ibn Sina's
> ud. This also applies to many modern dastgah.
> This comes as no surprise, since Ibn Sina was born
> and lived most of his life in Persia. Although all his
> major musical and medical works were written in
> Arabic, his later scientific treatises were written in
> Persian.
>
> Cris Forster, Music Director
> www.chrysalis-foundation.org
>
>
> --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
> >
> > Hi
> >
> >
> >
> > Although theories of farabi ( and not urmevi ) are a good basis for
> > persian music but we have different terms and trends:
> >

SNIP

🔗Cris Forster <cris.forster@comcast.net>

6/13/2006 9:51:02 AM

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
>`Avicenna and his
> catalogued books on music`, gives the following ratios of a 17-
> tone tuning
> attributed to Ibn Sina:
>
> 1/1
> 273/256
> 13/12
> 9/8
> 32/27
> 39/32
> 81/64
> 4/3
> 91/64
> 13/9
> 3/2
> 128/81
> 13/8
> 27/16
> 16/9
> 91/48
> 152/67
> 2/1

All correct for the lower octave, except 152/67.

Please note that for Fret #2, the Mathlath string
sounds 13/9, therefore the Mathna string sounds:
13/9 * 4/3 = 52/27.

>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 13 Haziran 2006 Salý 18:30
> Subject: [tuning] Ibn Sina and Persian Music
>
>
> > Mohajeri,
> >
> > The works of Al-Kindi, Al-Farabi, Safi Al-Din, and
> > Al-Jurjani have very little to do with Persian music.
> >
> > In contrast, the works of Ibn Sina have everything
> > to do with Persian music, especially the strategic
> > implementation of prime number 13.
> >
> > All the intervals described by Hormoz Farhat on the
> > modern tar and setar can be played on Ibn Sina's
> > ud. This also applies to many modern dastgah.
> > This comes as no surprise, since Ibn Sina was born
> > and lived most of his life in Persia. Although all his
> > major musical and medical works were written in
> > Arabic, his later scientific treatises were written in
> > Persian.
> >
> > Cris Forster, Music Director
> > www.chrysalis-foundation.org
> >
> >
> > --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@>
wrote:
> > >
> > > Hi
> > >
> > >
> > >
> > > Although theories of farabi ( and not urmevi ) are a good
basis for
> > > persian music but we have different terms and trends:
> > >
>
>
> SNIP
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

6/13/2006 3:46:23 PM

The source I have must have that printed wrong. I also had to correct
273/256 from 273/156.

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 13 Haziran 2006 Sal� 19:51
Subject: [tuning] Re: Ibn Sina and Persian Music

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
>`Avicenna and his
> catalogued books on music`, gives the following ratios of a 17-
> tone tuning
> attributed to Ibn Sina:
>
> 1/1
> 273/256
> 13/12
> 9/8
> 32/27
> 39/32
> 81/64
> 4/3
> 91/64
> 13/9
> 3/2
> 128/81
> 13/8
> 27/16
> 16/9
> 91/48
> 152/67
> 2/1

All correct for the lower octave, except 152/67.

Please note that for Fret #2, the Mathlath string
sounds 13/9, therefore the Mathna string sounds:
13/9 * 4/3 = 52/27.

🔗Cris Forster <cris.forster@comcast.net>

6/13/2006 6:35:15 PM

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> The source I have must have that printed wrong. I also had to
correct
> 273/256 from 273/156.

Excellent.

>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 13 Haziran 2006 Salý 19:51
> Subject: [tuning] Re: Ibn Sina and Persian Music
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
> >`Avicenna and his
> > catalogued books on music`, gives the following ratios of a 17-
> > tone tuning
> > attributed to Ibn Sina:
> >
> > 1/1
> > 273/256
> > 13/12
> > 9/8
> > 32/27
> > 39/32
> > 81/64
> > 4/3
> > 91/64
> > 13/9
> > 3/2
> > 128/81
> > 13/8
> > 27/16
> > 16/9
> > 91/48
> > 152/67
> > 2/1
>
>
> All correct for the lower octave, except 152/67.
>
> Please note that for Fret #2, the Mathlath string
> sounds 13/9, therefore the Mathna string sounds:
> 13/9 * 4/3 = 52/27.
>

🔗yahya_melb <yahya@melbpc.org.au>

6/14/2006 3:24:49 PM

Gentlemen,

Is this 17-note of ibn Sina's in Scala?
And what is it called? (Hopefully, what
he named it, if he did!)

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > The source I have must have that printed wrong. I also had to
> correct
> > 273/256 from 273/156.
>
> Excellent.
>
> > ----- Original Message -----
> > From: "Cris Forster" <cris.forster@>
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
> > >`Avicenna and his
> > > catalogued books on music`, gives the following ratios of a 17-
> > > tone tuning
> > > attributed to Ibn Sina:
> > >
> > > 1/1
> > > 273/256
> > > 13/12
> > > 9/8
> > > 32/27
> > > 39/32
> > > 81/64
> > > 4/3
> > > 91/64
> > > 13/9
> > > 3/2
> > > 128/81
> > > 13/8
> > > 27/16
> > > 16/9
> > > 91/48
> > > 152/67
> > > 2/1
> >
> >
> > All correct for the lower octave, except 152/67.
> >
> > Please note that for Fret #2, the Mathlath string
> > sounds 13/9, therefore the Mathna string sounds:
> > 13/9 * 4/3 = 52/27.

Regards,
Yahya

🔗Cris Forster <cris.forster@comcast.net>

6/14/2006 6:43:06 PM

Yahya,

I am not aware of any name Ibn Sina attributed to his
scale. He begins the discussion of his ud tuning in the
following manner:

******************************

The best known, most widely used, most popular
instrument is the lute. If there exists an instrument more
noble than this, it is not in general use among
practitioners. It is therefore necessary for us to discuss
the lute and the ratio[s] of its frets. We leave to others
the task of applying this theory to other instruments,
when they have accepted the principles that we are
going to explain.

******************************

Cris

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Gentlemen,
>
> Is this 17-note of ibn Sina's in Scala?
> And what is it called? (Hopefully, what
> he named it, if he did!)
>
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > The source I have must have that printed wrong. I also had to
> > correct
> > > 273/256 from 273/156.
> >
> > Excellent.
> >
> > > ----- Original Message -----
> > > From: "Cris Forster" <cris.forster@>
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > >
> > > > Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
> > > >`Avicenna and his
> > > > catalogued books on music`, gives the following ratios of a
17-
> > > > tone tuning
> > > > attributed to Ibn Sina:
> > > >
> > > > 1/1
> > > > 273/256
> > > > 13/12
> > > > 9/8
> > > > 32/27
> > > > 39/32
> > > > 81/64
> > > > 4/3
> > > > 91/64
> > > > 13/9
> > > > 3/2
> > > > 128/81
> > > > 13/8
> > > > 27/16
> > > > 16/9
> > > > 91/48
> > > > 152/67
> > > > 2/1
> > >
> > >
> > > All correct for the lower octave, except 152/67.
> > >
> > > Please note that for Fret #2, the Mathlath string
> > > sounds 13/9, therefore the Mathna string sounds:
> > > 13/9 * 4/3 = 52/27.
>
> Regards,
> Yahya
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

6/15/2006 7:16:29 AM

The closest scale to what I gave seems to be:

avicenna_19.scl

in the scala archive. Sorry! I don't have any other information on
Avicenna's intended gamut.

----- Original Message -----
From: "yahya_melb" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 15 Haziran 2006 Per�embe 1:24
Subject: [tuning] Re: Ibn Sina and Persian Music

>
> Gentlemen,
>
> Is this 17-note of ibn Sina's in Scala?
> And what is it called? (Hopefully, what
> he named it, if he did!)
>

🔗yahya_melb <yahya@melbpc.org.au>

6/15/2006 5:58:18 PM

Hi all,

Thank you, Cris!

I guess a reasonable name for it would
then be "ibn Sina's ud tuning".

BTW, for those who don't read Arabic,
the "mathlath" string is the third and
the "mathna" string is the second.

Regards,
Yahya

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...>
wrote:
>
> Yahya,
>
> I am not aware of any name Ibn Sina attributed to his
> scale. He begins the discussion of his ud tuning in the
> following manner:
>
> ******************************
>
> The best known, most widely used, most popular
> instrument is the lute. If there exists an instrument more
> noble than this, it is not in general use among
> practitioners. It is therefore necessary for us to discuss
> the lute and the ratio[s] of its frets. We leave to others
> the task of applying this theory to other instruments,
> when they have accepted the principles that we are
> going to explain.
>
> ******************************
>
> Cris
>
> --- In tuning@yahoogroups.com, "yahya_melb" <yahya@> wrote:
> >
> >
> > Gentlemen,
> >
> > Is this 17-note of ibn Sina's in Scala?
> > And what is it called? (Hopefully, what
> > he named it, if he did!)
> >
> > --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
> > wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > >
> > > > The source I have must have that printed wrong. I also had
to
> > > correct
> > > > 273/256 from 273/156.
> > >
> > > Excellent.
> > >
> > > > ----- Original Message -----
> > > > From: "Cris Forster" <cris.forster@>
> > > >
> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
> wrote:
> > > > >
> > > > > Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
> > > > >`Avicenna and his
> > > > > catalogued books on music`, gives the following ratios of
a
> 17-
> > > > > tone tuning
> > > > > attributed to Ibn Sina:
> > > > >
> > > > > 1/1
> > > > > 273/256
> > > > > 13/12
> > > > > 9/8
> > > > > 32/27
> > > > > 39/32
> > > > > 81/64
> > > > > 4/3
> > > > > 91/64
> > > > > 13/9
> > > > > 3/2
> > > > > 128/81
> > > > > 13/8
> > > > > 27/16
> > > > > 16/9
> > > > > 91/48
> > > > > 152/67
> > > > > 2/1
> > > >
> > > >
> > > > All correct for the lower octave, except 152/67.
> > > >
> > > > Please note that for Fret #2, the Mathlath string
> > > > sounds 13/9, therefore the Mathna string sounds:
> > > > 13/9 * 4/3 = 52/27.
> >
> > Regards,
> > Yahya
> >
>

🔗yahya_melb <yahya@melbpc.org.au>

6/15/2006 5:58:19 PM

Hi all,

Thank you, Cris!

I guess a reasonable name for it would
then be "ibn Sina's ud tuning".

BTW, for those who don't read Arabic,
the "mathlath" string is the third and
the "mathna" string is the second.

Regards,
Yahya

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...>
wrote:
>
> Yahya,
>
> I am not aware of any name Ibn Sina attributed to his
> scale. He begins the discussion of his ud tuning in the
> following manner:
>
> ******************************
>
> The best known, most widely used, most popular
> instrument is the lute. If there exists an instrument more
> noble than this, it is not in general use among
> practitioners. It is therefore necessary for us to discuss
> the lute and the ratio[s] of its frets. We leave to others
> the task of applying this theory to other instruments,
> when they have accepted the principles that we are
> going to explain.
>
> ******************************
>
> Cris
>
> --- In tuning@yahoogroups.com, "yahya_melb" <yahya@> wrote:
> >
> >
> > Gentlemen,
> >
> > Is this 17-note of ibn Sina's in Scala?
> > And what is it called? (Hopefully, what
> > he named it, if he did!)
> >
> > --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
> > wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > >
> > > > The source I have must have that printed wrong. I also had
to
> > > correct
> > > > 273/256 from 273/156.
> > >
> > > Excellent.
> > >
> > > > ----- Original Message -----
> > > > From: "Cris Forster" <cris.forster@>
> > > >
> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
> wrote:
> > > > >
> > > > > Ahmed Mahmud Hifni, in his 1977 Cairo publication entitled
> > > > >`Avicenna and his
> > > > > catalogued books on music`, gives the following ratios of
a
> 17-
> > > > > tone tuning
> > > > > attributed to Ibn Sina:
> > > > >
> > > > > 1/1
> > > > > 273/256
> > > > > 13/12
> > > > > 9/8
> > > > > 32/27
> > > > > 39/32
> > > > > 81/64
> > > > > 4/3
> > > > > 91/64
> > > > > 13/9
> > > > > 3/2
> > > > > 128/81
> > > > > 13/8
> > > > > 27/16
> > > > > 16/9
> > > > > 91/48
> > > > > 152/67
> > > > > 2/1
> > > >
> > > >
> > > > All correct for the lower octave, except 152/67.
> > > >
> > > > Please note that for Fret #2, the Mathlath string
> > > > sounds 13/9, therefore the Mathna string sounds:
> > > > 13/9 * 4/3 = 52/27.
> >
> > Regards,
> > Yahya
> >
>

🔗Cris Forster <cris.forster@comcast.net>

6/15/2006 6:56:55 PM

Yahya,

You're welcome.

The strings of the ud are traditionally named and numbered starting
with the lowest string:

String I: Bamm
String II: Mathlath
String III: Mathna
String IV: Zir
String V: Hadd

Cris

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Hi all,
>
> Thank you, Cris!
>
> I guess a reasonable name for it would
> then be "ibn Sina's ud tuning".
>
> BTW, for those who don't read Arabic,
> the "mathlath" string is the third and
> the "mathna" string is the second.
>
> Regards,
> Yahya
>
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
> wrote:
> >
> > Yahya,
> >
> > I am not aware of any name Ibn Sina attributed to his
> > scale. He begins the discussion of his ud tuning in the
> > following manner:
> >
> > ******************************
> >
> > The best known, most widely used, most popular
> > instrument is the lute. If there exists an instrument more
> > noble than this, it is not in general use among
> > practitioners. It is therefore necessary for us to discuss
> > the lute and the ratio[s] of its frets. We leave to others
> > the task of applying this theory to other instruments,
> > when they have accepted the principles that we are
> > going to explain.
> >
> > ******************************
> >
> > Cris
> >
> > --- In tuning@yahoogroups.com, "yahya_melb" <yahya@> wrote:
> > >
> > >
> > > Gentlemen,
> > >
> > > Is this 17-note of ibn Sina's in Scala?
> > > And what is it called? (Hopefully, what
> > > he named it, if he did!)
> > >
> > > --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
> > > wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
> wrote:
> > > > >
> > > > > The source I have must have that printed wrong. I also had
> to
> > > > correct
> > > > > 273/256 from 273/156.
> > > >
> > > > Excellent.
> > > >
> > > > > ----- Original Message -----
> > > > > From: "Cris Forster" <cris.forster@>
> > > > >
> > > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
> > wrote:
> > > > > >
> > > > > > Ahmed Mahmud Hifni, in his 1977 Cairo publication
entitled
> > > > > >`Avicenna and his
> > > > > > catalogued books on music`, gives the following ratios
of
> a
> > 17-
> > > > > > tone tuning
> > > > > > attributed to Ibn Sina:
> > > > > >
> > > > > > 1/1
> > > > > > 273/256
> > > > > > 13/12
> > > > > > 9/8
> > > > > > 32/27
> > > > > > 39/32
> > > > > > 81/64
> > > > > > 4/3
> > > > > > 91/64
> > > > > > 13/9
> > > > > > 3/2
> > > > > > 128/81
> > > > > > 13/8
> > > > > > 27/16
> > > > > > 16/9
> > > > > > 91/48
> > > > > > 152/67
> > > > > > 2/1
> > > > >
> > > > >
> > > > > All correct for the lower octave, except 152/67.
> > > > >
> > > > > Please note that for Fret #2, the Mathlath string
> > > > > sounds 13/9, therefore the Mathna string sounds:
> > > > > 13/9 * 4/3 = 52/27.
> > >
> > > Regards,
> > > Yahya
> > >
> >
>

🔗yahya_melb <yahya@melbpc.org.au>

6/16/2006 5:58:39 PM

Hi all,

Which names suggest that at some earlier stage,
the `ud had only three strings numbered from the
*highest* string!, thus:

> String III: Mathlath (from thalatha, 3)
> String II: Mathna (from ithnain, 2)
> String I: Hadd (from ahad, 1)

Funny how language changes ...

Zir (or Zirr) is probably from the same root as
zurrun, button. I have no clear idea what Bamm
comes from or means outside this context, and
can only speculate that it may represent a
contraction of "bi umm" or "bi amm", which would
relate it to umm, mother.

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...>
wrote:
>
> Yahya,
>
> You're welcome.
>
> The strings of the ud are traditionally named and numbered
> starting with the lowest string:
>
> String I: Bamm
> String II: Mathlath
> String III: Mathna
> String IV: Zir
> String V: Hadd
>
> Cris
...
[YA earlier]
> > BTW, for those who don't read Arabic,
> > the "mathlath" string is the third and
> > the "mathna" string is the second.
...
[CF earlier]
> > > > > > Please note that for Fret #2, the Mathlath string
> > > > > > sounds 13/9, therefore the Mathna string sounds:
> > > > > > 13/9 * 4/3 = 52/27.

Regards,
Yahya

🔗Cris Forster <cris.forster@comcast.net>

6/16/2006 7:26:20 PM

Yahya,

From: _Musical Mathematics: A Practice in the Mathematics of
Tuning Instruments and Analyzing Scales_,

Chapter 11, Section 50:

******************************

In the first half of the 9th century, the most famous teacher and
exponent of traditional Arabian music was Ishaq al-Mausili (d.
850). Unfortunately, all of his books, including the Kitab al-
aghani al-kabir (Grand book of songs) and Kitab al-naghm
wa'l-iqa' (Book of melody and rhythm) are lost. However, two
important related works by different authors have survived.
The first, written by Yahya b. `Ali b. Yahya b. Abi Mansur al-
Munajjim (d. 912), is called Risala fi'l-musiqi (Treatise on
music); in two critical passages cited below, Al-Munajjim refers
to Al-Mausili as an authority on the subject of Arabian modes.
The second, written by Abu'l-Faraj al-Isfahani (d. 976), is also
called Kitab al-aghani al-kabir, after Al-Mausili's work.
According to the historian Ibn Khallikan (d. 1282), Al-Isfahani
took fifty years to complete this book, which consists of twenty-
one volumes and contains nearly 2,000,000 words.

******************************

According to Farmer's description of the Risala fi'l-musiqi by
Al-Munajjim, in the ***Old Arabian System*** --- which also
occurs in the Rasa'il Ikhwan al-Safa (Treatises of the Brothers
of Sincerity) --- the strings are numbered in the following
direction:

String IV: Bamm (lowest in Brothers of Sincerity) - 1/1
String III: Mathlath - 4/3
String II: Mathna - 16/9
String I: Zir - 32/27

However, please note that in Al-Munajjim's text, the *Mathna*
string serves as the tonic for all *modes*. Here we have:

String IV: Bamm - 9/8 (D)
String III: Mathlath - 3/2 (G)
String II: Mathna - 2/1 (c)
String I: Zir - 4/3 (f)

The latter and former string numbers do *not* occur in Al-Kindi,
Al-Farabi, Ibn Sina, Safi Al-Din, and Al-Jurjani.

For example, Al-Farabi states:

******************************

The strings of the lute are stretched, according to common
practice, so that the second [Mathlath] produces, when it is
played open, a note identical to that given by the first [Bamm]
stopped at the little finger fret; the third open string [Mathna]
must produce a note identical to that of the little finger fret of
the second [Mathlath]; and the open fourth [Zir] gives a note
like that of the little finger fret of the third [Mathna].

******************************

Please see, http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm

******************************

This tuning sequence, which specifies that the tone of the little
finger fret determines the tone of the next higher open string,
holds true for all uds of the Arabian Renaissance.

Cris Forster, Music Director
www.chrysalis-foundation.org

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Hi all,
>
> Which names suggest that at some earlier stage,
> the `ud had only three strings numbered from the
> *highest* string!, thus:
>
> > String III: Mathlath (from thalatha, 3)
> > String II: Mathna (from ithnain, 2)
> > String I: Hadd (from ahad, 1)
>
> Funny how language changes ...
>
> Zir (or Zirr) is probably from the same root as
> zurrun, button. I have no clear idea what Bamm
> comes from or means outside this context, and
> can only speculate that it may represent a
> contraction of "bi umm" or "bi amm", which would
> relate it to umm, mother.
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
> wrote:
> >
> > Yahya,
> >
> > You're welcome.
> >
> > The strings of the ud are traditionally named and numbered
> > starting with the lowest string:
> >
> > String I: Bamm
> > String II: Mathlath
> > String III: Mathna
> > String IV: Zir
> > String V: Hadd
> >
> > Cris
> ...
> [YA earlier]
> > > BTW, for those who don't read Arabic,
> > > the "mathlath" string is the third and
> > > the "mathna" string is the second.
> ...
> [CF earlier]
> > > > > > > Please note that for Fret #2, the Mathlath string
> > > > > > > sounds 13/9, therefore the Mathna string sounds:
> > > > > > > 13/9 * 4/3 = 52/27.
>
> Regards,
> Yahya
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

6/17/2006 6:12:14 AM

Yahya,

>
> Hi all,
>
> Which names suggest that at some earlier stage,
> the `ud had only three strings numbered from the
> *highest* string!, thus:

Rauf Yekta says, that up to Al-Farabi, the Oud had 4 strings, each seperated
from the other by the interval of a pure fourth. Due to a lack of the
register of the instrument, Al-Farabi added a fifth string, and later on a
sixth was added after him.

Actually, I think Yekta means `course` instead of string, for he tunes the
strings:

1. A3 (bass)

2. G5
3. G5

4. D5
5. D5

6. A4
7. A4

8. E4
9. E4

10. D4
11. D4

And then he says that the tones are key transposed down an octave.

String I: Zir, meaning `down`, `low`... the lowest string according to the
player.

>
> > String III: Mathlath (from thalatha, 3)

Literally, `three by three`

> > String II: Mathna (from ithnain, 2)

Literally, `two by two`

> > String I: Hadd (from ahad, 1)
>

I don't think so. Hadd comes from hudud, meaning `border`, `boundary`,
`limit`, `furthest degree`.

SNIP

I have no clear idea what Bamm
> comes from or means outside this context, and
> can only speculate that it may represent a
> contraction of "bi umm" or "bi amm", which would
> relate it to umm, mother.
>

Nope! Bamm means `roof`, `dome`, `ceiling`, `sky`. Obviously, the highest
string according to the player.

In summary:

String 4: Bamm (roof)
String 3: Mathlath (3 by 3)
String 2: Mathna (2 by 2)
String 1: Zir (low... added by Al-Farabi?)
String 0: Hadd (limit... added by Allah knows who.)

> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...>
> wrote:
> >
> > Yahya,
> >
> > You're welcome.
> >
> > The strings of the ud are traditionally named and numbered
> > starting with the lowest string:
> >
> > String I: Bamm
> > String II: Mathlath
> > String III: Mathna
> > String IV: Zir
> > String V: Hadd
> >
> > Cris
> ...
> [YA earlier]
> > > BTW, for those who don't read Arabic,
> > > the "mathlath" string is the third and
> > > the "mathna" string is the second.
> ...
> [CF earlier]
> > > > > > > Please note that for Fret #2, the Mathlath string
> > > > > > > sounds 13/9, therefore the Mathna string sounds:
> > > > > > > 13/9 * 4/3 = 52/27.
>
> Regards,
> Yahya
>
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

6/17/2006 6:39:11 AM

Thank you for correcting the order of oud strings. I also wish to correct a
mistake in my previous message concerning the addition of the 5th string.
The 4th string (Zir) already existed prior to Al-Farabi, he added himself
the 5th (Hadd). It is the 6th nameless string that was anonymously added
later on.

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 17 Haziran 2006 Cumartesi 5:26
Subject: [tuning] Re: Ibn Sina and Persian Music

> Yahya,
>
> From: _Musical Mathematics: A Practice in the Mathematics of
> Tuning Instruments and Analyzing Scales_,
>
> Chapter 11, Section 50:
>
> ******************************
>
> In the first half of the 9th century, the most famous teacher and
> exponent of traditional Arabian music was Ishaq al-Mausili (d.
> 850). Unfortunately, all of his books, including the Kitab al-
> aghani al-kabir (Grand book of songs) and Kitab al-naghm
> wa'l-iqa' (Book of melody and rhythm) are lost. However, two
> important related works by different authors have survived.
> The first, written by Yahya b. `Ali b. Yahya b. Abi Mansur al-
> Munajjim (d. 912), is called Risala fi'l-musiqi (Treatise on
> music); in two critical passages cited below, Al-Munajjim refers
> to Al-Mausili as an authority on the subject of Arabian modes.
> The second, written by Abu'l-Faraj al-Isfahani (d. 976), is also
> called Kitab al-aghani al-kabir, after Al-Mausili's work.
> According to the historian Ibn Khallikan (d. 1282), Al-Isfahani
> took fifty years to complete this book, which consists of twenty-
> one volumes and contains nearly 2,000,000 words.
>
> ******************************
>
> According to Farmer's description of the Risala fi'l-musiqi by
> Al-Munajjim, in the ***Old Arabian System*** --- which also
> occurs in the Rasa'il Ikhwan al-Safa (Treatises of the Brothers
> of Sincerity) --- the strings are numbered in the following
> direction:
>
>
> String IV: Bamm (lowest in Brothers of Sincerity) - 1/1
> String III: Mathlath - 4/3
> String II: Mathna - 16/9
> String I: Zir - 32/27
>
> However, please note that in Al-Munajjim's text, the *Mathna*
> string serves as the tonic for all *modes*. Here we have:
>
> String IV: Bamm - 9/8 (D)
> String III: Mathlath - 3/2 (G)
> String II: Mathna - 2/1 (c)
> String I: Zir - 4/3 (f)
>
> The latter and former string numbers do *not* occur in Al-Kindi,
> Al-Farabi, Ibn Sina, Safi Al-Din, and Al-Jurjani.
>
> For example, Al-Farabi states:
>
> ******************************
>
> The strings of the lute are stretched, according to common
> practice, so that the second [Mathlath] produces, when it is
> played open, a note identical to that given by the first [Bamm]
> stopped at the little finger fret; the third open string [Mathna]
> must produce a note identical to that of the little finger fret of
> the second [Mathlath]; and the open fourth [Zir] gives a note
> like that of the little finger fret of the third [Mathna].
>
> ******************************
>
> Please see, http://www.chrysalis-foundation.org/Al-Farabi's_'Uds.htm
>
> ******************************
>
> This tuning sequence, which specifies that the tone of the little
> finger fret determines the tone of the next higher open string,
> holds true for all uds of the Arabian Renaissance.
>
> Cris Forster, Music Director
> www.chrysalis-foundation.org
>

🔗yahya_melb <yahya@melbpc.org.au>

6/17/2006 9:29:32 PM

Hi all,

--- In tuning@yahoogroups.com, "Ozan Yarman" wrote:
>
> Yahya,
>
> > Which names suggest that at some earlier stage,
> > the `ud had only three strings numbered from the
> > *highest* string!, thus:
>
> Rauf Yekta says, that up to Al-Farabi, the Oud had 4
> strings, each seperated from the other by the interval
> of a pure fourth. Due to a lack of the register of the
> instrument, Al-Farabi added a fifth string, and later
> on a sixth was added after him.
>
> Actually, I think Yekta means `course` instead of
> string, for he tunes the strings:
>
> 1. A3 (bass)
>
> 2. G5
> 3. G5
>
> 4. D5
> 5. D5
>
> 6. A4
> 7. A4
>
> 8. E4
> 9. E4
>
> 10. D4
> 11. D4

This arrangement of courses is reminiscent of that
of the Malay "gambus" lutes, which always have seven
strings in four courses, the lowest string being single
and all others in unison pairs. The word "gambus" seems
to relate to "qanbus", a lute of central Asia and Iran;
the gambus itself seems to have arrived in Malaysia at
least twice by different routes; there are two very
distinctive forms of the instrument, "gambus Melayu"
which is pear-shaped, and "gambus Hadramaut" with an
arched back, the latter being a recent arrival from the
Hadhramaut region of Yemen. The paper at:
http://tinyurl.com/qe6d6
some details of the history of these instruments.

> And then he says that the tones are key transposed
> down an octave.

Hmm!? How does this work?

> String I: Zir, meaning `down`, `low`... the lowest
> string according to the player.
>
> > > String III: Mathlath (from thalatha, 3)
> Literally, `three by three`
>
> > > String II: Mathna (from ithnain, 2)
> Literally, `two by two`
>
> > > String I: Hadd (from ahad, 1)
>
> I don't think so. Hadd comes from hudud, meaning
> `border`, `boundary`, `limit`, `furthest degree`.

[YA earlier]
> > I have no clear idea what Bamm
> > comes from or means outside this context, and
> > can only speculate that it may represent a
> > contraction of "bi umm" or "bi amm", which would
> > relate it to umm, mother.
>
> Nope! Bamm means `roof`, `dome`, `ceiling`, `sky`.
> Obviously, the highest string according to the player.
>
> In summary:
> String 4: Bamm (roof)
> String 3: Mathlath (3 by 3)
> String 2: Mathna (2 by 2)
> String 1: Zir (low... added by Al-Farabi?)
> String 0: Hadd (limit... added by Allah knows who.)

Thanks, Oz, it's good to have correct etymologies for
these terms.

Ozan later wrote to Cris Forster:
> Thank you for correcting the order of oud strings. I
> also wish to correct a mistake in my previous message
> concerning the addition of the 5th string. The 4th
> string (Zir) already existed prior to Al-Farabi, he
> added himself the 5th (Hadd). It is the 6th nameless
> string that was anonymously added later on.

Here is a corrected summary:

_Modern_ | __Old|__ | __Name__ |__Original meaning________
String 1 | String 4 | Bamm | roof
String 2 | String 3 | Mathlath | 3 by 3
String 3 | String 2 | Mathna | 2 by 2
String 4 | String 1 | Zir | low
String 5 | String 0 | Hadd | limit (added by al-Farabi)
String 6 | ___n/a__ |(nameless)| ___n/a____

> > --- In tuning@yahoogroups.com, "Cris Forster" wrote:
> > >
> > > Yahya,
> > >
> > > You're welcome.
> > >
> > > The strings of the ud are traditionally named and numbered
> > > starting with the lowest string:
> > >
> > > String I: Bamm
> > > String II: Mathlath
> > > String III: Mathna
> > > String IV: Zir
> > > String V: Hadd
> > >
> > > Cris
> > ...
> > [YA earlier]
> > > > BTW, for those who don't read Arabic,
> > > > the "mathlath" string is the third and
> > > > the "mathna" string is the second.
> > ...
> > [CF earlier]
> > > > > > > > Please note that for Fret #2, the Mathlath string
> > > > > > > > sounds 13/9, therefore the Mathna string sounds:
> > > > > > > > 13/9 * 4/3 = 52/27.

Regards,
Yahya

🔗Cris Forster <cris.forster@comcast.net>

6/18/2006 6:48:10 AM

From _Al-Faruqi, L.I. (1981). An Annotated
Glossary of Arabic Musical Terms. Greenwood
Press, Westport, Connecticut_

******************************

p. 29: BAMM (pl. BUMUM) (Pers.) "thick, low
sound" The lowest pitched string of the udÂ…

p. 89: HADD (pl. HUDUD) "sharp; at the edge" 1.
Name given in Classical Period to the fifth and
highest pitched string of the udÂ…

p. 402: ZIR (Pers.) "below; high pitched" 1. One of
he strings of the ud, according to the Classical
Period theorists. It was the highest pitched string
when the lute had four strings, the fourth (counting
from the lowest pitched)Â…

******************************

Cris Forster, Music Director
www.chrysalis-foundation.org

--- In tuning@yahoogroups.com, "yahya_melb" <yahya@...> wrote:
>
>
> Hi all,
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" wrote:
> >
> > Yahya,
> >
> > > Which names suggest that at some earlier stage,
> > > the `ud had only three strings numbered from the
> > > *highest* string!, thus:
> >
> > Rauf Yekta says, that up to Al-Farabi, the Oud had 4
> > strings, each seperated from the other by the interval
> > of a pure fourth. Due to a lack of the register of the
> > instrument, Al-Farabi added a fifth string, and later
> > on a sixth was added after him.
> >
> > Actually, I think Yekta means `course` instead of
> > string, for he tunes the strings:
> >
> > 1. A3 (bass)
> >
> > 2. G5
> > 3. G5
> >
> > 4. D5
> > 5. D5
> >
> > 6. A4
> > 7. A4
> >
> > 8. E4
> > 9. E4
> >
> > 10. D4
> > 11. D4
>
> This arrangement of courses is reminiscent of that
> of the Malay "gambus" lutes, which always have seven
> strings in four courses, the lowest string being single
> and all others in unison pairs. The word "gambus" seems
> to relate to "qanbus", a lute of central Asia and Iran;
> the gambus itself seems to have arrived in Malaysia at
> least twice by different routes; there are two very
> distinctive forms of the instrument, "gambus Melayu"
> which is pear-shaped, and "gambus Hadramaut" with an
> arched back, the latter being a recent arrival from the
> Hadhramaut region of Yemen. The paper at:
> http://tinyurl.com/qe6d6
> some details of the history of these instruments.
>
>
> > And then he says that the tones are key transposed
> > down an octave.
>
> Hmm!? How does this work?
>
>
> > String I: Zir, meaning `down`, `low`... the lowest
> > string according to the player.
> >
> > > > String III: Mathlath (from thalatha, 3)
> > Literally, `three by three`
> >
> > > > String II: Mathna (from ithnain, 2)
> > Literally, `two by two`
> >
> > > > String I: Hadd (from ahad, 1)
> >
> > I don't think so. Hadd comes from hudud, meaning
> > `border`, `boundary`, `limit`, `furthest degree`.
>
> [YA earlier]
> > > I have no clear idea what Bamm
> > > comes from or means outside this context, and
> > > can only speculate that it may represent a
> > > contraction of "bi umm" or "bi amm", which would
> > > relate it to umm, mother.
> >
> > Nope! Bamm means `roof`, `dome`, `ceiling`, `sky`.
> > Obviously, the highest string according to the player.
> >
> > In summary:
> > String 4: Bamm (roof)
> > String 3: Mathlath (3 by 3)
> > String 2: Mathna (2 by 2)
> > String 1: Zir (low... added by Al-Farabi?)
> > String 0: Hadd (limit... added by Allah knows who.)
>
> Thanks, Oz, it's good to have correct etymologies for
> these terms.
>
>
> Ozan later wrote to Cris Forster:
> > Thank you for correcting the order of oud strings. I
> > also wish to correct a mistake in my previous message
> > concerning the addition of the 5th string. The 4th
> > string (Zir) already existed prior to Al-Farabi, he
> > added himself the 5th (Hadd). It is the 6th nameless
> > string that was anonymously added later on.
>
>
> Here is a corrected summary:
>
> _Modern_ | __Old|__ | __Name__ |__Original meaning________
> String 1 | String 4 | Bamm | roof
> String 2 | String 3 | Mathlath | 3 by 3
> String 3 | String 2 | Mathna | 2 by 2
> String 4 | String 1 | Zir | low
> String 5 | String 0 | Hadd | limit (added by al-Farabi)
> String 6 | ___n/a__ |(nameless)| ___n/a____
>
>
> > > --- In tuning@yahoogroups.com, "Cris Forster" wrote:
> > > >
> > > > Yahya,
> > > >
> > > > You're welcome.
> > > >
> > > > The strings of the ud are traditionally named and numbered
> > > > starting with the lowest string:
> > > >
> > > > String I: Bamm
> > > > String II: Mathlath
> > > > String III: Mathna
> > > > String IV: Zir
> > > > String V: Hadd
> > > >
> > > > Cris
> > > ...
> > > [YA earlier]
> > > > > BTW, for those who don't read Arabic,
> > > > > the "mathlath" string is the third and
> > > > > the "mathna" string is the second.
> > > ...
> > > [CF earlier]
> > > > > > > > > Please note that for Fret #2, the Mathlath string
> > > > > > > > > sounds 13/9, therefore the Mathna string sounds:
> > > > > > > > > 13/9 * 4/3 = 52/27.
>
> Regards,
> Yahya
>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

6/28/2006 5:42:34 AM

SNIP

> >
> > Actually, I think Yekta means `course` instead of
> > string, for he tunes the strings:
> >
> > 1. A3 (bass)
> >
> > 2. G5
> > 3. G5
> >
> > 4. D5
> > 5. D5
> >
> > 6. A4
> > 7. A4
> >
> > 8. E4
> > 9. E4
> >
> > 10. D4
> > 11. D4
>
> This arrangement of courses is reminiscent of that
> of the Malay "gambus" lutes, which always have seven
> strings in four courses, the lowest string being single
> and all others in unison pairs. The word "gambus" seems
> to relate to "qanbus", a lute of central Asia and Iran;
> the gambus itself seems to have arrived in Malaysia at
> least twice by different routes; there are two very
> distinctive forms of the instrument, "gambus Melayu"
> which is pear-shaped, and "gambus Hadramaut" with an
> arched back, the latter being a recent arrival from the
> Hadhramaut region of Yemen. The paper at:
> http://tinyurl.com/qe6d6
> some details of the history of these instruments.
>
>
> > And then he says that the tones are key transposed
> > down an octave.
>
> Hmm!? How does this work?
>

Simple as a guitar staff!

SNIP

> Here is a corrected summary:
>
> _Modern_ | __Old|__ | __Name__ |__Original meaning________
> String 1 | String 4 | Bamm | roof
> String 2 | String 3 | Mathlath | 3 by 3
> String 3 | String 2 | Mathna | 2 by 2
> String 4 | String 1 | Zir | low
> String 5 | String 0 | Hadd | limit (added by al-Farabi)
> String 6 | ___n/a__ |(nameless)| ___n/a____
>

Excellent. But don't forget how Yekta categorized them:

1. BAMM now and of old
2-3. *unnamed*
4-5. HADD of old
6-7. ZIR of old
8-9. MATHNA of old
10-11. MATHLATH of old

It may be possible to revise the ordering in this way, from low to high:

String 1. BAMM (roof)
String 2a-2b. MATHNA (2 by 2)
String 3a-3b. MATHLATH (3 by 3)
String 4a-4b. MERBAA (4 by 4)
String 5a-5b. ZIR (down-low)
String 6a-6b. HADD (limit)

Guess which one is my addition!