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What are the names of maqams that correspond to these quarter-tone scales?

🔗calebmrgn@...

3/6/2014 6:27:04 AM

With the help of a programmer, I've put together a list of 7-note scales having 1 or more quarter-tones. There are certain restrictions. With those restrictions, it seems that there are 64 such scales total, which can be grouped into 10 groups. The groupings are by intervallic content: By rotations (meaning the same thing as modal shifts) and by inversion (meaning the same interval list backwards.) I have yet to confirm that there are exactly 64 -- I might have mistakenly left a few out, or something. (If anyone who understands the procedures here wishes to check to see if anything's missing, let me know.)

Now, here is my question, asked with some trepidation:

****To what maqams do these pitch-sets more-or-less correspond?****

The reason I ask is not to delve very deeply into the world of Arabic music. It's way too deep. For example, I'm aware that maqams are much more than mere unordered sets of pitches. I'm also aware that the actual practice of tuning is not well-expressed by quarter-tones.

Rather, I thought that the list would be more useful if there were some names of maqams that could be the beginning of links to further research -- just as A,B,C,D,E,F#,G could be linked to "Dorian" without that being an adequate explanation.

Here is the list. A minus sign (-) means the pitch is a quarter-tone lower. Scales under a line ( ----)

means the sets are related by inversion. The order and numbering of the groups are arbitrary; there is nothing inherently "first" about the group called "First". However, again, the groups are carefully chosen and clumped together by ordered interval content.

First Group
A,C-,D,D#,F,F#,G#
A,B,C,D#-,F,F#,G#
A,B,C,D,D#,F#-,G#
A,Bb,C#-,D#,E,F#,G
A,Bb,C,C#,D#,E,G-

Second Group
A,C-,C#,D#,F,F#,G#
A,B,C,D#-,E,F#,G#
A,B,C#,D,E,F,G#-
A,Bb,C#-,D,E,F#,G
A,B,C,D,D#,F#-,G
-------------------
A,B,C#,D#-,F,F#,G#
A,B,C,D,E,F#-,G#
A,B,C#-,D#,E,F#,G
A,B-,C#,D,E,F,G
A,Bb,C,C#,D#,F,G-

Third Group
A,C-,C#,D#,E,F#,G#
A,B,C,D,E,F,G#-
A,B,C,D#-,E,F#,G
A,Bb,C,D,D#,F#-,G
A,Bb,C#-,D,E,F,G
-----------------
A,B,C#-,D#,E,F#,G#
A,B,C#,D,E,F#-,G#
A,B,C#,D,E,F#-,G#
A,B-,C#,D,E,F#,G
A,Bb,C,D-,E,F,G
A,Bb,C,D,D#,F,G-

Fourth Group
A,B,C#,D#-,E,F#,G#
A,B,C#,D,E,F#,G#-
A,B,C,D,E,F#-,G
------------------------
A,B,C#-,D,E,F#,G
A,B-,C,D,E,F,G

Fifth Group
A,B,C#-,D,E,F#,G#
A,B,C#,D#,E,F#,G#-
A,B,C#,D,E,F#-,G
-----------------
A,B,C,D,E,F#,G#-
A,B,C#,D#-,E,F#,G
A,Bb,C,D,E,F#-,G
A,B,C#-,D,E,F,G
A,B-,C,D,D#,F,G
A,Bb,C,D-,D#,F,G

Sixth Group
A,B,C#-,D,E,F#-,G#
A,B-,C#,D,E,F#-,G
A,Bb,C,D-,D#,F,G-
------------------------
A,Bb,C#-,D,E,F#-,G

Seventh Group
A,B,C#-,D,E,F,G#
A,B,C,D#,E,F#,G#-
A,Bb,C#,D,E,F#-,G
A,Bb,C,D-,D#,F,F#
------------------------
A,B-,C,D,D#,F#,G

Eighth Group
A,B,C#,D#-,E,F#,G#-
A,B,C#-,D,E,F#,G#-
A,B-,C#-,D#-,E,F#-,G#-
A,B,C#-,D,E,F#-,G
-----------------------
A,B-,C,D,E,F#-,G

Ninth Group
A,B,C#-,D#-,E,F#,G#-
A,B,C#-,D#-,E,F#-,G#-
A,B,C#-,D,E,F#-,G#-
--------------------
A,B-,C#-,D,E,F#-,G#-
A,B-,C#-,D,E,F#-,G

Tenth Group
A,B,C,D#-,E,F#,G#-
A,B,C#-,D,E,F,G#-
A,B-,C,D,D#,F#-,G
------------------
A,C-,C#-,D#-,E,F#-,G#-

🔗Daniel Forró <dan.for@...>

3/6/2014 7:54:34 AM

Just few points.

I don't see much similarity:
- not all maqamat use quarter tones

- when yes, usually only one, maximally two, and tuning is not exact

- only few notes can have quarter tone accidentals, usually E, A, B

- even tonic can be shifted quarter tone down

- most maqamat have as a dominant fifth (like in Greek/Western modes), or fourth (in hypo- types) - at least one of these tones is there, or even both. Only few maqamat have together with one of these tones augmented fourth (or diminished fifth). I'm not aware about some maqam which would not have this structure and ignore it (by using quarter tones in the place of these important tones, or omit them somehow, for example by whole tone steps). Some of your scales have such structure.

- for most maqamat is typical interval augmented second, used at least in one tetrachord. Only some maqamat are same as Greek/Western modes and use only whole tones and halftones.

Check for example here:

http://www.maqamworld.com/maqamat.html

Daniel Forro

P.S.: Scales 7 and 8 in Third Group are the same. Mistake?

On 6 Mar, 2014, at 11:27 PM, <calebmrgn@...> <calebmrgn@...> wrote:

>
>
> With the help of a programmer, I've put together a list of 7-note > scales having 1 or more quarter-tones.
> There are certain restrictions. With those restrictions, it seems > that there are 64 such scales total, which can be grouped into 10 > groups. The groupings are by intervallic content: By rotations > (meaning the same thing as modal shifts) and by inversion (meaning > the same interval list backwards.) I have yet to confirm that there > are exactly 64 -- I might have mistakenly left a few out, or > something. (If anyone who understands the procedures here wishes to > check to see if anything's missing, let me know.)
>
> Now, here is my question, asked with some trepidation:
>
> ****To what maqams do these pitch-sets more-or-less correspond?****
>
> The reason I ask is not to delve very deeply into the world of > Arabic music. It's way too deep. For example, I'm aware that > maqams are much more than mere unordered sets of pitches. I'm also > aware that the actual practice of tuning is not well-expressed by > quarter-tones.
>
> Rather, I thought that the list would be more useful if there were > some names of maqams that could be the beginning of links to further > research -- just as A,B,C,D,E,F#,G could be linked to "Dorian" > without that being an adequate explanation.
>
> Here is the list. A minus sign (-) means the pitch is a quarter-> tone lower. Scales under a line ( ----)
> means the sets are related by inversion. The order and numbering of > the groups are arbitrary; there is nothing inherently "first" about > the group called "First". However, again, the groups are carefully > chosen and clumped together by ordered interval content.
>
> First Group
> A,C-,D,D#,F,F#,G#
> A,B,C,D#-,F,F#,G#
> A,B,C,D,D#,F#-,G#
> A,Bb,C#-,D#,E,F#,G
> A,Bb,C,C#,D#,E,G-
>
>
> Second Group
> A,C-,C#,D#,F,F#,G#
> A,B,C,D#-,E,F#,G#
> A,B,C#,D,E,F,G#-
> A,Bb,C#-,D,E,F#,G
> A,B,C,D,D#,F#-,G
> -------------------
> A,B,C#,D#-,F,F#,G#
> A,B,C,D,E,F#-,G#
> A,B,C#-,D#,E,F#,G
> A,B-,C#,D,E,F,G
> A,Bb,C,C#,D#,F,G-
>
>
> Third Group
> A,C-,C#,D#,E,F#,G#
> A,B,C,D,E,F,G#-
> A,B,C,D#-,E,F#,G
> A,Bb,C,D,D#,F#-,G
> A,Bb,C#-,D,E,F,G
> -----------------
> A,B,C#-,D#,E,F#,G#
> A,B,C#,D,E,F#-,G#
> A,B,C#,D,E,F#-,G#
> A,B-,C#,D,E,F#,G
> A,Bb,C,D-,E,F,G
> A,Bb,C,D,D#,F,G-
>
>
> Fourth Group
> A,B,C#,D#-,E,F#,G#
> A,B,C#,D,E,F#,G#-
> A,B,C,D,E,F#-,G
> ------------------------
> A,B,C#-,D,E,F#,G
> A,B-,C,D,E,F,G
>
>
> Fifth Group
>
> A,B,C#-,D,E,F#,G#
> A,B,C#,D#,E,F#,G#-
> A,B,C#,D,E,F#-,G
> -----------------
> A,B,C,D,E,F#,G#-
> A,B,C#,D#-,E,F#,G
> A,Bb,C,D,E,F#-,G
> A,B,C#-,D,E,F,G
> A,B-,C,D,D#,F,G
> A,Bb,C,D-,D#,F,G
>
>
> Sixth Group
> A,B,C#-,D,E,F#-,G#
> A,B-,C#,D,E,F#-,G
> A,Bb,C,D-,D#,F,G-
> ------------------------
> A,Bb,C#-,D,E,F#-,G
>
>
> Seventh Group
> A,B,C#-,D,E,F,G#
> A,B,C,D#,E,F#,G#-
> A,Bb,C#,D,E,F#-,G
> A,Bb,C,D-,D#,F,F#
> ------------------------
> A,B-,C,D,D#,F#,G
>
>
> Eighth Group
> A,B,C#,D#-,E,F#,G#-
> A,B,C#-,D,E,F#,G#-
> A,B-,C#-,D#-,E,F#-,G#-
> A,B,C#-,D,E,F#-,G
> -----------------------
> A,B-,C,D,E,F#-,G
>
>
> Ninth Group
> A,B,C#-,D#-,E,F#,G#-
> A,B,C#-,D#-,E,F#-,G#-
> A,B,C#-,D,E,F#-,G#-
> --------------------
> A,B-,C#-,D,E,F#-,G#-
> A,B-,C#-,D,E,F#-,G
>
>
> Tenth Group
>
> A,B,C,D#-,E,F#,G#-
> A,B,C#-,D,E,F,G#-
> A,B-,C,D,D#,F#-,G
> ------------------
> A,C-,C#-,D#-,E,F#-,G#-

🔗Caleb Morgan <calebmrgn@...>

3/6/2014 8:17:40 AM

Just a quick response for now.

Good catch on the duplicate!

That was indeed a mistake.

I need to get the programmer to modify the program, and confirm how many such scales there are.

Make it 63, for now.

On Thursday, March 6, 2014 10:56 AM, Daniel Forró <dan.for@...> wrote:

 
Just few points. 

I don't see much similarity:
- not all maqamat use quarter tones

- when yes, usually only one, maximally two, and tuning is not exact

- only few notes can have quarter tone accidentals, usually E, A, B

- even tonic can be shifted quarter tone down  

- most maqamat have as a dominant fifth (like in Greek/Western modes), or fourth (in hypo- types) - at least one of these tones is there, or even both. Only few maqamat have together with one of these tones augmented fourth (or diminished fifth). I'm not aware about some maqam which would not have this structure and ignore it (by using quarter tones in the place of these important tones, or omit them somehow, for example by whole tone steps). Some of your scales have such structure.

- for most maqamat is typical interval augmented second, used at least in one tetrachord. Only some maqamat are same as Greek/Western modes and use only whole tones and halftones.

Check for example here:

http://www.maqamworld.com/maqamat.html

Daniel Forro

P.S.: Scales 7 and 8 in Third Group are the same. Mistake?

On 6 Mar, 2014, at 11:27 PM, <calebmrgn@...> <calebmrgn@...> wrote:

>
>With the help of a programmer, I've put together a list of 7-note scales having 1 or more quarter-tones. 
>There are certain restrictions.  With those restrictions, it seems that there are 64 such scales total, which can be grouped into 10 groups.  The groupings are by intervallic content:  By rotations (meaning the same thing as modal shifts) and by inversion (meaning the same interval list backwards.)  I have yet to confirm that there are exactly 64 -- I might have mistakenly left a few out, or something. (If anyone who understands the procedures here wishes to check to see if anything's missing, let me know.)
>
>
>Now, here is my question, asked with some trepidation:
>
>
>****To what maqams do these pitch-sets more-or-less correspond?****  
>
>
>The reason I ask is not to delve very deeply into the world of Arabic music.  It's way too deep.  For example, I'm aware that maqams are much more than mere unordered sets of pitches.  I'm also aware that the actual practice of tuning is not well-expressed by quarter-tones.
>
>
>Rather, I thought that the list would be more useful if there were some names of maqams that could be the beginning of links to further research -- just as A,B,C,D,E,F#,G could be linked to "Dorian" without that being an adequate explanation.
>
>
>Here is the list.  A minus sign (-) means the pitch is a quarter-tone lower.   Scales under a line ( ----)
>
>means the sets are related by inversion.  The order and numbering of the groups are arbitrary; there is nothing inherently "first" about the group called "First".  However, again, the groups are carefully chosen and clumped together by ordered interval content.
>
>
>First Group
>A,C-,D,D#,F,F#,G# 
>A,B,C,D#-,F,F#,G# 
>A,B,C,D,D#,F#-,G# 
>A,Bb,C#-,D#,E,F#,G 
>A,Bb,C,C#,D#,E,G- 
>
>
>
>
>Second Group
>A,C-,C#,D#,F,F#,G# 
>A,B,C,D#-,E,F#,G# 
>A,B,C#,D,E,F,G#- 
>A,Bb,C#-,D,E,F#,G 
>A,B,C,D,D#,F#-,G 
>-------------------
>A,B,C#,D#-,F,F#,G# 
>A,B,C,D,E,F#-,G# 
>A,B,C#-,D#,E,F#,G
>A,B-,C#,D,E,F,G
>A,Bb,C,C#,D#,F,G-
>
>
>
>
>Third Group
>A,C-,C#,D#,E,F#,G#
>A,B,C,D,E,F,G#-
>A,B,C,D#-,E,F#,G
>A,Bb,C,D,D#,F#-,G
>A,Bb,C#-,D,E,F,G
>-----------------
>A,B,C#-,D#,E,F#,G#
>A,B,C#,D,E,F#-,G#
>A,B,C#,D,E,F#-,G#
>A,B-,C#,D,E,F#,G
>A,Bb,C,D-,E,F,G
>A,Bb,C,D,D#,F,G-
>
>
>
>
>Fourth Group
>A,B,C#,D#-,E,F#,G#
>A,B,C#,D,E,F#,G#-
>A,B,C,D,E,F#-,G
>------------------------
>A,B,C#-,D,E,F#,G
>A,B-,C,D,E,F,G
>
>
>
>
>Fifth Group
>
>
>A,B,C#-,D,E,F#,G#
>A,B,C#,D#,E,F#,G#-
>A,B,C#,D,E,F#-,G
>-----------------
>A,B,C,D,E,F#,G#-
>A,B,C#,D#-,E,F#,G
>A,Bb,C,D,E,F#-,G
>A,B,C#-,D,E,F,G
>A,B-,C,D,D#,F,G
>A,Bb,C,D-,D#,F,G
>
>
>
>
>Sixth Group
>A,B,C#-,D,E,F#-,G#
>A,B-,C#,D,E,F#-,G
>A,Bb,C,D-,D#,F,G-
>------------------------
>A,Bb,C#-,D,E,F#-,G
>
>
>
>
>Seventh Group
>A,B,C#-,D,E,F,G#
>A,B,C,D#,E,F#,G#-
>A,Bb,C#,D,E,F#-,G
>A,Bb,C,D-,D#,F,F#
>------------------------
>A,B-,C,D,D#,F#,G
>
>
>
>
>Eighth Group
>A,B,C#,D#-,E,F#,G#-
>A,B,C#-,D,E,F#,G#-
>A,B-,C#-,D#-,E,F#-,G#-
>A,B,C#-,D,E,F#-,G
>-----------------------
>A,B-,C,D,E,F#-,G
>
>
>
>
>Ninth Group
>A,B,C#-,D#-,E,F#,G#-
>A,B,C#-,D#-,E,F#-,G#-
>A,B,C#-,D,E,F#-,G#-
>--------------------
>A,B-,C#-,D,E,F#-,G#-
>A,B-,C#-,D,E,F#-,G
>
>
>
>
>Tenth Group
>
>
>A,B,C,D#-,E,F#,G#-
>A,B,C#-,D,E,F,G#-
>A,B-,C,D,D#,F#-,G
>------------------
>A,C-,C#-,D#-,E,F#-,G#-

🔗Caleb Morgan <calebmrgn@...>

3/6/2014 8:35:32 AM

Oh, and thanks for the link.  I'd looked at this.  I'll look again.

My intent here is *not* to generate maqams, exactly.

The list is for my own composition, and I explicitly want to *avoid* sounding like I'm trying to make Arabic music.

My intent is to generate all the possible 7-note scales with at least 1 quarter tone, no more than a certain number of 650 or 750-cent intervals (mod 24), nothing at 1150, 150, 650, or 750 cents, and no 3 pitches occupying a space of less than 7 quarter-tones.

There are no 7-note scales having a quarter-tone that do not have at least 1 "near 5th", so adjusting how many of those "wolves" (or perhaps "dingos" -- because they're not exactly wolves) affects how many scales the computer program will find.  It's just brute-force generate and test.

Out of these 63-or-so scales, some will match maqams.  It would be helpful to know which ones.

I can start to fill this in based on the information in the link.  But I'd rather ask someone.

Someone could look at my list, and say, "Ah yes, this one is Rast", or something.

The link tells me a great deal more, and a great deal less than I want to know for now.

On Thursday, March 6, 2014 11:17 AM, Caleb Morgan <calebmrgn@...> wrote:

 
Just a quick response for now.

Good catch on the duplicate!

That was indeed a mistake.

I need to get the programmer to modify the program, and confirm how many such scales there are.

Make it 63, for now.

On Thursday, March 6, 2014 10:56 AM, Daniel Forró <dan.for@...> wrote:

 
Just few points. 

I don't see much similarity:
- not all maqamat use quarter tones

- when yes, usually only one, maximally two, and tuning is not exact

- only few notes can have quarter tone accidentals, usually E, A, B

- even tonic can be shifted quarter tone down  

- most maqamat have as a dominant fifth (like in Greek/Western modes), or fourth (in hypo- types) - at least one of these tones is there, or even both. Only few maqamat have together with one of these tones augmented fourth (or diminished fifth). I'm not aware about some maqam which would not have this structure and ignore it (by using quarter tones in the place of these important tones, or omit them somehow, for example by whole tone steps). Some of your scales have such structure.

- for most maqamat is typical interval augmented second, used at least in one tetrachord. Only some maqamat are same as Greek/Western modes and use only whole tones and halftones.

Check for example here:

http://www.maqamworld.com/maqamat.html

Daniel Forro

P.S.: Scales 7 and 8 in Third Group are the same. Mistake?

On 6 Mar, 2014, at 11:27 PM, <calebmrgn@...> <calebmrgn@...> wrote:

>
>With the help of a programmer, I've put together a list of
7-note scales having 1 or more quarter-tones. 
>There are certain restrictions.  With those restrictions, it seems that there are 64 such scales total, which can be grouped into 10 groups.  The groupings are by intervallic content:  By rotations (meaning the same thing as modal shifts) and by inversion (meaning the same interval list backwards.)  I have yet to confirm that there are exactly 64 -- I might have mistakenly left a few out, or something. (If anyone who understands the procedures here wishes to check to see if anything's missing, let me know.)
>
>
>Now, here is my question, asked with some trepidation:
>
>
>****To what maqams do these pitch-sets more-or-less correspond?****  
>
>
>The reason I ask is not to delve very deeply into the world of Arabic music.  It's way too deep.  For example, I'm aware that maqams are much more than mere unordered sets of pitches.  I'm also aware that the actual practice of tuning is not well-expressed by quarter-tones.
>
>
>Rather, I thought that the list would be more useful if there were some names of maqams that could be the beginning of links to further research -- just as A,B,C,D,E,F#,G could be linked to "Dorian" without that being an adequate explanation.
>
>
>Here is the list.  A minus sign (-) means the pitch is a quarter-tone lower.   Scales under a line ( ----)
>
>means the sets are related by inversion.  The order and numbering of the groups are arbitrary; there is nothing inherently "first" about the group called "First".  However, again, the groups are carefully chosen and clumped together by ordered interval content.
>
>
>First Group
>A,C-,D,D#,F,F#,G# 
>A,B,C,D#-,F,F#,G# 
>A,B,C,D,D#,F#-,G# 
>A,Bb,C#-,D#,E,F#,G 
>A,Bb,C,C#,D#,E,G- 
>
>
>
>
>Second Group
>A,C-,C#,D#,F,F#,G# 
>A,B,C,D#-,E,F#,G# 
>A,B,C#,D,E,F,G#- 
>A,Bb,C#-,D,E,F#,G 
>A,B,C,D,D#,F#-,G 
>-------------------
>A,B,C#,D#-,F,F#,G# 
>A,B,C,D,E,F#-,G# 
>A,B,C#-,D#,E,F#,G
>A,B-,C#,D,E,F,G
>A,Bb,C,C#,D#,F,G-
>
>
>
>
>Third Group
>A,C-,C#,D#,E,F#,G#
>A,B,C,D,E,F,G#-
>A,B,C,D#-,E,F#,G
>A,Bb,C,D,D#,F#-,G
>A,Bb,C#-,D,E,F,G
>-----------------
>A,B,C#-,D#,E,F#,G#
>A,B,C#,D,E,F#-,G#
>A,B,C#,D,E,F#-,G#
>A,B-,C#,D,E,F#,G
>A,Bb,C,D-,E,F,G
>A,Bb,C,D,D#,F,G-
>
>
>
>
>Fourth Group
>A,B,C#,D#-,E,F#,G#
>A,B,C#,D,E,F#,G#-
>A,B,C,D,E,F#-,G
>------------------------
>A,B,C#-,D,E,F#,G
>A,B-,C,D,E,F,G
>
>
>
>
>Fifth Group
>
>
>A,B,C#-,D,E,F#,G#
>A,B,C#,D#,E,F#,G#-
>A,B,C#,D,E,F#-,G
>-----------------
>A,B,C,D,E,F#,G#-
>A,B,C#,D#-,E,F#,G
>A,Bb,C,D,E,F#-,G
>A,B,C#-,D,E,F,G
>A,B-,C,D,D#,F,G
>A,Bb,C,D-,D#,F,G
>
>
>
>
>Sixth Group
>A,B,C#-,D,E,F#-,G#
>A,B-,C#,D,E,F#-,G
>A,Bb,C,D-,D#,F,G-
>------------------------
>A,Bb,C#-,D,E,F#-,G
>
>
>
>
>Seventh Group
>A,B,C#-,D,E,F,G#
>A,B,C,D#,E,F#,G#-
>A,Bb,C#,D,E,F#-,G
>A,Bb,C,D-,D#,F,F#
>------------------------
>A,B-,C,D,D#,F#,G
>
>
>
>
>Eighth Group
>A,B,C#,D#-,E,F#,G#-
>A,B,C#-,D,E,F#,G#-
>A,B-,C#-,D#-,E,F#-,G#-
>A,B,C#-,D,E,F#-,G
>-----------------------
>A,B-,C,D,E,F#-,G
>
>
>
>
>Ninth Group
>A,B,C#-,D#-,E,F#,G#-
>A,B,C#-,D#-,E,F#-,G#-
>A,B,C#-,D,E,F#-,G#-
>--------------------
>A,B-,C#-,D,E,F#-,G#-
>A,B-,C#-,D,E,F#-,G
>
>
>
>
>Tenth Group
>
>
>A,B,C,D#-,E,F#,G#-
>A,B,C#-,D,E,F,G#-
>A,B-,C,D,D#,F#-,G
>------------------
>A,C-,C#-,D#-,E,F#-,G#-

🔗Caleb Morgan <calebmrgn@...>

3/6/2014 8:38:43 AM

Oh, error in previous email.  That should have been nothing at 50 cents, not 150 cents.

On Thursday, March 6, 2014 11:35 AM, Caleb Morgan <calebmrgn@...> wrote:

Oh, and thanks for the link.  I'd looked at this.  I'll look again.

My intent here is *not* to generate maqams, exactly.

The list is for my own composition, and I explicitly want to *avoid* sounding like I'm trying to make Arabic music.

My intent is to generate all the possible 7-note scales with at least 1 quarter tone, no more than a certain number of 650 or 750-cent intervals (mod 24), nothing at 1150, 150, 650, or 750 cents, and no 3 pitches occupying a space of less than 7 quarter-tones.

There are no 7-note scales having a quarter-tone that do not have at least 1 "near 5th", so adjusting how many of those "wolves" (or perhaps "dingos" -- because they're not exactly wolves) affects how many scales the computer program will find.  It's just brute-force generate and test.

Out of these 63-or-so scales, some will match maqams.  It would be helpful to know which ones.

I can start to fill this in based on the information in the link.  But I'd rather ask someone.

Someone could look at my list, and say, "Ah yes, this one is Rast", or something.

The link tells me a great deal more, and a great deal less than I want to know for now.

On Thursday, March 6, 2014 11:17 AM, Caleb Morgan <calebmrgn@yahoo.com> wrote:

 
Just a quick response for now.

Good catch on the duplicate!

That was indeed a mistake.

I need to get the programmer to modify the program, and confirm how many such scales there are.

Make it 63, for now.

On Thursday, March 6, 2014 10:56 AM, Daniel Forró <dan.for@tiscali.cz> wrote:

 
Just few points. 

I don't see much similarity:
- not all maqamat use quarter tones

- when yes, usually only one, maximally two, and tuning is not exact

- only few notes can have quarter tone accidentals, usually E, A, B

- even tonic can be shifted quarter tone down  

- most maqamat have as a dominant fifth (like in Greek/Western modes), or fourth (in hypo- types) - at least one of these tones is there, or even both. Only few maqamat have together with one of these tones augmented fourth (or diminished fifth). I'm not aware about some maqam which would not have this structure and ignore it (by using quarter tones in the place of these important tones, or omit them somehow, for example by whole tone steps). Some of your scales have such structure.

- for most maqamat is typical interval augmented second, used at least in one tetrachord. Only some maqamat are same as Greek/Western modes and use only whole tones and halftones.

Check for example here:

http://www.maqamworld.com/maqamat.html

Daniel Forro

P.S.: Scales 7 and 8 in Third Group are the same. Mistake?

On 6 Mar, 2014, at 11:27 PM, <calebmrgn@...> <calebmrgn@...> wrote:

>
>With the help of a programmer, I've put together a list of
7-note scales having 1 or more quarter-tones. 
>There are certain restrictions.  With those restrictions, it seems that there are 64 such scales total, which can be grouped into 10 groups.  The groupings are by intervallic content:  By rotations (meaning the same thing as modal shifts) and by inversion (meaning the same interval list backwards.)  I have yet to confirm that there are exactly 64 -- I might have mistakenly left a few out, or something. (If anyone who understands the procedures here wishes to check to see if anything's missing, let me know.)
>
>
>Now, here is my question, asked with some trepidation:
>
>
>****To what maqams do these pitch-sets more-or-less correspond?****  
>
>
>The reason I ask is not to delve very deeply into the world of Arabic music.  It's way too deep.  For example, I'm aware that maqams are much more than mere unordered sets of pitches.  I'm also aware that the actual practice of tuning is not well-expressed by quarter-tones.
>
>
>Rather, I thought that the list would be more useful if there were some names of maqams that could be the beginning of links to further research -- just as A,B,C,D,E,F#,G could be linked to "Dorian" without that being an adequate explanation.
>
>
>Here is the list.  A minus sign (-) means the pitch is a quarter-tone lower.   Scales under a line ( ----)
>
>means the sets are related by inversion.  The order and numbering of the groups are arbitrary; there is nothing inherently "first" about the group called "First".  However, again, the groups are carefully chosen and clumped together by ordered interval content.
>
>
>First Group
>A,C-,D,D#,F,F#,G# 
>A,B,C,D#-,F,F#,G# 
>A,B,C,D,D#,F#-,G# 
>A,Bb,C#-,D#,E,F#,G 
>A,Bb,C,C#,D#,E,G- 
>
>
>
>
>Second Group
>A,C-,C#,D#,F,F#,G# 
>A,B,C,D#-,E,F#,G# 
>A,B,C#,D,E,F,G#- 
>A,Bb,C#-,D,E,F#,G 
>A,B,C,D,D#,F#-,G 
>-------------------
>A,B,C#,D#-,F,F#,G# 
>A,B,C,D,E,F#-,G# 
>A,B,C#-,D#,E,F#,G
>A,B-,C#,D,E,F,G
>A,Bb,C,C#,D#,F,G-
>
>
>
>
>Third Group
>A,C-,C#,D#,E,F#,G#
>A,B,C,D,E,F,G#-
>A,B,C,D#-,E,F#,G
>A,Bb,C,D,D#,F#-,G
>A,Bb,C#-,D,E,F,G
>-----------------
>A,B,C#-,D#,E,F#,G#
>A,B,C#,D,E,F#-,G#
>A,B,C#,D,E,F#-,G#
>A,B-,C#,D,E,F#,G
>A,Bb,C,D-,E,F,G
>A,Bb,C,D,D#,F,G-
>
>
>
>
>Fourth Group
>A,B,C#,D#-,E,F#,G#
>A,B,C#,D,E,F#,G#-
>A,B,C,D,E,F#-,G
>------------------------
>A,B,C#-,D,E,F#,G
>A,B-,C,D,E,F,G
>
>
>
>
>Fifth Group
>
>
>A,B,C#-,D,E,F#,G#
>A,B,C#,D#,E,F#,G#-
>A,B,C#,D,E,F#-,G
>-----------------
>A,B,C,D,E,F#,G#-
>A,B,C#,D#-,E,F#,G
>A,Bb,C,D,E,F#-,G
>A,B,C#-,D,E,F,G
>A,B-,C,D,D#,F,G
>A,Bb,C,D-,D#,F,G
>
>
>
>
>Sixth Group
>A,B,C#-,D,E,F#-,G#
>A,B-,C#,D,E,F#-,G
>A,Bb,C,D-,D#,F,G-
>------------------------
>A,Bb,C#-,D,E,F#-,G
>
>
>
>
>Seventh Group
>A,B,C#-,D,E,F,G#
>A,B,C,D#,E,F#,G#-
>A,Bb,C#,D,E,F#-,G
>A,Bb,C,D-,D#,F,F#
>------------------------
>A,B-,C,D,D#,F#,G
>
>
>
>
>Eighth Group
>A,B,C#,D#-,E,F#,G#-
>A,B,C#-,D,E,F#,G#-
>A,B-,C#-,D#-,E,F#-,G#-
>A,B,C#-,D,E,F#-,G
>-----------------------
>A,B-,C,D,E,F#-,G
>
>
>
>
>Ninth Group
>A,B,C#-,D#-,E,F#,G#-
>A,B,C#-,D#-,E,F#-,G#-
>A,B,C#-,D,E,F#-,G#-
>--------------------
>A,B-,C#-,D,E,F#-,G#-
>A,B-,C#-,D,E,F#-,G
>
>
>
>
>Tenth Group
>
>
>A,B,C,D#-,E,F#,G#-
>A,B,C#-,D,E,F,G#-
>A,B-,C,D,D#,F#-,G
>------------------
>A,C-,C#-,D#-,E,F#-,G#-

🔗Daniel Forró <dan.for@...>

3/6/2014 8:47:54 AM

I would think you can get much more scales...

When we will not move tonic and dominant, and shift only the other 5 notes, there's 75 scales (similar to Indian raga theory).

Add quarter tones (on five basic notes and their nine possible chromatic shifts), and number of scales goes up. If my calculations are not wrong, there's:
75 x 5 = 375 scales with one quarter tone
75 x 10 = 750 scales with two quarter shifts
75 x 10 = 750 scales with three quarter shifts
75 x 5 = 375 scales with four quarter shifts
75 scales with five quarter shifts

Total number of possible scales is 2400.

Daniel Forro

On 7 Mar, 2014, at 1:17 AM, Caleb Morgan wrote:

>
>
> Just a quick response for now.
>
> Good catch on the duplicate!
>
> That was indeed a mistake.
>
> I need to get the programmer to modify the program, and confirm how > many such scales there are.
>
> Make it 63, for now.
>

🔗Caleb Morgan <calebmrgn@...>

3/6/2014 8:57:08 AM

Thanks for your response.

We're done, unless you have something that is again relevant, such as pointing out the duplicate scale in my list.

The reason what you're saying isn't relevant -- and therefore, is off-topic -- is that my restrictions are fairly carefully designed, but I'm still at an early stage.

It may well be that there are 75 scales according to my criteria, but that criteria is not raga theory, so that's irrelevant.

Thanks,

caleb

On Thursday, March 6, 2014 11:48 AM, Daniel Forró <dan.for@...> wrote:

 
I would think you can get much more scales...

When we will not move tonic and dominant, and shift only the other 5 notes, there's 75 scales (similar to Indian raga theory).

Add quarter tones (on five basic notes and their nine possible chromatic shifts), and number of scales goes up. If my calculations are not wrong, there's:
75 x 5 = 375 scales with one quarter tone
75 x 10 = 750 scales with two quarter shifts
75 x 10 = 750 scales with three quarter shifts
75 x 5 = 375 scales with four quarter shifts
75 scales with five quarter shifts

Total number of possible scales is 2400.

Daniel Forro

On 7 Mar, 2014, at 1:17 AM, Caleb Morgan wrote:

>
>
>Just a quick response for now.
>
>
>Good catch on the duplicate!
>
>
>That was indeed a mistake.
>
>
>I need to get the programmer to modify the program, and confirm how many such scales there are.
>
>
>Make it 63, for now.
>
>

🔗Daniel Forró <dan.for@...>

3/6/2014 8:58:48 AM

I see. It's interesting, and of course number of scales is not so
high, so checking which are similar to maqams is not so difficult. I
would check just those which have fourth or fifth (or both), or fourth
+ diminished fifth, or augmented fourth + fifth. Changing the tonic (=
root note) can help in some cases, because maqam structure can be
shifted (start from different root note).

Daniel Forro

On 7 Mar, 2014, at 1:38 AM, Caleb Morgan wrote:

>
>
> Oh, error in previous email. That should have been nothing at 50
> cents, not 150 cents.
>
>
> On Thursday, March 6, 2014 11:35 AM, Caleb Morgan
> <calebmrgn@...> wrote:
> Oh, and thanks for the link. I'd looked at this. I'll look again.
>
> My intent here is *not* to generate maqams, exactly.
>
> The list is for my own composition, and I explicitly want to *avoid*
> sounding like I'm trying to make Arabic music.
>
> My intent is to generate all the possible 7-note scales with at
> least 1 quarter tone, no more than a certain number of 650 or 750-
> cent intervals (mod 24), nothing at 1150, 150, 650, or 750 cents,
> and no 3 pitches occupying a space of less than 7 quarter-tones.
>
> There are no 7-note scales having a quarter-tone that do not have at
> least 1 "near 5th", so adjusting how many of those "wolves" (or
> perhaps "dingos" -- because they're not exactly wolves) affects how
> many scales the computer program will find. It's just brute-force
> generate and test.
>
> Out of these 63-or-so scales, some will match maqams. It would be
> helpful to know which ones.
>
> I can start to fill this in based on the information in the link.
> But I'd rather ask someone.
>
> Someone could look at my list, and say, "Ah yes, this one is Rast",
> or something.
>
> The link tells me a great deal more, and a great deal less than I
> want to know for now.
>
>
> On Thursday, March 6, 2014 11:17 AM, Caleb Morgan
> <calebmrgn@yahoo.com> wrote:
> Just a quick response for now.
>
> Good catch on the duplicate!
>
> That was indeed a mistake.
>
> I need to get the programmer to modify the program, and confirm how
> many such scales there are.
>
> Make it 63, for now.
>
>
> On Thursday, March 6, 2014 10:56 AM, Daniel Forró
> <dan.for@...> wrote:
>
> Just few points.
>
> I don't see much similarity:
> - not all maqamat use quarter tones
>
> - when yes, usually only one, maximally two, and tuning is not exact
>
> - only few notes can have quarter tone accidentals, usually E, A, B
>
> - even tonic can be shifted quarter tone down
>
> - most maqamat have as a dominant fifth (like in Greek/Western
> modes), or fourth (in hypo- types) - at least one of these tones is
> there, or even both. Only few maqamat have together with one of > these tones augmented fourth (or diminished fifth). I'm not aware
> about some maqam which would not have this structure and ignore it
> (by using quarter tones in the place of these important tones, or
> omit them somehow, for example by whole tone steps). Some of your
> scales have such structure.
>
> - for most maqamat is typical interval augmented second, used at
> least in one tetrachord. Only some maqamat are same as Greek/Western
> modes and use only whole tones and halftones.
>
> Check for example here:
>
> http://www.maqamworld.com/maqamat.html
>
> Daniel Forro
>
> P.S.: Scales 7 and 8 in Third Group are the same. Mistake?
>
>
> On 6 Mar, 2014, at 11:27 PM, <calebmrgn@...> <calebmrgn@...
> > wrote:
>
>>
>>
>> With the help of a programmer, I've put together a list of 7-note
>> scales having 1 or more quarter-tones.
>> There are certain restrictions. With those restrictions, it seems
>> that there are 64 such scales total, which can be grouped into 10
>> groups. The groupings are by intervallic content: By rotations
>> (meaning the same thing as modal shifts) and by inversion (meaning
>> the same interval list backwards.) I have yet to confirm that
>> there are exactly 64 -- I might have mistakenly left a few out, or
>> something. (If anyone who understands the procedures here wishes to
>> check to see if anything's missing, let me know.)
>>
>> Now, here is my question, asked with some trepidation:
>>
>> ****To what maqams do these pitch-sets more-or-less correspond?****
>>
>> The reason I ask is not to delve very deeply into the world of
>> Arabic music. It's way too deep. For example, I'm aware that
>> maqams are much more than mere unordered sets of pitches. I'm also
>> aware that the actual practice of tuning is not well-expressed by
>> quarter-tones.
>>
>> Rather, I thought that the list would be more useful if there were
>> some names of maqams that could be the beginning of links to
>> further research -- just as A,B,C,D,E,F#,G could be linked to
>> "Dorian" without that being an adequate explanation.
>>
>> Here is the list. A minus sign (-) means the pitch is a quarter-
>> tone lower. Scales under a line ( ----)
>> means the sets are related by inversion. The order and numbering
>> of the groups are arbitrary; there is nothing inherently "first"
>> about the group called "First". However, again, the groups are
>> carefully chosen and clumped together by ordered interval content.
>>
>> First Group
>> A,C-,D,D#,F,F#,G#
>> A,B,C,D#-,F,F#,G#
>> A,B,C,D,D#,F#-,G#
>> A,Bb,C#-,D#,E,F#,G
>> A,Bb,C,C#,D#,E,G-
>>
>>
>> Second Group
>> A,C-,C#,D#,F,F#,G#
>> A,B,C,D#-,E,F#,G#
>> A,B,C#,D,E,F,G#-
>> A,Bb,C#-,D,E,F#,G
>> A,B,C,D,D#,F#-,G
>> -------------------
>> A,B,C#,D#-,F,F#,G#
>> A,B,C,D,E,F#-,G#
>> A,B,C#-,D#,E,F#,G
>> A,B-,C#,D,E,F,G
>> A,Bb,C,C#,D#,F,G-
>>
>>
>> Third Group
>> A,C-,C#,D#,E,F#,G#
>> A,B,C,D,E,F,G#-
>> A,B,C,D#-,E,F#,G
>> A,Bb,C,D,D#,F#-,G
>> A,Bb,C#-,D,E,F,G
>> -----------------
>> A,B,C#-,D#,E,F#,G#
>> A,B,C#,D,E,F#-,G#
>> A,B,C#,D,E,F#-,G#
>> A,B-,C#,D,E,F#,G
>> A,Bb,C,D-,E,F,G
>> A,Bb,C,D,D#,F,G-
>>
>>
>> Fourth Group
>> A,B,C#,D#-,E,F#,G#
>> A,B,C#,D,E,F#,G#-
>> A,B,C,D,E,F#-,G
>> ------------------------
>> A,B,C#-,D,E,F#,G
>> A,B-,C,D,E,F,G
>>
>>
>> Fifth Group
>>
>> A,B,C#-,D,E,F#,G#
>> A,B,C#,D#,E,F#,G#-
>> A,B,C#,D,E,F#-,G
>> -----------------
>> A,B,C,D,E,F#,G#-
>> A,B,C#,D#-,E,F#,G
>> A,Bb,C,D,E,F#-,G
>> A,B,C#-,D,E,F,G
>> A,B-,C,D,D#,F,G
>> A,Bb,C,D-,D#,F,G
>>
>>
>> Sixth Group
>> A,B,C#-,D,E,F#-,G#
>> A,B-,C#,D,E,F#-,G
>> A,Bb,C,D-,D#,F,G-
>> ------------------------
>> A,Bb,C#-,D,E,F#-,G
>>
>>
>> Seventh Group
>> A,B,C#-,D,E,F,G#
>> A,B,C,D#,E,F#,G#-
>> A,Bb,C#,D,E,F#-,G
>> A,Bb,C,D-,D#,F,F#
>> ------------------------
>> A,B-,C,D,D#,F#,G
>>
>>
>> Eighth Group
>> A,B,C#,D#-,E,F#,G#-
>> A,B,C#-,D,E,F#,G#-
>> A,B-,C#-,D#-,E,F#-,G#-
>> A,B,C#-,D,E,F#-,G
>> -----------------------
>> A,B-,C,D,E,F#-,G
>>
>>
>> Ninth Group
>> A,B,C#-,D#-,E,F#,G#-
>> A,B,C#-,D#-,E,F#-,G#-
>> A,B,C#-,D,E,F#-,G#-
>> --------------------
>> A,B-,C#-,D,E,F#-,G#-
>> A,B-,C#-,D,E,F#-,G
>>
>>
>> Tenth Group
>>
>> A,B,C,D#-,E,F#,G#-
>> A,B,C#-,D,E,F,G#-
>> A,B-,C,D,D#,F#-,G
>> ------------------
>> A,C-,C#-,D#-,E,F#-,G#-
>
>
>
>
>
>
>
>
>
>