Arabic scales & cent calculations

> Hi, colleagues:
>
> Has anyone a convenient description of the intervals in the
> typical Arabic scale? I hear Arabic music frequently on the
> shortwave radio (as connected to a large sound system).
>
> Also, has anyone a formula for converting frequency ratios to
> "cent" values? I frequently notice ratios expressed in terms of
> unity as the base such that the fifth is at 1.5 in just tuning or
> slightly less than that in equal temperament.
>
> Thanks, Peter
>
>
>
> Peter Weeks
> St.Thomas University
> Fredericton, N.B., Canada
> Email PWEEKS@StThomasU.ca
>
> Peter Weeks
> St.Thomas University
> Fredericton, N.B., Canada
> Email PWEEKS@StThomasU.ca

Ratio to cents conversion
-------------------------

cents = 3986.313714 � log10(ratio)

log10(n) means, "log base 10 of (n)."

Cents to ratio conversion
-------------------------

ratio = 10 ^ (0.000250858 � cents)

^ means, "raised to the power of."

---
Glen Peterson
30 Elm Street North Andover, MA 01845
(978) 975-1527
http://www.OrganicDesign.org/Glen/Instruments

> -----Original Message-----
> From: weekswyl [mailto:weekswyl@nbnet.nb.ca]
> Sent: Monday, August 30, 1999 11:47 PM
> To: tuning@onelist.com
> Subject: [tuning] Arabic scales & cent calculations
>
>
> From: "weekswyl" <weekswyl@nbnet.nb.ca>
>
>
> > Hi, colleagues:
> >
> > Has anyone a convenient description of the intervals in the
> > typical Arabic scale? I hear Arabic music frequently on the
> > shortwave radio (as connected to a large sound system).
> >
> > Also, has anyone a formula for converting frequency ratios to
> > "cent" values? I frequently notice ratios expressed in terms of
> > unity as the base such that the fifth is at 1.5 in just tuning or
> > slightly less than that in equal temperament.
> >
> > Thanks, Peter
> >
> >
> >
> > Peter Weeks
> > St.Thomas University
> > Fredericton, N.B., Canada
> > Email PWEEKS@StThomasU.ca
> >
> > Peter Weeks
> > St.Thomas University
> > Fredericton, N.B., Canada
> > Email PWEEKS@StThomasU.ca
>
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> Has anyone a convenient description of the intervals in the
> typical Arabic scale? I hear Arabic music frequently on the
> shortwave radio (as connected to a large sound system).

Although medieval Arabic scales were described in terms of a Pythagorean
scale extended to 17 notes, most modern Arabic music is built on
quartertones. Manuel's list includes the following scales (in quartertones):

4 3 3 4 4 3 3 Arabic Diatonic, Maqam Rast
3 4 4 3 3 4 3 Maqam Sikah
4 3 3 4 3 3 4 Miha'il Musaqa's mode: Egyptian
3 3 4 4 2 4 4 Maqam 'Ushshaq Turki
3 3 4 4 2 1 3 4 Maqam Bayati
3 3 2 6 2 4 4 Maqam Saba, Maqam Mansuri
4 3 3 4 2 6 2 Maqam Suznak (Soznak)
4 3 3 4 4 2 1 3 Maqam Mahur, Maqam Dilkashidah, Maqam Rast
4 3 1 2 1 3 4 2 1 3 Maqam Yakah
3 3 4 2 6 2 4 Maqam Qarjighar
3 4 2 2 2 2 2 4 3 Maqam Huzam
3 4 2 6 2 4 3 Maqam Hizam
2 6 2 4 2 1 3 4 Maqam Hijaz
3 4 4 2 1 3 4 3 Maqam Musta'ar
3 2 6 2 4 4 3 Maqam 'Iraq
5 2 4 2 4 4 3 Maqam Bastanikar
4 2 6 2 4 2 1 3 Maqam Farah Faza, Maqam Nakriz
4 2 1 3 2 2 2 2 3 1 2 Maqam Hayyan
4 2 1 3 2 2 4 2 1 3 Maqam Basandida
4 4 2 1 3 2 2 4 2 Maqam Shawq Afza
2 1 3 2 2 4 2 4 2 2 Maqam Shawq Tarab
3 1 2 1 4 4 2 4 4 Maqam Jabburi
2 4 4 4 3 3 4 Maqam Nawa
2 5 3 4 2 5 3 Maqam Higaz-kar
3 4 4 2 4 4 3 Maqam Su'ar
3 6 1 5 2 6 1 Maqam Aug-ara
4 1 5 4 2 6 2 Maqam Buselik
4 2 6 2 2 5 3 Maqam Neuter

> Also, has anyone a formula for converting frequency ratios to
> "cent" values? I frequently notice ratios expressed in terms of
> unity as the base such that the fifth is at 1.5 in just tuning or
> slightly less than that in equal temperament.

The formula is cents=log(ratio)/log(2)*1200.

"Paul H. Erlich" wrote:

> Although medieval Arabic scales were described in terms of a Pythagorean
> scale extended to 17 notes, most modern Arabic music is built on
> quartertones. Manuel's list includes the following scales (in quartertones):

maybe some but not most. As I said before I have many,many examples of recent
recordings (over 60) with pictures of the instruments with 17 frets, none with
equally spaced fretting. I am sure you can find some pop belly dance stuff in
this but it is not representative of anything.

-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

I wrote,

>> Although medieval Arabic scales were described in terms of a Pythagorean
>> scale extended to 17 notes, most modern Arabic music is built on
>> quartertones. Manuel's list includes the following scales (in
quartertones):

Kraig Grady wrote,

>As I said before I have many,many examples of recent
>recordings (over 60) with pictures of the instruments with 17 frets, none
with
>equally spaced fretting.

If you have 17 frets chosen from quartertones, they won't be equally spaced.

Paul!
Do you really think I can't hear the difference much less see the
difference?

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> I wrote,
>
> >> Although medieval Arabic scales were described in terms of a Pythagorean
> >> scale extended to 17 notes, most modern Arabic music is built on
> >> quartertones. Manuel's list includes the following scales (in
> quartertones):
>
> Kraig Grady wrote,
>
> >As I said before I have many,many examples of recent
> >recordings (over 60) with pictures of the instruments with 17 frets, none
> with
> >equally spaced fretting.
>
> If you have 17 frets chosen from quartertones, they won't be equally spaced.
>
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-- Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com

Kraig Grady wrote,

>Paul!
> Do you really think I can't hear the difference much less see the
>difference?

Of course you can. I didn't mean to insult your intelligence. Clearly there
are dozens of distinct musical cultures within the Arabic world, and perhaps
as many schemes for fretted instruments. Although quartertones have become
"standard", you Kraig may be lucky enough to have recordings representing
older, more local traditions. Also, there is the question of what is
considered "Arabic" -- for example, where do you draw the lines between the
Turkish or Armenian worlds and the Arabic world?