Re: Arabic music half flat accidental shape

[Hans Aberg]

On 20 Jan 2008, at 04:12, josephHarfouch wrote:

> > Is this what they use on
> >    http://www.maqamworld.com/
> > They also use some accidentals with up-/down-arrows.
>
> Yes, that's it. You can see it in Maqam Bayatti for example, and I  
> can now
> plot it for the occasional accidental using the function Valentin  
> gave me in
> his reply. Here's another link that shows some of the more common  
> maqams
> that are used in Arabic music.
>
> http://www.turath.org/ProfilesMenu.htm

Thank you. For the transpositions,
  http://www.turath.org/Resources/MaqamTrans.htm
see below.

> I haven't noticed the up/down usage in maqamworld, but probably I just
> missed it.

It is written above and below the notes, as in
  http://www.maqamworld.com/maqamat/sikah.html#sikah-baladi
Perhaps in order to indicate finer pitch adjustments for practice only.

> I've seen other notations such as the use of series of + and -
> used against notes to alter the pitch. The use of the flat, sharp,  
> half flat
> and half sharp, three quarter sharp  (I don't see the three quarter  
> flat
> being used much in arabic pieces) is fairly standard in Arabic music
> notation, and the same as the LilyPond display except for the half- 
> flat.

Good to know.

> > The name "tonic" usually implies harmony, so I think a word like
> > "final", "finalis", might be better.
>
> Thanks. The arabic word is "qarar" which means literally a decision  
> but in
> the music context it means roughly the resting or the settling  
> point, and
> there is no implication of harmony.

Persian music has more qualities: beginning note, stop note,  
alternate finalis (cofinalis). This is described in the book by  
Hormoz Farhat on Persian dastgah.

> > If I look at Maqamworld <http://www.maqamworld.com/>, the Bayati in D
> > has a flat on B. How is this written in notation? Is the Bb written
> > as a key signature, or is it always written as a temporary accidental
> > within the piece? Of it is Bayati in G, what is the key signature.
>
> The short answer is that it is written in the key signature, and  
> the key
> signature would modulate if you shift the finalis, but there is a long
> answer as well -).

So it is similar to that in the book by Hormoz Farhat.

> Here it is :
>
> I have been trying to work out the rules on this for the last few  
> days, but
> I don't think there are any that are set in stone,  so I've been going
> through example pieces and theory books that I have and looking for
> patterns. There are some inconsistencies even within the same book,  
> but
> there are also some patterns. I guess in the end, it doesn't matter  
> much how
> accidentals are marked if the composer or even the editor wishes to  
> change
> it, but here's what I found so far.

I have made a system for Persian dastgahs (see below), following the  
description in Hormoz Farhat's book. I am interested to know if a  
similar system works in Arab music.

> A key signature reflects a group or family of modes, so the family of
> Bayatti modes that have the same default finalis (re or e) would  
> all have
> the same key signature of mi half-flat  and si flat (e half-flat and b
> flat). So , if we take for example a Husseini maqam which is close  
> enough to
> Bayatti to be considered as a member of the same group, it would  
> usualy
> written with the key signature of Bayatti, and the  accidentals  
> where it
> differs from Bayatti are written in the body of the piece. Even  
> Saba that is
> sometimes considered in a different group from Bayatti is still  
> considered
> similar enough to have the same signature of Bayatti, and the  
> fourth note
> (sol) that is almost always flat is written as a flat throughout  
> the piece
> rather than in the key signature. This is in some way good news,  
> because it
> means that I only need to define few additional key signatures for  
> Arabic
> music, but can lead to somewhat  strange results, where sometimes a  
> note in
> the key signature is actually never played that way, and another  
> that is
> always an accidental is not in the key signature. It seems that in  
> the books
> I have seen at least, the key signature is used to indicate the  
> group or
> family.
>
> If we then take a family key signature such as Bayatti, and want  
> another
> finalis such as sol rather than re, then the key signature would be
> modulated, so it will be la half-flat, si flat, mi flat (a half- 
> flat, b
> flat, e flat), and husseini on sol if there is such a thing, or  
> saba on sol
> would have the same key signature.
>
> Even though the key signature indicates the group or the more maqam  
> in the
> group, rather than necessarily the particular maqam, the particular  
> mode or
> maqam is often indicated in the title of the piece, as well as the  
> form, so
> one piece for example would have a title of "Longa Saba" and a key  
> signature
> of bayatti. Here Longa indicates the form, and Saba the maqam.
>
> I think that most of  these pieces that I'm looking at in Oud  
> instruction
> books, have a Turkish origin, given  the names of the forms and the  
> authors.
> It is not usual in Arabic culture, to adopt forms from other  
> cultures, and
> then change them drastically, so I would just guess, but I'm not  
> sure, that
> the practices in writing Arabic music, the names of maqams, and so  
> on, are
> not very different from what is used in Turkish music, although  
> there is
> usually no attempt  in Arabic music, as I mentioned previously, to  
> indicate
> microtones precisely.

Arab, Persian and Turkish music all seem to derive from the  
Pythagorean tuning, but took a different path than Western music. The  
Pythagorean tuning is built up around the minor second m = m2 =  
256/243, and the major second M = M2 = 9/8. It is easily understood  
in 53-equal temperament, where the tonesteps are called "commas" - 53- 
equal is such a good approximation, that for practical purposes, it  
is Pythagorean tuning. (Historically, if one iterates the rational  
interval 3/2, the perfect fifth, one arrives at 12, 41, and 53-equal;  
or use continued fractions on log_2 3/2.) In 53-equal, m = 4 and M =  
9 commas.

Now, the traditional Western key signatures with sharps # and flats b  
only work in a true diatonic scale - scales made up of exactly two  
intervals, not as in Just intonation, where there are three (wide and  
narrow whole tones). Then it is easy to see that one must have
  # = b = M - m
In 53-equal
  # = b = M - m = 9 - 4 = 5
So, in fact, in Pythagorean tuning and 53-equal, sharps and flats are  
wider than the half-tone m, and a doubleflat or a doublesharp is  
wider than a whole tone M. (So, for example, F# is higher than Gb.)

Now, one of the Turkish 53-equal systems makes the mistake of setting  
sharps and flats equal, so that, for example F# = Gb. It means that  
this notation is not transposable. (Of course, Arab music avoid the  
problem by not assigning specific pitches - I just want to point out  
a pitfall.)

Now, in Hormoz Farhat describes Persian music as having additional  
intervals
  n   small neutral
  N   large neutral
  P   plus-tone
The way he uses them, they should satisfy the relations
  n + N = M + m
  n + P = 2M
He writes out the intervals of the dastgah, along with notation with  
microtone lowering koron and raising sori, which I will write as
  p  koron
  >  sori
From the way he uses them, one can see that
  p = M - n
  b = # = M - m = p + >
It follows that if one fixes the size of one of the p, >, n, N, P,  
assuming that m, M have been fixed, the others can be computed.

Now, when I computed it, I got koron p = 3 commas. Then sori > = # -  
p = 5 - 3 = 2 commas. So koron lowers with an amount different than  
sori raises. This seems to be a new thing - experts of the past seems  
to have jumped to the conclusion that they are the same amounts. But  
they have a different musical function, indicating intervals  
different from m and M, from sharps of flats, which are used to  
indicate transpositions.

Now, the Western key signatures can be computed from the following  
diagram:
  Fb Cb Gb Db Ab Eb Bb
  F  C  G  D  A  E  B
  F# C# G# D# A# E# B#
View this as a single line, wrapping around downwards at the end of  
the lines. Then raising a perfect fifth moves the pitches forward/ 
down the line. And lowering a perfect fifth moves the pitches back/up  
on the line. If the set of pitches in the middle row are shifted, the  
pithes of the staff lines, then you will get the key signatures.

Now, for the koron and sori, do the same:
  Fp Cp Gp Dp Ap Ep Bp
  F> C> G> D> A> E> B>
The relation
  p + > = # = b
ensures that it works correctly.

Now, try working through the maqams you know, using
  F- C- G- D- A- E- B-
  F+ C+ G+ D+ A+ E+ B+
where
  -  halfflat
  +  halfsharp

Does this work?

> > Otherwise, have you looked at the church modes? If you take the C
> > major scale, there is a church mode with a final for each of the
> > scale degrees, indicating the final(is).
>
> The finalis problem is not such a big deal now that I understand the
> grouping of key signatures,
> so now I can say
>
> \key re \bayatti
>
> and
>
> \key sol \bayatti
>
> ideally, I should be able to omit the re, since it is the default
> NOTENAME_PITCH but it is not a big deal.

The Persian music, using the system above, is fully transposable. So  
the key signature note name should be there, I think.

The same applies to Arab music: it may not be transposed much, due to  
actual practice and limitations of musical instruments, but if there  
is an underlying transposable theory, then the key signature note  
name, or "key" for short, should be there.

> > And in Persian music, one uses koron and sori pasted into the Western
> > key signatures. So if this would be used with Bayati in D, it would
> > have a key signature consisting of Bb plus a E-halfflat.
>
> Yes, that's right, but I don't quit understand how korons and  
> sori's come
> into it, but I'll look into Persian music sometime.

Look into the book by Hormoz Farhat. The things he writes there seems  
to be similar to Balkan music, and perhaps for Arab and Turkish music.

> btw, I enjoyed your
> reference to turkish maqam theory, although it is quite complex,  
> and there
> is as always a background of theory to learn, before I can  
> understand this
> too.

As the reference noted, there are problems with the Turkish  
notational systems, such as that one of them is not transposable.  
Therefore I am interested to know if my suggestion above woks for  
Arab music.

  Hans Åberg