fernandoamartin - 8-28-2016 at 09:22 AM
There are countless discussions about intonation in arabic music. Most of them are about Eb in nahawand, E1/2b in rast and bayati, lowered 3rd in
jiharkah and ajam etc. The most common answers are that it has to be learned by ear and changes over time and from place to place.
However, if we go further into the past we find that arabic and european music have roots in the studies of the greeks. For example, the concept of
authentic and plagal modes with dominant and final notes is very similar to the way some maqamat are built and played.
Then, arabic music was already well structured when the idea of equal temperament dominated western music and also influenced arabic music. Now we
find much information about how just intonation, pythagorean intonation and others that were used in european from medieval to baroque. But what about
arabic music? What intonation system did it use before equal temperament became famous? I don't think it's reasonable to believe that aside the
"micro-tunes" of arabic music all the other notes would have to be equally tempered.
For example: If we take the following common just intonatation scale we have a Jiharkah (or Ajam Ashyran) maqam. Better yet is that many sources claim
that the third of ajam or jiharkah is lowered and in the intonation bellow we can form ajam jins in the 1st, in the 4th and in the 5th and all of them
will have the 3rd note a little lowered. Very nice! 
0: 1/1 0.000000
1: 16/15 111.731285
2: 9/8 203.910002
3: 6/5 315.641287
4: 5/4 386.313714
5: 4/3 498.044999
6: 45/32 590.223716
7: 3/2 701.955001
8: 8/5 813.686286
9: 5/3 884.358713
10: 16/9 996.089998
11: 15/8 1088.268715
12: 2/1 1200.000000
But now if take the same scale above and lower the 3rd and the 7th by one comma (+/-22cents), we get a good rast scale. But this rast would have a
jins rast in C with notes reasonably tuned in place and a second rast jins in G where the A would be lowered to 884.358713, something that doesn't
have much to do with rast.
Then here are the questions: Arabic music is older then equal temperament. What intonation systems did they use for natural notes (that is C, D, E, F,
G, A, B, leaving aside the quarter-tones)? Does just intonation, pythagorean intonation or other similar systems work nicely in arabic music? Did
arabs had their own intonation systems? What intonation systems may work better for traditional arabic music?
Brian Prunka - 9-2-2016 at 06:53 PM
Pythagorean is a form of just intonation (JI); it is 3-limit JI, referring to the limit of the third harmonic, which generates a P12th above the
fundamental (or a P5th if we compress the octaves). All the chromatic tones in Pythagorean tuning are generated by P5ths and octaves.
The usual JI we refer to is 5-limit JI, which allows up to the 5th harmonic (so both P5ths, M3rds and octaves are used).
The descriptions of the positions of the "natural" notes (from a wester perspective) in old Arabic sources (Farabi, etc.) which describe fret
placement seem to suggest that it is primarily Pythagorean. However, many maqamat evolved to use further adjustments. For example, Jiharkah has both
a lowered third and 4th degree and a "quarter tone" for the 7th.
Since the oud is tuned in 4ths, a Pythagorean basis is very obvious and logical. However, the primacy of vocal music in the Arab tradition means that
intonation is far more complex than simple instrument mechanics would suggest.
If you consider the notes C D F G A you get a very obvious Pythagorean arrangement:
F C G D A, coincidentally (or not) the common tuning of the oud's open strings. The E and B are less obviously connected. And again coincidentally
(or not) these are the tones with the most variation in intonation.
In practice, the intonation must be learned by ear, and the "E" used in Ajam on C will be different than the one used in Kurd on A or Hijaz on C.
fernandoamartin - 9-14-2016 at 11:17 AM
Thank you Brian for your very clarifying answer.
Really C D F G A seem to be the most "stable" notes in maqamat. And they really fit well to pythagorean tuning.
E and B seem to completely "unstable" points and most intonation discussions revolve around them.
IF we take each jins that form a maqam into account we really find the need to adjust some notes.
But pythagorean C D F G A seem to be a nice idea where no further adjustment is needed.
Thank you.