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8/2: Arabic Theorists

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Chapter 8: Ancient Scales and Modes: Middle East

*Simple* [more ancient scales you can hear]

Each sound on each tongue is Love singing a song to its own ears. – Fakruddin Araqi

As I explore the many ancient cultures, I often wonder how much interaction the theorists of each culture had with each other. With Middle Eastern music, I believe a case can be made that there was cross-fertilization of musical thought with both the West (the Greeks and their musical protégés) and the East (India). Theirs is a rich intellectual, emotional and spiritual tradition which is still alive today.

The Arabian theorist Al-Farabi (~900-950 A.D.) incorporated Ptolemy’s musical systems into his own, accepting 5-limit harmonies such as the major and minor thirds (5/4 and 6/5) into Arabic musical tradition. Ibn Sina (980-1037) and Safi Al-Din (d. 1294) classified these ratios as bona fide consonances as well.

Around 700 A.D., Zalzal the Lutenist reformed the tuning systems of the Middle East, incorporating many 5th, 7th and 11th-harmonic ratios. Some lineages of Middle Eastern music theory employ 24-eq or quarter-tone scales, but like everywhere else, musicians themselves tend to instinctively hit the “sweet spots” which actually land near the “quarter tone” only when they are evoking 11-limit harmonies.  Many theorists after Zalzal stayed in the Pythagorean or 24-eq mold; the ruling Arab families of the 8th through 14th century hired teams of translators to preserve the ancient Greek writings, including those of Pythagoras.

The tenth century theorist Al-Farabi agreed with the 8th century Zalzal and also advocated five-limit harmonic theory.  Al-Farabi also described a lute with 22 unequal frets in an octave. The eleventh century Ibn Sina and the 13th century Safi Al-Din said the same.

Performers and singers tended to play the five-limit harmonies just because they sound so good, whatever theorists of the time may have said. In the 13th and 14th centuries, Mahmoud and Abdulqadir tried to bring Middle Eastern music back into line with Pythagoras. Here again is their system of seventeen perfect fifths (fifths up and fourths down because seventeen fifths up is just too many octaves), sometimes built off of D or more often G: (Figure 8-1)

Gb – Db – Ab – Eb – Bb – F – C – G – D – A – E – B – F# – C# – G# – D# – A#

Since the 3-limit Gb and the 5-limit F1# have almost identical pitches (they create the Skhisma, or 2-cent gap), a seventeen – note Pythagorean system that effectively allows for some very close enharmonic equivalences of several  5-limit relationships. Since oud players perform with an instinct for those harmonic “sweet spots” as do sitar players from India, dulcimerists from China, and singers and string players in the West, the 17-note Pythagorean system still allowed musicians to go on playing what naturally sounded the best. (Figure 8-2) Pythagoreanizing the 5-limit scales

.                                                      F1# C1#  G1# D1#  A1#

.                                                        |      |       |      |       |

.Gb-  Db-  Ab-   Eb-    Bb- F- C- G- D–   A-    E-    B-   F#-   A#-   D#-   A#

Mikha’il Mishaqa is credited with describing a 24-eq scale for Arabic music, but his “Essay on the Art of Music” showed that his own measurements of the tunings of performing musicians of the time didn’t match the 24-eq system.

In Harmonic Secrets of Arabic Music Scales by Cameron Powers, the author offers a very different series of thirteen essential notes which he believes are the basis for all of the most important notes in the Arabic Maqams or scales. He believes that musicians actually employ 58 different just intervals, including some in 13-limit, which performers employ in live performance. He starts on the note G, and the notes he picks include one 11th-harmonic note (which plays 8 cents flat in 53-eq). The seventh harmonic-based note is 4.5 cents sharp, and the rest of the 3 and 5-limit notes are all very much in tune in 53-eq! Here is his list with ratios, which he derived from years of study of Arabian theorists and modern performance practices:

Figure 8-3 Cameron Powers’ Ratios

G   1/1

A1b  16/15

A    9/8

B1b   6/5

B2b   11/9

B1    5/4

C    4/3

C1#   7/5

D   3/2

E1b   8/5

E1    5/3

F   9/5

F1#   15/8

G   2/1

Let’s see how these notes form the basis of dozens of deeply expressive Arabic maqams (scales). First, as a living tradition, performers may play slightly sharper notes in ascending passages and slightly flatter notes on the descent. Local customs vary from city to city, with different degrees of precision. Depending on which starting note you use, the perfect-fourth-based tunings of the oud may cause some notes to play a bit differently as well. The notes for the maqams in the next section are therefore subject to variation. If you are obsessed with standardizing and doing music The One Right Way, the intuitive sensibilities of Arabic musicians may drive you insane! But if you’re like the Arabic mystics, you will drink deeply the sound of Love singing a song to its own ears.

If you would like to learn more about the ancient tunings worldwide you can buy the entire book, The Grand Unified Theory of Music, in pdf form for $25 with hundreds of embedded musical examples of scales and chords from all over the world.

A free introduction to what The Grand Unified Theory of Music offers is on this website and includes both text and a few musical examples from each webpage. If you would like to learn more about this chapter and the full contents of this entire e-book, you can buy The Grand Unified Theory of Music for $25, with hundreds of embedded musical examples of scales and chords from all over the world — and ideas for how to set up your computer system —


You’ll get a personalized password you can use to see the entire e-book. Inside the full book, you will also get a link to the complete pdf file of this e-book, which you can read on your Kindle or similar device. The links to the hundreds of mp3 sound files – the same ones you can hear on the website — will also be included. This is “Version 1.0” of The Grand Unified Theory of Music. Because it is an e-book, additions, corrections and improvements in the sound may be added at any time. The Grand Unified Theory of Music is Copyright © 2018 by Christopher Mohr. All rights reserved.

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Next Page: 8/3 – Ajnas and Maqams