Pohlit, S. \u0026 Weiss, J. B. † Divisions of the Apotome on the Middle-Eastern Qānūn

$Page 1: Pohlit, S. \u0026 Weiss, J. B. † Divisions of the Apotome on the Middle-Eastern Qānūn$
Mikrotonalität. Praxis und Utopie, Walter C-J. & C. Pätzold (Hg.), Stuttgart: Schott, pp. 202-18

1

Divisions of the Apotome on the Middle-Eastern Qānūn

Julien Bernard Jalâl Ed-Dine Weiss & Stefan Pohlit, Ph. D.

Biographical Notes

Julien Bernard Jalâl Ed-Dine Weiss, born in 1953, abandoned a career as a classically trained

guitar player in 1978 for studying the Near-Eastern qānūn with famous masters in Cairo,

Tunis, Istanbul, Baghdad, Beirut, Aleppo, and Tehran. In 1983 he founded the “al-Kindi”

ensemble that, until today, belongs to the foremost formations of maqām music on the

international stage, with more than twenty records, most of them being produced by

“Harmonia Mundi”. Residing in Aleppo in Northern Syria since the 1990’s, he collaborated

with legendary Soufi singers. Weiss is laureate of the prestigious Villa Médici award and, in

2001, was appointed Officer of Arts and Letters by the French Minister of Culture. Besides

his artistic agenda, he continues to investigate extensively in rhythmic patterns and micro-

tonal intonation of the maqām tradition. Feeling unsatisfied with the common tempered qānūn

models, he has, so far, conceived nine prototypes that, for the first time, fully rely on just

intonation. http://al-kindi.org

Stefan Pohlit, born in 1976, studied Composition and Music Theory in Saarbrücken, Basel,

Lyon, and Karlsruhe, most notably with Wolfgang Rihm and Sandeep Bhagwati. Since 1999,

he studied the Near-Eastern maqām tradition and traveled extensively both in Turkey and the

Arab world. In 2008, the Ankara State Conservatory appointed him as a Composition teacher

in the rarely granted position of a “foreign expert” of the Turkish State. In 2011 he defended

his doctoral thesis on the tuning system of Julien Bernard Jalâl Ed-Dine Weiss at the music

research center MĐAM of the Istanbul Technical University. Besides his activities as a

composer, Pohlit continues to investigate in conditions and meanings of cross-cultural art-

music. http://www.stefanpohlit.com


2

Introduction

As the most complicate instrument with fixed pitch supply within the maqām tradition, the

qānūn plays a central role in the definition of the Near-Eastern tuning system. Originally this

instrument had to be retuned separately for every scale structure, comparably to the Iranian

santur. During the first half of the 20th century, mandal-s, movable levers, were applied to

every course of strings with which the intonation can be adjusted during performance. These

small metal bridges, however, have also caused confusion between theory and practice

because they are tuned, on all common models, upon the tempered twelve-note scale that has

little in common with pure Pythagorean and harmonic intervals as they are described in the

traditional treatises. This article shall provide a brief account, containing four existing systems

that were invented during the 20th century.

Other than the Western piano and the pedal-harp, the strings on the qānūn are structured on

the foundation of a Pythagorean heptatonic scale – which equals the scale of ‘aĝam on C in

the Arab world and Çargâh in Turkey:

Figure 1: Pythagorean Heptatonic Scale

While the common Arab-Egyptian qānūn is based on a simple division of the octave into 24

notes, the modern Turkish system offers 13 different pitches on every course of strings and

amounts in a pitch supply of 72 notes within one octave. The Turkish system may, thus, be

compared to the 72-note scale of Byzantine church music since the reform of Chrysanthos

(Giannelos 1996, Karas 1989). The mandal-s on both of those common models always detune

a course of strings within a tempered whole-tone (200c). In case of “partial temperament”

(Weiss 2004), the basic gamut may be tuned according to just harmonic fifths 3/2, but then,

the division of the bridges, due to the tempered intervals that it produces, may lead to notable

distortions within the instrument’s intonation. Furthermore, not all octaves on the Turkish

model contain the same amount of mandal-s. In many cases, mandal-s on affected courses of


3

strings may still divide a tempered whole-tone mechanically upon equal distances, and,

consequently, many microtonal pitches may not allow parallel ocatve-doubling in consistent

intonation.

The qānūn of Aleppo, customarily invented for the tradition of Northern Syria, offered a

highly practical solution, with ten mandal-s being arrayed upon specific interval sizes, as they

appeared in common performance practice. However, this model has practically vanished

since the 1980’s. In 1990, the renowned French qānūn virtuoso and founder of the “Al-Kindi”

ensemble, Julien Jalâl Ed-Dine Weiss constructed a novel prototype, that, for the first time,

uses strictly just interval ratios. Weiss’ system includes 14 mandal-s that divide detune strings

on the basis of twice the Pythagorean apotome (2187/2048, 113.69c). In abandoning the

concept of temperament, Weiss, has, thus, successfully attempted to reconcile theory and

practice while understanding the different regional variations and characteristics within the

Near-Eastern tradition from a trans-national perspective.1

Temperament and Traditional Tuning Theories

In practice, the qānūn may shift to an audible extent from a correctly intonated lute. Some of

the most central interval ratios of the Near-Eastern tradition cannot be produced on the basis

of temperament, although the theoretical tradition distinguishes them neatly. Scholarly theory

and empirical practice in Near-Eastern music may always have coexisted without necessarily

supporting each other, since the Arab Middle-Ages (Chabrier 2001:601) until the modern era

(D’Erlanger 2001-V:x&6, Marcus 1993:40, Wright 2005:226). The use of a tempered

semitone of 100c, however, obscurs certain intervallic distinctions that appear vital to the

characteristics of many fundamental modal genres. Both theory and practice account for a

minor and a major semitone, traditionally conceived as the Pythagorean limma (90.23c) and

apotome (113.69c) and separated by the Pythagorean comma. Although musicians may resort

to the tempered twelve-tone scale when describing scale degrees, all experienced perfoemrs

discern certain modal genres, such as ĝins Kurdī and ĝins Hiĝāz, by this difference.

The Pythagorean tradition of the Arab Middle-Age, as in ’Abu Nasr Muhammad al-Farābī

(D’Erlanger 2001-I) and ’Ibn Sīnā (D’Erlanger 2001-II), was, furthermore, extended to a

1 More detailed information as well as a complete bibliography may be obtained from Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss. “A Novel Tuning System for the Middle-Eastern Qānūn.” Ph.D. Thesis in Music, Submitted to the Đstanbul Technical University, Institute of Social Sciences, MĐAM. http://www.stefanpohlit.com/dissertation.engl..htm


4

characteristic inventory of harmonic ratios that, traditionally, were referred to the fretting

conceived by the lutist Mansūr Zalzal al-Dārib of Baghdad (died 791, Farmer 2001: 118):

Table 1: Division of the Fourth on the Zīr String of Farābī’s lute (D’Erlanger 2001-I: 46,

During 1985: 81, Chabrier 2001: 603, Tura 1988b: 107, also cited in D’Erlanger 2001-III:

116).2

0

1 1

cents

1

256 243

90.23

2

18 17

98.96

3

162 149

144.82

4

54 49

168.21

5

9 8

203.91

6

32 27

294.14

7

81 68

302.86

8

27 22

354.55

9

81 64

407.82

10

4 3

498.05

└──────────────── 9 ───────────────┘ └──────────────── 8 └────────────── 9 ───────────┘ └──────────────── 8 └────────────── 8 └─────────── 2187 ──────────┘ └──────── 2187 ───────┘ └─────────── 2048 ──────────┘ └──────── 2048 ───────┘

These so-called “Zalzal frets”, usually described as “quarter-tones” were conceived with

different ratios and appear in notably low tuning on the lute of ’Ibn Sīnā:

Table 2: The Lute of ’Ibn Sīnā, Zīr String (D’Erlanger 2001-II: 103-245, Manik 1969: 47-51,

During 1985: 91-93, Chabrier 2001: 606, and Wright 2005: 225-29).

0

1 1

cents

1

2187 2048

113.69

2

13 12

138.57

3

9 8

203.91

4

32 27

294.14

5

39 32

342.48

6

81 64

407.82

7

4 3

498.05

└─────────── 9 ─────────┴──────────── 9 ────────────┘ └─────────── 8 └──────────── 8 ───────────┘

└────────────── 9 ───────────┘ 8

└── 2187 ──┘ └──────── 2187 ───────┘ └ ─ 2048 ──────────┘ └─── ─────2048 ───────┘

2 In this article the struck-out flat accidental is used for signifying a general concept of “quarter-tone”, as it is used, for example, in publications such as Shiloah 1981 & Touma 2003.


5

Safīyy al-Dīn’s 17-note scale from the 13th century may remind of Farābī’s Khorasan tunbur

from the 10th century (D’Erlanger 2001,I: 218-42, During 1985: 87 et seq., Chabrier 2001:

608, Tura 1988e) but differs from all other Arab systems in relying exclusively on

Pythagorean ratios. This system, built entirely of Pythagorean limma-s and comma-s,

translates the “quarter-tone” degrees into complex products of fifths and octaves and raises

them substantially. The “neutral” second and third were, thus, converted into interval that

differ from the harmonic minor whole-tone 10/9 and from the harmonic third 5/4 only by the

negligible amount of the schisma:

Table 3: Division of the Fourth in Safīyy al-Dīn’s 17-Note Scale (D’Erlanger 2001-III: 220-

233, Manik 1969: 62 et seqq., Tura 1988e: 182-85, and Chabrier 2001: 610 et seq.).

0

1 1

cents

1

256 243

90.23

2

65536 59049

180.45

3

9 8

203.91

4

32 27

294.14

5

8192 6561

384.36

6

81 64

407.82

7

4 3

498.05

└─────────── 9 ─────────┴──────────── 9 ────────────┘ └─────────── 8 └─────────────8 ───────────┘

└────────────── 9 ───────────┘ 8

└─ 2187 ──┴ 531441 ┴───2187 ──┴── 256 ─┴── 256 ───┴── 2187────┴── 256 ───┘ └ ─2048 ── 524288 2048 243 243─── ─2048 ─────── 243

It appears evident that the fundamental scale of 17 notes was completed to 24 notes until the

middle of the 19th century (Popescu-Judetz 2002:169-71, table I). On the other hand, the

controversy over the “neutral” scale degrees Segāh, ‘awĝ, and their octave equivalents

continues to divide Turkey and the Arab world within the maqām tradition: While the modern

Turkish systems after Raûf Yektâ (Yektâ 1921, D’Erlanger 2001-V: 27), Hüseyin Sadettin

Arel, and Suphi Ezgi (Signell 2006:41&44-45 & Özkan 2006:38&62) resurrected the

Systematist scale of Safīyy al-Dīn with its potentially unrealistic Pythagorean deduction

method, Arab theorists concentrated on the calculation of intervals for approximating quarter-

tones. The Congress of Cairo of 1932 took stock of the variety of different proposals, such as

the systems of Maurice Collengettes (D’Erlanger 2001-V:23, fig. 7), Raûf Yektâ (op.cit.: 27,

fig. 8), ‘alī al-Darwīš (op.cit.: 29, fig. 9), Miĥā’īl ’Ibn Ĝurĝus Mušāqah (op.cit.: 34, fig. 10),

Mansūr ’Awad (op.cit.: 37, fig. 11), ’Āmīn al-Dīk Affendī (op.cit.: 42, fig. 13, ’Idrīs Rāġib


6

Bey, and Iskandar Šalfūn (op.cit.: 40, fig. 12) , although the participants departed without

solving their general disagreements (D’Erlanger 2001-V:12).

Some modern Arab theorists, such as ‘alī al-Darwīš and Tawfīq al-Sabbāġ (Al-Dalīl al-

Mūsīqā al-’Amm: fī ’Atrab al-Anġām, 1950, referenced in Racy 2003:107), introduced the

comma into their scale concepts and, similarly to the Turks, divided the major whole-tone 9/8

into nine comma-s. As the Pythagorean comma (23.46c) does not fit exactly into a closed

cycle, the general scale was referred to a pitch supply of 53 Holdrian comma-s (21.82c) in

order to please the general interest in tempered systems. However, al-Sabbāġ also criticized

the lack of precision of a tempered 24-note scale and, therefore, introduced additional

symbols and refinements to the general tuning (Racy ibid.). In this manner, it became more

and more apparent that a modern tuning theory would not simply force all available pitches of

intonation practice into one simplified method of deduction but rather account for the various

aspects that a note may obtain in different contexts. The Turk Mustafa Ekrem Karadeniz, a

contemporary of Arel and Ezgi, proposed another highly individual attempt to such broader

conception in creating a scale of 42 notes (1985:10 et seqq.) that, however, has not found its

way into general practice.

The Arab-Egyptian Qānūn

Contrarily to the ambitious attempts of the diverse historic and modern treatises, tempered

modern qānūn-s neither produce the Pythagorean and harmonic ratios of the theoretical

tradition nor do their mandal-s conform with the theory of comma-s that appears so

prominently in discussions on Near-Eastern music. Rather than relying on specific theoretical

postulations, their mechanically applied division of the tempered whole-tone involves yet

additional tuning cycles. The modern qānūn may, thus, easily perform together with a

tempered piano or synthesizer, but serious approaches to the handed-down pitch supply of the

maqām tradition may be obscured by its lack of reliable interval sizes.

The Egyptian model, common in the Arab world and prominently conceived by instrument-

makers such as Rabīy‘a Šaraf and Gābīyy Tutunjī, insists on the specifically Arab preference

for quarter-tones. As many qānūn players perform in popular contexts and together with

synthesizers (Rasmussen 1996), the instrument may be tuned consistently upon the tempered

scale. Between C and D, D and E, F and G, G and A, and A and B, a sharp interval is meant to

equal the flat one of the next higher course of strings:


7

� 200c ┌─────────────────────── = ─────────────────────┘

└────── 50c ────┴──── 50c ───┴──── 50c ────┴──── 50c ──┘

Figure 2: Mandal Tuning on the Egyptian Qānūn. Comparison Between C and D Strings In a completely tempered context, the second halves of the E and, respectively, B courses

produce the same pitches as the first halves of the F and, respectively, C courses:

� � = └─────────┴───────┘ 100c ┌─────────────┬──────────┐

Figure 3: Mandal Tuning on the Egyptian Qānūn. Comparison Between E and F Strings.

In case of full temperament, some of the most crucial interval ratios may be reached in close

approximation. The more essential deficiency of this solution originates in the unification of

the limma and the apotome into one single semitone:

18/17 (98.95c ─┘ 12/11 (150.64c) ────┘

9/8 (203.91c) ────────┘

81/68 (302.55c) ───────────┘

27/22 (354.55c) ───────────────┘ 81/64 (407.82c) ──────────────────┘ 4/3 (498.05c) ───────────────────────┘

Figure 4: The Fourth on the Egyptian Qānūn, Full Temperament.


8

Many older masters have preferably tuned the heptatonic frame of the strings by ear and, thus,

upon Pythagorean ratios. In that case the scale may be based either on the fundamental of C or

on B flat. Due to the shifts between tempered mandal-s and contextual Pythagorean interval

sizes, the consequences are different for some of the resulting pitches:

17/16 (104.96c ─┘ 59/54 (153.31c) ────┘

9/8 (203.91c) ────────┘

153/128 (308.87c) ───────────┘

59/48 (357.22c) ───────────────┘ 81/64 (407.82c) ──────────────────┘ 4/3 (498.05c) ───────────────────────┘

Figure 5: The Fourth on the Egyptian Qānūn, Based on ‘aĝam in C.

17/16 (104.96c ─┘ 59/54 (153.31c) ────┘

9/8 (203.91c) ────────┘

32/27 (294.14c) ───────────┘

72/59 (344.74c) ───────────────┘ 64/51 (393.09c) ──────────────────┘ 4/3 (498.05c) ───────────────────────┘

Figure 6: The Fourth on the Egyptian Qānūn, Based on ‘aĝam in B flat.

On the professional Arab qānūn prior to the 1970’s an additional lever was provided, serving

for the production of the major semitone of genre Hiĝāz and the diminished fourth of genre

Sabā. Consequently, this model contained six different notes on one course of strings:


9

17/16 (104.96c ─┘ 15/14 (119.44c) ────┘

59/54 (153.31c) ───────┘

9/8 (203.91c) ────────────┘

153/128 (308.87c) ────────────┘

135/112 (323.35c) ───────────────┘ 59/48 (357.22c) ────────────────────┘ 81/64 (407.82c) ───────────────────────┘ 4/3 (498.05c) ─────────────────────────────┘

Figure 7: The Fourth on the Extended Arab Qānūn, Based on ‘aĝam in C.

17/16 (104.96c ─┘ 16/15 (111.73c) ────┘

59/54 (153.31c) ───────┘

9/8 (203.91c) ────────────┘

32/27 (294.14c) ──────────────┘

6/5 (315.64c) ───────────────────┘ 72/59 (344.74c) ─────────────────────┘

64/51 (393.09c) ─────────────────────────┘ 4/3 (498.05c) ─────────────────────────────┘

Figure 8: The Fourth on the Extended Arab Qānūn, Based on ‘aĝam in B Flat.

This system provides genre Hiĝāz with a desired higher minor second:

Figure 9: Optional Addition to the Egyptian Qānūn: Major Semitone for Genre Hiĝāz.

While this solution can be compared to certain lute types with lesser amount of frets such as

the buzūqī, an entirely correct tetrachord of this genre would also lower the third by one

comma:


10

16/15 ──┘ 5/4 ───────┘ 4/3 ──────────┘

Figure 10: Requirement for a Correctly Tuned Ĝins Hiĝāz.

The Qānūn of Aleppo

Julien Jalâl Ed-Dine Weiss discovered this model during his early years in Paris in an old

publication owned by Jean-Claude Chabrier and, while living in Aleppo, was able to take

precise measurements from an existing instrument. This qānūn is closely related to the

Aleppian instrument-maker Šukrīyy Antaqlī, a contemporary of ‘alī al-Darwīš. Conceived

specifically for the abundant local tradition of Northern Syria, the model was adopted and

refined by other instrument-makers, such as ‘alī Wa’ez and Sāfīyy Zaynab.

This instrument has practically ceased to exist since the 1980’s. It provided eleven different

pitches on every course of strings. They were arrayed according to two tempered semitones.

However, the inner mandal positions were tuned customarily for the production of specific

interval sizes, as they appeared in the local tradition of Aleppo. The cent values given in fig.

11 shall only offer an impression of the approximate location of the bridges:

� 200c ┌─────────────────────── = ─────────────────────┘ �

└ ~16c ─┴─ ~32c ─┴─ ~12c ─┴─ ~32c ─┴─ ~12c ┴─ ~12c ┴ ~32c ─┴ ~12c─┴─ ~32c ─┴─ ~ 12c ┘

└───────── 100c ───────┴─────── 100c ────────┘

Figure 11: Aliquot Division of the Tempered Apotome on the QŒnń of Aleppo. C and D Strings.

In the case of full temperament, the following ratios for the crucial seconds and thirds appear

in close approximation:


11

~18/17 (98.95c) ──┘

~16/15 (111.73c ──────┘

~88/81 (143.5c) ──────────┘

~128/117 (155.56c) ────────────┘

~512/459 (189.18c) ─────────────────┘

~9/8 (203.91c) ───────────────────────┘

Figure 12: Approximated Seconds on the QŒnń of Aleppo.

~81/68 (302.86c) ──┘

~6/5 (315.64c ──────┘

~11/9 (347.41c) ──────────┘

~16/13 (359.47c) ──────────────┘

~64/51 (393.09c) ──────────────────┘

~81/64 (407.82c) ──────────────────────┘

Figure 13: Approximated Thirds on the QŒnń of Aleppo.

It should be mentioned that the distribution of micro-steps on this model does not neatly

conform with the ultra-Pythagorean tuning system of ‘alī al-Darwīš (D’Erlanger 2001-V:29,

fig.9):


12

~16000/15580 (46.05c) ──┘

~256/243 (90.23c) ────────┘

~2187/2048 (113.69c) ───────────┘

~ 35073/32000 (158.75c) ───────────────┘

~9/8 (203.91c) ───────────────────────────┘

Figure 14: Minor to Major Seconds According to the Tuning Theory of Šayĥ ‘alī al-Darwīš.

While the mandal-s rely on the tempered semitone, the fundamental heptatonic scale was, in

practice, tuned by ear upon Pythagorean ratios, in “unequally Pythagorean temperament”

(Weiss 2004). As its division of the semitone was built systematically upon musically

meaningful interval sizes, this system offered, at the time, the most rational qānūn. The

following representation, again, show the resulting ratios, whether the instrument was tuned

upon C or upon B flat:

18/17 (98.95c ─┘ 15/14 (119.44c) ───┘

88/81 (143.5c) ──────┘

128/117 (155.56c) ───────┘

512/459 (189.18c) ───────────┘

9/8 (203.91c) ────────────────┘

81/68 (302.86c) ───────────────────┘

135/112 (323.35c) ──────────────────────┘

11/9 (347.41c) ───────────────────────────┘

16/13 (359.47c) ───────────────────────────────┘

64/51 (393.09c) ───────────────────────────────────┘ 81/64 (407.82c) ──────────────────────────────────────┘ 4/3 (498.05c) ───────────────────────────────────────────┘

Figure 15: The Fourth on the Qānūn of Aleppo, Based on ‘aĝam in C.


13

18/17 (98.95c ─┘ 16/15 (111.73c) ───┘

88/81 (143.5c) ──────┘

128/117 (155.56c) ───────┘

512/459 (189.18c) ───────────┘

9/8 (203.91c) ────────────────┘

32/27 (294.14c) ───────────────────┘

6/5 (315.64c) ────────────────────────┘

39/32 (342.48c) ───────────────────────────┘

27/22 (354.55c) ───────────────────────────────┘

5/4 (386.31c) ───────────────────────────────────┘ 398c ───────────────────────────────────────────┘ 4/3 (498.05c) ───────────────────────────────────────────┘

Figure 16: The Fourth on the Qānūn of Aleppo, Based on ‘aĝam in B Flat.

This highly sophisticated pitch supply was designed in order to respond on the specific local

tuning customs of Aleppo. The semitone 18/17, thus, serves for the Aleppian understanding of

the third in genre Nahāwand in F (81/68), the harmonic semitone 16/15 for genre Hiĝāz in G;

88/81 was used in Bayātī in G, 128/117 for Rast in F (16/13), 512/459 for the third of Hiĝāz

in F (64/51).

The Turkish Qānūn

This model, standardized in modern Turkey, uses twelve mandal-s (= 13 pitches) per course

of strings while at least one pitch is shared with the next adjacent string and distributed 72

notes within one octave mechanically onto the heptatonic frame tuning. The tempered

wholetone is neatly divided into two tempered semitones:


14

n � � � � � � � #

� 200c ┌─────────────────────── = ─────────────────────┘ �

└ ~17c ─┴ ~17c─┴ ~17c ─┴ ~17c ┴ ~16c ┴ ~16c ┴ ~17c ─┴ ~17c─┴ ~17c ┴ ~17c ┴ ~16c ┴ ~16c ┘

└───────── 100c ───────┴─────── 100c ────────┘

Figure 17: Aliquot Division of the Tempered Apotome on the Turkish QŒnń. C and D Strings.

In case that the heptatonic frame of the instrument is tuned upon Pythagorean intervals – and

by means of melodic scale steps –, this distribution could be explained upon the following

ratios:

└───── 18 ────┴──── 17 ─────┘

└───── 17 ────┴──── 16

└─────────── 9 ────────────┘

└───── ────── 8

98.95c 105.44c

Figure 18: Approximation of Harmonic Ratios on the Turkish QŒnń.

Due to the equidistant array of the bridges next to each course of strings, a slight aliquot

division from one end of a semitone to another must be accounted:

102 x 101 x 100 x 99 x 98 x 97 101 100 99 98 97 96

└─────────────────── 18 ─────────────────┘

└─────────────────── 17

98.96c └───────────────

b � � � � � � � n

Figure 19: Aliquot Division of the Tempered Apotome on the Turkish Qānūn. Approximation with 18/17.


15

The following representation shall give an impression of the Pythagorean and harmonic ratios

that are closely touched by this system:

Pythagorean and Harmonic Ratios

ratios (sums) 256 15 13 12 11 10 9 32 6 39 27 99 5 81 4 243 14 12 11 10 9 8 27 5 32 22 80 4 64 3

cents 9 0.23 119.44 138.57 150.64 165.0 182.0 203.91 294.14 315.64 342.48 354.55 368.91 386.31 407.82 498.05

Tempered Turkish Qānūn

cents 100 117 134 151 168 184 200 300 317 334 351 368 384 400 500

Figure 20: Division of the Fourth: Comparison of Ratios from the Theoretical Tradition with

Approximate Interval Sizes on the Turkish Qānūn.

The Prototypes of Julien Jalâl Ed-Dine Weiss

In 1990, together with his first custom-built qānūn, Julien Jalâl Ed-Dine Weiss also invented a

reliable notation system, based on accidentals that appear prominently in Arab, Turkish, and

Persian theories. They relate the 14 mandal-s of his system with specific interval ratios:

Figure 21: Weiss’ Specified Mandal Notation With this notation, all so far accounted tuning systems are included and coexist in a broader

concept of acoustic and theoretical derivation. For example, Weiss is able to play subtle

distinctions such as the schisma between an F flat and an E natural that appear at exactly the

right places on his heptatonic frame and are justly tuned. Both the Pythagorean (2187/2048)

and the harmonic (16/15) aptome can be provided, each at its specifically assigned place. The

augmented prime signifies the Pythagorean apotome (2187/2048), a minor second the

Pythagorean limma that, which 90.23c, is by one Pythagorean comma smaller. In comparison,

Arel-Ezgi,Uzdilek, in their today standardized Turkish notation system, confounded this

theoretical distinction by equating the one with the other and relying on a tempered keyboard

rather than on acoustic evidence:


16

Arel-Ezgi-Uzdilek (Modern Turkey) Weiss

└── 256──┘ └── 256─┘ └──2187─┘ └── 256─┘ 243 243 2048 243

90.23 c 90.23 c 113.69 c 90.23 c

Figure 22: Minor and Major Semitone. Comparison between the Notation Systems of Arel-

Ezgi-Uzdilek’s and Weiss.

Weiss divides each course of strings upon twice the Pythagorean apotome. The symmetrical

distribution of the following fig. 23 applies to all prototypes that have been built to this day:

┌──┬────────────────┬──┬──┬────────────────┬───┐

ratios 81 25 (“Zarlino semitone”) 81 81 25 (“Zarlino semitone”) 81 80 24 80 80 24 80

cents 21.51 70.67 22.51 21.51 70.67 21.51

└──┴────────────────┴──┴──┴────────────────┴───┘

└──────── 135/128 ─────┘ └──────── 135/128──────┘

└───────135/128 ───────┘ └───────135/128 ────────┘

└───── 2187/2048 ≈ 113.69 ct.────┴───── 2187/2048 ≈ 113.69 ct. ────┘

2x the Pythagorean apotome

Figure 23: Weiss’ Qānūn Systems – Basic Division of the Pythagorean Apotome.

System 1 was conceived in 1990 and built by the Đzmir-based instrument-maker Ejder Güleç,

explicitly for performances with Weiss’ “Al-Kindi” ensemble in Arab contexts. The first half

of the D course in the following table describes an almost perfect series of harmonic ratios:

Table 4: Weiss’ Qānūn System 1 – Ratios on the D String in Regard to C Natural

cents: 21.51 14.2 12.65 12.06 14.37 17.4 21.51 21.51 14.2 12.65 12.06 14.37 17.4 21.51 ratios: 256 16 784 13 12 11 10 9 729 147 9477 6561 24057 1215 19683 su 243 15 729 12 11 10 9 8 640 128 8192 5632 20480 1024 16384

cents: 90.23 111.73 125.92 138.57 150.64 165.0 182.4 203.91 225.41 239.61 252.62 264.32 278.89 296.09 317.6

Eight instruments in different sizes were constructed upon this system until Weiss, in 2007,

conceived a slightly different tuning that, by simply reversing the interval ratios of the first


17

system, should primarily serve the interpretation of the Ottoman-Turkish repertoire. This new

prototype was built by the Đstanbul-based instrument-maker Kenan Özten:

Table 5: Weiss’ Qānūn System 2 – Ratios on the D String in Regard to C Natural

cents: 21.51 16.57 15.2 12.06 12.35 14.49 21.51 21.51 16.57 15.2 12.06 12.35 14.49 21.51

ratios: 256 16 14 88 128 119 10 9 729 23 297 243 273 1215 19683 m ratios: 243 15 13 81 117 108 9 8 640 20 256 208 232 1024 16384

cents: 90.23 111.73 128.3 143.5 155.56 167.92 182.4 203.91 225.41 241.96 257.18 269.25 275.38 296.09 317.6

Tables 6 and 7 show the full range of the microtonal pitch supply that both systems offer. In

reconciling theory and practice in a, finally, acoustically consistent approach, Weiss’ qānūn

models could be compared to Dimitrie Cantemir’s tanbūr from the 17th century (Feldman

1996:206 et seqq.). They reflect various aspects of Near-Eastern tuning customs, modal

genres, and pitch supply both from an historic and contemporary viewpoint.

Table 6: Weiss’ System 1 – Available Pitch Content per Octave in Relationship to C Natural.

DO

2048 2187

113.69c

128 135

92.18c

2560 2673

74.78c

704 729

60.41c

1053 1024

48.35c

48 49

35.70c

80 81

21.51c

1 1

0

81 80

21.51c

49 48

35.70c

1053 1024

48.35c

729 704

60.41c

2673 2560

74.78c

135 128

92.18c

2187 2048

113.69c

RE

256 243

90.22c

16 15

111.73c

784 729

125.92c

13 12

138.57c

12 11

150.63c

11 10

165.00c

10 9

182.40c

9 8

203.91c

729 640

225.41c

147 128

239.60c

9477 8192

252.26c

6561 5632

264.32c

24057 20480

278.68c

1215 1024

296.09c

19683 16367

319.39c

MI

32 27

294.14c

6 5

315.64c

98 81

329.83c

39 32

342.48c

27 22

354.55c

99 80

368.91c

5 4

386.31c

81 64

407.82c

6561 5120

429.32c

1323 1024

443.52c

85293 65536

456.17c

59049 45056

468.23c

216513 163840

482.59c

10935 8192

500c

177147 131072

521.51c

FA

8192 6561

384.36c

512 405

405.87c

25088 19683

420.06c

104 81

432.71c

128 99

444.77c

176 135

459.13c

320 243

476.54c

4 3

498.05c

27 20

519.55c

49 36

533.74c

351 256

546.39c

243 176

558.46c

891 640

572.82c

45 32

590.22c

729 512

611.73c

SOL

1024 729

588.27c

64 45

609.78c

3136 2187

623.97c

13 9

636.62c

48 36

648.69c

22 15

663.05c

40 27

680.45c

3 2

701.96c

243 160

723.46c

147 96

737.65c

3159 2048

750.30c

2187 1408

762.37c

8019 5120

776.73c

405 256

794.13c

6561 4096

815.64c

LA

128 81

792.18c

8 5

813.69c

392 243

827.88c

13 8

840.52c

18 11

852.59c

33 20

866.96c

5 3

884.36c

27 16

905.87c

2187 1280

927.37c

441 256

941.56c

28431 16384

954.21c

19683 11284

963.21c

72171 40960

980.64c

3645 2048

998.04c

59049 32768

1019.55c

SI

16 9

996.09c

9 5

1017.6c

49 27

1031.79c

117 64

1044.44c

81 44

1056.5c

297 160

1070.87c

15 8

1088.27c

243 128

1109.78c

19683 10240

1131.28c

3969 2048

1145.47c

255879 131079

1158.03c

177147 90112

1170.19c

649539 327680

1184.55c

32805 16384

1201.95c

531441 262144

1223.46c

DO

4096 2187

1086.31c

256 135

1107.82c

5120 2673

1122.01c

52 27

1134.66c

64 33

1146.73c

88 45

1161.09c

160 81

1178.49c

2 1

1200c

81 40

1221.51c

49 24

1235.70c

1053 512

1248.35c

729 352

1260.41c

2673 1280

1274.78c

135 64

1292.18c

2187 1024

1313.69c


18

Table 7: Weiss’ System 2 – Available Pitch Content per Octave in Relationship to C Natural.

DO

2048 2187

113.69c

128 135

92.18c

232 243

80.2c

26 27

65.34c

32 33

53.27c

1664 1701

38.07c

80 81

21.51c

1 1

0

81 80

21.51c

1701 1664

38.07c

33 32

53.27c

27 26

65.34c

243 232

80.2c

135 128

92.18c

2187 2048

113.69c

RE

256 243

90.22c

16 15

111.73c

14 13

128.29c

88 81

143.49c

128 117

155.56c

119 108

167.92c

10 9

182.40c

9 8

203.91c

729 640

225.41c

15309 13312

241.98c

297 256

257.18c

243 208

269.25c

9639 8192

281.60c

1215 1024

296.09c

19683 16367

319.39c

MI

32 27

294.14c

6 5

315.64c

63 52

332.21c

11 9

347.41c

16 13

359.47c

119 96

371.83c

5 4

386.31c

81 64

407.82c

6561 5120

429.32c

137781 106496

445.89c

2673 2048

461.09c

2187 1664

473.16c

86751 65536

485.51c

10935 8192

500c

177147 131072

521.51c

FA

8192 6561

384.36c

512 405

405.87c

448 351

422.43c

2816 2187

437.63c

4096 3159

449.7c

952 729

462.05c

320 243

476.54c

4 3

498.05c

27 20

519.55c

567 416

536.12c

11 8

551.32c

18 13

563.38c

357 256

575.74c

45 32

590.22c

729 512

611.73c

SOL

1024 729

588.27c

64 45

609.78c

56 39

626.34c

352 243

641.54c

512 351

653.61c

119 81

665.96c

40 27

680.45c

3 2

701.96c

243 160

723.46c

5103 3328

740.03c

99 64

755.23c

2187 1404

767.29c

3213 2048

779.65c

405 256

794.13c

6561 4096

815.64c

LA

128 81

792.18c

8 5

813.69c

21 13

830.25c

44 27

845.45c

64 39

857.52c

119 72

869.87c

5 3

884.36c

27 16

905.87c

2187 1280

927.37c

45927 26624

943.94c

891 512

959.14c

19683 11232

971.20c

28917 16384

983.56c

3645 2048

998.04c

59049 32768

1019.55c

SI

16 9

996.09c

9 5

1017.6c

189 104

1034.16c

11 6

1049.36c

24 13

106143c

119 64

1073.78c

15 8

1088.27c

243 128

1109.78c

19683 10240

1131.28c

413343 212992

1147.85c

8019 4096

1163.05c

6561 3328

1175.11c

260253 131072

1187.46c

32805 16384

1201.95c

531441 262144

1223.46c

DO

4096 2187

1086.31c

256 135

1107.82c

672 351

1124.39c

4224 2187

1139.59c

12288 6318

1151.65c

476 243

1164.01c

160 81

1178.49c

2 1

1200c

81 40

1221.51c

1701 832

1238.07c

33 16

1253.27c

27 13

1265.34c

243 116

1280.2c

135 64

1292.18c

2187 1024

1313.69c

Figure 24: Weiss’ Qānūn Nr. 9, System 2


19

Figure 25: Weiss’ Qānūn Nr. 9, System 2, Mandal-s

Bibliography

Arel, Hüseyin Sadettin. 1993 (1953). Türk Musıkîsi Nazariyatı Dersleri. Onur Akdogu, (ed.). Ankara: Kültür Bakanlıgı Yayınları

Chabrier, Jean-Claude. 2001 (1996). “Musical Science.” In: Rāshid, R. & R. Morélon (eds.)

Encyclopedia of the History of Arab Science. London: Routledge D’Erlanger, Rodolphe. 2001 (1935 & 1938) La Musique Arabe. Vol. I-VI. Paris: Geuthner. During, Jean. 1985. Théories et Pratiques de la Gamme Iranienne. In: Revue de

Musicologie, vol. 71 (1-2: Échelles Musicales: Modes Et Tempéraments), 79-118. Published by: Société Française de Musicologie. Stable URL: http://www.jstor.org/stable/928594. Accessed 12/07/2010 17:44 on JSTOR

Farmer, Henry George. 2001 (1929). A History of Arabian Music. New Delhi: Goodword

Books Feldman, Walter. 1996. Music of the Ottoman Court – Makam, Composition and the Early

Ottoman Instrumental Ensemble. Berlin: Intercultural Music Studies. VWB – Verlag für Wissenschaft und Bildung

Giannelos, Dimitri. 1996. La Musique Byzantine. Le Chant Ecclésiaque Grec, sa Notation et

sa Pratique Actuelle. Paris-Montréal: L’Harmattan Helmholtz, Hermann. 1954 (1885). On the Sensations of Tone. Ellis, A. J. (trans.). Mineola

(NY): Dover Karadeniz, Mustafa Ekrem. 1985. Türk Musıkîsinin Nazariye ve Esaslari. Ankara: Türkiye

Đş Bankası Kültür Yayınları Karas, Simon. 1989. Harmoniká. Des Consonances (Syn-Phonies) par Moyennes

Harmoniques : Les Intervalles Musicaux. Athens (GR): Manoutios.


20

Manik, Liberty. 1969. Das arabische Tonsystem im Mittelalter. Leiden (NL): Brill. Marcus, Scott. 1993. “The Interface between Theory and Practice: Intonation in Arab

Music.” In: Asian Music, Vol. 24, No. 2 (Spring - Summer 1993), 39-58. Published by: University of Texas. Press Stable URL: http://www.jstor.org/stable/834466. Accessed: 22/07/2010 12:47 on JSTOR

Özkan, Đsmail Hakkı. 2006 (1982). Türk Mûsıkîsi Nazariyatı ve Usûlleri. Đstanbul: Ötüken. Popescu-Judetz, Eugenia. 2002. Tanburi Küçük Artin. A Musical Treatise of the Eighteenth

Century. Istanbul: Pan. Racy, Ali Jihad. 2003. Making Music in the Arab World: The Culture and Artistry of Tarab.

Cambridge UK): Cambridge University Press Rasmussen, Anne K. “Theory and Practice at the 'Arabic Org': Digital Technology in

Contemporary Arab Music Performance.” In: Popular Music, Vol. 15, No. 3, Middle East Issue (Oct. 1996), 345-365. Published by: Cambridge University Press.

Shiloah, Amnon. 1981. “The Arabian Concept of Mode.” In: Journal of the American

Musicological Society. Vol. 34, Nr. 1 (1981), 19-42.

Signell, Karl Lloyd. 2006 (1977). Makam: Modal Practice in Turkish Art Music. Đstanbul: Yapı Kredi Yayınları

Touma, Habib Hassan. 2003. The Music of the Arabs. Schwartz, L. (trans.). Portland:

Amadeus Press Weiss, Julien Bernard Jalâl Ed-Dine. 2004. “Safiyuddin et la Musique Arabe Moderne. ”

Unpublished lecture upon the International Symposium of the Iranian Academy of Arts, Jan. 15th-19th 2005 in Tehran. Retrieved from the author in digital format

Wright, Owen. 2005. “Die melodischen Modi bei Ibn Sīnā und die Entwicklung der Modalpraxis von Ibn al-Muna−−im zu êāfī al-Dīn al-Urmawī.” In: Sezgin, F. (ed.): Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften. Sonderdruck, Nr.16 (2004/05), 224-308

Yektâ, Raûf. 1921 (1913). “La Musique Turque.” In: Lavignac, A. et L. de Laurencie (eds.). Encyclopédie de la Musique et Dictionnaire du Conservatoire, vol. I/5 (1921), Paris : Delagrave, 2945-3†

Documents

Pohlit, S. \u0026 Weiss, J. B. † Divisions of the Apotome on the Middle-Eastern Qānūn