Notes

 
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start: 7 january 2007, up-date: 7 january 2007
1) The study is based on the Arabic text that I have written by examining the three oldest copy of al-Sharafiyyah in Turkey (The Language and History-Geography Faculty, Saib Sencer Manuscripts no: I/4810; Topkapý Palace Museum Library, III. Ahmad, no: 3460; Nuruosmani Library, no: 3647) and the copy in Paris Bibliotheque Nationale numbered 2479).
2) See the subjects on the theory of sound; al-Fârâbi, Ebû Nasr Muhammad b. Muhammad b. Tarhân, (d. 950) Kitâb al-Mûsîqi al-Kabîr, ed, Gattâs Abd al-Melik Hashebe, Mahmûd Ahmad al-Hifnî, Cairo, n.d. pp. 211-224; Ikhwan al-Safâ, Rasâil, al-Risâlah al-Hâmise fi al-Mûsiqi, ed, Hayr al-Dîn al-Ziriklî, Cairo, 1928, i, 137-141; Ibn Sîna, (d. 1037), Kitâb al-Shifâ, Cawâmi Ilm al-Mûsiqi, ed. Zekeriyya Yusuf, Cairo, 1956. pp. 4-13; d'Erlanger, "Traite anonyme dedie au Sultan Osmanli Muhammed II", La Musique Arabe, Paris, 1939, iii, 17-25, Fath Allah al-Shirwânî Majallah fi al-Mûsiqi, ed. Fuat Sezgin, Frankfurt 1986, v. 26, fols. 47-54; Muhammad b. Abd al-Hamid al-Lâdhiqî, al-Risâlah al-Fathiyyah fi al-Mûsiqi Istanbul Municipality Taqsim Ataturk Library no. K. 23, fols: 13b-16b; Rauf Yekta, Türk Mûsikîsi Nazariyâti, (Turkish Music Theoretic), Istanbul, 1924, pp. 14-34.
3) These 11 ratios which are out of the numbers of equality are mentioned in Mukaddimat al-Usûl as how it was mentioned in al-Sharafiyyah, Alishah b. Haci Buke, Mukaddimat al-Usûl, University of Istanbul, The Library of Ancient Works, The Department of Persian Manuscripts, no. 1097, fol. 5a. In addition, for the information al-Shirwâni gives over the intervals and ratios see: al-Shirwâni, Majallah fi al-Mûsiqi, fol. 39…
4) In the Treatises of Al-Kindî, the terms of octave, pentachord, tetrachord and tanînî (9/8) are frequently encountered. See Ahmed Hakki Turabi, el-Kindî'nin Mûsikî Risâleleri, MA Thesis, Istanbul 1996, (Risalah fi Khubr Sinâat al-Ta'lîf) p. 113.
In the Risâlah fi al-Mûsiqi of Ikhwân al-Safâ, there is no information on the ratios of the numbers with each other in the way Safi al-Dîn put forward. However, the sentences in Ikhwân al-Safâ about this subject are important. "The best compositions are the ones produced with the most consonant ratios" Ikhwân al-Safâ, Risâlah fi al-Mûsiqi, i, 161. Then, it is pointed out that these consonant ratios are 2/1, 3/2, 4/3, 5/4, 9/8. Ikhwân al-Safâ, Risâlah fi al-Mûsiqi, i, 164.
In the Sixth Risâlah of Ikhwân al-Safâ where "numbers, the effect of numerical ratios on the people and the ratios related to music" mostly take place, these subjects are examined: "The ratio is a measure between two amounts. When the two numbers are compared to each other, both are either equal or not. If there is no equality between the two numbers, one is either smaller or bigger than the other. When small one is compared to the big one, there are nine positions. These are 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10…Besides, the ratios of di'f (two fold), mithl and cuz, mithl and ecza, di'f and cuz, di'f and ecza and eda'f are taken place. Ikhwân al-Safâ, al-Risâlah al-Sadise fi al-Nisbat al-Adadiyyah ve al-Handasiyyah, i, 181-182.
After naming nine harmonious intervals as octave, pentachord, tetrachord, tanînî, mujannab, bakiyye, two octaves, octave and pentachord, octave and tetrachord, Shirwanî points out that the consonant intervals are 12 in practice and he adds three octaves, two octaves and pentachord, two octaves and tetrachord to the ones mentioned above. al-Shirwâni Majallah fi al-Mûsiqi, fols. 59-66.
5) For the same definition see; al-Shirwâni Majallah fi al-Mûsiqi, fol. 59.
6)Ibn Sîna divides the intervals into three as large, middle and small intervals. Octave interval were classified by Ibn Sîna as grand interval, tetrachord and pentachord intervals as middle, and the others coming after tetrachord are classified as lahnî . And also to him, the grand lahnî intervals are the ones with 5/4, 6/5, 7/6, 8/7, 9/8, 10/9, 11/10, 12/11, 13/12, 14/13 ratios. Middle lahnî intervals are the ones from 15/14 to 29/28. The others starting with 30/29 are the small lahnî intervals. Ibn Sîna, Cawâmi Ilm al-Mûsiqi, pp. 23-25.
Al-Lâdhiqî classified intervals as grand, middle and small like Safi al-Dîn did and he pointed out that this classification belongs to Safi al-Dîn. Besides, this classification exists in Al-Shirwâni as well. al-Lâdhiqî, al-Risâlah al-Fathiyyah, fol. 35b; Also see; al-Shirwânî Majallah fi al-Mûsiqi, fols. 92-93.
The big and middle interval Rauf Yekta pointed out with a heading of "consonant intervals" are the same as the ones Safi al-Dîn recorded. Yekta pointed out all the other intervals except these as "small intervals" and showed them on the staff. Yekta, Türk Musikisi Nazariyâti, p. 94; Also see Traite Anonyme, pp. 34-41.
7) The subjects of the addition, the division and the subtraction of the intervals don't take place in Treatises of al-Kindi, and Rasâil of Ikhwân al-Safâ.Al-Fârâbi studied this subject at the heading of "simple numerical relations between the intervals" and studied it in detail. Al-Fârâbi, Kitâb al-Mûsîqi al-Kabîr, pp. 188-204.
Ibn Sîna allocated the second discourse of his work into this subject. The first part of the second discourse, which he divided into two, is about the addition of the intervals with each other and subtraction of them from each other and the second part is about redoubling of the intervals and the division of them. Ibn Sîna, Cawâmi, pp. 33-41.
The addition, subtraction and division of the intervals of the following periods are carried on to be examined. Al-Ladhiqî allocated the second part into these subjects. Rauf Yekta dealt with this subject in detail with a heading of "Mûsikînin Mebâdi-i Riyaziyesi" (The Preliminary Mathematics of Music). Türk Musikisi Nazariyati, pp. 35-45.

8) As it is seen Safi al-Dîn emphasizes on the kinds so much in his work. This subject is also taken place in detail in al-Fârâbi. But al-Kindi also explains three kinds, tanînî,(including every diatonic kinds) lawnî (including every chromatic kinds) and te'lîfî (composed kind-including every enharmonic kinds) with a heading of kinds. Tanînî is composed of "tanînî-tanînî-fadla (ton-ton-limma)" intervals. Lawnî is arranged as fadla-fadla-three halves tanînî; (1 ½ tone). Te'lîfî kind is arranged as irkha-irkha-two tanînî (tones). For detailed information see Risalah fi Khubr Sinâat al-Ta'lif, (Turabi, p. 124).
Al-Fârâbi examined layyin and kawî kinds with a heading of "the arrangement and classes of the kinds" in detail. Although it has a great similarity with al-Fârâbi, Safi al-Dîn never names al-Fârâbi in the third discourse where he mentions about the arrangement of the kinds. Al-Fârâbî, Kitâb al-Mûsîqa al-Kabîr, pp. 278, 317.
Ibn Sîna allocated the third discourse of Cawâmi into kinds. He calls the kinds, which he explains they are composed of three intervals and a four notes, as "lahni". Kawî kinds are explained in the third discourse and lawnî ones are in the fourth part. For details see: Ibn Sîna, Cawâmi, pp. 45-46.
While al-Ladhiqî writes a great deal about the kinds in his work, al-Shirwâni never mentions it with a reason that "his brief work would exceed the capacity". See. Al-Ladhiqî, al-Risâlah al-Fathiyyah, fols. 53a…; Traite Anonyme, pp. 51-76; al-Shirwâni, Majallah fi al-Mûsiqi, fol. 99.
Rauf Yekta takes this subject into his work and explains it completely parallel with Safi al-Dîn. After examining all the kinds Safi al-Dîn did, Rauf Yekta explains: "After this tiring work, maybe it will be asked how many tetrachords consonants with each other were obtained. As a respond we would say with shyness that only four consonants were decided and tetrachord was obtained. The others were confined into the theoretical books. Additionally, these obscured the ideas of the European artists who attempted to do unfruitful works to realize them while they were unveiling the mystery of the kinds in Greek music so many centuries later. Yekta, Türk Musikisi Nazariyati, pp.59, 63.
9) See. Al-Fârâbi, Kitâb al-Mûsîqi al-Kabîr, p. 329-332; This subject was taken place in al-Ladhiqî and Traite Anonyme just like the one in al-Sharafiyyah. See. Al-Risâlah al-Fathiyyah, fols. 38a-41a; Traite Anonyme, pp. 78-91.
10) Safi al-Dîn, Kitâb al-Adwâr, Yale University, The Beineke Rare Book and Manuscript Library, No. S. 73. fol. 30.
11) Alishah presented seven scales of one octave he showed in an Ushshâq scale of two octaves with their names and he pointed out these full scales are called as "all sort of kinds". Alishah b. Haci Buke, Mukaddimat al-Usûl, fol. 29b; also see for bahr Al-Ladhiqî, al-Risâla al-Fathiya, fol. 76a; for common notes see. Traite Anonyme, p. 103.
12) Ikhwan al-Safâ, al-Risâlah fi al-Mûsiqi, i, 148.
13) Al-Fârâbi, Kitâb al-Mûsiqi al-Kabîr, p. 498.
14) Al-Ladhiqî, al-Risâlah al-Fathiyyah, fol. 88a.
15) Al-Kindi talks about the strings of this instrument in detail both in the book Kitâb al-Musavvitat al-Vatariyyah (See, Turabi, pp. 149-153) and in Risâlah fi Aczâ Khubriyyah (Turabi, pp. 163-167) and he connects celestial bodies, natural events, and human morality with emotions and behaviours. Also see; Ikhwan al-Safâ, i, 149, al-Fârâbi, Kitâb al-Mûsiqi al-Kabîr, p. 502; Ibn Sîna, Cawâmi, p. 148.
16) Kitâb al-Musavvitat al-Vatariyyah (Turabi, p. 142).
17) Al-Fârâbî, Kitâb al-Mûsiqi al-Kabîr, pp. 588-592.
18) Ibn Sîna, Cawâmi, p. 148; Alishah, Mukaddimat al-Usûl, fols. 89a-89b.
19) Al-Fârâbi, Kitâb al-Mûsiqi al-Kabîr, p. 597. Here al-Fârâbi tells about various accord orders of ûd.
20) Al-Kindi, al-Risâlah al-Kubrâ fi al-Ta'lîf (Turabi, p. 176); Ikhvan al- Safa, i, 149, Ibn Sîna, Cewâmi, p. 148.
21) Safi al-Dîn, Kitâb al-Adwâr, fol. 33.
22) Safi al-Dîn, Kitâb al-Adwâr, fols. 4-6; Alishah b. Haci Buke, Mukaddimat al-Usûl, fols. 48a-49a; Traite Anonyme, pp. 27-28; Al-Ladhiqî, al-Risâlah al-Fathiyyah, fols. 25a-26a; Also see; Yalçin Tura, Türk Musikisinin Meseleleri (The Pproblems of Turkish Music) Istanbul, 1988, pp. 182-184; M. Cihat Can, XV. Yüzyýl Türk Mûsikîsi Nazariyâti (Ses Sistemi), Ph.D. Thesis, Istanbul, 2001, pp. 156-157; Murat Bardakçi, Meragali Abdulkadir, Istanbul, 1986, pp. 56-57.
23) This is the kind as Safi al-Dîn indicates, having a value of 5/4. The ratio is the average value of the major third with a value of 8192/6561 used in practice.
24) Safi al-Dîn gives the ratio of 6/5 for Râhewî. But the ratio of 6/5 is the ratio used in stead of the minor third with the ratio of 32/27.
25) In the Treatises of al-Kindi, although the maqams which Safi al-Dîn mentioned with the names above are not taken place, together with tanînî, lawnî and te'lîfi names consisting the maqams, three more kinds and seven maqam ranges are presented. These are shown with the notes of modern time by the editors studying on al-Kindi. These maqams do not have a special names in al-Kindi but they are shown with their equal maqams in the Greek music. Turabi, pp. 83-84.
The subject of maqam is in the important topics of following music manuscripts. The source of these adwars is Safi Al-Dîn. However, there have been substantial differentiations in defining maqams and their numbers and existed important variaties about this subject between these manuscripts. See Alishah, fols. 14b-24b; al-Ladhiqî, al-Risâlah al-Fathiyyah, fols. 74a-74b; al-Shirwâni, Majallah fi al-Mûsiqi, fol. 100; Hizir b. Abd Allah, Kitâb al-Adwâr, Topkapi Rewan no: 1728, fol. 63b; Traite Anonyme, pp, 107-120.