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These two terms, which occur in the late thirteenth-century Anonymus IV treatise (De mensuris et discantu), have often been cited as evidence of Arab musical influence in Western Europe: either in connexion with developments in melodic style, since they are identified as currentes, or, perhaps more ambitiously, in support of the contention that the emergence of mensural music in Western Europe was prompted by contact with Arab musical practice, which had long possessed a complex system of rhythmic modes
1 Described by al-Kindi, (Farmer, H. G., Sa'adyah Goon on the influence of music, London, 1943, 19)Google Scholar, and in greater detail by Sīnā, Ibn (d'Erlanger, R., La musique arabe, II, Paris, 1935, 167–228)Google Scholar, and, especially, al-Fārābī, (Kitāb al-mūsīqā al-kabīr, Cairo, n.d., 435–71, 983–1062Google Scholar; Neubauer, E., ‘Die Theorie vom īqā'. I. Übersetzung des Kitāb al-īqā'āt von Abū Nasr al-Fārābi’, Oriens, XXI, 1968, 196–232)CrossRefGoogle Scholar.
2 Farmer, H. G., ‘Clues for the Arabian influence on European musical theory’, Journal of the Royal Asiatic Society, 1925, pt. 1, 61–80Google Scholar.
3 ‘Music’, in Arnold, T. and Guillaume, A. (ed.), The legacy of Islam, London, 1931, 372Google Scholar; and (somewhat more guardedly) ‘The music of Islam’, in Wellesz, E. (ed.), New Oxford history of music, I. Ancient and Oriental music, London, 1957, 470–1Google Scholar.
Farmer's case was accepted in general outline by Trend, J. B. (Legacy of Islam, 18–19)Google Scholar and Sarton, G. (Introduction to the history of science, II, pt. I, Washington, D.C., 1931, 25 and 407)Google Scholar but does not appear to have gained any adherents among Western musicologists.
4 Seybold, C. F., Glossarium latino-arabicum (Semitistische Studien. Ergänzungshefte zur Zeitschrift für Assyriologie, 15–17), Berlin, 1900, 337Google Scholar.
5 ‘Clues’, 76.
6 ibid.
7 Handschin, J., ‘Zur Leonin-Perotin Frage’, Zeitschrift, für Musikwissenschaft, XIV, 1931–1932, 319–22Google Scholar.
8 The Arabic equivalents show that it is quite simply the feminine of nolus, which is also recorded in the Glossarium (p. 338), and is rendered by mashhür and ma'rūf.
9 Schmidt, H., ‘Zur Melodiebildung Leonins und Perotins’, Zeitschrift für Musikwissenschaft, XIV. 1931–1932, 129–34Google Scholar. The following passage (pp. 129–30) is especially pertinent. ‘Diese Portamenti und Glissandi konnen ebenfalls als ein Beweis fiir den mit orientalischen Gesangsmanieren verwandten, stark naturalistischen Stil dieser Kompositionen gotten, zumal selbst die Musiktheorie fiir die einzelnen Tonzeiohen dieser Läufe Ausdriieke orientalischen Ursprungs gebraucht. … Elmuahym und Elmuarifa sind kleine Notenwerte. welche moistens zu Gruppen vereinigt auftreten und bei den Theoretikern auch “currentes” genannt werden.’
10 Reese, G., Music in the Middle Ages, London, 1941, 298Google Scholar.
11 Chailley, J., ‘Elmuahym et Elmuarifa’, in Tischler, H. (ed.), Essays in musicology, a birthday offering for Willi Apel, Bloomington, 1968, 61–2Google Scholar.
12 See Neubauer, E., ‘Neuere Bücher zur arabischen Musik’, Der Islam, XVLIII, 1972, 13Google Scholar.
13 Chailley, art. cit. In al-Hasan, b.Ahmad, b. ‘Ali al-Kātib, La perfection des connaissances musicales (Kitāb kamāl adab al-ghinā’, tr. et comm. A.Shiloah) (Bibliothèqued'Études Islamiques, V), Paris, 1972, 128Google Scholar, the text is: ‘La muhāhā. C'est une expression qui rappelle les sanglote (ŝahaqāt); elle se produit sur la lettre hā' comnie par exemple: hā-hā …’.
14 However, since this word is defined as meaning ‘celle qui donne la connaissance, qui determine, qui définit’, it would seem that it is rather al-mu'arrif(a) that is intended.
15 Reokow, F., Der Musiktraktat des Anonymus 4, Teil I. Edition (zum, BeihefteArchiv für Musikwissenschaft, IV), Wiesbaden, 1967, 41Google Scholar.
16 The other contexts also imply shapes and figures: ‘fao tractum descendendo et protrahe a tractu unum simile elmuahim longum vel breve’ (ibid., 42); ‘fac quadrangulum … et iunge obliquo modo … elmuahim’ (p. 43); ‘Iterate est quaedam figura, quae dicitur elmuahim vel simil <e> sibi, , Et semper iacet obliquo modo quodammodo' (p. 45)Google Scholar.
17 art. cit., 321. Handschin's findings are noted and accepted in Ursprung, O., ‘Um die Frage nach dem arabischen bzw. maurischen Einfluss auf die abendländische Musik des Mittelalters (Nachtrag)’, Zeitschrift für Musikwissenschaft, XVI, 1934, 355–7Google Scholar.
18 Tahrīr Ūqlīdis, British Museum Add. MS 23387, fol. 3v: thumma dhū al-arba'at al-alā' wa-minhu al-murabba' …wa 'l-mu'ayyan wa-huwa al-mutasāwī al-adlā' wa 'l-shabīh bi 'l-mu'ayyan huwa alladhī lā takūn alā'uhu mutasāwiya wa-lā zawāyāhu qā'ima wa-lākin yatasāwā kull mutaqābilayn min alā'ihi wa-zawāyāhu wa'l-munarif wa-huwa mā'adāhā.
19 See ‘Euclid’, Dictionary of scientific biography, IV, New York, 1971, 440Google Scholar.
20 Besthorn, B. O. and Heiberg, J. L., Euclidis Elementa ex interpretatione al-Hadschdschadschii, I, fasc. II, Copenhagen, 1897, 148Google Scholar (proposition 35).
21 Kitāb Üqlīdis fī'l-usūl al-handasiyya, naql Ishāq b. Hunayn wa-islāh Abi'l-Ḥasan Thābit b. Qurra, Bodleian MS Thurston 11, fol. 2r: wa-ammā al-ashkāl dhawāt al-aḍlā' al-arba'a fa-inna minhā al-murabba' …wa-minhā al-mu'ayyan wa alladhī al-aḍlā' wa-laysa bi-qā'im al-zawāyā wa-minhā al-shabīh bi 'l-mu 'ayyan wa-huwa alladhī kull ḍil'ayn min aḍlā'ihi mutaqā-bilayn (MS mutaqābilān) mutasāwiyān wa-kull zāwiyatayn min zawāyāhu mutaqābilatayn mvtasāwiyatān wa-laysa bi-mutasāwi al-aḍlā' wa-lā qā'im al-zawāyā wa-mā kān ‘alā ghayr mā wasafnā min al-ashkāl dhawāt al-aḍlā' al-arba'a fa-l-yusamma (MS fa-l-yusammā) al-munharif.
22 Variants 1–4 occur in MSS of Anonymus IV, 4–7, in Adelard of Bath, while 8 is recorded in Latham, R. E., Revised Medieval Latin word-list from British and Irish sources, London, 1965Google Scholar, and given the reference presumably also derives from Adelard. Variants 4–7 are given in Oerberti … Opera mathematica, collegit N. Bubnov, Berlin, 1899, 176Google Scholar.
23 Variants 1 and 2 are in Anonymu s IV, 2–4, in Adelard.
24 It might seem equally justifiable to assume a sequence muhaijin > muhaim > muahim > muhahim (the last by dittography), but the above—which must still be regarded as largely conjectural—accords rather better with the chronology of the existing MSS. Even so, it should be noted that muain is one of the earliest forms to appear, and might therefore represent a direct derivation from muhaijin.
25 The formulation of the last part of the Isḥāq b. Ḥunayn-Thābit b. Qurra translation given in n. 21 above suggests that there might possibly have been another version in which the phrase al-ashkāl al-munḥarifa appeared, thus accounting for the final a in the Latin forms. The addition of a final a would, however, be by no means exceptional (see Latham, J. D., ‘Arabic into Medieval Latin’, Journal of Semitic Studies, XVII, 1, 1972, 30–67CrossRefGoogle Scholar (examples p. 40)).
28 ibid., 33–8.
27 Since it represented a sound foreign to most of those whose native speech was Romance (and even in Old French the occurrence of h was restricted to word-initial position).
28 In the British Museum Royal 12C VI MS of Anonymus IV, for example, elmuahym is only written thus on its first occurrence, being subsequently contracted to elmuahī.
29 Schirmer, A., ‘Der Wortschatz der Mathematik’, Zeitschrift fur devtsche Wortforschung, XIV, Beiheft, 1912Google Scholar, s. v. ‘Rhombus’. These forms are said to be derived not from Adelard's translation of an Arabic Euclid but from that of Campanus—but since Campanus' version falls broadly within the Adelard tradition the distinction is of no great consequence in the present context. The forms found in the 1509 edition (Euclidis megarensis … opa a Campano … translota, Venice) are helmuaim, simil-hdmuaī (fol. 4r, diagrams); helmuaripha (ibid., and fol. 4v); and helmuaym (fol. 4v). elmuahin does not appear.
30 He does, however, list (op. cit., s. v. ‘Trapez’) the forms elmuharifa and elmifarifa (occurring in the Geometria Culmensis of c. 1400).
31 Lokotsch, K., Etymologisches Wōrterbuch der europäischen Wörter orientalischen Ursprungs (Sammlung Indogermanischer Lehr- und Handbücher, II. Reihe: Wörterbücher. Dritter Band), Heidelberg, 1927Google Scholar, s.v. mu'ajjan.
34 ibid., s.v. mu'arrif.
33 The only flaw in Handschin's argument is that he paid insufficient attention to, or misinterpreted, the deliberately cautious way in which Farmer couched his comments on al-ma'luma and al-ma'lūfa. Handschin accepted these as the correct etymologies (art. cit., 322) and concluded: ‘Die Frage ist nun, wie der arabische Vorgänger des Adelard darauf kam, Euklids Rhombos, Rhomboeides und Trapezion durch Wörter wiederzugeben, die “die Bekannte, die durch das Wissen Erfasste” bedeuten; dies ist indessen eine Frage für den Arabisten’.