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Such transposition is always indicated by a B flat in the signature.In these cases the true final will be either a fourth below or a fifth above the closing note.But any phrase except the last- of a melody., may also end upon these tones.; Hence they are also called cadences or modula- tions .As in a long melody a feeling of monot- ony would be produced by the constant employ- ment of these modulations, two or more tones are admitted.It is significant that only about 31,000,000, or less than 15 per cent, of this Mohammedan popula- tion are found in politically independent Moslem states, viz. Deutsch, Essay on Islam (ib., 1874) ; Arinin Vambgry, Der Islam im 19 ten Jahr- hundert (Leipzig, 1875) ; Blunt, The Future of Islam (London, 1880) ; J.: in Turkey, 16,500,000 ; Persia, 9,200,000; Afghanistan, 5,000,000; while Great Britain has about 95,000,000, Holland about 30.000. Dozy, Set Islamisme (Ley- den, 1863; French trans., J Essai sur Fhistoire de V Islamisme, Paris, 1879) ; Alfred von Kremer, Geschichte der herrschenden Ideen des Islam (Leipzig, 1868) ; Ahmed Khan Bahadur, A Series of Essays on the Life of Mahomet and Subjects Subsidiary thereto (London, 1870) ; E. Hauri, Der Islam in seinem Einfluss auf das Leben seiner Beken- ner (Leyden, 1881) ; C. Pischon, Der Einfluss des Islam auf das hausliche, sociale und polit- ische Leben seiner Bekenner (Leipzig, 1881); Poole, Studies in a Mosque (London, 1883) ; T. Hughes, A Dictionary of Islam (ib., 1885) ; August Muller, Der Islam im Morgen- und Abendlande (Berlin, 1885-87) ; Le Cha- telier, L’Islamisme aw 19e siecle (Paris, 1889) ; Ameer Ali, The Life and Teachings of Moham- med (London, 1891), a defense of Islam by an intelligent and educated Moslem; De Castries, L’Islam (Paris, 1897; 5th ed., 1912); H. I slams ( Friedrichshagen, 1897) ; Sachau, Muhammedanisches Recht naeh schafiitischer Lehre (Stuttgart, 1897) ; Bernard Carra de Vaux, Le Mahometisme (Paris, 1898) ; Atterbury, Islam in Africa (New York, 1899) ; Le Chatelier, L’Islamisme dans VAfrique occi- dental (Paris, 1899) ; Martin Hartmann, Der islamische Orient (Berlin, 1899) ; D. Forget, L’Islam et le Christianisme dans I’Afrique cen- trale (ib., 1900) ; D. Macdonald, Develop- ment of Muslim Theology , Jurisprudence, and Constitutional Theory (New York, 1903) ; T. de Boer, Geschichte der Philosophic im Islam (Stuttgart, 1901; Eng. Houdas, L’Islamisme (Paris, 1904) ; Hubert Grimme, Mohammed : Die weltgeschichtliche Bedeutung Arabiens (Munich, 1904) ; D. Margoliouth, Mohammed and the Rise of Islam (London, 1905) ; Hogarth, The Penetration of Arabia (ib., 1905) ; Armin Vamb4ry, Western Culture in Eastern Lands (New York, 1906) ; Martin Hartmann, Islam, Mission, Politik (Leipzig, 1912) ; id., Fuhf Yortrdge uber den Islam (ib., 1912) ; * S. Zwemer, Arabia (2d ed., New York, 1912) ; Ignaz Goldziher, Die Religion des I slants' • (2d ed., ^ Berlin, 1913)4' MOHAMMEDAN SECTS 88 MOHAMMEDAN SECTS T. Arnold, The Preaching of Islam: A His- tory of the Propagation of the Muslim Faith ( 2d ed., London, 1913) ; C. Becker, “The Expan- sion of the Saracens, 5 ’ in The Cambridge Mediae- val History, vol. Consult also the journals recently established dealing especially with Mohammedan subjects, such as Revue du Monde Musulman (Paris, 1909 et seq.) ; JDer Islam (Strassburg, 1910 et seq.) ; the Moslem World (London, 1911 et seq.) ; Die islamische Welt (Berlin, 1911 et seq.); Mir Islama (Petrograd, 1911 et seq.) ; the excellent summaries in Rimsta degli studi oriental i (Rome, 1908 et seq.) ; the Enzyklopaedie des Islam (Leyden, 1908 et seq.). 6 “ “ glare, care, and as e in there, a “ u am, at. In these two modes the pentachord represents the compass of a di- minished fifth, the tetrachord that of an aug- mented fourth (tritonus). a “ “ final, regal, pleasant, a “ “ all, fall, e u u eve. In examining the above table it will be noticed that the pentachords and tetrachqrds of all the modes, except the Locrian and Hypolocrian, exhibit the compass of a perfect fifth or fourth.

One of the most frequent of these conceded modulations is the seventh tone of the mode.

The mediamt derives its name from the fact that in the authentic modes it always lies midway between the final and the dominant; it is always the third tone of the mode.

In the plagal modes the position of the mediant is rather unsettled, owing to the necessity of ob- taining a convenient tone for cadences, as in the case of the dominant, and for the same reason B can never appear as a mediant. The participant in the authentic modes lies either between the final and the mediant, or between the mediant and the dominant.

000, France about 22,000,000, Russia about 14,000,000, China about 12,000,000, and Abyssinia about 5,000,000 Mohammedans. The works mentioned in the articles Koran and Mohammed are all impor- tant for the general subject of Islam. Lane, The Man- ners and Customs of the Modem Egyptians (London, 1836; many subsequent editions), the best popular account of Mohammedan life and customs; R. See Koran; Mohammed; Shiites; Sunna; Mohammedan Sects; Mecca; Medina; Wahabi. The movement which led to the division of Islam into opposing parties was at first a political one, though reli- gious, theological, and philosophical questions soon arose which added to the complexity of the situation and caused a further subdivision into sects.

Consult also: Geiger, Was hat Mohammed axis dem Judenthum aufgenommenf (Bonn, 1833; Eng. Mohammed died without naming his suc- cessor; and while Abu Bekr was looked upon by many as the natural leader, others felt that Ali, who was not only the cousin and son-in- law but also a decided favorite of the Prophet, should be his successor.