Page:The New International Encyclopædia 1st ed. v. 13.djvu/727

MODULATION. 649 HCEKIS. passing UKxlulatiou. ]5iit even here the choice of keys is not arbitrary. However, no rule.s can be given ; tlie artistic and ustlietie instinct of the composer is the sole guide. Ac- cording to the theory of the present day, all modulation is regarded in its relation to the principal key of the piece, and, in a wider sense, all keys are but steps within the unlimited domain of tonality (q.v.). Older composers are very sparing and careful in the use of modula- tion, but those of the nineteentli ci'iit my (espe- cially Wagner, Schumann. Chopin) practically re- moved all barriers. The means of moilulation are various and cannot be discussed in an article like the present. The most frequent expedient is the different interpretations put upon the same chord. Thus the chord c, e, g may lie conceived as tonic of C, dominant of F, .sub- dominant of G, etc.. and consequently can be used to modulate at once to those keys. In modern music the chord of the diminished seventh plays an important part in modulation. Thus cjt, e, g, bb leads into D minor; the same chord conceived as e, g, bb, djj into F minor; as g, b), db, fb to A flat minor; as aJt, cj{, e, g into B minor, etc. The principal works on modulation are: Draseke, Antceisunfi ziiin kunstgerechten ModuUeren ( Freienwalde. 1876) ; Riemann. Hiir- monie und Modulatiotislehre (Leipzig, 1900): Jadassohn, Die Kiinst xu modulieren (Leipzig, 1890). MOiyULE (Fr. module, from Lat. modulus, small measure). In classic architecture, an arbitrary measure or standard for determining the proportions of the various members of the col- umnar orders. It is based upon the width of the temple fagade. Vitruvius. upon whose statement all such calculations have been based, divides a he.xastyle Doric front, for example, into 44 moduli, the capital being the modulus, the diameter of the shaft two moduli, the total height of the column 14 moduli, etc. Such a scheme was undoubtedly a (Jreek idea incor- porated in the writings of the Greek architects whom Vitruvius copied. But no such cast-iron rules could have been formulated .is were laid down by the neo-classic architects of the Renais- sance, such as Serlio and Vignola, who made the modulus the one determining iinit of proportion. By them the diameter, semi-diameter, or one- third of the diameter are most frequently used ; the first being usually divided into 60 parts (or minutes), the second into 30 parts, and the third into 20 parts. MODULUS (Lat., small measure). A term variously used in mathematics. In the theory of logarithms (q.v.) it designates the multiplier by which one system of logarithms is trans- formed into another. The expression ^'ar + 6" is often called the modulus of the complex num- ber, o + bi, where i stands for ■^/ — I. (See CoM- I'l.EX Number.) In the theory of numbers, the term congruence (q.v.) is applied to an equality in which we neglect certain quantities which are called 'moduli;' e.g. 26=12 (mod. 7) denotes that 26 is congruent to 12 to the modulus 7, i.e. that 26— 12 is a mul1i]ile iif 7. MODULUS OF ELASTICITY. See Elas- ticity. MOE, mo'e. .Torqen (1815-82). A Norwegian poet and folklorist. He was born at Holm, in the District of Kingerike. and before his entry at the University of Cliristiania became well acquainted with Asbjiirnscn (q.v.), later bis col- laborator. From 1835 to 1852 hardly a year passed during which Moe did not nuike a long tour of I lie country in search of jiopular legends. The first collection of these tales, edited by Moe and Asbjornsen under the title A'ocsA-e folkceventyr, appeared in 1842-44; was republished by Moe in 1852, and was translated into English by Dascnt (1859). His Hamlvde Hkrifler (1877) include the popular poems (1850) and the juvenile stories, / Briindi n og i Kjiirnct ( 1851 ) . Moe died at Christiansand, where he had been bishop for seven years. MOEL, moil (Welsh, hill). A hill having a rounded outline in its u|)per portion because the sunmiit is protected from rapid denudation by a layer of soil and a growth of forest trees or grass, or by marshes of peat. Consult Marr, The Ge- ograiihical Journal (London, 1901). MCELLER, mel'ler, Louis (1856—). An American genre painter, born in New York City. He was a pupil of E. M. Ward and Will Low in New York C!ity, and of Dietz and Duveneck in Munich. He is a clever delineator of character. In 1884 he won the first Hallgar- ten Prize with his picture "I'uzzled," and he was made a National Academician in 1895. MOEN, me'en. A Danish island in the Baltic Sea, separated from Seeland on the northwest by the Ulv Sound, and from Falster on the south- west by the Grijn Sound (Map: Denmark, F 4). Area, 82 square miles. Population, in 1901, 14,504. Its surface is remarkably irregular com- pared with the rest of Denmark. The limestone formation which underlies a large ])art of the country here crops out in the form of high and steep chalk clifl's of great natural beauty. The soil is very fertile. Agriculture and fisheries are the leading industries. The chief town and seaport is Stege, on the west coast, with :i popula- tion (1901) of 2247. MCE'R^. The Greek name of the Fates. See Pakc.e. MCERIS, me'ns (Lat., from Gk. Moipis, Moi- ri.i). Lake. The ancient name of a sheet of water in Central Eg^'pt, a remnant of which, it is generally agreed, exists in tlu^ present liirkrt- Karun or Birket el-Kerun ('lake of horns'), 34 miles long by iU miles wide, extending along the northwestern borders of the Province of Fayum. The classical writers have left Very confused descriptions of a great artificial reservoir at this locality for storing the water of the Nile and irrigating the surrounding coun- try by means of sluices. As the lake is at pres- ent 130 feet below the level of the sea. it must, within historic times, have hollowed out its bed 200 feet, or the artificial lake must have been a small reservoir southeast of it, or else the an- cients must have totally misrepresented the whole matter. The investigations of Major Brown, which have been fully confirmed by Petrie, seem to point to the last-named solution. The lake formed by the Bahr-Yusuf (.Joseph's Canal) must have been much larger, until the kings of Dynasty XII., and later the second Ptolemy, diked off considerable portions. The semi-mythi- cal King Moeris of Herodotus is Amenemhat III., the builder of the Labyrinth (q.v.), whose two