THE ENCYCLOPEDIA BRITANNICA ELEVENTH EDITION FIRST edition, published in three volumes, 1768— 1771. SECOND 99 » ten 99 1777— 1784. THIRD >» ,, eighteen 99 1788— 1797. FOURTH >» „ twenty 99 l80I l8lO. FIFTH IS ,, twenty 99 l8lS—l8l7. SIXTH 99 „ twenty 99 l823 1824. SEVENTH 99 „ twenty-one 99 183O 1842. EIGHTH 99 „ twenty-two 99 l8S3 — l860. NINTH 99 „ twenty-five 91 I875— 1889. TENTH- 99 ninth edition and eleven supplementary volumes, I902 I9O3. ELEVENTH 1) published in twenty-nine volumes, I9IO I9II. COPYRIGHT in all countries subscribing to the Bern Convention by THE CHANCELLOR, MASTERS AND SCHOLARS , of the UNIVERSITY OF CAMBRIDGE All rights reserved THE ENCYCLOPAEDIA BRITANNICA A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION ELEVENTH EDITION VOLUME XIII HARMONY to HURSTMONCEAUX New York Encyclopaedia Britannica, Inc. 342 Madison Avenue Copyright, in the United States of America, 1910, by The Encyclopaedia Britannica Company. INITIALS USED IN VOLUME XIII. TO IDENTIFY INDIVIDUAL CONTRIBUTORS, 1 WITH THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED. A. E. G.* Rev. Alfred Ernest Garvie, M.A., D.D. f Principal of New College, Hampstead. Member of the Board of Theology and J Heresv (in 6ar£\ the Board of Philosophy, London University. Author of Studies in the Inner Life | pan), of Jesus, &c. L Henry Austin Dobson, LL.D. I Hogarth. See the biographical article, Dobson, H. A. L Alfred Edward Thomas Watson. f w n rc« Bo»imr c * ,\ Editor of the Badminton Library and Badminton Magazine. Formerly Editor J « or5 «;-Kacing \m part); of the Illustrated Sporting and Dramatic News. Author of The Racing World and Hunting. its Inhabitants: &c. Algernon Charles Swinburne. J Hugo Victor. See the biographical article, Swinburne, A. C. I ' Arthur Ernest Cowley, M.A., Litt.D. / Hebrew Language; Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen College. \ Hebrew Literature. Albert Frederick Pollard, M.A., F.R.Hist.S. ("Heath, Nicholas; Professor of English History in the University of London. Fellow of All Souls Henry VIII. of England* College, Oxford. Assistant Editor of the Dictionary of National Biography, 1893- -\ rr nnn -, t}! C \,„„. ' iqoi. Lothian Prizeman (Oxford), 1892, Arnold Prizeman, 1898. Author of England cooper, msaof, under the Protector Somerset; Henry VIII. ; Life of Thomas Cranmer; &c. I Humphrey, Lawrence. A. Go.* Rev. Alexander Gordon, M.A. J Hofmann, Melchior; Lecturer on Church History in the University of Manchester. I Hotman. A. H. S. Rev. Archibald Henry Sayce; D.D. , Litt.D., LL.D. /Humboldt Karl W. Von. See the biographical article, Sayce, A. H. \ ' A. H.-S. Sir A. Houtum-Schindler, CLE. f „___,,_ , . . General in the Persian Army. Author of Eastern Persian Irak. \ Hormuz (m part). A. J. H. Alfred J. Hipkins, F.S.A. (1826-1003). r Formerly Member of Council and Hon. Curator of the Royal College of Music, London. Member of Committee of the Inventions and Music Exhibition, 1885; of -j Harp {in part). the Vienna Exhibition, 1892; and of the Paris Exhibition, 1900. Author of Musical I Instruments; &c. A. D. A. E. T. w A. C.S. A. cy. A. P. P. A. L. Andrew Lang. J Hauntings. See the biographical article, Lang, Andrew. I A. M. C. Agnes Mary Clerke. See the biographieal article, Clerke, A. M. A. N. Alfred Newton, F.R.S. See the biographical article, Newton, Alfred. A. SI. Arthur Shadwell, M.A., M.D.', LL.D., F.R.CP. Herschel, Sir F. W. (in part); Herschel, Sir J. F. W. (in part). Hevelius; Hipparehus; Horrocks; Huggins; Humboldt. Harpy; Harrier; Hawfinch; Hawk; Heron; Hoactzin; Honeyeater; Honey Guide; Hoopoe; Hornbill; Humming-Bird. IUR SHADWELL, 1VI. A., 1V1.JJ., L,L,.D., r.K.U.r. r Member of Council of Epidemiological Society. Author of Industrial Efficiency ; J Housing. The London Water Supply; Drink, Temperance and Legislation. | A. W. H.* Arthur William Holland. f Henry IV.: Roman Emperor; Formerly Scholar of St John's College, Oxford. Bacon Scholar of Gray's Inn, 1900. < Hide; Hohenzollern; [Honorius II.; Anti-Pope. A. W. W. Adolphus William Ward, Litt.D., LL.D. r See the biographical article, Ward, A. W. \ Hrosvitha. C. A. M. F. Charles Augustus Maude Fennell, M.A., Litt.D. f Formerly Fellow of Jesus College, Cambridge. Editor of Pindar's Odes and Frag- -j Hercules. ments; and of the Stanford Dictionary of Anglicised Words and Phrases. [ 1 A complete list, showing all individual contributors, appears in the final- volume. VI C. B.* C. El. C. F. A. C. H. Ha. C. J. L. C. L. K. C. Mo. C. P. INITIALS AND HEADINGS OF ARTICLES Charles Bemont, Litt.D. (Oxon.). JHavet; See the biographical article, Bemont, C. \ Hozier. Sir Charles Norton Edgcumbe Eliot, K.C.M.G., C.B., M.A., LL.D., D.C.L. r Vice-Chancellor of Sheffield University. Formerly Fellow of Trinity College, HlSSar (in part); Oxford. H.M.'s Commissioner and Commander-in-Chief for the British East -j Hungary: Language; Africa Protectorate; Agent and Consul-General at Zanzibar; and Consul-General Huns. for German East Africa, 1900-1904. I Charles Francis Atkinson, Formerly Scholar of Queen's College, Oxford. Captain, 1st (Royal Fusiliers). Author of The Wilderness and Cold Harbour. Carlton Huntley Hayes, A.M., Ph.D. Assistant Professor of History in Columbia University, New York City, of the American Historical Association. ' City of London 1 Hohenlohe (in part). Member ] Honorius II., III., IV. L Hindostani Literature. J Henry IV., V., VI.: [ of England. 1 Hunt, W. Holman. Herschel, Sir P. W. (in part) ; Herschel, Sir J. F, (in part). c. PI. c. R. B. c. s. c. w. W Author i Hunald. Hayton; Henry the Navigator. Hayes, Rutherford B. D. B. M. D. F. T. D. Gi. D. G. H. D. H. D. Mn. D. S.* E. C. B. E. D. B. Sir Charles James Lyall, K.C.S.I., CLE., LL.D. (Edin.). Secretary Judicial and Public Department, India Office. Fellow of King's College London. Secretary to Government of India, Home Department, 1889-1894. " Chief Commissioner, Central Provinces, India, 1895-1898. Author of Translations of Ancient Arabic Poetry; &c. Charles Lethbridge Kingsford, M.A., F.R.Hist.S., F.S.A. Assistant Secretary to the Board of Education. Author of Life of Henry V. Editor of Chronicles of London, and Stow's Survey of London. William Cosmo Monkhouse. See the biographical article, Monkhouse, W. C. Rev. Charles Pritchard, M.A. See the biographical article, Pritchard, Charles. Christian Pfister, D.-es-L. Professor at the Sorbonne, Paris. Chevalier of the Legion of Honour, of Etudes sur le regne de Robert le Pieux. Charles Raymond Beazley, M.A., D.Litt. Professor of Modern History in the University of Birmingham. Formerly Fellow of Merton College, Oxford, and University Lecturer in the History of Geography. Author of Henry the Navigator; The Dawn of Modern Geography; &c. Carl Schurz, LL.D. See the biographical article, Schurz, Carl. ' Sir Charles William Wilson, K.C.B., K.C.M.G., F.R.S, (1836-1907). Major-General, Royal Engineers. Secretary to the North American Boundary- Commission, 1858-1862. British Commissioner on the Servian Boundary Com- mission. Director-General of the Ordnance Survey, 1886-1894. Director-General" of Military Education, 1895-1898. Author of From Korti to Khartoum; Life of Lord Clive ; &c. David Binning Monro, M.A., Ltrr.D. See the biographical article, Monro, David Binning. Donald Francis Tovey. f Author of Essays in Musical Analysis: comprising The Classical Concerto, The< Harmony. Goldberg Variations, and analyses of many other classical works. |_ Sis David Gill, K.C.B., LL.D., F.R.S., F.R.A.S., D.Sc. H.M. Astronomer at Cape of Good Hope, 1879-1907. Served in Geodetic Survey of Egypt, and on the expedition to Ascension Island to determine the Solar Parallax by observations of Mars. Directed Geodetic Survey of Natal, 1 Cape Colony and Rhodesia. Author of Geodetic Survey of South Africa ; Catalogues of Stars for the Equinoxes (1850, i860, 1885, 1890, 1900); &c. David George Hogarth, M.A. Keeper of the Ashmolean Museum, Oxford. Fellow of Magdalen College, Oxford. Fellow of the British Academy. Excavated at Paphos, 1888; Naucratis, 1899 and 1903; Ephesus, 1904-1905; Assiut, 1906-1907. Director, British School at Athens, 1897-1900. Director, Cretan Exploration Fund, 1899. David Hannay. Formerly British Vice-Consul at Barcelona. Author of Short History' of the Royal Navy ; Life of Emilio Castelar ; &c. w. Hierapolis (in part). { Homer. Heliometer. Heraclea (in part); Hierapolis (in part); Hittites. Heyn; Hood, Viscount; Howe, Earl; Humour. Rev. Dugald Macfadyen, M.A. Minister of South Grove Congregational Church, Highgate. Congregational Ideals ; &c. . ^, , „ . , . f Henderson, Alexander Author of Constructive < , . ' (in part). David Sharp, M.A., M.B., F.R.S., F.Z.S. Editor of the Zoological Record. Formerly Curator of Museum of Zoology, Univer- J Hexapoda (in part). sity of Cambridge. President of Entomological Society of London. Author of | " Insecta " (Cambridge Natural History) ; &c. ' I Rt. Rev. Edward Cuthbert Butler, O.S.B., M.A., D.Litt. Abbot of Downside Abbey, Bath. Author of " The Lausiac History of Palladius ' in Cambridge Texts and Studies, vol. vi. Edwin Dampier Brickwood. Author of Boat-Racing; &c. Hierony mites; Hilarion, Saint. f Horse: History; \ Horse-Racing (in part). INITIALS AND HEADINGS OF ARTICLES Vll E. D. Bu. E. E. S. E. F. S. E. G. Ed . M. E. M. W E. 0.* E. Pr. E. Re * E. R. B. F. B. F. C. C. F. G. M. B F. G. P. F. G. S. F. H. B. F. LI. G. F. 0. B. F Px. G. A. Gr. G. C. R. G. C. W. Hungary: Literature (in part). Edward Dundas Butler. Formerly Assistant in the Department of Printed Books, British Museum. Foreign Member of the Hungarian Academy of Sciences. Author of Hungarian Poems and Fables for English Readers ; &c. *- Ernest Edward Sikes, M.A. f „„.„.,„. Fellow, Tutor and Lecturer, St John's College, Cambridge. Newton Student at J nepnaesius, Athens, 1890. Editor of the Prometheus Vinctus of Aeschylus, and of The Homeric ] Hera; Hermes. Hymns. L Edward Fairbrother Strange. f Assistant- Keeper, Victoria and Albert Museum, South Kensington. Member of J Hiroshige; Council, Japan Society. Author of numerous works on art subjects. Joint-editor | Hokusai. of Bell's " Cathedral " Series. I Edmund Gosse, LL.D. See the biographical article, Gosse, Edmund, W. f Heroic Romances; i Heroic Verse; [Herrick; Holberg. Eduard Meyer, Ph.D., D.Litt. (Oxon.), LL.D. f" Professor of Ancient History in the University of Berlin. Author of Geschichte < Hormizd. des Alterthums ; Geschichte des alien Aegyptens ; Die Israeliten und ihre Nachbarstdmme. { Herodotus (in part). Heart: Surgery; Hernia. ■I Hungary: Literature (in part), Rev. Edward Mewburn Walker, M.A. J Fellow, Senior Tutor and Librarian of Queen's College, Oxford. I Edmund Owen, M.B., F.R.C.S., LL.D., D.Sc. Consulting Surgeon to St Mary's Hospital, London, and io the Children's Hospital, Great Ormond Street, London. Chevalier of the Legion of Honour. Late Examiner " in Surgery at the Universities of Cambridge, London and Durham. Author of A Manual of Anatomy for Senior Students. Edgar Prestage. ~ r Special Lecturer in Portuguese Literature at the University of Manchester. Com- J Herculano de CarvalnO 6 mendador, Portuguese Order of S. Thiago. Corresponding Member of Lisbon | Araiyo. Royal Academy of Sciences and Lisbon Geographical Society. I Emil Reich, Doc.Juris., F.R. Hist. S. Author of Hungarian Literature ; History of Civilization ; &c. Edwyn Robert Bevan, M.A. f New College, Oxford. Author of Tlie House of Seleucus ; Jerusalem under the High -j Hellenism. Priests. I Felice Barnabei, Litt.D. f „ Formerly Director of Museum of Antiquities at Rome. Author of archaeological "j HeTCUlaneum. papers in Italian reviews and in the Athenaeum. I Frederick Cornwallis Conybeare, M.A., D.Th. (Giessen). f Fellow of the British Academy. Formerly Fellow pf University College, Oxford. -{ Holy Water. Author of The Ancient Armenian Texts of Aristotle; Myth, Magic and Morals; &c. I Frederick George Meeson Beck, M.A. Fellow and Lecturer of Clare College, Cambridge. Frederick Gymer Parsons, F.R.C.S., F.Z.S., F.R.Anthrop.Inst. Vice-President, Anatomical Society of Great Britain and Ireland. Lecturer on Anatomy at St Thomas's Hospital and the London School of Medicine for Women. Formerly Hunterian Professor at the Royal College of Surgeons. F. G. Stephens. Formerly art critic of the Athenaeum. Author of Artists at Home; George Cruik- shank; Memorials of W. Mulready; French and Flemish Pictures; Sir E. Landseer; T. C. Hook, R.A.; &c. ■i Heruli. -j Heart: Anatomy. Holl, Frank. f Honey; Hunter, John; \ Hunter, William. Francis Henry Butler, M.A. Worcester College, Oxford. Associate of the Royal School of Mines. Francis Llewellyn Griffith, M.A. , Ph.D., f.S. A. f Heliopolis- Reader in Egyptology, Oxford University. Editor of the Archaeological Survey J w „ pm£ . c Tricmoaicfiic and Archaeological Reports of the Egypt Exploration Fund. Fellow of Imperial 1 " ermes msmeglSlUS, German Archaeological Institute. l_ Horus. Frederick Orpen Bower, D.Sc, F.R.S. r Regius Professor of Botany in the University of Glasgow. Author of Practical } Hofmeister. Botany for Beginners. [ Frank Puaux. r President of the Societe de l'Histoire du Protestantisme frangais. Author of J __ . Les Precurseurs francais de la tolerance ; Hisloire de I'ctablissement des protestants 1 Huguenots. franQais en Suede ; L'Eglise reformee de France ; &c. [ George Abraham Grierson, CLE. Ph.D., D.Litt. Member of the Indian Civil Service, 1873-1903. In charge of Linguistic Survey of India, 1898-1902. Gold Medallist, Asiatic Society, 1909. Vice-President of ^ HindostariT. the Royal Asiatic Society Formerly Fellow of Calcutta University. Author of The Languages of India ; &c. George Croom Robertson, M.A. See the biographical article, Robertson, G. George Charles Williamson, Litt.D. Hobbes, Thomas (in part). Chevalier of the Legion of Honour. Author of Portrait Miniatures; Life of Richard J I r-„. a _j' H -„ k .i,.. n^i,;.. Cos-way, R.A.; George Engleheart; Portrait Drawings; &c. Editor of new edition ] " ima ™> Hicnoias, H0SK1DS. of Bryan's Dictionary of Printers and Engravers. f Hilliard, Lawrence; A Hilliard, Nicholas [Humphry, Ozias. vlii 6. G. S. G. E. G. H. C. G. J. T. G. K. G. R. G. W. T. H. H.Br. H. Bt H. Cta. H. De. H. L. H. L. C. H. M. V. H. W. C. D. H. W. R.* H. W. S. INITIALS AND HEADINGS OF ARTICLES H Y. I. A. J. A. C. J. A. R. I. Bt George Gregory Smith, M.A. Professor of English Literature, Queen's University of Belfast. Author of The- Days of James IV.; The Transition Period; Specimens of Middle Scots; &c. Rev. George Edmundson, M.A., F.R.Hist.S. Formerly Fellow and Tutor of Brasenose College, Oxford. Ford's Lecturer, 1909. . Hon. Member, Dutch Historical Society, and Foreign Member, Netherlands Associa- tion of Literature. Henryson. Holland: History. Holland: County and Province of. George Herbert Carpenter, B.Sc. f n.miMoM • Professor of Zoology in the Royal College of Science, Dublin. President of the) nemipiera. Association of Economic Biologists. Member of the Royal Irish Academy. Author ] Hexapoda {-in part). of Insects: their Structure and Life ; &c. George James Turner. Barrister-at-Law, Lincoln's Inn. Editor of Select Pleas for the Forests for the Selden Society. Gustav Kruger. Professor of Church History in Papsttum; &c. Rev. George Rawlinson, M.A. See the biographical article, Rawlinson, George. the University of Giessen. Author Hundred. of r(M |HIppolytUB. Rev. Grifeithes Wheeler Thatcher, M.A., B.D. Warden of Camden College, Sydney, N.S.W. Formerly Tutor in Hebrew and Old Testament History at Mansfield College, Oxford. Lord Houghton. See the biographical article, Houghton, ist Baron. Henry Bradley, M.A., Ph.D. J „ .. . Joint-editor of the New English Dictionary (Oxford). Fellow of the British Academy. 1 "euano. Author of The Story of the Goths ; The Making of English ; &c. *• Sir Henry Burdett, K.C.B., K.C.V.O. _ f Founder and Editor of The Hospital. Formerly Superintendent of the Queen's - Hospital, Birmingham, and the Seamen's Hospital, Greenwich. Author of Hospitals and Asylums of the World; &c. Hugh Chisholm, M.A. Formerly Scholar of Corpus Christi College, Oxford. Editor of the nth edition" of the Encyclopaedia Britannica; Co-editor of the 10th edition. Herodotus (in part). Hasan-ul-Basn; Hassan ibn Thabit; Hisham ibn al-Kalbi. i Hood, Thomas. Hospital. Howe, Samuel Gridley. HlPPOLYTE DELEHAYE, S.J. Assistant in the compilation of the Bollandist publications: Analecta Bollandiana ' and Acta sanctorum. Henri Labrosse. Assistant Librarian at the Bibliotheque Nationale, Paris. Officer of the Academy Hugh Longbourne Callendar, F.R.S., LL.D. Professor of Physics, Royal College of Science, London. Formerly Professor of Physics in McGill College, Montreal, and in University College, London. Herbert M. Vaughan, F.S.A. Keble College, Oxford. Author of The Last of the Royal Stuarts; The Medici Popes; The Last Stuart Queen. Helena, St; Hubert, St. J Hugh of Heat. St Cher. Henry, Stuart (Cardinal York). Henry I., II., Ill,: Of England. Henry of Huntingdon. Henry William Carless Davis, M.A. Fellow and Tutor of Balliol College, Oxford. Fellow of All Souls College, Oxford, 1895-1902. Author of England under the Normans and Angevins; Charlemagne. Rev. Henry Wheeler Robinson, M.A. f Professor of Church History in Rawdon College, Leeds. Senior Kennicott Scholar, j Hosea (in part). Oxford, 1901. Author of Hebrew Psychology in Relation to Pauline Anthropology \ (in Mansfield College Essays) ; &c. <■ H. Wickham Steed. [ Correspondent of The Times at Vienna. Correspondent of The Times at Rome, i Humbert, King. 1 897-1902. L Sir Henry Yule, K.C.S.I., C.B. See the biographical article, Yule, Sir H. Israel Abrahams, M.A. Reader in Talmudicrand Rabbinic Literature in the University of Cambridge. J Herzl; Hormuz (in part); Hsttan Tsang (in part). Hasdai ibn Shaprut; Formerly President, Jewish Historical Society of England. Author of A Short History of Jewish Literature; Jewish Life in the Middle Ages; Judaism; &c. Sir Joseph Archer Crowe, K.C.M.G. See the biographical article, Crowe, Sir J. A. Very Rev. Joseph Armitage' Robinson, D.D. ___ Dean of Westminster. Fellow of the British Academy.^ Hon. Fellow of Christ's College, Cambridge. Formerly Fellow of Christ's College, Cambridge, and Norris- ian Professor of Divinity in the University. Author of Some Thoughts on the Incarnation; &c. James Bartlett. f Lecturer on Construction, Architecture, Sanitation, Quantities, &c, at King's J Heating. College, London. Member of Societv Of Architects., Member of Institute of j Junior Engineers. I Hirsch, Samson R. Hobbema; Holbein. Hippolytus, The Canons of. INITIALS AND HEADINGS OF ARTICLES IX J. B. T. J. Da. J. E. J. F. F. J. F. H. B. J. G.* J. Ga. J. G. M. J. G. R. J. Hn. J. H. A. H. J. H. F. J. H. Mu. J. H. R. J. J. F. J. K. L. J. M. M. J. P.-B. J. P. Pe. J. S. Co. J. S. F. h T. Be. Sir John Batty Tuke, M.D., F.R.S. (Edin.), D.Sc, LL.D. f President of the Neurological Society of the United Kingdom. Medical Director J HiDDOcrates of New Saughton Hall Asylum, Edinburgh. M. P. for the Universities of Edinburgh | vv and St Andrews, 1900-1910. I Rev. James Davies, M.A. (1820-1883). f Formerly Head Master of Ludlow Grammar School and Prebendary of Hereford . Cathedral. Translated classical authors for Bohn's " Classical Library." Author of volumes in Collins's Ancient Classics for English Readers. Hesiod {in part). H. Julius Eggeling, Ph.D. Professor of Sanskrit and Comparative Philology, University of Formerly Secretary and Librarian to Royal Asiatic Society. Edinburgh, i Hinduism. John Faithfull Fleet, CLE. Commissioner of Central and Southern Divisions of Bombay, 1891-1897. Author'! Hindu Chronology. of Inscriptions of the Early Gupta Kings; &c. Sir John Francis Harpin Broadbent, Bart., M.A., M.D. r Physician to Out-Patients, St Mary's Hospital, London, and to the Hampstead I Tr oar *. rr , n- General Hospital. Assistant Physician to the London Fever Hospital. Author 1 Hearl - Heart Disease. of Heart Disease and Aneurysm ; &c. |_ Rev. James Gow, M.A., Litt.D. r Head Master of Westminster School. Fellow of King's College, London. Formerly] „ , . . Fellow of Trinity College, Cambridge. Editor of Horace's Odes and Satires. Author] uoraee \™ part). of A Companion to the School Classics; &c. I. Henry VII.: of England. James Gairdner, C.B. See the biographical article, Gairdner, J. John Gray McKendrick, M.D. , LL.D., F.R.S., F.R.C.P. (Edin.) fHearine- Emeritus Professor of Physiology at" the University of Glasgow. Author of Life •{ „ , . ,. in Motion ; Life of Helmholtz ; &c. [ HelmnoltZ. John George Robertson, M. A., Ph.D. f Heine (in part); Professor of German at the University of London. Formerly Lecturer on the English -| Hiidebrand, Lay of" Language, Strassburg University. Author of History of German Literature ; &c. Hoffmann E T W Justus Hashagen, Ph.D. Privatdozent in Medieval and Modern History, University of Bonn. Author of- Das Rheinland unter der franzosischen Herrschdft. John Henry Arthur Hart, M.A. Fellow, Theological Lecturer and Librarian, St John's College, Cambridge. John Henry Freese, M.A. Formerly Fellow of St John's College, Cambridge. John Henry Muirhead, M.A. , LL.D. r „ . „ ,. . Professor of Philosophy in the University of Birmingham. Author of Elements J Me & el - Hegelianism m of Ethics; Philosophy and Life; &c. Editor of Library of Philosophy. } England. John Horace Round, M.A., LL.D. (Edin.). r Author of Feudal England; Studies in Peerage and Family History; Peerage and J Hereward. Pedigree. 1 Hecker, F. F. K.; Hertzberg, Count Von; I Hormayr. -j Herod; Herodians. 4 Herald; Hesiod {in part). Hecker, I. T. Hood of Avalon. Heraclitus; Hume, David {in part). Rev. James J. Fox. St Thomas's College, Brookland, D.C., U.S.A. Sir John Knox Laughton, M.A., Litt.D. Professor of Modern History, King's College, London, Secretary of the Navy Records Society. Served in the Baltic, 1854-1855; in China, 1856-1859. Honorary Fellow, Gonville and Caius College, Cambridge. Fellow, King's College, London. Author of Physical Geography in its Relation to the Prevailing Winds and Currents; Studies in Naval History; Sea Fights and Adventures; &c. John Malcolm Mitchell. Sometime Scholar of Queen's College, Oxford. Lecturer in Classics, East London College (University of London). Joint-editor of Grote's History of Greece. James George Joseph Penderel-Brodhurst. Editor of the Guardian (London). Rev. John Punnett Peters, Ph.D., D.D. Canon Residentiary, Cathedral of New York. Formerly Professor of Hebrew in the University of Pennsylvania. Director of the University Expedition to Babylonia, 1888-1895. Author of Nippur, or Explorations and Adventures on the Euphrates. James Sutherland Cotton, M.A. , Editor of The Imperial Gazetteer of India. Hon. Secretary of the Egyptian Explora- J „ ,. „. tion Fund. Formerly Fellow and Lecturer of Queen's College, Oxford. Author | Hastings, Warren. of India in the " Citizen " Series; &c. [ John Smith Flett, D.Sc, F.G.S. r Petrographer to the Geological Survey. Formerly Lecturer on Petrology in Edinburgh University. Neill Medallist of the Royal Society of Edinburgh. Bigsby Medallist of the Geological Society of London. L John T. Bealby. r Joint-author of Stanford's Europe. Formerly Editor of the Scottish Geographical \ Hissar (in part). Magazine. Translator of Sven Hedin's Through Asia, Central Asia and Tibet; &c. L -j Hepplewhite. Hillah; Hit. Hornfels. X J. T. C. J. T. Mo. J. T. S.* J. v.* J. V. B. J. Ws. J. W.* J. W. F. J W. Fo INITIALS AND HEADINGS OF ARTICLES K. S. L H. B. L J. S. L. W M. G. M. Ha. M. H. C. M. N. T. M. 0. B. C. M. T. M. N. D. M. 0. Ba. O.Br. Herring. Joseph Thomas Cunningham, M.A. ,F.Z.S. Lecturer on Zoology at the South- Western Polytechnic, London. Formerly Fellow . of University College, Oxford. Assistant Professor of Natural History in the University of Edinburgh and Naturalist to the Marine Biological Association. John Torrey Morse, Jr. Author of The Life and Letters of Oliver Wendell Holmes. James Thomson Shotwell, Ph.D. Professor of History in Columbia University, New York City. Jules Viard. . % Archivist at the National Archives, Paris. Officer of Public Instruction. Author 1 WUnared Years War. of La France sous Philippe VI. de Valois ; &c. James Vernon Bartlet, M.A., D.D. (St Andrews). Professor of Church History, Mansfield College, Oxford. Author of The Apostolic Age; &c. John Weathers, F.R.H.S. Lecturer on Horticulture to the Middlesex County Council. Guide to Garden Plants; French Market Gardening; &c. James Ward, D.Sc, LL.D. f Professor of Mental Philosophy and Logic in the University of Cambridge. Fellow J „ . , of Trinity College, Cambridge. Fellow of the British Academy. Fellow of the | """a"- New York Academy of Sciences. I J. Walter Ferrier. f Translated George Eliot and Judaism from the German of Kaufmann. Author of A Heine (in Part) Mottisclijfe. I r '' The Hon. John Watson Foster, A-M., LL.D. f Professor of American Diplomatics, George Washington University, Washington, i Harrison, Benjamin. U.S.A. Formerly U.S. Secretary of State. Author of Diplomatic Memoirs; &c. I Author of Practical i Holmes, Oliver WendelL -| History. Hebrews, Epistle to the; Hermas, Shepherd of. Hippeastrum; Honeysuckle; Horticulture (in part). Kathleen Schlesinger. Editor of The Portfolio of Musical Archaeology. Orcliestra. Author of The Instruments of the Harp (in part); Harp-Lute; Harpsichord; Holztrorr.pete; L Horn; Hurdy-Gurdy. . J Horticulture: Chairman of Roosevelt "i Calendar Liberty Hyde Bailey, LL.D. Director of the College of Agriculture, Cornell University Commission on Country Life. Leonard James Spencer, M.A. Assistant in Department of Mineralogy, British Museum. Formerly Scholar of Sidney Sussex College, Cambridge, and Harkness Scholar. Editor of the Mineralo- gical Magazine. Lucien Wolf. Vice-President of the Jewish Historical Society of England. Formerly President of the Society; Joint-editor of the Bibliotheca Anglo- judaica. Moses Gaster, Ph.D. (Leipzig). Chief Rabbi of the Sephardic Communities of England! Vice-President, Zionist Congress, 1898, 1899, 1900. Ilchester Lecturer at Oxford on Slavonic and Byzantine - Literature, 1886 and 1891. President, Folk lore Society of England. Vice-President Anglo-Jewish Association. Author of History of Rumanian Popular Literature; &c. Marcus Hartog, M.A., D.Sc, F.L.S. C Professor of Zoology, University College, Cork. Author of " Protozoa " in Cam- < Heliozoa, bridge Natural History; and papers for various scientific journals.: (_ Montague Hughes Crackanthorpe, K.C., D.C.L. President of the Eugenics Education Society. Honorary Fellow, St John's College, Oxford. Bencher of Lincoln's Inn. Formerly Member of the General Council of - the Bar and of the Council of Legal Education, and Standing Counsel to the Univer- sity of Oxford. Marcus Niehbur Tod, M.A. Fellow and Tutor of Oriel College, Oxford. University Lecturer in Epigraphy. - Joint-author of Catalogue of the Sparta Museum. L Maximilian Otto Bismarck Caspari. f Reader in Ancient History at London University. Lecturer in Greek at Birmingham ■{ Heraelius, University, 1905-1908. I Maxwell T. Masters, M.D., F.R.S. (1833-1907). f Formerly Editor of Gardeners' Chronicle ; and Lecturer on Botany, St George's Hos- pital, London. Author of Plant Life; Botany for Beginners; and numerous mono- graphs in botanical works. American U» part). Harmotome; Kemimorphite; Heulandite; Hornblende; Humite. Hirsch, Baron. Hasdeu. Herschell, 1st Baron. Helots. Horticulture (in part). Newton Dennison Mereness, A.M., Author of Maryland as a Proprietary Ph.D. Province. f Henry, Patrick; \ Homestead and Exemption [ Laws. Oswald Barron, F.S.A. Editor of The Ancestor, 1 902- 1 905. Honourable Society of the Baronetage Oscar Briliant. f Heraldry; Hon. Genealogist to Standing Council of the J Herbert: family; [Howard: family. f Hungary: Geography \ and Statistics. INITIALS AND HEADINGS OF ARTICLES XI 0. c. w. P. A. P. C. M. P. C. Y. p. H. p. H. P.-S. p. La R. A. * R. Ad . R. A. S. M R A. W. R H S. R I. P. R J. M. R J. S. R .K . D. R. L.* R. N. B. R. Po. R. P. S. R. S. C. R. S. T. { Rev. Owen Charles Whitehouse, M.A., D.D. Christ's College, Cambridge. Professor of Hebrew, Biblical Exegesis and Theology, and Theological Tutor, Cheshunt College. Cambridge. Paul Daniel Alphandery. Professor of the History of Dogma, Ecole pratique des hautes etudes, Sorbonne, Paris. Author of Les Idees morales chez les heterodoxes Latines au debut du XIII' si'ecle. Peter Chalmers Mitchell, M.A., F.R.S., F.Z.S., D.Sc, LLD. Secretary to the Zoological Society of London. University Demonstrator in Com- parative Anatomy and Assistant to Linacre Professor at Oxford, 1 888-1 891. Examiner in Zoology to the University of London, 1903. Author of Outlines of Biology; &c. Philip Chesney Yorke, M.A. Magdalen College, Oxford. Editor of Letters of Princess Elizabeth of England. Peter Henderson (1823-1890). Formerly Horticulturist, Jersey City and New York Profit; Garden and Farm Topics. Philip Henry Pye-Smith, M.D., F.R.S. I Consulting Physician to Guy's Hospital, London. Formerly Vice-Chancellor of the -j University of London. Joint-author of A Text Book of Medicine ; &c. ' Philip Lake, M.A., F.G.S. I Lecturer on Physical and Regional Geography in Cambridge University. Formerly J of the Geological Survey of India. Author of Monograph of British Cambrian ] Trilobites. Translator and Editor of Kayser's Comparative Geology. Robert Anchel. Archivist to the Department de l'Eure. Robert Adamson, LL.D. See the biographical article, Adamson, R. Robert Alexander Stewart Macalister, M.A., F.S.A. St John's College, Cambridge. Director of Excavations for the Palestine Explora- ■ tion Fund. Robert Alexander Wahab, C.B., C.M.G., CLE. Colonel, Royal Engineers. Formerly H.M. Commissioner, Aden Boundary Delimi- tation, and Superintendent, Survey of India. Served with Tirah* Expeditionary Force, 1 897-1 898; Anglo-Russian Boundary Commission, Pamirs, 1895; &c. Richard Henry Stoddard. See the biographical article, Stoddard, Richard Henry. Hebrew Religion. Henry of Lausanne; Hugh of St Victor; Humiliati. Hemiehorda; Heredity. Holies, Baron. ,', ,.,.,! Horticulture: American Author of Gardening for y CaUndar {in p art) _ Harvey, William. Himalaya: Geology. Herault de Seehelles. Hume, David {in part). Hebron; Hor, Mt. Hasa, El; Hejaz. I Hawthorne, Nathaniel. J" Harvester; Hibernation. Reginald Innes Pocock, F.Z.S. Superintendent of the Zoological Gardens, London. Ronald John McNeill, M.A. C Christ Church, Oxford. Barrister-at-Law. Formerly Editor of the St James's -i Hely-Hutchinson. Gazette, London. I , Hon. Robert John Strutt, M.A. , F.R.S. f Professor of Physics in the Imperial College of Science and Technology, South J Helium. Kensington. Fellow of Trinity College, Cambridge. [_ Sir Robert Kennaway Douglas. f Formerly Keeper of Oriental Printed Books and MSS. at the British Museum, _ and Professor of Chinese, King's College, London. Author of The Language and* Literature of China ; &c. Richard Lydekker, F.R.S., F.G.S., F.Z.S. Member of the Staff of the Geological Survey of India, 1874-1882. Author of Catalogue of Fossil Mammals, Reptiles and Birds in the British Museum; The Deer of all Lands; The Game Animals of Africa; &c. Robert Nisbet Bain (d. iqoq). Assistant Librarian, British Museum, 1883-1909. Author of Scandinavia, the Political History of Denmark, Norway and Sweden, 1$ 13-1900; The First Romanovs - 1613-172$ ; Slavonic Europe, the Political History of Poland and Russia from 1469 to 1796 ; Slc. Rene Poupardin, D.-es-L. Hsttan Tsang {in part). Hedgehog; Hippopotamus; Horse {in part); Howler. H'opken; Horn, A. B., Count; Hungary: History {in part); Hunyadi, Janos; Hu'nyadi, Laszl6. Secretary of the Ecole des Chartes. Honorary Librarian at the Bibliotheque J jij nema « Nationale, Paris. Author of Le Royaume de Provence sous les Carolingiens ; Recueil\ n,n cmar. des chartes de Saint-Germain; &c. I R. Phene Spiers, F.S.A. , F.R.I.B. A. Formerly Master of the Architectural School, Royal Academy, London. Past President of Architectural Association. Associate and Fellow of King's College, -j HoUSe. London. Corresponding Member of the Institute of France. Editor of Fergusson' s History of Architecture. Author of Architecture: East and West; &c. Robert Seymour Conway, M.A. , D.Litt. (Cantab.). r _ _ Professor of Latin and Indo-European Philology in the University of Manchester. J Hernici; Formerly Professor of Latin in University College, Cardiff; and Fellow of Gonville 1 Hirpini. and Caius College, Cambridge. Author of The Italic Dialects. { Ralph Stockman Tarr. J Hudson River Professor of Physical Geography, Cornell University. , I ■■ ■ Xll R.W. S. P. B. S. A* C. T. A. I. T. As. T. Ba. iMTMLSi aito amftornGS of articles T. B.* T. F. H. T. Gi. T. H. H.* T. L. H. T. Se. T. Wo, T. W. A. W. A. B. C. W. A. P. w. Ba w. Fr. w. F. C. w. G. H. w. H. F. w. H. Ha Robert Wallace, F.R.S. (Edin.), F.L.S. ':'■' : Pr«>fdstSofcof Agriculture and Rural Economy at Edinburgh University, and Garton Lecturer on Colonial and Indian Agriculture. Professor of Agriculture, R.A.C.,. Cirencester, 1882-1885. Author of Farm Live Stock of Great Britain; The Agricul- ture and Rural Economy of Australia and New Zealand; Farming Industries of Cape Colony; &c. Spencer Fuller-ton Baird, LL.D. See the biographical article, Baird, S. F. Horse (m part). { Henry, Joseph. Hezekiah; Hoshea. Stanley Arthur Cook, M.A. Lecturer in Hebrew and Syriac, and formerly Fellow, Gonville and Caius College, Cambridge. Editor for Palestine Exploration Fund. Examiner in Hebrew and Aramaic, London University, 1904-1908. Author of Glossary of Aramaic Inscrip- tions ; The Laws of Moses and ihe Code of Hammurabi ; Critical Notes en Old Testament History; Religion of Ancient Palestine; &c. Thomas Allan Ingram, M.A., LL.D. Trinity College, Dublin. Thomas Ashby, M.A., D.Litt. (Oxon.). Director of British School of Archaeology at Rome. Formerly Scholar of Christ Church, Oxford. Craven Fellow, 1897. Conington Prizeman, 1906. Member of the Imperial German Archaeological Institute. Sir Thomas Barclay, M.P. (" Member of the Institute of International Law. Member of the Supreme Council] tij-j, q oa « of the Congo Free State. Officer of the Legion of Honour. Author of Problems | nlsn OBa!> of International Practice and Diplomacy; &c. M.P. for Blackburn, 1910. I J Holiday. Heraclea (in part)- Hispellum. { Hosiery. Thomas Brown. Incorporated Weaving, Dyeing and Printing College, Glasgow. T. F. Henderson. Author of The Casket Letters and Mary Queen of Scots; Life of Robert Burns; &c. Thomas Gilray, M.A. Formerly Professor of Modern History and English Literature, University College, < Dundee. • |_ Colonel Sir Thomas Hungerford Holdich, K.C.M.G., K.C.I.E., Hon. D.Sc. Superintendent Frontier Surveys, India, 1892-1898. Gold Medallist, R.G.S., London, 1887. Author of The Indian Borderland; The Countries of the King's Award; India; Tibet; &c. Sir Thomas Little Heath, K.C.B., D.Sc. Assistant Secretary to the Treasury. Formerly Fellow of Trinity College, Cam- " bridge. Thomas Seccombe, M.A. Balliol College, Oxford. Lecturer in History, East London and Birkbeck Colleges, University of London. Stanhope Prizeman, Oxford, 1887. Assistant Editor' of Dictionary of National Biography, 1891-1901. Author of The Age of Johnson; joint-author of Bookman History of English Literature; &c. Thomas Woodhouse. Head of the Weaving and Textile Designing Department, Technical College, Dundee. "^ Thomas William Allen, M.A. Fellow and Tutor of Queen's College, Oxford. Joint-editor of The Homeric Hymns. \ ' Rev. William Augustus Brevoort Coolidge, M.A. , F.R.G.S., Ph.D. THautes Alpes* Fellow of Magdalen College, Oxford. Professor of English History, St David's I xi_„f c», „• .' College, Lampeter, 1880-1881. Author of Guide to Switzerland; The Alps in Nature') H auie-aavoie, and in History; &c. Editor of The Alpine Journal, 1 880-1 889. [ Herzog, Hans. 4 Hooker, Richard. [Henderson, Alexander (in part). Helmund; Herat; Himalaya; Hindu Kush. Hero of Alexandria. Hayward> Abraham; Hughes, Thomas. -I Hose-Pipe. Si -j Homer Q n part). Walter Alison Phillips, M.A. rHohenlohe (in part). Formerly Exhibitioner of Mer'ton College and Senior Scholar of St John's College, J Holy A1,iance > Tne : Oxford. Author oi Modern Europe; &c. Hononus I.; [Hungary: History (in part). William Bacher, D.Ph. Professor of Biblical Studies at the Rabbinical Seminary, Budapest. Hillel. William Fream, LL.D. (d. 1907). r„ . Formerly Lecturer on Agricultural Entomology, University of Edinburgh, and J ™°P' Agricultural Correspondent of The Times. 1 Horse (in part). William Feilden Craies, M.A. r Barrister-at-Law, Inner Temple. Lecturer on Criminal Law at King's College, J Homicide. London. Editor of Archbold's Criminal Pleading (23rd ed.). [ Walter George Headlam (1866- 1908). r Fellow of King's College, Cambridge. Editor of Herodas. Translator of the plays J Herodas. of Aeschylus. 1 Sir William Henry Flower, F.R.S. f _ t See the biographical article, Flower, Sir W. H. ^ *"TSe \m part). William Henry Hadow, M.A., Mus.Doc. r Principal, Armstrong College, Newcastle-on-Tyne. Formerly Fellow and Tutor) tj„ v j_ of Worcester College, Oxford. Member of Council, Royal College of Music. Editor 1 Ma J an * of Oxford History of Music. Author of Studies in Modern Music; &c. | 13 INITIALS AND HEADINGS OF ARTICLES X1U w. M R. w. P. J. w. R. Ni. w. R. S. w. R. S.-R Howe, Joseph. s,|) j Harris, Thomas Lake. j Hosea W. L. G. William Lawson Grant, M.A. Professor at Queen's University, Kingston, Canada. Formerly Beit Lecturer in . Colonial History at Oxford University. Editor of Acts of the Privy Council, Colonial Series ; Canadian Constitutional Development (in collaboration). L William Michael Rossetti JHaydon, Benjamin Robert. See the biographical article, Rossetti, Dante Gabriel. L William Price James. University College, Oxford. Barrister-at-Law. High Bailiff of County Courts, -j Henley, W. E. Cardiff. Author of Romantic Professions ; &c. Sir William Robertson Nicoll, LL.D. See the biographical article, Nicoll, Sir W. R. William Robertson Smith, LL.D. H .. See the biographical article, Smith, William Robertson. "^nosea [m part). William Ralston Shedden-Ralston, M.A. J" Assistant in the Department of Printed Books, British Museum. Author of Russian ~i Hertzen. Folk Tales ; &c. I W. R. W. William Robert Worthington Williams, F.L.S. f Superintendent of London County Council Botany Centre. Assistant Lecturer J tinrtipnHnro t m *■ -A in Botany, Birkbeck College (University of London). Member of the Geologists' | norucuuure U» part). Association. I W. T. H. William Tod Helmtjth, M.D., LL.D. (d. iooi). Formerly Professor of Surgery and Dean of the Homoeopathic and Medical College and Hospital New York. President of the Collins State Homoeopathic Hospital. Sometime President of the American Institute of Homoeopathy and the New York State Homoeopathic Medical Society. Author of Treatise on Diphtheria; System of Surgery ; &c. W. W. William Wallace, LL.D. See the biographical article, WALLACE, WlLLIAM (1844-1897). W. Wr. Williston Walker, Ph.D., D.D. Professor of Church History, Yale University. Author of History of the Congrega- tional Churches in the United States ; The Reformation ; John Calvin ; &c. W. Y. S. William Young Sellar, LL.D. See the biographical article, Sellar, W. Y. Homoeopathy. 4 Hegel {in part). { Hopkins, Samuel. Horace (in pari). PRINCIPAL UNSIGNED ARTICLES Harrow. Hartford. Hartlepool. Harvard University. Harz Mountains. Hat. Havana. Hawaii. Hazel. Health. Heath. Hebrides, The. Heidelberg Catechism. Heligoland. Heliostat. Hellebore. Helmet Hemp. Herbarium. Herefordshire. Hero. Hertfordshire. Hesse. Hesse-Cassel. Hesse-Darmstadt. High Place. Highway. Hockey. Holly. Homily. Honduras. Hong-Kong. Hostage. Hottentots. Household, Royal. Hudson's Bay Company. Huntingdonshire. ENCYCLOPEDIA BRITANNICA ELEVENTH EDITION VOLUME XIII HARMONY (Gr. apuovia, a concord of musical sounds, apfiofav to join; apjMVLK-q (sc. rexvif) meant the science or art of music, novaiK-q being of wider significance), a combination of parts so that the effect should be aesthetically pleasing. In its earliest sense in English it is applied, in music, to a pleasing combination of musical sounds, but technically it is confined to the science of the combination of sounds of different pitch. I. Concord and Discord. — By means of harmony modern music has attained the dignity of an independent art. In ancient times, as at the present day among nations that have not come under the influence of European music, the harmonic sense was, if not altogether absent, at all events so obscure and undeveloped as to have no organizing power in the art. The formation by the Greeks of a scale substantially the same as that which has received our harmonic system shows a latent harmonic sense, but shows it in a form which positively excludes harmony as an artistic principle. The Greek perception of certain successions of sounds as concordant rests on a principle identifiable with the scientific basis of concord in simultaneous sounds. But the Greeks did not conceive of musical simultaneity as consisting of anything but identical sounds; and when they developed the practice of magadizing — i.e. singing in octaves — they did so because, while the difference between high and low voices was a source of pleasure, a note and its octave were then, as now, perceived to be in a certain sense identical. We will now start from this fundamental identity of the octave, and with it trace the genesis of ether concords and discords; bearing in mind that the history of harmony is the history of artistic instincts and not a series of progressive scientific theories. The unisonous quality of octaves is easily explained when we examine the " harmonic series " of upper partials (see Sound). Every musical sound, if of a timbre at all rich (and hence pre-eminently the human voice), contains some of these upper partials. Hence, if one voice produce a note which is an upper Ex. i. — The notes marked * are out of tune. m.-^-^L rf»_ pti_ i 2 3 4 s 6 7 8 9 10 ii 12 partial of another note sung at the same time by another voice, the higher voice adds nothing new to the lower but only rein- forces what is already there. Moreover, the upper partials of the higher voice will also coincide with some of the lower. Thus, if a note and its octave be sung together, the upper octave is itself No. 2 in the harmonic series of the lower, No. 2 of its own series is No. 4 of the lower, and its No. 3 is No. 6, and so on. The impression of identity thus produced is so strong that we often find among people unacquainted with music a firm conviction that a man is singing in unison with a boy or an instrument when he is really singing in the octave below. And even musical people find a difficulty in realizing more than a certain brightness and richness of single tone when a violinist plays octaves per- fectly in tune and with a strong emphasis on the lower notes. Doubling in octaves therefore never was and never will be a process of harmonization. Now if we take the case of one sound doubling another in the 1 2th, it will be seen that here, too, no real addition is made by the higher sound to the lower. The 1 2th is No. 3 of the harmonic series, No. 2 of the higher note will be No. 6 of the lower, No. 3 will be No. 9, and so on. But there is an important difference between the 12th and the octave. However much we alter the octave by transposition into other octaves, we never get anything but unison or octaves. Two notes two octaves apart are just as devoid of harmonic difference as a plain octave or unison. But, when we apply our principle of the identity of the octave to the 1 2th, we find that the removal of one of the notes by an octave may produce a combination in which there is a distinct harmonic element. If, for example, the lower note is raised by an octave so that the higher note is a fifth from it, No. 3 of the harmonic series of the higher note will not belong to the lower note at all. The 5th is thus a combination of which the two notes are obviously different; and, moreover, the principle oLthe identity of octaves can now operate in a contrary direction aUd transfer this positive harmonic value of the. 5th to the 12th, so that we regard the 12th as a 5th plus an octave, instead of regarding the 5th as a compressed 12th. 1 At the same time, the relation between the two is quite close enough to give the 5th much of the feeling of harmonic poverty and reduplication that characterizes the octave; and hence when medieval musicians 1 Musical intervals are reckoned numerically upwards along the degrees of the diatonic scales (described below). Intervals greater than an octave are called compound, and are referred to their simple forms, e.g. the 12th is a compound 5th. HARMONY doubled a melody in sths and octaves they believed themselves to be doing no more than extending and diversifying the means by which a melody might be sung in unison by different voices. How they came to prefer for this purpose the 4th to the 5th seems puzzling when we consider that the 4th does not appear as a fundamental interval in the harmonic series until that series has passed beyond that part of it that maintains any relation to our musical ideas. But it was of course certain that they obtained the 4th as the inversion of the 5th; and it is at least possible that the singers of lower voices found a peculiar pleasure in singing below higher voices in a position which they felt harmonically as that of a top part. That is to say, a bass, in singing a fourth below a tenor, would take pleasure in doubling in the octave an alto singing normally a 5th above the tenor. 1 This should also, perhaps, be taken in connexion with the fact that the interval of the downward 4th is in melody the earliest that became settled. And it is worth noticing that, in any singing-class where polyphonic music is sung, there is a marked tendency among the more timid members to find their way into their part by a gentle humming which is generally a 4th below the nearest steady singers. The limited compass of voices soon caused modifications in the medieval parallelisms of 4ths and 5ths, and the introduction of independent ornaments into one or more of the voices increased to an extent which drew attention to other intervals. It was long, however, before the true criterion of concord and discord was attained; and at first the notion of concord was purely acoustic, that is to say, the ear was sensitive only to the difference in roughness and smoothness between combinations in them- selves. And even the modern researches of Helmholtz fail to represent classical and modern harmony, in so far as the pheno- mena of beats are quite independent of the contrapuntal nature of concord and discord which depends upon the melodic intelligi- bility of the motion of the parts. Beats give rise to a, strong physical sense of discord akin to the painfulness of a flickering light (see Sound). Accordingly, in the earliest experiments in harmony, the ear, in the absence of other criteria, attached much more importance to the purely acoustic roughness of beats than our ears under the experience of modern music. This, and the circumstance that the imperfect concords 2 (the 3rds and 6ths) long remained out of tune owing to the incom- pleteness of the Pythagorean system of harmonic ratios, sufficiently explain the medieval treatment of these combinations as discords differing only in degree from the harshness of 2nds and 7ths. In the earliest attempts at really contrapuntal writing (the astonishing 13th and 14th- century motets, in which voices are made to sing different melodies at once, with what seems to modern ears a total disregard of sound and sense) we find that the method consists in a kind of rough-hewing by which the concords of the octave, 5th and 4th are provided at most of the strong accents, while the rest of the. harmony is left to take care of itself. As the art advanced the imperfect concords began to be felt as different from the discords; but as their true nature appeared it brought with it such an increased sense of the harmonic poverty of octaves, 5ths and 4ths, as ended in a complete inversion of the earliest rules of harmony. The harmonic system of the later 15th century, which cul- minated in the "golden age" of the 16th-century polyphony, may be described as follows: Imagine a flux of simultaneous inde- pendent melodies, so ordered as to form an artistic texture based not only on the variety of the melodies themselves, but also upon gradations between points of repose and points in which the roughness of sound is rendered interesting and beautiful by means of the clearness with which the melodic sense in each part indicates the convergence of all towards the next point of repose. The typical point of repose owes its effect not only to the acoustic smoothness of the combination, but to the fact that it actually 1 It is at least probable that this is one of the several rather obscure reasons for the peculiar instability of the 4th in modern harmony, which is not yet satisfactorily explained. ■ The 'jerfect concords are the octave, unison, 5th and 4th. Other diatonic combinations, whether concords or discords, are called imperfect. consists of the essential elements present in the first five notes of the harmonic series. The major 3rd has thus in this scheme asserted itself as a concord, and the fundamental principle of the identity of octaves produces the result that any combination of a bass note with a major 3rd and a perfect 5th above it, at any distance, and with any amount of doubling, -g- may constitute a concord available even as the Ex QE^pzE final point of repose in the whole composition. z^E— And by degrees the major triad, with its major ~ & 3rd, became so familiar that a chord consisting of a bare 5th, with or without an octave, was regarded rather as a skeleton triad without the 3rd than as a concord free from elements of imperfection. Again, the identity of the octave secured for the combination of a note with its minor 3rd and minor 6th a place among concords; because, whether so recognized by early theorists or not, it was certainly felt as an inversion of the major triad. The fact that its bass note is not the fundamental note (and therefore has a series of upper partials not compatible with the higher notes) deprives it of the finality and perfection of the major triad, to which, however, its relationhsip is too near for it to be felt otherwise than as a concord. This sufficiently explains why the minor 6th ranks as a concord -y ■ — - — . in music, though it is acoustically nearly Ex. 3. SESEbEgE3 as rough as the discord of the minor 7th, » and considerably rougher than that of the 7th note of the harmonic series, which has not become accepted in our musical system at all. But the major triad and its inversion are not the only concords that will be produced by our flux of melodies. From time to time this flux will arrest attention by producing a combination which, while it does not appeal to the ear as being a part of the harmonic chord of nature, yet contains in itself no elements not already present in the major triad. Theorists have in vain tried to find in " nature " a combination of a note with its minor 3rd and perfect 5th; and so long as harmony was treated unhistori- cally and unscientifically as an a priori theory in which every chord must needs have a " root," the minor triad, together with nearly every other harmonic principle of any complexity, remained a mystery. But the minor triad, as an artistic and not purely acoustic phenomenon, is an inevitable thing. It has the character of a concord because of our intellectual percep- tion that it contains the same elements as the major triad; but its absence of connexion with the natural harmonic series deprives it of complete finality in the simple system of 16th-century harmony, and at the same time gives it a permanent contrast with the major triad; a contrast which is acoustically intensified by the fact that, though its intervals are in themselves as con- cordant as those of the major triad, their relative position produces decidedly rough combinations of "resultant tones." By the time cur flux of melodies had come to include the major and minor triads as concords, the notion of the independence of parts had become of such paramount importance as totally to revolutionize the medieval conception of the perfect concords/ Fifths and octaves no longer formed an oasis in a desert of cacophony, but they assumed the character of concord so nearly approaching to unison that a pair of consecutive sths or octaves began to be increasingly felt as violating the independence of the parts. And thus it came about that in pure 16th-century counterpoint (as indeed at the present day whenever harmony and counterpoint are employed in their purest significance) consecutive 5ths and octaves are strictly forbidden. When we compare our laws of counterpoint with those of medieval discant (in which consecutive 5ths and octaves are the rule, while con- secutive 3rds and 6ths are strictly forbidden) we are sometimes tempted to think that the very nature of the human ear has changed. But it is now generally recognized that the process was throughout natural and inevitable, and the above account aims at showing that consecutive 5ths are forbidden by our harmonic system for the very reason which inculcated them in the system of the 12th century. II. Tonality. — As soon as the major and minor triad and their first inversions were well-defined entities, it became evident that HARMONY the successions of these concords and their alternations with discord involved principles at once larger and more subtle than those of mere difference in smoothness and artificiality. Not only was a major chord (or at least its skeleton) necessary for the final point of repose in a composition, but it could not itself sound final unless the concords as well as the discords before it showed a well-defined tendency towards it. This tendency was best realized when the penultimate concord had its fundamental note at the distance of a 5th or a 4th above or below that of the final chord. When the fundamental note of the penultimate chord is a 5th above or (what is the same thing) a 4th below that of the final chord, we have an " authentic " or " perfect " cadence, and the relation between the two chords is very clear. While the contrast between them is well marked, they have one note in common — for the root of the penultimate chord is the 5th of the final chord; and the statement of this common note, first as an octave or unison and then as a 5th, expresses the first facts of harmony with a force which the major 3rds of the chords can only strengthen, while it also involves in the bass that melodic interval of the 4th or the 5th which is now known 3 to be the germ of all melodic scales. The EEjjEgEd relation of the final note of a scale with its ■3- upper 5th or lower 4th thus becomes a fundamental fact of complex harmonic significance — that is to say, of harmony modified by melody in so far as it concerns the succession of sounds as well as their simultaneous combination. In our modern key-system the final note of the scale is called the tonic, and the 5th above or 4th below it is the dominant. (In the 1 6th century the term " dominant " has this meaning only in the " authentic " modes other than the Phrygian, but as an aesthetic fact it is present in all music, though the theory here given would not have been intelligible to any composers before the 18th century). Another penultimate chord asserts itself as the converse of the dominant — namely, the chord of which the root is a 5th below or a 4th above the final. This chord has not that relationship to the final which the dominant chord shows, for its fundamental note is not in the harmonic series of the final. But the fundamental note of the final chord is in its harmonic series, and in fact stands to it as the dominant stands to the final. Thus the progression from subdominant, as it is called, to tonic, or final, forms a full close known as the " plagal cadence," second only in importance to the " perfect " _o or " authentic cadence." In our modern i--^--jp=^z : \ key-system these three chords, the tonic, * the dominant and the subdominant, form Ex. 5. a firm harmonic centre in reference to which all other chords are grouped. The tonic is the final in which everything ultimately resolves: the dominant stands on one side of it as a chord based on the note harmonically most closely related to the tonic, and the subdominant stands on the other side as the converse and opposite of the dominant, weaker than the dominant because not directly derived from the tonic. The other triads obtainable from the notes of the scale are all minor, and of less importance; and their relationship to each other and to the tonic is most definite when they are so grouped that their basses rise and fall in 4th and 5ths, because they then tend to imitate the relation- ship between tonic, dominant and subdominant. Ex. 6. Tonic. Supertonic. Mediant. Sub- Dominant. Sub- dominant. mediant. 1 =t Here are the six common chords of the diatonic scale. The triad on the 7th degree or " leading-note " (B) is a discord, and is therefore not given here. Now, in the 16th century it was neither necessary nor desirable that chords should be grouped exclusively in this way. The relation between tonic, dominant and subdominant must necessarily appear at the final close, and in a lesser degree at 1 The submediant is so-called because if the subdominant is taken a 5th below the tonic, the submediant will come midway between it and the tonic, as the mediant comes midway between tonic and dominant. subordinate points of repose; but, where no harmonies were dwelt on as stable and independent entities except the major and minor triads and their first inversions, a scheme in which these were confined to the illustration of their most elementary relationship would be intolerably monotonous. It is therefore neither surprising nor a sign of archaism that the tonality of modal music is from the modern point of view often very in- definite. On the contrary, the distinction between masterpieces and inferior works in the 16th century is nowhere more evident than in the expressive power of modal tonality, alike where it resembles and where it differs from modern. Nor is it too much to say that that expressive power is based on the modern sense of key, and that a description of modal tonality in terms of modern key will accurately represent the harmonic art of Palestrina and the other supreme masters, though it will have almost as little in common with 16th-century theory and inferior 16th- century practice as it has with modern custom. We must conceive modal harmony and tonality as a scheme in which voices move independently and melodiously in a scale capable of bearing the three chords of the tonic, dominant and sub- dominant, besides three other minor triads, but not under such restrictions of symmetrical rhythm and melodic design as will necessitate a confinement to schemes in which these three cardinal chords occupy a central position. The only stipulation is that the relationship of at least two cardinal chords shall appear at every full close. At other points the character and drift of the harmony is determined by quite a different principle — namely, that, the scale being conceived as indefinitely extended, the voices are agreed in selecting a particular section of it, the position of which determines not only the melodic character of each part but also the harmonic character of the whole, according to its greater or less remoteness from the scale in which major cardinal chords occupy a central position. Historically these modes were derived, with various errors and changes, from the purely melodic modes of the Greeks. Aesthetically they are systems of modern tonality adapted to conditions in which the range of harmony was the smallest possible, and the necessity for what we may conveniently call a clear and solid key-perspective incomparably slighter than that for variety within so narrow a range. We may thus regard modal harmony as an essentially modern scheme, presented to us in cross-sections of various degrees of obliquity, and modified at every close so as either to take us to a point of view in which we see the harmony sym- metrically (as in those modes 2 of which the final chord is normally major, namely the Ionian, which is practically our major scale, the Mixolydian and the Lydian, which last is almost invariably turned into Ionian by the systematic flattening of its 4th degree) or else to transform the mode itself so that its own notes are flattened and sharpened into suitable final chords (as is necessary in those modes of which the triad on the final is normally minor, namely, the Dorian, Phrygian and Aeolian). In this way we may describe Mixolydian tonality as a harmonic scheme in which the keys of G major and C major are so combined that sometimes we feel that we are listening to harmony in C major that is disposed to overbalance towards the dominant, and sometimes that we are in G major with a pronounced leaning towards the subdominant. In the Dorian mode our sensations of tonality are more confused. We seem to be wandering through all the key-relationships of a minor tonic without defining anything, until at the final close the harmonies gather strength and bring us, perhaps with poetic surprise, to a close in D with a major chord. In the Phrygian mode the difficulty in forming the final close is such that classical Phrygian compositions actually end in what we feel to be a half-close, an impression which is by the great masters rendered perfectly artistic by the strong feeling that all such parts of the composition as do not owe their ex- pression to the variety and inconstancy of their harmonic drift are on the dominant of A minor. It cannot be too strongly insisted that the expression of modal music is a permanent artistic fact. Its refinements may be crowded out by the later tonality, in which the much greater 2 See Plain. Song. HARMONY Ex. 7. Suspension. No. 8. Passing Notes. ?H^Et m variety of fixed chords needs a much more rigid harmonic scheme to control it, but they can never be falsified. And when Beethoven in his last " Bagatelle " raises the 6th of a minor scale for the pleasure he takes in an unexpectedly bright major chord; or when, in the Incarnatus of his Mass in D, he makes a free use of the Dorian scale, he is actuated by precisely the same harmonic and aesthetic motives as those of the wonderful opening of Palestrina's eight-part Stabat Mater; just as in the Lydian figured chorale in his A minor Quartet he carries out the principle of harmonic variety, as produceable by an oblique melodic scale, with a thoroughness from which Palestrina himself would have shrunk. (We have noted that in 16th-century music the Lydian mode is almost invariably Ionicized.) III. Modern Harmony and Tonality. — In the harmonic system of Palestrina only two kinds of discord are possible, namely, suspensions and passing-notes. The principle of the suspension is that while parts are moving from one concord to another _ one of the parts remains I * » behind, so as to create a -^— *-«-«z«! zzfrr^ — i discord at the moment when V ~ji : SS5=fei£^=J the other parts proceed. The ^ — ' suspended part then goes on to its concordant note, which must lie on an adjacent (and in most cases a lower) degree of the scale. Passing-notes are produced transiently by the motion of a part up or down the scale while other parts remain stationary. The possibilities of these two devices can be worked out logically so as to produce combinations of extreme harshness. And, when combined with the rules which laid on the performers the responsibility for modifying the strict scale of the mode in order to form satis- factory closes and avoid melodic harshness, they some- times gave rise to combinations which the clearest artistic intellects of the 16th century perceived as incompatible with the modal style. For example, in a passage written thus the singer of the lower part would be obliged Ex »• , Op. 130 (where we again note that the flat submediant of the exposition is temporarily answered by the flat mediant of the recapitulation). c. Artificial Key-relationships. — Early in the history of the minor mode it was discovered that the lower tetrachord could be very effectively and naturally altered so as to resemble the upper (thus producing the scale C Db Et( F, G Ab Btf C). This produces a flat supertonic (the chord of which is generally pre- sented in its first inversion, and is known as the Neapolitan 6th, from its characteristic use in the works of the Neapolitan school which did so much to establish modern tonality) and its origi*, as just described, often impels it to resolve on a major tonic chord. Consequently it exists in the minor mode as a pheno- menon not much more artificial than the mode itself; and although the keys it thus connects are extremely remote, and the effect of their connexion very surprising, the connexion is none the less real, whether from a major or a minor tonic, and is a crucial test of a composer's sense of key-perspective. Thus Philipp Emanuel Bach in a spirit of mere caprice puts the charming little slow movement of his D major Symphony into Eb and obliterates all real relationship by chaotic operatic HARMONY 7 connecting links. Haydn's greatest pianoforte sonata (which, being probably his last, is of course No. i in mo«:t editions) is in Eb, and its slow movement is in F^ major ( = Fb). That key had already appeared, with surprising effect, in the wander- ings of the development of the first movement. No attempt is made to indicate its connexion with Eb; and the finale begins in Eb, but its first bar is unharmonized and starts on the one note which most contradicts El| and least prepares the mind for Eb. The immediate repetition of the opening phrase a step higher on the normal supertonic strikes the note which the open- ing had contradicted, and thus shows its function in the main key without in the least degree explaining away the paradoxical effect of the key of the slow movement. Brahms's Violoncello Sonata Op. 99, is in F; a prominent episode in the development of the first movement is in E# minor ( = Gb), thus preparing the mind for the slow movement, which is in F# major ( = Gb), with a central episode in F minor. The scherzo is in F minor, and begins on the dominant. Thus if we play its first chord immedi- ately after the last chord of the slow movement we have exactly that extreme position of flat supertonic followed by dominant which is a favourite form of cadence in Wagner, who can even convey its meaning by its mere bass without any harmonies (Walkiire, Act 3, Scene 2:"Was jetzt du bist,das sage dir selbst"). Converse harmonic relationships are, as we have seen, always weaker than their direct forms. And thus the relation of C major to B major or minor {as shown in the central episode of the slow movement just mentioned) is rare. Still more rare is the obtain- ing of indirect artificial relationships, of which the episode in the first movement just mentioned is an illustration in so far as it enhances the effect of the slow movement, but is incon- clusive in so far as it is episodic. For with remote key-relation- ships everything depends upon whether they are used with what may be called cardinal function (like complementary keys) or not. Even a near key may occur in the course of wandering modula- tions without producing any effect of relationship at all, and this should always be borne in mind whenever we accumulate statistics from classical music. d. Contrary and Unconnected Keys. — There remain only two pairs of keys that classical music has not brought into connexion, a circumstance which has co-operated with the utter vagueness of orthodox theories on the subject to confirm the conventionally progressive critic in his conviction that all modulations are alike. We have seen how the effect of modulation from major tonic to minor supertonic is, on a large scale, obscured by the identity of the primary dominant with the secondary sub- dominant, though the one chord is major and the other minor. Now when the supertonic becomes major this difference no longer obviates the confusion, and modulation from C major to D major, though extremely easy, is of so bewildering effect that it is used by classical composers only in moments of intensely dramatic surprise, as, for example, in the recapitulation of the first subject of Beethoven's Eroica Symphony, and the last variation (or coda) of the slow movement of his Trio in B\>, Op. 97. And in both cases the balance is restored by the converse (and equally if not more contradictory) modulation between major tonic and major flat 7th, though in the slow movement of the B\> Trio the latter is represented only by its dominant chord which is " enharmonically " resolved into quite another key. The frequent attempts made by easy-going innovators to treat these key-contrasts on another footing than that of paradox, dramatic surprise or hesitation, only show a deficient sense of tonality, which must also mean an inability to see the intensely powerful effect of the true use of such modulations in classical music, an effect which is entirely inde- pendent of any ability to formulate a theory to explain it. 1 1 Many theorists mistake the usual extreme emphasis on the dominant chord of the dominant key, in preparation for second subjects, for a modulation to the major supertonic, but this can deceive no one with any sense of tonality. A good practical test is to see what becomes of such passages when translated into the minor mode. Illusory modulation to the flat 7th frequently occurs as a bold method of throwing strong emphasis on to the subdominant at the outset of a movement, as in Beethoven's Sonata, Op. 31, No. 1. There now remains only one pair of keys that have never been related, namely, those that (whether major or minor) are at the distance of a tntone 4th. In the first place they are unrelated because there is no means of putting any form of a tonic chord of F# into any form of the key of C, or vice versa; and in the second place because it is impossible to tell which of two precisely opposite keys the second key may be (e.g. we have no means of knowingthat a direct modulation from C to F# is not from C to Gb, which is exactly the same distance in the opposite direction) . And this brings us to the only remaining subjects of importance in the science and art of harmony, namely, those of the tempered scale, enharmonic ambiguity and just intonation. Before proceeding we subjoin a table of all the key-relationships from major and minor tonics, representing the degrees by capital Roman figures when the second key is major and small figures TABLES OF KEY-RELATIONSHIPS A. From Major Tonic Direct Relationships li iii IV V vi Indirect through both \ i and the second key i ..... Indirect, through i III* yu \ \ Indirect through the i second key ' <--- ' 1 1 1 Doubly indirect through the former indirect keys iii^ vi* s , \ 1 V » s l \ 1 Artificial, direct \ VII & vfi Artificial, indirect* ^ 1 * \ ! \ 1 Unrelated 1 > IV* & iv» =V k & »k Contradictory i V VIIf & viit> B. i From Minor Tonic 3 Direct Relationships III iy v VI V,II .1 I 1 \ 1 1 Indirect through both J I and the second key , ■ ■■< 1 1 1 1 1 • » ' iV v 1 ; Indirect, through I iii# vi# Indirect through the ' 1 second key ill i/ 1 i Doubly indirect III* V»* 1 1 1 / / / * Artificial, direct 1 \ I* * f f Artificial, Indirect 4 1 ilk vn«''a vii# 1 r / Unrelated f. V IV# & iv# = 1 V* & v|> Contradictory 5 li II vii> 2 Very rare, but the slow movement of Schubert's C major String Quintet demonstrates it magnificently. 3 All the indirect relationships from a minor tonic are distinctly strained and, except in the violently contrasted doubly indirect keys, obscure as being themselves minor. But the direct artificial modulation is quite smooth, and rich rather than remote. See Beethoven's C# minor Quartet. 4 No classical example, though the clearer converse from a major tonic occurs effectively. 5 Not (with the exception of II) so violent as when from major tonic. Bach, whose range seldom exceeds direct key-relationships, is not afraid to drift from D minor to C minor, though nothing would induce him to go from D major to C major or minor. 8 HARMONY when minor. Thus I represents tonic major, iv represents subdominant minor, and so on. A flat or a sharp after the figure indicates that the normal degree of the standard scale has been lowered or raised a semitone, even when in any particular pair of keys it would not be expressed by a flat or a sharp. Thus vit> would, from the tonic of Bb major, express the position of the slow movement of Beethoven's Sonata, Op. 106, which is written in F# minor since Gb minor is beyond the practical limits of notation. VI. Temperament and Enharmonic Changes. — As the facts of artistic harmony increased in complexity and range, the purely acoustic principles which (as Helmholtz has shown) go so far to explain 16th-century aesthetics became more and more inadequate; and grave practical obstacles to euphonious tuning began to assert themselves. The scientific (or natural) ratios of the diatonic scale were not interfered with by art so long as no discords were " fundamental "; but when discords began to assume independence, one and the same note often became assignable on scientific grounds to two slightly different positions in pitch, or at all events to a position incompatible with even tolerable effect in performance. Thus, the chord of the diminished 7th is said to be intolerably harsh in " just intonation," that is to say, intonation based upon the exact ratios of a normal minor scale. In practical performance the diminished 7th contains three minor 3rds and two imperfect 5ths (such as that which is present in the dominant 7th), while the peculiarly dissonant interval from which the chord takes its name is very nearly the same as a major 6th. Now it can only be said that an intonation which makes nonsense of chords of which every classical composer from the time of Corelli has made excellent sense, is a very unjust intonation indeed; and to anybody who realizes the universal relation between art and nature it is obvious that the chord of the diminished 7th must owe its naturalness to its close approximation to the natural ratios of the minor scale, while it owes its artistic possibility to the extremely minute instinctive modification by which its dissonance becomes tolerable. As a matter of fact, although we have shown here and in the article Music how artificial is the origin and nature of all but the very scantiest materials of the musical language, there is no art in which the element of practical compromise is so minute and so hard for any but trained scientific observation to perceive. If a painter could have a scale of light and shade as nearly approaching nature as the practical intonation of music approaches the acoustic facts it really involves, a visit to a picture gallery would be a severe strain on the strongest eyes, as Ruskin constantly points out. Yet music is in this respect exactly on the same footing as other arts. It constitutes no exception to the universal law that artistic ideas must be realized-, not in spite of, but by means of practical necessities. However independent the treatment of discords, they assert themselves in the long run as transient. They resolve into permanent points of repose of which the basis is natural; but the transient phenomena float through the harmonic world adapting themselves, as best they can, to their environment, showing as much dependence upon the stable scheme of " just intonation " as a crowd of metaphors and abstractions in language shows a dependence upon the rules of the syllogism. As much and no more, but that is no doubt a great deal. Vet the attempt to determine the point in modern harmony where just intonation should end and the Tempered scale begin, is as vexatious as the attempt to define in etymology the point at which the literal meaning of a word gives places to a metaphorical meaning. And it is as unsound scientifically as the conviction of the typical circle-squarer that he is unravelling a mystery and measuring a quantity hitherto unknown. Just intonation is a reality in so far as it emphasizes the contrast between concord and discord; but when it forbids artistic interaction between harmony and melody it is a chimera. It is sometimes said that Bach, by the example of his forty-eight preludes and fugues in all the major and minor keys, first fixed the modern scale. This is true practically, but not aesthetically. By writing a scries of movements in every key of which the keynote was present in the normal organ and harpsichord manuals of his and later times, he enforced the system by which all facts of modern musical harmony are represented on keyed instruments by dividing the octave into twelve equal semitones, instead of tuning a few much-used keys as accurately as possible ■ and sacrificing the euphony of all the rest. This system of equal temperament, with twelve equal semitones in the octave, obviously annihilates important distinctions, and in the most used keys it sours the concords and blunts the discords more than unequal temperament; but it is never harsh; and where it does not express harmonic subtleties the ear instinctively supplies the interpretation; as the observing faculty, indeed, always does wherever the resources of art indicate more than they express. Now it frequently happens that discords or artificial chords are not merely obscure in their intonation, whether ideally or practically, but as produced in practice they are capable of two sharply distinct interpretations. And it is possible for music to take advantage of this and to approach a chord in one signifi- cance and quit it with another. Where this happens in just intonation (in so far as that represents a real musical conception) such chords will, so to speak, quiver from one meaning into the other. And even in the tempered scale the ear will interpret the change of meaning as involving a minute difference of intonation. The chord of the diminished 7th has in this way four different meanings — Ex. 11 and the chord of the augmented 6th, when accompanied by the fifth, may become a dominant 7th or vice versa, as in the passage already cited in the coda of the slow movement of Beethoven's B\> Trio, Op. 97. Such modulations are called enharmonic. We have seen that all the more complex musical phenomena involve distinctions enharmonic in the sense of intervals smaller than a semitone, as, for instance, whenever the progression D E in the scale of C, which is a minor tone, is identified with the progression of D E in the scale of D, which is a major tone (differing from the former as f from ^). But the special musical meaning of the word " enharmonic " is restricted to the difference between such pairs of sharps with fiats or naturals as can be represented on a keyboard by the same note, this difference being the most impressive to the ear in " just intonation " and to the imagination in the tempered scale. Not every progression of chords which is, so to speak, spelt enharmonically is an enharmonic modulation in itself. Thus a modulation from D flat to E major looks violently enharmonic on paper, as in the first movement of Beethoven's Sonata, Op. no. But E major with four sharps is merely the most convenient way of expressing F flat, a key which would need six flats and a double flat. The reality of an enharmonic modula- tion can be easily tested by transporting the passage a semi- tone. Thus, the passage just cited, put a semitone lower, becomes a perfectly diatonic modulation from C to E flat. But no transposition of the sixteen bars before the return of the main theme in the scherzo of Beethoven's Sonata in Eb, Op. 31, No. 3, will get rid of the fact that the diminished 7th (G Bb Db Efl), on the dominant of F minor, must have changed intoGBb Db Fb (although Beethoven does not take the trouble to alter the spelling) before it could resolve, as it does, upon the dominant of Ab. But though there is thus a distinction between real arid apparent enharmonic modulations, it frequently happens that a series of modulations perfectly diatonic in themselves returns to the original key by a process which can only be called an enharmonic circle. Thus the whole series of keys now in practical use can be arranged in what is called the circle of fifths (C G D A E B F# [ = Gb] Db Ab Bb F C, from which series we now see the meaning of what was said in the discussion of key-relationships as to the ambiguity of the relationships between keys a tritone fourth apart). Now no human memory is capable of distinguishing the difference of pitch between the HARMONY keys of C and B# after a wide series of modulations. The difference would be perceptible enough in immediate juxta- position, but after some interval of time the memory will certainly accept two keys so near in pitch as identical, whether in "just intonation " or not. And hence the enharmonic circle of fifths is a conception of musical harmony by which infinity is at once rationalized and avoided, just as some modern mathematicians are trying to rationalize the infinity of space by a non-Euclidian space so curved in the fourth dimension as to return upon itself. A similar enharmonic circle progressing in major 3rds is of frequent occurrence and of very rich effect. For example, the keys of the movements of Brahms's C Minor Symphony are C minor, E major, Ab major ( = G#), and C ( = B#). And the same circle occurs in the opposite direction in the first movement of his Third Symphony, where the first subject is in F, the transi- tion passes directly to Db and thence by exactly the same step to A (= Bbb). The exposition is repeated, which of course means that in " just intonation " the first subject would begin in Gbb and then pass through a transition in Ebbb to the second subject in Cbbb. As the development contains another spurious enharmonic modulation, and the recapitulation repeats in another position the first spurious enharmonic modulation of the exposition, it would follow that Brahms's movement began in F and ended in C sextuple-flat! So much, then, for the application of bad metaphysics and circle-squaring mathematics to the art of music. Neither in mathematics nor in art is an approximation to be confused with an imperfection. Brahms's movement begins and ends in F much more exactly than any wooden diagonal fits a wooden square. The following series of musical illustrations show the genesis of typical harmonic resources of classical and modern music. Ex. 12. — Three concords (tonic, first inversion of sub- dominant, and dominant of A minor, a possible 16th- century cadence in the Phrygian mode). Ex. T3- — The pension I*). same chords v Ex. 14 —Ditto, with the further addition of a double suspension {*) and two passing notes (tt>. Ex. 15. — Di'-to, with a chromatic alteration of the second chord (*) and an "essential" discord (dominant 7th) at (t). Ex. passin