Part 2
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 of _A Companion to the School Classics_; &c.
Horace (_in part_).
J. Ga. JAMES GAIRDNER, C.B.
See the biographical article, GAIRDNER, J.
Henry VII.: _of England_.
J. G. M. JOHN GRAY MCKENDRICK, M.D., LL.D., F.R.S., F.R.C.P. (Edin.)
Emeritus Professor of Physiology at the University of Glasgow. Author of _Life in Motion_; _Life of Helmholtz_; &c.
Hearing; Helmholtz.
J. G. R. JOHN GEORGE ROBERTSON, M.A., PH.D.
Professor of German at the University of London. Formerly Lecturer on the English Language, Strassburg University. Author of _History of German Literature_; &c.
Heine (_in part_); Hildebrand, Lay of; Hoffmann, E. T. W.
J. Hn. JUSTUS HASHAGEN, PH.D.
Privatdozent in Medieval and Modern History, University of Bonn. Author of _Das Rheinland unter der franzosischen Herrschaft_.
Hecker, F. F. K.; Hertzberg, Count Von; Hormayr.
J. H. A. H. JOHN HENRY ARTHUR HART, M.A.
Fellow, Theological Lecturer and Librarian, St John's College, Cambridge.
Herod; Herodians.
J. H. F. JOHN HENRY FREESE, M.A.
Formerly Fellow of St John's College, Cambridge.
Herald; Hesiod (_in part_).
J. H. Mu. JOHN HENRY MUIRHEAD, M.A., LL.D.
Professor of Philosophy in the University of Birmingham. Author of _Elements of Ethics_; _Philosophy and Life_; &c. Editor of _Library of Philosophy_.
Hegel: _Hegelianism in England_.
J. H. R. JOHN HORACE ROUND, M.A., LL.D. (Edin.).
Author of _Feudal England_; _Studies in Peerage and Family History_; _Peerage and Pedigree_.
Hereward.
J. J. F. REV. JAMES J. FOX.
St Thomas's College, Brookland, D.C., U.S.A.
Hecker, I. T.
J. K. L. 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.
Hood of Avalon.
J. M. M. 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_.
Heraclitus; Hume, David (_in part_).
J. P.-B. JAMES GEORGE JOSEPH PENDEREL-BRODHURST.
Editor of the _Guardian_ (London).
Hepplewhite.
J. P. Pe. 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_.
Hillah; Hit.
J. S. Co. JAMES SUTHERLAND COTTON, M.A.
Editor of _The Imperial Gazetteer of India_. Hon. Secretary of the Egyptian Exploration Fund. Formerly Fellow and Lecturer of Queen's College, Oxford. Author of _India_ in the "Citizen" Series; &c.
Hastings, Warren.
J. S. F. JOHN SMITH FLETT, D.SC., F.G.S.
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.
Hornfels.
J. T. Be. JOHN T. BEALBY.
Joint-author of Stanford's _Europe_. Formerly Editor of the _Scottish Geographical Magazine_. Translator of Sven Hedin's _Through Asia, Central Asia and Tibet_; &c.
Hissar (_in part_).
J. T. C. 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.
Herring.
J. T. Mo. JOHN TORREY MORSE, Jr.
Author of _The Life and Letters of Oliver Wendell Holmes_.
Holmes, Oliver Wendell.
J. T. S.* JAMES THOMSON SHOTWELL, PH.D.
Professor of History in Columbia University, New York City.
History.
J. V.* JULES VIARD.
Archivist at the National Archives, Paris. Officer of Public Instruction. Author of _La France sous Philippe VI. de Valois_; &c.
Hundred Years' War.
J. V. B. JAMES VERNON BARTLET, M.A., D.D. (St Andrews).
Professor of Church History, Mansfield College, Oxford. Author of _The Apostolic Age_; &c.
Hebrews, Epistle to the; Hermas, Shepherd of.
J. Ws. JOHN WEATHERS, F.R.H.S.
Lecturer on Horticulture to the Middlesex County Council. Author of _Practical Guide to Garden Plants_; _French Market Gardening_; &c.
Hippeastrum; Honeysuckle; Horticulture (_in part_).
J. W.* JAMES WARD, D.SC., LL.D.
Professor of Mental Philosophy and Logic in the University of Cambridge. Fellow of Trinity College, Cambridge. Fellow of the British Academy. Fellow of the New York Academy of Sciences.
Herbart.
J. W. F. J. WALTER FERRIER.
Translated _George Eliot and Judaism_ from the German of Kaufmann. Author of _Mottiscliffe_.
Heine (_in part_).
J. W. Fo. THE HON. JOHN WATSON FOSTER, A.M., LL.D.
Professor of American Diplomatics, George Washington University, Washington, U.S.A. Formerly U.S. Secretary of State. Author of _Diplomatic Memoirs_; &c.
Harrison, Benjamin.
K. S. KATHLEEN SCHLESINGER.
Editor of _The Portfolio of Musical Archaeology_. Author of _The Instruments of the Orchestra_.
Harp (_in part_); Harp-Lute; Harpsichord; Holztrompete; Horn; Hurdy-Gurdy.
L. H. B. LIBERTY HYDE BAILEY, LL.D.
Director of the College of Agriculture, Cornell University. Chairman of Roosevelt Commission on Country Life.
Horticulture: _American Calendar_ (_in part_).
L. J. S. 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 _Mineralogical Magazine_.
Harmotome; Hemimorphite; Heulandite; Hornblende; Humite.
L. W. LUCIEN WOLF.
Vice-President of the Jewish Historical Society of England. Formerly President of the Society. Joint-editor of the _Bibliotheca Anglo-judaica_.
Hirsch, Baron.
M. G. 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.
Hasdeu.
M. Ha. MARCUS HARTOG, M.A., D.SC., F.L.S.
Professor of Zoology, University College, Cork. Author of "Protozoa" in _Cambridge Natural History_; and papers for various scientific journals.
Heliozoa.
M. H. C. 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 University of Oxford.
Herschell, 1st Baron.
M. N. T. MARCUS NIEHBUR TOD, M.A.
Fellow and Tutor of Oriel College, Oxford. University Lecturer in Epigraphy. Joint-author of _Catalogue of the Sparta Museum_.
Helots.
M. O. B. C. MAXIMILIAN OTTO BISMARCK CASPARI.
Reader in Ancient History at London University. Lecturer in Greek at Birmingham University, 1905-1908.
Heraclius.
M. T. M. MAXWELL T. MASTERS, M.D., F.R.S. (1833-1907).
Formerly Editor of _Gardeners' Chronicle_; and Lecturer on Botany, St George's Hospital, London. Author of _Plant Life_; _Botany for Beginners_; and numerous monographs in botanical works.
Horticulture (_in part_).
N. D. M. NEWTON DENNISON MERENESS, A.M., PH.D.
Author of _Maryland as a Proprietary Province_.
Henry, Patrick; Homestead and Exemption Laws.
O. Ba. OSWALD BARRON, F.S.A.
Editor of _The Ancestor_, 1902-1905. Hon. Genealogist to Standing Council of the Honourable Society of the Baronetage.
Heraldry; Herbert: _family_; Howard: _family_.
O. Br. OSCAR BRILIANT.
Hungary: _Geography and Statistics_.
O. C. W. 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.
Hebrew Religion.
P. A. 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^e siecle_.
Henry of Lausanne; Hugh of St Victor; Humiliati.
P. C. M. PETER CHALMERS MITCHELL, M.A., F.R.S., F.Z.S., D.SC., LL.D.
Secretary to the Zoological Society of London. University Demonstrator in Comparative Anatomy and Assistant to Linacre Professor at Oxford, 1888-1891. Examiner in Zoology to the University of London, 1903. Author of _Outlines of Biology_; &c.
Hemichorda; Heredity.
P. C. Y. PHILIP CHESNEY YORKE, M.A.
Magdalen College, Oxford. Editor of _Letters of Princess Elizabeth of England_.
Holles, Baron.
P. H. PETER HENDERSON (1823-1890).
Formerly Horticulturist, Jersey City and New York. Author of _Gardening for Profit_; _Garden and Farm Topics_.
Horticulture: _American Calendar_ (_in part_).
P. H. P.-S. PHILIP HENRY PYE-SMITH, M.D., F.R.S.
Consulting Physician to Guy's Hospital, London. Formerly Vice-Chancellor of the University of London. Joint-author of _A Text Book of Medicine_; &c.
Harvey, William.
P. La. PHILIP LAKE, M.A., F.G.S.
Lecturer on Physical and Regional Geography in Cambridge University. Formerly of the Geological Survey of India. Author of _Monograph of British Cambrian Trilobites_. Translator and Editor of Kayser's _Comparative Geology_.
Himalaya: _Geology_.
R. A.* ROBERT ANCHEL.
Archivist to the Department de l'Eure.
Herault de Sechelles.
R. Ad. ROBERT ADAMSON, LL.D.
See the biographical article, ADAMSON, R.
Hume, David (_in part_).
R. A. S. M. ROBERT ALEXANDER STEWART MACALISTER, M.A., F.S.A.
St John's College, Cambridge. Director of Excavations for the Palestine Exploration Fund.
Hebron; Hor, Mt.
R. A. W.
Robert Alexander Wahab, C.B., C.M.G., C.I.E. Colonel, Royal Engineers. Formerly H.M. Commissioner, Aden Boundary Delimitation, and Superintendent, Survey of India. Served with Tirah Expeditionary Force, 1897-1898; Anglo-Russian Boundary Commission, Pamirs, 1895; &c.
Hasa, El; Hejaz.
R. H. S. RICHARD HENRY STODDARD.
See the biographical article, STODDARD, RICHARD HENRY.
Hawthorne, Nathaniel.
R. I. P. REGINALD INNES POCOCK, F.Z.S.
Superintendent of the Zoological Gardens, London.
Harvester; Hibernation.
R. J. M. RONALD JOHN MCNEILL, M.A.
Christ Church, Oxford. Barrister-at-Law. Formerly Editor of the _St James's Gazette_, London.
Hely-Hutchinson.
R. J. S. HON. ROBERT JOHN STRUTT, M.A., F.R.S.
Professor of Physics in the Imperial College of Science and Technology, South Kensington. Fellow of Trinity College, Cambridge.
Helium.
R. K. D. SIR ROBERT KENNAWAY DOUGLAS.
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.
Hsuan Tsang (_in part_).
R. L.* 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.
Hedgehog; Hippopotamus; Horse (_in part_); Howler.
R. N. B. ROBERT NISBET BAIN (d. 1909).
Assistant Librarian, British Museum, 1883-1909. Author of _Scandinavia, the Political History of Denmark, Norway and Sweden, 1513-1900_; _The First Romanovs 1613-1725_; _Slavonic Europe, the Political History of Poland and Russia from 1469 to 1796_; &c.
Hopken; Horn, A. B., Count; Hungary: _History_ (_in part_); Hunyadi, Janos; Hunyadi, Laszlo.
R. Po. RENE POUPARDIN, D.-ES-L.
Secretary of the Ecole des Chartes. Honorary Librarian at the Bibliotheque Nationale, Paris. Author of _Le Royaume de Provence sous les Carolingiens_; _Recueil des chartes de Saint-Germain_; &c.
Hinemar.
R. P. S. 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, London. Corresponding Member of the Institute of France. Editor of _Fergusson's History of Architecture_. Author of _Architecture: East and West_; &c.
House.
R. S. C. ROBERT SEYMOUR CONWAY, M.A., D.LITT. (Cantab.).
Professor of Latin and Indo-European Philology in the University of Manchester. Formerly Professor of Latin in University College, Cardiff; and Fellow of Gonville and Caius College, Cambridge. Author of _The Italic Dialects_.
Hernici; Hirpini.
R. S. T. RALPH STOCKMAN TARR.
Professor of Physical Geography, Cornell University.
Hudson River.
R. W. ROBERT WALLACE, F.R.S. (Edin.), F.L.S.
Professor of 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 Agriculture and Rural Economy of Australia and New Zealand_; _Farming Industries of Cape Colony_; &c.
Horse (_in part_).
S. F. B. SPENCER FULLERTON BAIRD, LL.D.
See the biographical article, BAIRD, S. F.
Henry, Joseph.
S. A. C. 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 Inscriptions_; _The Laws of Moses and the Code of Hammurabi_; _Critical Notes on Old Testament History_; _Religion of Ancient Palestine_; &c.
Hezekiah; Hoshea.
T. A. I. THOMAS ALLAN INGRAM, M.A., LL.D.
Trinity College, Dublin.
Holiday.
T. As. 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.
Heraclea (_in part_); Hispellum.
T. Ba. SIR THOMAS BARCLAY, M.P.
Member of the Institute of International Law. Member of the Supreme Council of the Congo Free State. Officer of the Legion of Honour. Author of _Problems of International Practice and Diplomacy_; &c. M.P. for Blackburn, 1910.
High Seas.
T. B.* THOMAS BROWN.
Incorporated Weaving, Dyeing and Printing College, Glasgow.
Hosiery.
T. F. H. T. F. HENDERSON.
Author of _The Casket Letters and Mary Queen of Scots_; _Life of Robert Burns_; &c.
Hooker, Richard.
T. Gi. THOMAS GILRAY, M.A.
Formerly Professor of Modern History and English Literature, University College, Dundee.
Henderson, Alexander (_in part_).
T. H. H.* 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.
Helmund; Herat; Himalaya; Hindu Kush.
T. L. H. SIR THOMAS LITTLE HEATH, K.C.B., D.SC.
Assistant Secretary to the Treasury. Formerly Fellow of Trinity College, Cambridge.
Hero of Alexandria.
T. Se. 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.
Hayward, Abraham; Hughes, Thomas.
T. Wo. THOMAS WOODHOUSE.
Head of the Weaving and Textile Designing Department, Technical College, Dundee.
Hose-Pipe.
T. W. A. THOMAS WILLIAM ALLEN, M.A.
Fellow and Tutor of Queen's College, Oxford. Joint-editor of _The Homeric Hymns_.
Homer (_in part_).
W. A. B. C REV. WILLIAM AUGUSTUS BREVOORT COOLIDGE, M.A., F.R.G.S., PH.D.
Fellow of Magdalen College, Oxford. Professor of English History, St David's College, Lampeter, 1880-1881. Author of _Guide to Switzerland_; _The Alps in Nature and in History_; &c. Editor of _The Alpine Journal_, 1880-1889.
Hautes Alpes; Haute-Savoie; Herzog, Hans.
W. A. P. WALTER ALISON PHILLIPS, M.A.
Formerly Exhibitioner of Merton College and Senior Scholar of St John's College, Oxford. Author of _Modern Europe_; &c.
Hohenlohe (_in part_); Holy Alliance, The; Honorius I.; Hungary: _History_ (_in part_).
W. Ba. WILLIAM BACHER, D.PH.
Professor of Biblical Studies at the Rabbinical Seminary, Budapest.
Hillel.
W. Fr. WILLIAM FREAM, LL.D. (d. 1907).
Formerly Lecturer on Agricultural Entomology, University of Edinburgh, and Agricultural Correspondent of _The Times_.
Hop; Horse (_in part_).
W. F. C WILLIAM FEILDEN CRAIES, M.A.
Barrister-at-Law, Inner Temple. Lecturer on Criminal Law at King's College, London. Editor of _Archbold's Criminal Pleading_ (23rd ed.).
Homicide.
W. G. H. WALTER GEORGE HEADLAM (1866-1908).
Fellow of King's College, Cambridge. Editor of Herodas. Translator of the plays of Aeschylus.
Herodas.
W. H. F. SIR WILLIAM HENRY FLOWER, F.R.S.
See the biographical article, FLOWER, SIR W. H.
Horse (_in part_).
W. H. Ha. WILLIAM HENRY HADOW, M.A., MUS.DOC.
Principal, Armstrong College, Newcastle-on-Tyne. Formerly Fellow and Tutor of Worcester College, Oxford. Member of Council, Royal College of Music. Editor of _Oxford History of Music_. Author of _Studies in Modern Music_; &c.
Haydn.
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).
Howe, Joseph.
W. M. R. WILLIAM MICHAEL ROSSETTI.
See the biographical article, ROSSETTI, DANTE GABRIEL.
Haydon, Benjamin Robert.
W. P. J. WILLIAM PRICE JAMES.
University College, Oxford. Barrister-at-Law. High Bailiff of County Courts, Cardiff. Author of _Romantic Professions_; &c.
Henley, W. E.
W. R. Nl. SIR WILLIAM ROBERTSON NICOLL, LL.D.
See the biographical article, NICOLL, SIR W. R.
Harris, Thomas Lake.
W. R. S. WILLIAM ROBERTSON SMITH, LL.D.
See the biographical article, SMITH, WILLIAM ROBERTSON.
Hosea (_in part_).
W. R. S.-R. WILLIAM RALSTON SHEDDEN-RALSTON, M.A.
Assistant in the Department of Printed Books, British Museum. Author of _Russian Folk Tales_; &c.
Hertzen.
W. R. W. WILLIAM ROBERT WORTHINGTON WILLIAMS, F.L.S.
Superintendent of London County Council Botany Centre. Assistant Lecturer in Botany, Birkbeck College (University of London). Member of the Geologists' Association.
Horticulture (_in part_).
W. T. H. WILLIAM TOD HELMUTH, M.D., LL.D. (d. 1901).
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.
Homoeopathy.
W. W. WILLIAM WALLACE, LL.D.
See the biographical article, WALLACE, WILLIAM (1844-1897).
Hegel (_in part_).
W. Wr. WILLISTON WALKER, PH.D., D.D.
Professor of Church History, Yale University. Author of _History of the Congregational Churches in the United States_; _The Reformation_; _John Calvin_; &c.
Hopkins, Samuel.
W. Y. S. WILLIAM YOUNG SELLAR, LL.D.
See the biographical article, SELLAR, W. Y.
Horace (_in part_).
PRINCIPAL UNSIGNED ARTICLES
Harrow. Heligoland. High Place. Hartford. Heliostat. Highway. Hartlepool. Hellebore. Hockey. Harvard University. Helmet. Holly. Harz Mountains. Hemp. Homily. Hat. Herbarium. Honduras. Havana. Herefordshire. Hong-Kong. Hawaii. Hero. Hostage. Hazel. Hertfordshire. Hottentots. Health. Hesse. Household, Royal. Heath. Hesse-Cassel. Hudson's Bay Company. Hebrides, The. Hesse-Darmstadt. Huntingdonshire. Heidelberg Catechism.
FOOTNOTE:
[1] A complete list, showing all individual contributors, appears in the final volume.
ENCYCLOPAEDIA BRITANNICA
ELEVENTH EDITION
VOLUME XIII
HARMONY (Gr. [Greek: harmonia], a concord of musical sounds, [Greek: harmozein] to join; [Greek: harmonike] (sc. [Greek: techne]) meant the science or art of music, [Greek: mousike] 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 other 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.
[Illustration: Ex. 1.--The notes marked * are out of tune.]
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 partial of another note sung at the same time by another voice, the higher voice adds nothing new to the lower but only reinforces 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 perfectly 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 12th, it will be seen that here, too, no real addition is made by the higher sound to the lower. The 12th 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 12th, 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 of the identity of octaves can now operate in a contrary direction and 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 doubled a melody in 5ths 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.[2] 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.