Rhyolite

RHYOLITE (Gr. fxtv, to flow, because of the frequency with which they exhibit fluxion structures), the group name of a type of volcanic rock, occurring mostly as lava flow?, and characterized by a highly acid composition. They are the most siliceous of all lavas, and, with the exception of the dacites, are the only lavas which contain free primary quartz. In chemical composition they very closely resemble the granites which are the corresponding rocks of plutonic or deep-seated origin; their minerals also present many points of similarity to those of granite though they are by no means entirely the same. Quartz, orthoclase and plagioclase felspars, and biotite are the commonest ingredients of both rocks, but the quartz of rhyolites is full of glass enclosures and the potash felspar is pellucid sanidine, while the quartz of granite contains dust-like fluid cavities of very minute size and its potash felspar is of the turbid variety which is properly called orthoclase. The granites also are holocrystalline, while in the rhyolites there are usually porphyritic crystals floating in a fine ground-mass. Rhyolites have also been called liparites because many of the lavas of the Lipari Islands are excellent examples of this group. Above all rocks they have a disposition to assume vitreous forms, as when fused they crystallize with great difficulty. "Hence it has long baffled experimenters to produce rhyolite synthetically by fusion; it is stated that these difficulties have now been overcome, but geologists believe that the presence of steam and 'other gases in the natural state expedites crystallization. In crucibles these cannot be retained at the temperatures employed; when the rocks are melted the gases escape and on cooling a pure glass is formed. The vitreous forms of rhyolite are known as obsidian, perlite and pumice (qq.v.).

The minerals of the first generation, or phenpcrysts, of rhyolite are generally orthoclase, oligoclase, quartz, biotite, augite or hornblende. The felspars are usually glassy clear, small but of welldeveloped crystalline form: the potash felspar is sanidine, usually Carlsbad twinned ; the soda-lime felspar is almost always oligoclase, with characteristic polysynthetic structure. Both of these may be corroded and irregular in their outlines; their cleavage and twinning then distinguish them readily from quartz. Glass enclosures, sometimes rectangular with small immobile bubbles, are frequent. The quartz occurs as blebs or sub-rounded grains, which are corroded double hexagonal pyramids. Its glass enclosures are many and nearly always rounded or elliptical in section. No proper cleavage is seen in the quartz, though arcuate (conchoidal) fractures may often be noticed; they may have been produced by strain on cooling. Phenocrysts of micropegmatite are known in some rhyolites; they may have the shape of felspar or of quartz crystals; in the former case Carlsbad twinning is by no means uncommon, but in other cases hour-glass structure is very conspicuous. Biotite is always deep brown or greenish brown, in small hexagonal tabjets, generally blackened at their edges by magmatic corrosion. Muscovite is not known in rhyolites. Hornblende may be green or brown; in the quartz-pantellarites it sometimes takes the form of strongly pleochroic brown cossyrite. Like biotite it is eumorphic but often corroded in a marked degree. Augite, which, is equally common or more common than the other ferro-magnesian minerals, is always green; its crystals are small and perfectly shaped, and corrosion phenomena are very rarely seen in it. Zircon, apatite and magnetite are always present in rhyolites, their crystals being often beautifully perfect though never large. Olivine is never a normal ingredient, but occurs in the hollow spherulites or lithophysae of some rhyolites with garnet tridymite, topaz and other minerals which indicate pneumatolytic action. Amonij the less common accessory minerals of the rhyolites are cordierite in crystals which resemble hexagonal prisms but break up under polarized light into six radiating sectors owing to complicated twinnine: they weather to green aggregates of chlorite and muscovite (pinite) ; garnet sphene and orthite may also be met with in rhyolites.

The ground-mass of rhyolitic rocks is of three distinct types which are stages in crystalline development, viz. the vitreous, the felsitic or cryptocrystalline, and the microcrystalline. Hence some authorities have proposed to subdivide the group into the vitrophyres, the felsophyres and the granophyres, but this is not now in use, and the last of these terms has obtained a signification quite different from that originally assigned to it. Mixtures of the different kinds occur; thus a vitreous rhyolite has often felsitic areas in its ground-mass, and in the same lava flow some parts may be vitreous while others are felsitic. The vitreous rhyolites are identical in most respects with the obsidians, from which they can only be separated in an artificial classification; and in their glassy base the banded or eutaxitic, spherulitic and perlitic structures of pure obsidians are very frequently present (see OBSIDIAN; PERLITE). The felsoliparites or liparites with stony ground-mass are especially common among the pre-Tertiary igneous rocks (see QUARTZ- PORPHYRY), as liparite glass is unstable and experiences devitrification in course of time. Many of these felsites have fluxion banding, spherulites and even perlitic cracks, which are strong evidence that they were originally glassy. In other cases a hyaloliparite, obsidian, or pitchstone becomes felsitic along its borders and joint planes, or even along perlitic cracks, and we may assume that the once fibrous rock has changed into felsite under the action of percolating moisture or even by atmospheric decomposition. In many rhyolites the felsite is original and represents an incipient crystallization of the vitreous material which took place before the rock was yet cold. The felsite in turn is liable to change; it becomes a fine mosaic of quartz and alkali felspar; and in this way a matrix of the third type, the microcrystalline, may develop. This is proved by the occurrence of the remains of spherulitic and perlitic structures in rocks which are no longer felsitic or glassy. Many microcrystalline rhyolites have a ground-mass in which much felsitic matter occurs; but as this tends to recrystallize in course of time, the older rocks of this group show least of it. Whilst no quartz-bearing rhyolites are known to have been erupted in recent years, Lacroix proved that portions of the " dome " which rose as a great tower or column out of the crater of Mont Pelee after the eruption in 1906 contained small crystals of quartz in the ground-mass. The rock was an acid andesite, and it was ascribed by Lacroix to the action of steam retained in the rock under considerable pressure. The microcrystalline groundmass of rhyolites is never micrographic as in the porphyries (granophyres) ; on the other hand it is often micropoikilitic, consisting of small felspars, often sub-rectangular, embedded in little rounded or irregular plates of quartz.

The ground-mass of rhyolites is liable to other changes, of which the most important are silicification, kaolinization and sericitization. Among the older rocks of this group it is the exception to find that secondary quartz has not been deposited in some parts of them. Often indeed the matrix is completely replaced by silica in the form of finely crystalline quartz or chalcedony; and these rocks on analysis prove to contain over 90% of silica. In the recent rhyolites of Hungary, New Zealand, etc., the deposit of coarse opal in portions of the rock is a very common phenomenon.

Kaolinization may be due to weathering, and the stony dull appearance of the matrix of many microcrystalline rhyolites is a consequence of the decomposed state of the felspar grains in them; it is even more typically developed by fumarole action, which replaces the felspars with soft, cloudy white products which belong to a mineral of the kaolin group. Sericitization, or the development of fine white mica after felspar, is usually associated with shearing, and is commonest in the older rhyolites.

Vesicular structure is very common in rhyolites; in fact the pumiceous obsidians have this character in greater perfection than any other rocks (see PUMICE); but even the felsorhyolites are very often vesicular. The cavities are usually lined with opal and tridymite; in the older rocks they may be filled with agate and chalcedony. The " mill-stone porphyries," extensively used in Germany for grinding corn, are porous rhyolites; the abundance of quartz makes them hard, and their rough surfaces render them peculiarly suitable for this purpose. In some of them the cavities are partly secondary. These rocks are obtained in the Odenwald, Thuringerwald and Fichtelgebirge.

In Britain a pale grey Tertiary rhyolite occurs at Tardree, Antrim (the only British rock containing tridymite), and in Skye. Felsitic rhyolites occur among the Old Red rocks of Scotland ( Pentland Hills, Lome, etc.), in Devonshire, and in large numbers in North Wales. The Carnarvonshire rhyolites are often much altered and silicified; many of them have a nodular structure which is very conspicuous on weathered surfaces. The spheroids may be two or three inches in diameter; some of them are built up of concentric shells. Rhyolites are also known from Fishguard, Malvern, Westmorland and Co. Waterford. One of the oldest volcanic rocks of Britain (pre-Cambrian, Uriconian) is the spherulitic rhyolite of the Lea Rock near Wellington in Shropshire. It shows bright red spherulites in great numbers and is probably an obsidian completely devitrified. Perlitic structure is also visible in it.

In other parts of Europe rhyolites have a fairly wide distribution though they are not very numerous. In Hungary (Hlinik, etc.) there are many well-known examples of this class. They extend along the margin of the Carpathians and are found also in Siebenburgen. In Italy they occur in the Euganean Hills and in the Lipari Islands; the latter being the principal source of pumice at the present day. Rhyolites of Recent age occur in Iceland (Myvatn, etc.), where they are characterized by the frequent absence of quartz, and the presence of much plagioclase and pyroxene. Some of these rocks have been called trachyte-obsidians, but they seem to be rhyolites which contain an exceptionally large amount of soda. The older rhyolites, which are generally called quartzporphyries in Germany, are mostly of Permian or Carboniferous age and are numerous in the Vosges, Odenwald, Thuringerwald, etc. They are often accompanied by basic rocks (melaphyres). Permian rhyolites occur also at Lugano in Italy. Rhyolites are known also in Asia Minor and the Caucasus, in New Zealand, Colorado, Nevada and other parts of western North America. In the Yellowstone National Park there is a well-known cliff of obsidian which shows remarkably perfect columnar jointing. Some of the rhyolites of Nevada are exceedingly rich in porpnyritic minerals, so that they appear at first sight to be holocrystalline rocks, since the groundmass is scanty and inconspicuous. To this type the name nevadite has been given, but it is rare and local in its distribution.

In the island of Pantellaria, which lies to the south-west of Sicily, there are rocks of rhyolitic affinities which present so many unusual features that they have been designated pantellarites. They contain less silica and alumina and more alkalis and iron than do ordinary rhyolites. Their felspars are of the anorthoclase group, being rich in soda together with potash, and are very variable in crystalline development. Aeginne-augite and forms of sodaamphibole are also characteristic of these rocks: dark brown aenigmatite or cossyrite often occur in them. Quartz is not very plentiful; other ingredients are olivine, arfvedsonite and tridymite. The ground-mass varies much, being sometimes quite vitreous, at other times a glass filled with swarms of microliths, while in certain pantellarites it is a microcrystalline aggregate of quartz and alkali felspar. The absence of plagioclase and biotite are marked distinctions between these rocks and the rhyolites, together with the scarcity of quartz and the prevalence of soda-bearing pyroxenes and amphiboles.

Among the Palaeozoic volcanic rocks of Germany there is a group of lavas, the quartz-keratophyres, which are of acid composition and rich in alkali felspar. Their dominant alkali is soda: hence their felspars are albite and cryptoperthite, not sanidine as in rhyolites. Quartz occurs sometimes as corroded phenocrysts, but is often scarce even in the ground-mass. Porphyritic biotite or augite are very rare, but occur in the matrix along with felspars and quartz. Micropegmatite is not infrequent in these rocks, and they may be silicified like the rhyolites. As quartz-keratophyres mostly occur in districts where there has been a good deal of folding, they are often crushed and more or less sericitized. They are best known from the Devonian rocks of Westphalia and the Harz, but are also found in Queensland, and similar rocks have been described (as soda-felsites) from Ireland. The rocks which they accompany are usually diabases and spilites.

The other group of rhyolitic rocks rich in alkali felspars and soda pyroxenes and amphiboles are the comendites. They are often porphyritic, with crystals of quartz, sanidine, microperthite or albite: the ground-mass is microcrystalline or rarely micrographic, and often filled with spongy growths of aegirine and riebeckite. They are known from the recent eruptive districts of East Africa, from Sardinia and Texas, and very similar rocks occur as intrusive masses which may be grouped with the porphyries.

The following analyses show the composition of some of the principal types of rhyolites:

SiO 2 Al 2 Oi I- 76-34 13-22 II. 72-15 13-50 III. 77-59 12-75 IV. 67-48 9-70 V. 70-97 I3-84 VI. 74-76 n-6o Fe 2 s CaO K 2 O Na 2 O 1zz -93 1zz -85 0-21 3-67 2-84 0-61 3-12 o-93 0-16 4-54 4-20 0-85 0-67 7-42 n.f.

2-21 0-04 1-45 0-16 0-77 3-99 2-94 2-56 7-21 0-96 3-21 0-78 1-26 O-2O 1-57 6-27 0-74 3-50 O-I9 0-07 0-18 4-92 4-35 0-64 I. Rhyolite, Telki Banya, Hungary. II. do. Mafahlid, Iceland.

III. do. Omahu, New Zealand.

IV. Pantellarite, Pantellaria.

V. Quartz-keratophyre, Muhlenthal, Harz. VI. Comendite, Sardinia.

We note in the rhyolites I. -1 1 1. the very high silica, with alkalis and alumina also in considerable amount, while lime, magnesia and iron are very low. In the pantellarite, keratophyre and comendite the silica tends to be less abundant, while the alkalis, especially soda increase; they have less alumina but are richer in iron and magnesia. It is easy to see why the latter types contain less quartz, felspars often very rich in soda, and femic minerals which contain iron and alkalis in notable amounts such as aeginne, nebeckite and arfvedsonite. Jj. a.r.J RHYTHM (Greek t>v6nk, from fxlv, to flow), the measured flow of movement, or beat, in verse, music or by analogy in other connexions, e.g. " rhythm of life." The early critic of prosody, Aristoxenus, distinguished as the three elements out of which rhythm is composed, the spoken word, Xew, the tune of music and song, /wXos, and the bodily motion, dvijaa ffunaTudi. The art of the early Greek poets was devoted to S harmonious combination of these three elements, language, instrument and gesture uniting to form perfect rhythm. Aristoxenus proceeds to define the rhythm so produced as an arrangement of time-periods, TO.& xPv, but other early theorists make not the time but the syllable the measurement of poetic speech. Both music and poetry depend, and have depended from the earliest times, on rhythm. But in music melody and harmony have to be taken into consideration, whereas in poetry the rhythmical value of the tone is modified by the imaginative value and importance of the words themselves. In earliest times the fundamental unity of the two arts was constantly manifest, but as 'the world has progressed, and they have ramified into countless forms, the difference between them has been emphasized more and more.

Rhythm in Verse. Professor Jakob Minor has adduced a figure, valuable in helping us to realize what poetic rhythm is, when he remarks that to strike a bell twelve times, at exactly equal intervals, is to produce what may be called, indeed, a rhythmic effect, but not to awaken anything resembling the sensation of poetical rhythm. Into the idea of poetic rhythm enters an element of life, of pulse, of a certain inequality of time based upon an equality of tone. Rhythm ceases to be poetic rhythm if it is mechanical or lifeless. Aristotle, from whom a definition might be expected, is very vague in dealing with the subject, and most of the old rhetorical writers darken counsel with statements that are obscure or irrational. The fact is that rhythm is an expression of the instinct for order in sound which naturally governs the human ear, and little practical knowledge is gained by following Suidas when he says that rhythm is the father of metre, or Quintilian in his epigram that rhythm is male and metre is female. These definitions arise from a rhetorical desire to measure a delicate instinct by rule of three, and, as a matter of fact, Greek criticism on this subject often lost itself in arithmetical absurdities. It is sufficient to say that rhythm is the law which governs the even and periodical progress of sounds, in harmony with the exigencies of human emotion. For the passions, as expressed in verse, various movements are appropriate. Joy demands that the voice should leap and sing; sorrow that it should move solemnly and slowly; and poetry, which is founded on rhythm, requires that the movement of words should respond to this instinctive gradation of sounds. The finer the genius of the metrist the more exquisitely does his rhythm convey, as upon an instrument, the nature of the passion which burdens his verses. Ecstasy takes a quick, eager, rising movement:

" Give him the nectar! Pour out for the poet, Hebe, pour free! Quicken his eyes with celestial dew, That Styx the detested no more he may view.

Mystery and suspense demand a faint, languid and throbbing movement:

" There is not wind enough in the air To move away the ringlet curl From the lovely lady's cheek There is not wind enough to twirl The one red leaf, the last of its clan, That dances as often as dance it can."

An overpowering sadness interprets itself in rhythm that is full and slow and emphatic:

" My genial spirits fail, And what can these avail To lift the smothering weight from off my breast? It were a vain endeavour, Though I should gaze for ever On that green light that lingers in the west : I may not hope from outward forms to win The passion ana the life, whose fountains are within."

The rhythm so produced, intimately linked, almost beyond the disintegrating power of analysis, with human feeling, may depend either on accentuation or quantity. The latter forms the principle upon which all classic metre was composed, while the former is dominant in nearly every description of modem verse. Greek and Latin verse depends entirely upon the relation of syllables, long or short. It was a question of time with the ancients, of stress or weight with us. It is an error to say, as is often done, that ancient verse did not recognize accent, and that in modern verse there is no place for quantity. These statements are generally true, but there are various exceptions to both rules. Schiffer, in his Englische Melrik, specially points out that " long and short syllables have no constant length, no constant relation, but they depend on their place in the verse, and on the context; though they do not determine the rhythm of verse, they still act as regulators of our metre in a very important degree." Pauses take an essential importance in the construction of modern rhythm, of the variety and vitality of which they are the basis. They are introduced for the purpose of relieving the monotony of successive equal groups of syllables. The pause often takes the place of a light syllable, and there are instances in the verse of Shakespeare and Milton where it is even allowed to fill up the space of a heavy syllable. But still more often the pause does not imply the dropping of a syllable at all, but simply dictates a break in the sound, equivalent to a break in the sense. The following extract from a " Psalm " in Crashaw's Steps to the Temple (1646), in which the pauses are numerous and energetic, will exemplify the variety of this artifice:

In the blank verse of Milton the free use of pauses constitutes the principal element in the amazing metrical art of the poet, and is the source of the sublime originality of his music. In speaking of rhythm, it is customary to think of the formal rules which govern the fixed cadence of feet in poetry, but there is also a rhythm in prose, which imitates the measured movements of the body in stately speech. According to Renan, the rhythm of the ancient poetry of the Hebrews is solely founded on this prose movement, which differs, in fact, from that of modern European poetry merely in its undefined and indeterminate character.

See I. Minor, Neuhochdeutsche Melrik (Strassburg, 1893); W. Christ, Die Melrik der Greichen (Leipzig, 1874); Roderick Benadix, Das Wesen des deutschen Rhythmus (Leipzig, 1862); Jakob Schiffer, Englische Melrik (Leipzig, 1895); Edwin Guest, History of English Rhythms (London, 1838; and ed., 1882); Theodore de Banville, Petit Traite de la poesie franfaise (Pans, 1881); F. B. Gummere, Handbook of Poetics (Boston, 1902).

Rhythm in Music. The rhythm of modem music began to develop through the attempts of learned medieval musicians to adapt the rhythms of spoken language to the necessities of choral singing; but before the process had gone far, certain much more ancient and powerful principles, always manifest in folk-song and dance, gained ascendancy, so that even the simplest classical music has a rhythm for which no criteria of poetic metre can be made adequate. From the musical point of view, the rhythm of speech, whether in prose or verse, is very subtle and almost uniformly fluent. The metrical feet which constitute the details of poetic rhythm are musically very minute; and the exaggerated forms in which music represents them are many and varied. On the other hand, the groups of metrical feet which constitute any one kind of verse are of a uniformity which for music on a large scale would be intolerable. Artistic music is soon compelled to draw upon infinite resources of its own, which preserve an appropriate accentuation of the sense and feeling, while obliterating or hugely exaggerating the poet's rhythmic effects. Musical rhythm cannot be studied on a sound basis unless its radical divergences from speechrhythm are recognized from the outset.

In the earliest extant musical settings of poetry the treatment of accent and quantity was strictly arithmetical ; and purely aesthetic requirements were satisfied by ex post facto inference from the arithmetical laws, rather than treated as the basis of the laws. Accent, when translated into music, is a rhythmic sensation resembling the stress we put on the left foot in marching; while quantity rarely suggests any bodily movement at all, since it can correspond only to variations in the length of steps. Now in modern music a sense akin to that of bodily movement is of overwhelming importance. Changes of tempo, and of the grouping of musical beats, are incidents as obvious in their effect as changes in the pace of a running horse. One consequence is that the laws of musical accent are simple and cogent, while the laws of musical quantity, if such exist, are far beyond analysis. Fluent speech and energetic physical exercise cannot be carried on simultaneously by the same person; and hence the laws of quantity belong to speech rather than to dance. Before we could form adequate notions of the musical rhythms of classical Greece, we should need to settle, firstly, how far the dancing in Greek drama included movements other than idealized dramatic gesticulation; secondly, how much bodily energy was involved in all dancing that may have gone beyond this; and lastly, how much dancing of any kind was executed by the singers while singing. What is certain is that ancient Greek musical rhythms were exact translations of verse rhythms, with the quantities interpreted arithmetically.

The extant fragments of Greek music are, whether we have read them correctly or not, undoubtedly very different in rhythm from the system of discant on which European music of the 12th and 13th centuries first developed; but they resemble discant in so far as the modern sense of rhythm is absent and its place is supplied by a sense of the rhythmic expression of unusually slow and emphatic speech. In ordinary speech there is an important difference between long syllables and short; but it is not naturally regulated by an exact rhythm, and the art by which it is organized in verse admits (or indeed demands) considerable freedom on the part of the reciter in varying his pace within such limits as do not destroy the structure of the lines. But when a chorus is made to sing words, it must, if the words are to reach the hearer, sing them slowly; and moreover, it must sing them exactly together, unless, as in much classical music, it can repeat them until they are either understood or dismissed from the mind as a mere pretext for the employment of voices in a merely musical design. In any case, if a chorus is to sing well together, the contrast between short and long syllables must be placed on an arithmetical basis, the simpler the better. Now the sole function of ancient Greek music was to enhance the emotional effect of poetic words by regulating their rise and fall in a musical scale and their length in a metrical scheme; and it was natural and right that its rhythms should, though accurate, have no stronger ictus than those of the words. To make them as rigid and forcible as the rhythms of a non-vocal music would produce an effect as intolerable to a Greek ear as a schoolboy's worst jog-trotting scansion of poetry. We need not, then, imagine that the human sense of rhythm has suffered any mysterious change, when our best attempts at deciphering the extant fragments of ancient Greek music yield us a rhythm which scholars can explain by the structure of Greek verse, but which gives us no musical sense. Neither here nor in such strange harmonic phenomena as our complete inversion of medieval harmonic ideas as to the treatment of " perfect concords " (see HARMONY) do we find any principle involved which is not as true at the present day as it ever was. Ancient musical rhythm shared in the general qualities of that " Flatland " which we know ancient music to have been; modern musical rhythm, like harmony, belongs, as it were, to a three-dimensioned musical space with the vast artistic resources of a consistent perspective.

Indeed, we need much the same kind of mental gymnastic in studying the origins of musical rhythm as we need for the much more abstruse subject of harmonic origins. The two subjects soon begin to show interaction. During the period of discant we find metrical conceptions already strongly modified by two purely musical factors. Firstly, the attempt to make voices produce a harmony from different simultaneous melodies (instead of from combinations conceived as disguised unison) brought with it the necessity for differences of length enormously larger than any possible metrical differences. The metrical influence, however, still so predominated, even in the 14th century, as to produce a rhythm based almost exclusively on what would now be called triple time. Secondly, that sense of bodily movement, for which the less clumsy term " dancerhythm " is far too narrow, gained ground as the only means powerful enough to hold the various rhythms of the new and growing polyphony together. In the later stages of discant the old metrical conceptions struggled against the grain of the polyphony for awhile, only to succumb in a tangle of inextricable technicality: and the new art, which became coherent in the 15th century, disregarded poetic metre, with little or no loss in capacity to interpret words if the composer had leisure or desire to do so; since, after all, poetic rhythm in its highest forms has a subtle freedom which renders mechanical musical translation worse than useless, while the rhythmic swing of the lighter forms of poetry was soon discovered by the composers of the " Golden Age " to be practically identical with the refined dance-rhythm which they in their lighter moments idealized from folk-music. 1 By the middle of the 15th century polyphony attained such independence that the only rhythms which would hold the flow of independent melodious voices together were those in which a steadily duple or steadily triple rhythm (either of which might be subdivided by the other or by itself) could be felt as an absolutely regular musical tread. Such a rhythm is capable of expressing every poetic foot, either by the difference of stress between notes or by a difference in their length. Moreover, emphasis may be obtained by the pitch of the note, or, again, by its harmonic significance. All these forms of emphasis combine and counteract each other in an infinite variety, till the sense of musical movement becomes as remote from crude dance-rhythm as it is from poetic metre. But though the part thus played by accent was already of paramount importance in the " Golden Age " of music, it was not allowed to become evident to the ear except in the lighter and more coarse-grained art-forms. Its highest purpose was served as soon as the listener was able to lose all crude rhythmic impulses in a secure feeling that the mass of polyphonic harmony was held together by a general grouping of the rhythmic beats in fours or threes; and individual parts were at least as free to indulge in other rhythms across the main rhythm as they are in the most complex modern music, so long as the harmony was held together by the average grouping, or " time," as we now call it. Hence the rhythmic variety of 16th-century 1 It would be interesting and fruitful to consider how far the growing preference, In modern European languages, of accent to quantity, may not only have modified the conception of musical rhythm, but may itself have been enhanced by the rhythmic tendencies of popular song, which had so great an influence on the learned music of the middle ages. And it can hardly be said that the subject of musical rhythm has yet been so clearly treated on these lines as to shed the light it seems capable of shedding upon many vexed questions in poetic rhythm.

music is exactly like the harmonic variety, and the limitations and waywardness of the one are no more archaic than those of the other.

When the resources of later music and the treatment of instruments necessitated the publishing of music in score as well as in separate parts, it became necessary to guide the eye by drawing vertical lines (" bars ") at convenient distances. Hence the term " score " (Ger. Partitur, FT. partition). These divisions naturally coincided with the main rhythmic groups, and eventually became equidistant. This purely practical custom has co-operated with the great increase of rhythmic firmness necessary for the coherence of those large modern forms which decree the shape rather than the texture of the music, until our notions of rhythm may fairly be described as bar-ridden. And, since the vast majority of our musical rhythms absorb the utmost complexity of detail into the most square and symmetrical framework possible, we are taught to regard the " 4-bar period " as a normal (or even ultimate) rhythmic principle, instead of contenting ourselves with broader conceptions which treat symmetry and proportion in time as freely as they are treated in space. It cannot be too strongly emphasized that the bar indicates no universal musical principle. The havoc wrought by mechanical teaching on this point is incalculable, especially in the childish crudeness of current ideas as to the declamation of words in classical and modern music: ideas which mislead even some composers who might have been expected to know better.

As rhythm is contemplated in larger measures, it becomes increasingly difficult to say where the sense of rhythm ends and the sense of proportion begins. The same melody that may be felt as a square and symmetrical piece of proportion in four-bar rhythm if it is taken slowly, will be equally rational as a single bar of " common time " (see below) if it is taken very quickly; and between these two extremes there may be insensible gradations. All that can be laid down is that composers are apt to use short bars where they demand constant strong accent, while long bars will imply smoother rhythms. For example, if the scherzo of Beethoven's Ninth Symphony were written in " instead of ! bars, then the passages now marked Ritmo di tre battute would have to appear in ! time, and so the changes of rhythm would be much more visible on paper. But the tendency to put a strong accent on the first beat of every bar would make this notation an undesirable substitute for Beethoven's, since it would lead to a neglect of the subordinate accents (all of them bar-accents, as Beethoven writes them). The trio of this scherzo shows the opposite case in the fact that Beethoven first intended to write it in * time, but, in order to indicate a more tranquil flow at the same pace, doubled the quantity contained in a bar, substituting alia breve bars, each equal to two of the preceding J bars. The alteration produced a discrepancy in the metronome marks, which has always caused controversy among conductors, but the facts admit of only one interpretation. It is clear, then, that the only sound theory of musical rhythm will be that in which accent, beat, bar, and even form and proportion are relative terms.

The kinds of time (i.e. rhythmic groups forming, as it were, invariable molecules in the structure of any continuous piece of music) that are used in all music from the 15th century onwards are nowadays classified as duple and triple, and each of these may be simple or compound. Simple time is that in which the normal subdivision of its beats is by two, whether the number of the beats themselves is duple or triple. Compound time is that in which the beats are regularly divided by three, which three subdivisions are reckoned as subordinate beats. The beats are in all kinds of time reckoned as halves, quarters, 8ths, i6ths or even 32nds of the standard note in modern music, the semibreve: and the timesignature placed at the beginning of a piece of music is really a fraction, of which the numerator expresses the number of beats in a bar, while the denominator expresses the size of a beat. Thus J signifies three crotchets in a bar. Compound time is expressed, not by using normal fractions of a semibreve as main beats and dividing them into triplets, 1 but by using dotted beats. A dot after 1 Triplets are groups of three equal notes crowded into the time normally taken by two. Binary and ternary subdivision answer a note adds another half to its value, and so not only do we obtain the means of expressing a great variety of rhythmic effects ( especially quantitative effects of iambic and trochaic character) in all kinds of time, but we are able to use normal fractions of a semibreve as the subordinate beats of compound time. Thus 5 is the compound time obtained by dotting the two crotchets of * time, and is thus totally different in accent and meaning from J time though that also contains six quavers in a bar. The most highly compound times in classical music are to be found in the last movement _of Beethoven's Sonata, Op. in. He begins by dividing bars of J into their usual compound time ,V He then divides the six half-beats of J time by three, producing \l (which he incorrectly calls ,1), and lastly he divides the 12 quarter-beats by 3, producing JJ (which he calls JJ). The special signatures C for 4 time, and C for * time are the last survivals of the time system of the middle ages (see MUSICAL NOTATION). That complicated system of mood, time and prolation was capable of expressing even more highly compound rhythms than our usual time-signatures, though the complexity was in most cases unreal, since the small rhythmic ictus of ecclesiastical polyphony renders little but the general distinction between duple and triple rhythm audible: especially as the more compound rhythms were not subdivisions but multiples, involving lengths better measurable by an eight-day clock than by human ears. The second Kyrie of Palestrina s Missa L'Homme Arme is one of the rare cases which remain both rhythmic and complex when transcribed in modern score. 1 For genuine articulate complexity the ballroom scene in Mozart's Don Giovanni has never been surpassed. So real are its three simultaneous rhythms of minuet, contredanse and waltz that the persons on the stage actually dance to whichever suits their character. Anomalous measures such as { and J time, whether divisible into alternations of I and I or not, are aesthetically best regarded not as rhythmic units, but as extreme- cases of unsymmetncal phrase-rhythm erected into a system for special effect. They tend, however, to group themselves into musical sentences of reactionary squareness; and the 5 movement of Tschaikovsky's Pathetic Symphony consists of twenty 8-bar periods (twenty-four, counting the repeats) before an unpaired 4-bar phrase is heard in the short coda. Even the last bar is not odd, though it is the I79th, for the rhythm ends with an unwritten iSoth bar of silence.

There is, no doubt, a germ of truth in current doctrine as to the fundamental character of 4-bar phrase-rhythms, inasmuch as the human anatomy has a bilateral symmetry with either limb on one side slightly stronger than that on the other. This is probably the basis of our natural tendency to group rhythmic units in pairs, with a stress on the first of each pair; and hence, if our attention is drawn to larger groups, we put more stress on the first of the first pair than on the first of the second; and so with still greater groups, until our immediate and unanalysed sense of rhythm merges into a sense of proportion distributed through time with a clear consciousness of past, present and future. The point at which this merging takes every ordinary purpose of musical rhythm, "being capable of expressing clear distinctions far more minute than have ever been regulated in speech. It is impossible to pronounce a syllable in less than a tenth of a second; but it is easy to play 1 6 notes in a second on the pianoforte. (That is to say, musical rhythm continues to be measurable up to the point at which atmospheric vibrations coalesce in the ear as low musical notes!) In a series of such rapid notes a single break twice in a second would have a very obvious rhythmic effect directly measured by the ear. If the broken series were levelled into an even series of fourteen notes a second, the rhythmic effect would be entirely different, though the actual difference of pace would be only j"j of a second. The special sign for triplets is readily adapted to other subdivisions where necessary; but such adaptation generally indicates rather a freedom of declamatory rhythm than any abstruse arithmetical accuracy. Among the worst barbarisms in musical editing is the persistent reduction of Chopin's septoles, groups of 13 and other indeterminables, into mutton-cutlet frills._ A natural freedom in performance is as necessary for the minutiae of musical rhythm as it is in speech; but where all but the finest players fail is in basing this freedom on the superlative accuracy of the rhythmic notation of the great composers.

4 In the critical edition of Palestrina's complete works, vol. xii. p. 177 (Breitkppf and Hartel), the editor has violently simplified it. He is justified in using the ordinary < bars to hold the piece together, and he is not called upon to reproduce the riddles of the original notation ; but some secondary time signatures ought to have been added to indicate the strong swing of the tune in its conflicting shapes; and there is no justification, in a full score intended for scholars, in supplanting the true rhythm of the quintus by a rough practical compromise.

place depends on the extent to which these larger groups can dominate the details of the rhythm, and this again depends on the listener's capacity for grasping large and slow rhythms. In any case, the only " ultimate " rhythmic element is the tendency to mark off rhythmic beats into pairs, with a stress on the first of each pair. Where this tendency is resisted, the mind will follow the line of least resistance, which will vary according to the pace and detail of the music. Thus in rapid triple time it is easier to seek duple rhythm in the grouping of bars than in the details within the bars; but if the groups of bars are also triple, or irregular, the mind will fix on the first recurring salient feature for a secondary beat, regardless of inequality in length; rather than, so to speak, hop on one leg indefinitely. On this principle there is a distinct tendency in moderate and slow triple times to throw a secondary accent on the third beat; or sometimes on the second, as in the springing step of the mazurka, where the spring gives energy to the first beat and the descent from it gives poise to the second.

The tendency of small rhythmic groups to build themselves into large and square ones, such as 8-bar, i6-bar and even 32-bar periods, is doubtless important; but the converse tendency of large phrase-rhythms to break up in a tapering series is far more significant, since even in its most regular forms it not only produces more variety the further it goes, but always increases in obvious effect, until the subdivisions attain the minuteness (and therewith the expression) of speech rhythms. (A crude example of the device is Diabelli's waltz, on which Beethoven wrote his gigantic 33 variations. See VARIATIONS, where the point is illustrated by a diagram.) Regularly expanding rhythm, on the other hand, not only becomes imperceptible as it is carried further, but tends merely to make musical proportions resemble those of a chess-board. In great music the expanding principle is therefore always contrasted with or modified by the tapering principle, which can indeed exist simultaneously with it and with any other. For, to take only three categories, the harmonic changes of a passage may be designed in tapering rhythm while the melodic phrases expand, and the entries of instruments or parts occur on some third principle, regular or irregular. Such interplay need produce no feeling of complexity; indeed, it is an art most neglected by those composers who most rely on the effect of complex rhythm. It is the main discoverable source of that almost dramatic sense of movement that distinguishes the great musical styles from the academic methods which play for safety, and from the anti-academic novelties which end in monotony.

Square rhythms become desirable at climaxes where physical energy dominates thought. Strong final cadences accordingly require that the last chord should fall on an accent; and if the pace is rapid the final chord will probably be not only on an accented beat but on an accented bar. Thus it is quite obvious that there is by a mere oversight one bar too many in the four bars of tremolo quavers at the end of the first movement of Beethoven's Fourth Symphony; for they are followed by an important bar leading to the last three chords, which chords can only mean (counting bars as beats) " ONE, two, THREE " (" four " being silent and therefore unwritten). A fifth bar of tremolo would correct the rhythm in a more vigorous but more vulgar way by bringing the last chord onto " ONE " of the next imaginary group of four. The former correction is so obviously right that the imagination makes it in spite of the presence of the superfluous bar, which is instinctively ignored as an accidental prolongation of the tremolo. Where the composer writes in bars so short as to be permanently less than the phrases of the piece (as in Beethoven's scherzos), or in bars that are frequently longer than the phrases (as in most of Mozart's movements in slow or moderate common time) , it sometimes becomes impossible to construe the music without carefully calculating where the accents come; and this calculation is most easily made on the assumption that the strongest cadences bring the tonic chord on an accent. Thus, in Beethoven's Sonata in E flat, Op. 27, No. i, the first bar of the second movement must be preliminary and the first accent must come on the second bar, since the piece refuses to make sense in any other way. Indeed, Beethoven has written some notes twice over in order to bring his doublebars and repeat-marks where they will indicate the true rhythmic joints to the eye. (A double-bar is a mere graphic indication of some important sectional division, not necessarily rhythmic or even coincident with a normal bar-stroke.)

Theorists, however, have developed a tendency to assume that all cadences must be strong. More than one critic has told us that the scherzo of Beethoven's Sonata, Op. 28, is in the same predicament as that of Op. 27, No. i; though it not only makes excellent sense with its cadences in the light and weak form in which they appear, but, when reconstrued on the " strong cadence " theory, entirely fails in its middle portion to uphold that theory or to make any other rhythmic sense. And when Professor Prout tells us that the overture to Figaro begins with a silent bar, and that Schubert's Impromptu in B flat is positively ungrammatical in its cadences unless it is entirely rebarred, and when Dr Riemann turns half the ritornello of a Bach concerto from into f time, simply in order to make the sequences coincide with the hardest possible accents; then we can only protest that this is regulating musical aesthetics by criteria too crude for the aesthetics of bricklaying. An edition of Paradise Lost, in which the lines were so rearranged as to bring all punctuation marks (except perhaps commas) at the end of the line, would be on precisely the same level of ingenious barbarity.

Few technical terms are entirely peculiar to the subject of musical rhythm; but some obvious terms of syntax, such as phrase, period and section are used with varying degrees of system by all writers on music; and the whole terminology of prosody has been annexed with such success that we are told in Grove's Dictionary (article " Metre ") that " the theme of Weber's Rondo brillante in E flat (Op. 62) is in Anapaestic Tetrameter Brachycatalectic, very rigidly maintained."

One important term has acquired a special significance in music: viz. Syncopation. It means a cross-accent of such strength as to equal or even suppress the main accent; but the use of the term is generally restricted to cases in which the crossaccent is produced by shifting the notes of a melody or a formula so that they fall between the beats instead of upon them. From what we have said as to the almost physical energy of musical rhythm it is obvious that such a phenomenon is of far greater effect and importance in music than it could possibly be in verse; and, to whichever subject the term may belong by priority, extreme caution is needed in extending any musical notion of it to the structure of poetry. (D. F. T.)

Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)

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