we have a crotchet solved into a triplet of quavers, but then, each triplet-quaver into two semiquavers. We have, therefore, again a group of six notes, a sextriplet (and this is the forementioned second kind of sextuplet), but differently derived. Further on (in the 10th section of this division), we shall see, that the derivation has an influence on its nature, and distinguishes the last from the first. Hitherto we have been occupied with the dual and triform values; and moreover with the development of groups of crotchets and quavers (for instance, four quavers to a minim, and eight quavers to a semibreve), and in the explanation of the other groups of six notes, that is the so-called sextriplet or double triplet, and both kinds mingled together. Now, let us proceed to (D) MORE NUMEROUS GROUPS. We divide a note into five instead of four parts: for example, a minim into five quavers, a crotchet into five semiquavers; whereby the notes, quavers and semiquavers, again lose their proper or legitimate values. Thus these,— d FEEL FFFF taken collectively have only the original value of four. Such a group is called A QUINTUPLET. In like manner is formed A SEPTUPLET. in which ten parts appear in lieu of eight or four; and so any value may be divided at pleasure into eleven, thirteen, &c. For example, here, 59. 15 is a crotchet in fifteen parts instead of four or eight, and the cypher placed over it is sufficient for universal intelligence, without any rigorous+ inquiry into the number of the lines of duration: everywhere the same value is attributed to the notes alone, without regard to their derivation. A more distinct recognition of similar groups, which are, however, not of frequent occurrence, will be obtained from the study of the formation of bars, and its distributive arrangements. SECOND SECTION.-OF RESTS. We have now determined the duration of the tones, and also how to regulate the succession of time for whole of tones. For the latter case we have ranges presupposed that one tone immediately follows another without any intervention of time. But the contrary is possible; that between the end of one tone and the beginning of another, some time may intervene, may pass without sound. These moments of silence, called RESTS, In which there are seven parts instead of four-or also instead of six.* Or the NONUPLET, If it were desired to place seven quavers instead of six in a sixeight bar (what to understand by this will be explained further on) this would be a septuplet, in which seven would not be instead of four, but of six. demisemiquaver, semidemisemiquaver, demisemidemisemiquaver + It is usual to write from the next preceding subdivision-for example, nonuplets, from the next preceding subdivision of eight notes: therefore a nonuplet of a minim with semiquavers, a nonuplet of a crotchet with demisemiquavers. Others content themselves with dashing the group together with a single or double line of duration. J. Haydn wrote so in the introduction to the Creation (page 5 of the score) that genial volley of clarinets of 15 notes on a minim, with quavers : 60. It is of no consequence on which line these rests are placed. Indeed, if two or more successions of tones are written upon one staff, and a rest be necessary in one of the successions in a position where there is not the value of the notation, they are marked staccato (detached), or with little thin lines, thus ;— 62. or, if they are not to be made so short, with dots against or over the notes, thus : 63. How much shorter notes so marked should be, is not determined. The foregoing, with dots, may be, perhaps, as quavers equal to three demisemiquavers instead of four, those with little lines, still shorter, perhaps equal to only one semiquaver, thus: Written, 64. Played, while the remainder of the value is occupied in momentary rests after each note. If a still shorter duration is desired for each note, the staccato and rests may be used in conjunction, thus:— 65. or staccatissimo may be written over the passage. 2. LEGATO. If in any passage, every sound is to be held on, or continued until the immediate commencement of the following sound, or longer if possible, so that the two sounds may melt as it were into each other, Legato (bound) is placed over the notes, or Legato assai (very bound), or Legatissimo (bound in the utmost degree); or in lieu of these, a bind is placed over them with the same effect, thus : 66. Here, therefore, the value of each separate tone is secured against any diminution, or even extended into the time of the next tone. If any particular tone is to endure quite its full time, or rather more, it is marked Tenuto (ten.) or Ben tenuto-held on, sustained fully. Of late it has become customary, particularly when several notes after each other are to be played tenuto, to place a little dash over every such note. So here, 67. the three last crotchets must be allowed their full time, and perhaps a little more. When the time or value is unappreciably taken from or added to the notes, such a passage is marked Tempo rubato (stolen time), or also, a piacere, ad libitum, at the will of the performer. If in any principal part (such, for example, as the voice in a song), an ad libitum, or a piacere, should occur, the accompanying parts must govern themselves by it; FOURTH SECTION.-OF TIME. ABSOLUTE. All the foregoing varieties of duration gave the notes and rests merely a relative value. They determined that a crotchet should be equal to two quavers, or half as much as a minim; and this, again, half as much as a semibreve. But how long any one of them-that is, how many seconds for example, or what part of a second, a semibreve should last, that the valuation does not determine. Now it is clear, that in some compositions a lively quick motion would be appropriate; while in others, the sentiment would require the time to be slow, lingering, and solemn. Joyful, excited sensations, animate and hasten all our motions, and, therefore, our voices: sad and dejected feelings, on the other hand, render us in all respects slothful and torpid. Different degrees and kinds of motion have been adopted, therefore, with suitable designations, as expressive of various states of the mind, whereby an attempt is made to give an approximate idea of absolute time. Motion may be considered as divided into five chief gradations, each of which may again be subdivided into smaller variations. They are all indicated by the following list of words, which are generally written at the beginning of the composition over the notes. 1. THE SLOWEST MOTION. Largo-slow; Largo assai-assai means very; or Larghissimo-extremely slow. Adagio-slow; Adagiosissimo-very slow. Largo and its augmentatives generally mean the slowest motion; Adagio and Grave are often taker as less slow than Lento. 2. MODERATELY SLOW MOTION. Larghetto-rather slow. Andante-going, but walking, not running. Andantino-somewhat slower than Andante. Sostenuto-sustained, maintained without change. Commodo-leisurely. Here also the names are arranged in the gradation of increasing swiftness. There is, however, no unanimity among composers and teachers in these fine distinctions; there are many, for instance, who consider Andantino as quicker than Andante. 3. MODERATELY QUICK MOTION has the following signs:Allegretto-rather lively. Moderato-moderate. Allegramente-approaching to Allegro, nearly as lively. Allegro Moderato-moderately lively. Allegro-merry, cheerful. Allegro con brio (or brioso)-joyful and bold. 5. THE QUICKEST MOTION. Allegro assai-very cheerful or joyful. Allegro vivace, or Allegrissimo-most lively. Vivace, Vivacissimo-most animated or lively. Presto quick; Presto assai, Prestissimo-as quick as possible. That with these expressions, and any definite number more, all possible gradations of musical motion would not be exhausted, must be abundantly evident. We seek for assistance, therefore, from augmentatives and diminutives. Such are Più-more. So, for instance,— Più allegro means more lively (than before). Meno allegro means less lively (than before). Più moto, and mosso, means with more motion. Più vivo means more animated. And after all, the most apt, minute, and vivid directions must be intrusted to the comprehension of the performer and the taste of the moment. All these expressions serve to give a sufficiently definite style and character to the whole course of a musical composition. But it may be desirable that some portions of the composition be played faster or slower than the general time of the piece. On such occasions we use— Vivo, più vivo-lively, more lively. Ritenuto (riten., rit., and ritardando)—slower. And afterwards A tempo-return to the original time. Or, it may be the object to proceed by imperceptible gradations from one kind of motion to another. For this, there are many technical expressions, and moreover, the general direction Tempo assimilando al movimento seguente-assimilating in time to the following movement. If the time is to become gradually slower, the words used are Rilasciando-relaxing, slackening. Ritardando-retarding, keeping back. Rallentando or rallent. or rall., also allentand. and lentando-becoming slower. The last expression is generally used as the strongest for indicating a diminution or cessation of motion; also the word Calando-sinking, declining, falling away, has the intention of producing a slower motion. If a slower motion is to be quickened into swiftness, the following expressions are employed :Accelerando-accelerating. Precipitando-urging onwards. Stringendo-pressing forwards. If the increase or diminution of speed is desired to be by very small degrees, the foregoing expressions are accompanied by Poco a poco-little by little; thus Poco a poco rallentando-becoming slower little by little. Poco a poco più moto-faster and faster by small degrees. If a considerable movement throughout, or towards the conclusion, is to be urged constantly faster, the words Più stretto more strained or urged, are written over the movement. The movement so marked is also called the STRETTA. So concludes, for example, the first finale in Don Giovanni, with a stretta. When the state of changing from one condition of motion to another ceases, the new or required condition is indicated; thus, for example, Allegro | Accelerando | Presto starting from Allegro, we meet on our way with Accelerando, which we put into practice until we fall in with Presto, which we then continue. Or, if after a change in time we are to revert to the original prescription, this intention is indicated by Tempo primo (t. p.) meaning the original time. *When it is desired that the time marked should be rigidly adhered to, without either acceleration or retardation, we use the words Tempo giusto (exact time). *This paragraph is my own, in lieu of the original, in which the Author gives to the Italian words "Tempo giusto" a meaning of which they may indeed be in some cases susceptible, but which they certainly do not mean in this instance. The paragraph of Marx would run thus, in English:-"An extraordinary indication of time must be noticed in conclusion. The direction is sometimes found Tempo giusto,' that is to say 'the right time.'-The motion is to be as fast or as slow as we please or think proper.-A very innocent determination, for it determines just nothing." -TRANSLATOR. APPENDIX.-THE CHRONOMETER. tion, nor the fixed relative durations in the first Neither the descriptions of time in the last sec(both of this division), have furnished us with a measure for absolute time. They merely determine that the motion in one passage, according to the determined value of the notes, shall be quicker or slower than in another passage; or again, that a crotchet, for example, in an Andante movement, should be of longer duration than in an Allegro, and shorter duration than in a Largo movement. There still remains the question, how long should they be in any one of these designations of time? This can be determined only by our absolute astronomical divisions of time into minutes, seconds, &c. If we could obtain, therefore, the means of measuring motion with precision, we might establish, that a crotchet or a minim should have the duration of any certain fraction of a minute or of a second. Many expedients have been thought of for this object. The most generally known, however, is Mälzel's METRONOME. An instrument consisting of a pendulum with movable weight and wheelwork. Behind the pendulum there is a table divided into 110 degrees, No. 50 to 160. If the weight be applied to the pendulum at one of these degrees, the pendulum vibrates so many times in a minute as is the number itself of the degree. It vibrates, therefore, in the minute from 50 to 160 times, according to its being placed on the uppermost or the undermost degree. By this instrument a quantity of absolute duration can be measured for any note. We determine, for instance, that any value, as that of a crotchet, for example, shall be the sixtieth or hundred-and-twentieth of a minute. We place the weight at 60 or 120, accordingly, and the vibration of the pendulum will give the desired absolute measure. The measure of the crotchet being known, those of the minim and semibreve follow of course. In this manner the time may be signified in the most definite and absolute sense. The above cases would be indicated in the following manner :— M.M. (Mälzel's Metronome) = 60 If the motion be too slow to measure (according to the degree table) one kind of note, a smaller note must be measured. Thus, for example, if it were desired to show a motion in which the crotchet would require only 30 vibrations in a minute (and would therefore last two seconds), it might be represented thus: M.M. 60, = the vibrations of the metronome would then be quavers, from which the crotchets would become known. If on the other hand we wished to express so quick a motion, that it could not be shown for any value on the degree table, we must then have the assistance of larger denominations. If, for example, we want to express three crotchets as lasting a second (or 180 in the minute), we may do it so :— We We can understand in this way, how one and the same degree of motion, may have various ways of expression. More simple, cheaper, and liable to no derangement (as with the wheelwork of Mälzel), is the CHRONOMETER (OR STRING PENdulum) of Gottfried Weber, which with any weight, for instance a ball of clay and a string marked into lengths, any how, by knots for example, is at once complete. The shorter such a string is, the quicker are its vibrations; the longer, of course the slower are the vibrations. So, therefore, the degree of motion can be determined by the length of the string. A string, for example, of 55 Rhenish inches vibrates 50 times, and of five such inches, 160 times in a minute. The first of these measures applied to a crotchet would be thus expressed != 55′′ Rh., (56g English.) the latter, applied also to a crotchet, thus:T=5′′ Rh., (5} English.) Here follows a comparative table of the measures of Weber and Mälzel [and the approximate English measures are added] Metron. Rh. inches. : 56 = ... 512 96 48 100 = 14 ... 45% 104 13 42 108 Eng. 16 15 14 13 12 11 101 91 81 73 7 6 whereby we may be enabled to use both or either. If the string be fastened by the extreme end, it makes fifty vibrations in a minute; if it be fastened so that thirty-eight inches remain free, it will vibrate seconds, that is sixty vibrations in a minute, as the metronome when at sixty. If only nine inches of the string be allowed to be free, each vibration lasts only half a second, as the metronome indicates at 120. Now, it may be asked what quantity of absolute time is occupied by each of our signs or prescriptions for time? It has been suggested that the crotchet in the movement Andante, of our second gradation (page 31), should be considered as a second of absolute time. In truth, however, music is little concerned wit the mathematically-exact division of quantities Her object is to excite and to manifest the emotion of the heart and of the soul; and in that view, the approximative directions of the composer are more appropriate for her and true to nature, than metronomic exactitude.† The leader or conductor of a great performance, is bound most assuredly to comprehend perfectly, and endeavour to produce as faithfully as possible, the conceptions and feelings of the composer; and it therefore is incumbent upon him, to acquaint himself intimately with the composer's intentions as to time. But after all, everything depends upon his having formed a correct apprehension of his subject, and his having made the work a living thing in his own heart and mind; for from his own inward emotion alone can it issue forth with life and effect. Produced from outward mechanical tradition or prescription, without inward appropriation in feeling, it is dead-it neither has nor can give vitality. Moreover, there are other circumstances, which in the metronomic system of time cannot be provided for. In great compositions, for example, and large places, the time, particularly in florid passages, must be taken slower, because the sound spreads more slowly, and therefore in rapid motion, the sounds become confused, notwithstanding the most correct execution. It is necessary, therefore, to have a strong impression of the approximate time which is commonly attributed to the various expressions used in its indication, consistently always with the usual meaning of the words. Further minutiæ should and must be left to the artistic judgment and inspiration of the executants. We shall have a more intimate comprehension of these matters when we get to the instructions on Performance. FIFTH SECTION.-THE NATURE AND REGULATION OF BARS. We can now produce whole successions of sounds of equal or various value. But such a range, if it be of considerable extent, would not be appreciable by the eye it would not have the advantage of order, even though it proceeded regularly in single notes of the same value. How then are we to make any mass of notes intelligible? By dividing them into smaller and more comprehensible totals. So we distribute, for example, a heap of coin into small rows of four or five each, and we then easily reckon the whole quantity. Let us apply this to our string of notes. We take in the first instance, notes of the same value, crotchets for example, and we will call the notes separately. parts of the string. A long line of such notes or parts and so forth. On this point,, see the Author's Article Metronom, in the Universal Lexikon der Tonkunst C |