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INTRODUCTORY Remarks 1

MINERALOGY AND GEOLOGY.

BOTANY.

ZOOLOGY.

PHYSICS AND CHEMISTRY.

MISCELLANEOUS.

THE

JOURNAL OF SCIENCE, &c.

The age in which we live is not less distinguished by a vigorous and successful cultivation of physical science, than by its numerous and important applications to the practical arts, and to the common purposes of life.

In every enlightened country, men illustrious for talent, worth, and knowledge, are ardently engaged in enlarging the boundaries of natural science; and the history of their labours and discoveries is communicated to the world chiefly through the medium of Scientific Journals. The utility of such Journals has thus become generally evident; they are the heralds of science; they proclaim its toils and its achievements; they demonstrate its intimate connexion as well with the comfort, as with the intellectual and moral improvement of our species; and they often procure for it enviable honours and substantial rewards.

In England the interests of science have been, for a series of years, greatly promoted by the excellent Journals of Tilloch and Nicholson; and for the loss of the latter, the scientific world has been fully compensated by Dr. Thomson's Annals of Philosophy, and by the Journal of Science and the Arts, both published in London.

In France, the Annales de Chimie et de Physique, the Journal des Mines, the Journal de Physique, &c. have long enjoyed a high and deserved reputation. Indeed, there are few countries in Europe which do not produce some similar publication; not to mention the transactions of learned societies and numerous medical Journals.

But all these facts go only to prove the strong tendency which exists in this country towards the cultivation of physical science, and the inadequacy of the existing means for its effectual promulgation.

Although our limits do not permit us, however much inclined, to be more particular in commemorating the labours and in honouring the performances of our predecessors and cotemporaries, there is one effort which we are not willing to pass by without a more particular notice; and we are persuaded that no apology is necessary for naming the Journal of the late Dr. Bruce, of New-York, devoted principally to mineralogy and geology.

The hopes of its revival have now, unhappily, become completely extinct, by the lamented death of Dr. Bruce.

No one, it is presumed, will doubt that a Journal devoted to science, and embracing a sphere sufficiently extensive to allure to its support the principal scientific men of our country, is greatly needed; if cordially supported, it will be successful, and if successful, it will be a great public benefit.

As regards the subjects of this work, it is in our power to do much in the department of the natural history of this country. Our Zoology has been more fully investigated than our mineralogy and botany; but neither department is in danger of being exhausted. The interesting travels of Lewis and Clark have recently brought to our knowledge several plants and animals before unknown. Foreign naturalists frequently explore our territory; and, for the most part, convey to Europe the fruits of their researches, while but a small part of our own productions is examined and described by Americans: certainly, this is little to our credit, and still less to our advantage. Honourable exceptions to the truth of this remark are furnished by the exertions of some gentlemen in our principal cities, and in various other parts of the Union.

Such are the disguises worn by many most useful mineral substances, that an unskilful observer is liable to pass a thing by, as worthless, which, if better informed, he would seize with avidity; and, still more frequently, a worthless substance, clothed perhaps in a brilliant and attractive exterior, excites hopes altogether delusive, and induces expense, without a possibility of remuneration. A diffusion of correct knowledge on this subject is the only adequate remedy for either evil.

Our geology, also, presents a most interesting field of inquiry. A grand outline has recently been drawn by Mr. Maclure, with a masterly hand, and with a vast extent of personal observation and labour: but to fill up the detail, both observation and labour still more extensive are demanded; nor can the object be effected, till more good geologists are formed, and distributed over our extensive territory.

The outlines of American geology appear to be particularly grand, simple, and instructive; and a knowledge of the important facts, and general principles of this science, is of vast practical use, as regards the interests of agriculture, and the research for useful minerals. Geological and mineralogical descriptions, and maps of particular states and districts, are very much needed in the United States; and to excite a spirit to furnish them will form one leading object of this journal.

The science of natural philosophy, with its powerful auxiliary, mathematics, and the science of chemistry, the twin sister of natural philosophy, are of incalculable importance to this country. A volume would not suffice to trace their applications, and to enumerate the instances of their utility.

The successful execution of this magnificent design was first witnessed upon the waters of the Hudson, but is now imitated in almost every civilized country; and it remains to be seen whether they will emulate us by transporting, by the same means, and against the same obstacles, the most formidable trains of artillery.

The mechanical inventions of this country are numerous; many of them are ingenious, and some are highly important. In no way can a knowledge of them be so readily and extensively diffused as in a scientific journal. To this object, therefore, a part of our labours will be devoted, and every necessary aid will be given by plates and descriptions.

Science and art mutually assist each other; the arts furnish facts and materials to science, and science illuminates the path of the arts.

In a word, the whole circle of physical science is directly applicable to human wants, and constantly holds out a light to the practical arts; it thus polishes and benefits society, and every where demonstrates both supreme intelligence, and harmony and beneficence of design in THE CREATOR.

It is well known to those who have attended to the subject of musical ratios, that a fixed scale of eight degrees to the octave, which shall render all its concords perfect, is impossible. It has been demonstrated by Dr. Smith, from an investigation of all the positions which the major, the minor, and the half-tone can assume, that the most perfect scales possible, of which there are two equally so, differing only in the position of the major and the minor tone above the key note, must have one Vth and one 3d too flat, and consequently the supplementary 4th and VIth too sharp, by a comma. In vocal music, and in that of perfect instruments, this defect in the scale is not perceived, because a small change may be made in the key, whenever the occurrence of either of those naturally imperfect intervals renders such a change necessary to perfect harmony. But in instruments with fixed scales, such as the guitar, the piano-forte, and the organ, if we begin with tuning as many concords as possible perfect, the resulting chords above-mentioned will be necessarily false in an offensive degree. Hence it is an important problem in practical harmonics, to distribute these imperfections in the scale among the different chords, in such a manner as to occasion the least possible injury to harmony.

But this is not the only nor the principal difficulty which the tuner of imperfect instruments has to encounter. In order that these instruments may form a proper accompaniment for the voice, and be used in conjunction with perfect instruments, it is necessary that music should be capable of being executed on them, in all the different keys in common use; and especially that they should be capable of those occasional modulations which often occur in the course of the same piece. Now only five additional sounds to the octave are usually inserted for this purpose, between those of the natural scale, which, of course, furnish it with only three sharps and two flats. Hence, when a greater number of flats or sharps is introduced, the music can be executed only by striking, in the former case, the sharp of the note next below; and, in the latter, the flat of the note next above. But as the diatonic semitone is more than half the major, and much more than half the minor tone, if the additional sounds in the common artificial scale be made perfect for one of the above employments, they must be extremely harsh for the other. Hence arises the necessity of adjusting the position of these five inserted sounds so that they may make tolerable harmony, whichever way employed. A change in these will require corresponding changes in the position of the several degrees of the natural scale; so that it is highly probable that the best scheme of temperament will leave no concord, either of the natural or artificial scale, absolutely perfect.

In adjusting the imperfections of the scale, the three following considerations have been usually taken into view.

But if the above consideration deserves any weight at all, it deserves to be accurately investigated. Not only ought the relative frequency of different chords to be ascertained with the greatest accuracy, of which the nature of the subject is susceptible, but the degree of weight which this consideration ought to have, when compared with the two others above-mentioned, should be determined: for it is plain that neither of them ought to be ever left out of view.

Accordingly, the principal design of the following propositions will be to investigate the actual frequency of occurrence of different chords in practice; and from this and the two other above-mentioned considerations united, to deduce the best system of temperament for a scale, containing any given number of sounds to the octave, and particularly for the common Douzeave, or scale of twelve degrees.

All consonances may be regarded, without any sensible error in practice, as equally harmonious in their kinds, when equally tempered; and when unequally tempered, within certain limits, as having their harmoniousness diminished in the direct ratio of their temperaments.

That different consonances, in this sense, are equally harmonious in their kinds, when equally tempered, or, at least, sufficiently so for every practical purpose, may be illustrated in the following manner:

which is evidently the tempering ratio of the imperfect unisons.

Hence, so far as any reasoning, founded on the abstract nature of coexisting pulses can be relied on, we are led to conclude that the harmoniousness of different consonances is proportionally diminished when they are equally tempered.

The remaining part of the proposition, viz. that consonances differently tempered have their harmoniousness diminished, or their harshness increased, in the direct ratio of their temperaments, will be evident, when we consider that the temperament of any consonance is the sole cause of its harshness, and that the effect ought to be proportioned to its adequate cause. We may add, that the rapidity of the beats, in a given consonance, increases very nearly in the ratio of the temperament; and universal experience shows, that increasing the rapidity of the beats of the same consonance, increases its harshness. This is on the supposition that the consonance is not varied so much as to interfere with any other whose ratio is equally simple.

It will be proper to explain, in this place, the notation of musical intervals, which will be adopted in the following pages. It is well known that musical intervals are as the logarithms of their corresponding ratios. If, therefore, the octave be represented by .30103, the log. of 2, the value of the Vth will be expressed by .17509; that of the major tone by .05115; that of the comma by .00540, &c. But in order to avoid the prefixed ciphers, in calculations where so small intervals as the temperaments of different concords are concerned, we will multiply each of these values by 100,000, which will give a set of integral values having the same ratio. The octave will now become 30103, the comma 540, &c.; and, in general, when temperaments are hereafter expressed by numbers, they are to be considered as so many 540ths of a comma. Had more logarithmic places been taken, the intervals would have been expressed with greater accuracy; but it was supposed that the additional accuracy would not compensate for the increased labour of computation which it would occasion. This notation has been adopted by Dr. Robinson, in the article Temperament, and for every practical purpose, is as much superior to that proposed by Mr. Farey, in parts of the Schisma, lesser fraction and minute, as all decimal measures necessarily are, to those which consist of different denominations.

It has been generally assigned as the reason for neglecting the consonances, usually termed discords, in ascertaining the best scheme of temperament, that they are of less frequent occurrence than the concords. This, however, if it were the only reason, would lead us, not to neglect them entirely, but merely to give them a less degree of influence than the concords, in proportion as they are less used.

Again, the 5th, whose perfect ratio has been generally laid down as 45 : 64, but which is in reality 25 : 36, cannot be sharpened more than 1/3 of a comma, before it becomes more harmonious by having its temperament increased, as approaching nearer the simpler ratio 7 : 10. At the same time, the effect of this interval in melody would not be sensibly varied. The limits, within which the harmoniousness of the IVth is inversely as its temperament, are still narrower.

Hence it appears that no inference can be drawn from the temperaments of such consonances as the 7th, 5th, IVth, &c. respecting their real harmoniousness. The other perfect ratios which have nearly the same value with those of these chords, and which are in equally simple terms, are so numerous that by increasing their temperament they alternately become more and less harmonious; and in a manner so irregular, that to attempt to subject them to calculation, with the concords, would be in vain. Even when unaltered, they may be considered either as greater temperaments of more simple, or less temperaments of more complex ratios. Suppose the 5th, for example, to be flattened 1/5 of a comma: shall it be considered as deriving its character from the perfect ratio 25 : 36, and be regarded as flattened 108; or shall it be referred to the perfect ratio 7 : 10, and considered as sharpened 239? No one can tell.--On the whole, it is manifest that no consonances more complex than those included in the proposition, can be regarded in adjusting the temperaments of the scale.

Each of these results makes the harmony of all the consonances as nearly equal as possible; but as the sum of the temperaments in the first case is much the least, it follows that the temperaments stated in the proposition constitute the best scheme of intervals for the natural scale, in which the harmony of all the different consonances is rendered as nearly equal as possible.

To find a set of numbers, expressing the ratio of the probable number of times that each of the different consonances in the scale will occur, in any set of musical compositions.

It was judged that 200 scores, taken promiscuously from all the varieties of music for the organ, would afford a set of numbers expressing, with sufficient accuracy, the chance that a given consonance will occur in a single major, and its relative minor key. Accordingly 200 scores were examined, 150 in the major, and 50 in the minor mode, of the various species of music for the organ, comprising a proper share both of the simpler and of the more rapid and chromatic movements. As the selecting and reducing to their proper keys all the occasional modulations which occur in the same piece would render the labour of ascertaining the relative frequency of different signatures very tedious, it was thought best to consider all those modulations which are too transient to be indicated by a new signature, as belonging to the same key. This will account for the occurrence of the chords in the following table, which are affected by flats and sharps.

The minim, or the crotchet, was taken for unity, according to the rapidity of the movement. Bases of greater or less length had their proper values assigned them; although mere notes of passage, which bore no proper harmony, were generally disregarded. The scores were taken promiscuously from all the different keys; and were reduced, when taken down, to the same tonic; the propriety of which will evidently appear from the foregoing remarks. The following table contains the result of the investigation.

The following anomalous chords were found in the major mode, and are subjoined, to make the list complete:

Besides the following chromatic intervals:

Caleb Atwater, Esq. of Circleville, Ohio, is engaged in writing Notes on the State of Ohio, a work which is intended to embrace the most important features and interests of this new and rising State.

To this laudable effort, and to that of the Western Museum Society, whose address is published above, we cordially wish success. From the zeal, talent, and industry of the gentlemen concerned, we have every reason to expect a happy result.

We view, with much satisfaction, the efforts which have been already made, and are rapidly increasing, to bring to light the resources, and to develope the history, of the western States; and it will always give us pleasure, if through the medium of this Journal, or in any other manner, we can contribute to promote them.

SUNSWICK, June, 1818.

DEAR SIR,

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