The hexachords in their several octaves only made up the following register of sounds represented in our present notation- (Fig. 1).

FIG. 1.-REGISTER OF GUIDO.

GABC D E F g a bbc def gg aa bb hh cc dd ee These sounds were distributed in hexachords as in the annexed diagram (Fig. 2).

FIG. 2.-1. HEXACHORD OF G, OR DURUM HEXACHORD.

ut re mi fa sol la ut re mi fa sol la ut re mi fa sol la

2. HEXACHORD OF C, OR NATURAL HEXACHORD.

Ꮎ

ut re mi fa sol la ut re mi fa sol la

3. HEXACHORD OF F, OR MOLLE HEXACHORD.

До

ut re mi fa sol la ut re mi fa sol la

Thus Guido's register comprised twenty-two sounds, and these were distributed in three scales. Our present vocal register comprises fiftytwo sounds, and we have thirteen scales. Guido's entire register embraced only the sounds of two of our present scales (C and F).

If, then, the adoption of a common set of names was a facility to learners at the time of Guido, how much greater a facility must it be to learners at the present day. Each of Guido's hexachords would contain fifteen intervals, and his pupils would have to master in all forty-five intervals. Each of our scales contains twenty-eight intervals, and our pupils have to master 28 x 13, or 364 intervals. Guido, by teaching his forty-five intervals as repetitions of fifteen, reduced the work of his pupils to one-third of what it would otherwise have been. We, by teaching 364 intervals as repetitions of 28, reduce the work of our pupils to one-thirteenth of what it would be. On this plan, the pupil by learning one scale learns all; and if he is properly taught, one scale becomes as easy to him as another. He has a common measure for all the scales; and only let him know where to lay on his measure, to what sounds to apply the syllables, and he is equally at home, whatever the signature may be.

And not only does this device lessen his labour, but it brings the scales before his mind in their true scientific relation. Though he may not understand the scientific explanation of the common character of the scales, he sees that they have this character. The common series of syllables represents the same fact to him practically, that the common series of ratios represents theoretically to the scientific musician. Thus the plan is founded on scientific truth, and, while it facilitates the practice, also prepares the learner for the scientific explanation.

From these considerations, it would appear that Guido's was indeed a great invention, and that the award of history has in his case been a just one. His invention is certainly the greatest that has ever been made in relation to the teaching of vocal music. Any method of instruction which adopts this fundamental principle will have in it a scientific unity which will carry it over all obstacles, internal and external; while a method which does not proceed upon this principle is devoid of scientific unity, is devoid of method, and, whatever may be its excellence of detail, will assuredly fail of accomplishing its general object,―teaching people to sing at sight.

We insist upon this principle, not only because we consider it to be the vital point in teaching music, but because, strange to say, we of the present generation, living eight centuries after the date of this important invention, have lived to see the Governments of France and England, in a praiseworthy endeavour to spread a knowledge of singing among the people of their respective countries, give the sanction of their "authority" to a method which ignores the invention. In both cases, the method (itself originally German and imported from Rhenish Prussia) was introduced in the face of a prevalent national method based upon the correct principle. Not only does the method in question forego all the aid to be derived from the adoption of Guido's plan, but it commits the absurdity and mockery of using his syllables as fixed names for the sounds of one scale only, and that not even the one corresponding to the hexachord to which the inventor originally applied them. On this subject, that learned and "cunning" musician, General Thompson, remarks, in his unique little treatise on his Enharmonic Organ :*"There is no more striking evidence that knowledge does sometimes retrograde, than that the sol-fa of the scientific monk should have degenerated, in the hands of modern musicians, into a nomenclature for fixed sounds. It is as if the x y z of algebra were found serving as digits in keeping accounts."

According to this method, the pupil has to learn each of the thirteen scales as a distinct department of music, and each presents to his mind a different degree of difficulty in proportion to the number of sharps or flats in its signature. The so-called natural scale, which is free from these artificial incumbrances, is comparatively easy; the scale of one sharp is difficult; the scale of two sharps is very difficult; the scale of three sharps very difficult indeed; four sharps insuperable: and similarly with the flat scales. The consequence is, that, although the pupil learns the natural scale very thoroughly, he seldom gets much further.

This is the whole mystery of movable do and fixed do, which, for the last quarter of a century, has divided the teachers of singing, first in

* We much regret that this work is out of print.

France and then in England, and which, in our opinion, has tended much to retard the progress of musical education among the people of both countries. Every elementary teacher who would teach vocal music in his school must decide the question for himself and choose his method accordingly.

General Thompson recommends that the numerals should be employed instead of the sol-fa syllables. His remarks are as follows:-" A conclusion pointed to by the practice of the enharmonic instrument is the desirableness of returning to something like the original system of solfaing, or what in French is called solfier par transposition, where do is always applied to the key-note. But, instead of the syllables do, re, mi, &c., it would be simpler and better in every way to sing the words one, two, three, &c., as directed by Mr. W. E. Hickson in his Singing Master.' If it is objected that these are of more difficult articulation,— unless poetry is to be divorced from music, and we are to be entertained with solfeggi and gorgheggi instead, the necessity for practising articulation is a good and not an evil.”

We think it is very certain that teachers will find it easier, in the first stages of the instruction, to teach their pupils to read the different scales by means of the numerals, because the application of these involves only a single act of thought, while the application of the syllables involves a twofold act. In singing by the numerals, the pupils have merely to count the number of degrees at which the note stands from the given key-note, and this at once gives them the appropriate numeral ; but in singing by the syllables, they have first to find the degree of the note, and then to apply the syllable corresponding to that degree. But we should advise teachers, as soon as they have rendered their pupils expert in the application of the numerals, to avail themselves of the solfa syllables, which have several advantages over the numerals, irrespectively of the question of articulation; among which we may particularize the following:

1. So soon as the pupils begin to beat time, the numerals are required for counting the beats in a bar, and it would obviously be confusing to them to have to use these words for two distinct purposes at the same time.

2. The numerals, denoting mere numerical sequence, are liable to be applied to any succession of sounds; for instance, Mr. Hickson counts forwards in descending as well as in ascending the scale.

3. The numerals, being of general application, are not sufficiently distinctive as names for the sounds of the scale.

One

4. The syllables furnish an excellent means of hitting the semitones, which is the most essential thing in singing a piece of music. principal reason why Guido adopted the six original syllables for the notes of his hexachords seems to have been, that he "observed a dissimilarity between the closeness of the syllable mi and the broad, open sound of fa, which he thought could not fail to impress upon the mind a lasting idea of their congruity;" and a similar fitness may be observed in the syllables si and do.

[In the celebrated Pestalozzian singing method of Nägeli and Pfeiffer, the numerals were employed as recommended by General Thompson; but in the professed improvement on it, which the Rev. W. J. Unwin has recently edited, the syllables are adopted in preference.]

J. T.

Notes of New Books.

Aristotle's Ethics, with English Notes. By W. E. Jelf, B.D., late Student of Christ Church, Oxford. Pp. 470. London and Oxford: J. H. & J. Parker.

Although it may be true that, in the words of the thoughtful author of "Oxford Studies,"*" the popular conception of philosophical principles must ever remain περιττὰ καὶ θαυμαστὰ, καὶ χαλεπὰ, καὶ δαιμόνια, ἀχρηστὰ dé," yet, perhaps, one cause of this may be found in the indifference which pioneers have too often shown in clearing away difficulties and incumbrances from the way of science. Editions of the best-known philosophical treatises of Aristotle have till lately multiplied, without commensurate increase of light being shed upon their subjects by a careful and accurate grammatical examination of the text; books and tutors alike furnishing every requisite for a due appreciation of the Stagirite, save only the sine qua non of minute and critical scholarship. Thanks to the learned labours of Mr. Jelf, this will no longer be a hinderance to the study of the Ethics. The edition before us presents a thorough examination into the philosophical tenets of his author, with no stint of illustration of one passage by another, or of this particular treatise by other works of Aristotle: but what will be hailed with most satisfaction, is the exact and scholarly explanation of sentence after sentence, which must render this volume no inconsiderable boon to future students of the Ethics. Let any one compare Mr. Jelf's edition with the in many respects valuable work of Mr. Brewer, or with the accepted English translation by a well-known Oxford tutor, and this will be readily apparent. On approaching a difficulty, in lieu of unsatisfactory silence, or a too general rendering, always liable to mislead, this edition affords every reasonable aid to the student towards the grammatical comprehension of his author's words. To dilate on this feature may seem needless, when the very high repute of Mr. Jelf's Greek Grammar would in itself be a sufficient guarantee for his thoroughly editing any Greek author to whom he might put his hand : but we are the more disposed to notice it, because it is not evidenced by obtrusive display of collateral scholarship, but always in strict subservience to the better understanding of Aristotle's language. Thus, in Book vii. c. 1, at note (5), 2, ɛi kaláπep paoív, k. 7. λ., Mr. Jelf's grammatical acuteness leads him to suggest that the use of the indicative yívovrai, and not the conditional, may indicate that the passage expresses Aristotle's own opinion a nice point, on which other editors are silent. Again, in c. 2 of the same book, note (16), 2, ötɩ yáρ ovк oiɛrai yɛ, where Michelet has unaccountably blundered in translating our OLETαι non opinione distrahitur," Mr. Jelf at once supplies the proper ellipse, dεiv πράtteiv, as also at c. 3, (35), 3. In page 156, (8), 3, we have this short note, "Zetos, Lac. for Ocios;" where a book-maker would probably have drawn from his common-places the parallel use of r o σúμaroc in Thucyd. v. 77; of σáλλɛ for Oάλλɛ elsewhere, and have referred to a curious section

* Oxford Studies in Oxford Essays, 1855, p. 282.

(§ 473) in Donaldson's New Cratylus. But where philology may elucidate the precise meaning of Aristotle's words (e. g., evdaiμovía, I. iv. (51), 2; dεivórηs, vi. note (136), 9; and a remark at rò ȧyalòv respecting the fact that the comparative of 'good' is irregular in almost all languages,- -see X. iii. (16), 2), we never fail to derive from Mr. Jelf's notes apt illustration from kindred words in other tongues, involving kindred notions.

A careful perusal of the Ethics with this work will realize, we feel sure, Mr. Jelf's modest wish "to guide students to an understanding of what Aristotle says." No philosophical difficulty (e. g., Book vii. note (60), 5) is left unsolved, or at least not manfully grappled with: no opportunity lost of illustrating up and down his book the three points among others, to which his preface (p. x.) calls attention; viz., Aristotle's use, and opinion of induction (e. g., p. 157, (3), 5); his way of speaking of the gods (see X. viii. (79), 7); and the reverential way in which he mentions his instructor Plato (cf. Notes, p. 11 (80), 1). This last point receives additional confirmation, we may observe, from Aristotle's language in his Politics, ii. 6, p. 64, in a passage which Mr. Congreve translates -"All the dialogues of Plato are characterized with brilliancy and grace, originality and profound inquiry."

One word, and that of praise, is due to the good taste, sound judgment, and practical consideration for the wants of students evinced in the getting up of this volume. The duodecimo text (of Bekker), printed on an octavo page, so as to leave ample margin for note or comment, a liberal supply of blank leaves of good paper, whereupon the reader may draw out his own analysis after a model given on a sample page, and a clear broad type in the portion of the volume given up to notes, are luxuries for the scholar, which must be seen to be appreciated. May this work, which deserves to rank with Liddell and Scott's Lexicon, Linwood's Lexicon to Eschylus, and the editor's own Greek Grammar, among the most creditable productions of ripe and good Oxford scholars, find that wide favour which must needs follow its diligent perusal.

The First Step in Chemistry. By R. Galloway, F.C.S. Second edition. Pp. 302. London: Churchill.

The author of this manual complains, and with some justice, that the elementary works on the science of chemistry do not begin at the beginning, and, consequently, do not follow up the various stages in their natural and proper order. Chemistry should be taught as arithmetic ; the notation should be studied first of all; the power of the elements, as of single figures, should next be understood; then the effects of the combination of the elements, analogous to the processes of multiplication, division, &c.; then the combinations of these compound substances; and so on to the most complex problems of the science. The counter process of decomposition and the effects of the various modifying agents, such as heat, cohesion, elasticity, light, and electricity, would form the last stage in the course of instruction.

This is the plan pursued by Mr. Galloway, and the arrangement of the subject is one of the distinctive features of his book. But, besides this, he lays great stress on instruction by working examples: to lay