"thb Wobth Of Aet Appbabs Most Eminent In Mnsic, SINCE It Bequiees Ko Material, No Sbbject-matteb, Whose Effect Must


STJBSCEIPTI01T:—Stamped for Postage, 20s. per annum—Payable in advance, by Cash or Post Office Order, to BOOSEY & SONS, 28, Holies Street, Cavendish. Square.

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HER MOST GRACIOUS MAJESTY THE QUEEN, H.R.H. THE PRINCE CONSORT, THEIR ROYAL HIGHNESSES THE PRINCESSES AND PRINCES OF THE ROYAL FAMILY, The Most Worshipful the |Grand Master of Ireland, His Grace the DUKE of LEIN8TER, And Several other Diitinguished Freematont; His Excellency the Lord Lieutenant of Irelaud, tho EARL nf EGLINTON and WINTON, The LORD BISHOP OF MANCHESTER, The Bight Worshipful the MAYOR OF MANCHESTER, IVIE MACKIE, Esq. His Worship the Mayor of Salford, W. HARVEY, Esq. SIR FREDERICK GORE OUSELEY, Bart., Director of Music at the University of Oxford. A,\d many 0/ the Nobility, Gentry, Clergy, and distinguished Families of the Empire.



Organised in 1848, and developed at THE ROYAL COLLEGE OF MUSIC BRIDGE STREET, MANCHESTER, established by him expressly as a Great National Institution to facilitate the Encouragement and Promotion of NATIVE MUSICAL TALENT, and tlie GENERAL ADVANCEMENT OF MUSIC AMONG THE RISING GENERATION, upon his new and effective system, also as a Normal School for the training of masters to conduct Consprvatoirks o» Music to be established throughout tho United Kingdom, for Little Children, the whole comprising an entirely new scheme of NATIONAL EDUCATION, by blending music with general instruction, so that tho study of music shall become a branch of education in tho humblest of schools of this country. To illustrate and to rouse an interest iu every town and city for these institutions, Dr. Mark travels with a number of his pupils occasionally through the country—giving lectures, and introducing his highly approved and pleasing Musical Entertainment, entitled DR MARK AND HIS LITTLE MEN, who number upwards of Thirty Instrumentalists, and a most Efficiout Chorus, the whole forming a most unique and complete Juvenile Orchestra, composed of LITTLE ENGLISH, IRISH. SCOTCH AND WELCH BOYS. FROM FIVE TO SIXTEEN YEARS OF AGE, who play Operatic Selections, Solos, Marches, Quadrilles, Galops, Ac., and sing Songs and Choruses in a most effectivo manner, and to whom Dr. Mark gives a gratuitous General and Musical Education. APPOINTMENTS OF MASTERS AND ARRANGEMENTS OF CLASSES IN THE ABOVE INSTITUTION. Principal of the Royal College of Music; Director, Composer, and \ Conductor; Lecturer to both Private and Public, Theoretical >Dr. Marx,

and Practical Instrumental and Vocal Classes )

Master of the General Educational Departments Mr povveLL Writing,Reading, Arithmetic, Grammar, Dictation, I au'dTwo ^eeptng' Geo8^aphyPractical Geometry. and Book- j Alslatant Teachers.

Organ' Mr. Baker.


Vinlin J Mons ROGDIER.

¥,omi1 Mr. Beard.

Violoncello. Double Bass, and Viol. 12^.^TMTM!*

Flute, Piccolo, Oboe, and Clarionet Big, Cortesi.

Cornet and other Brass Instruments Mr. H. Russell.

Concertina (German and English) Mr. Elder.

Vocal Classes { """^j1*^ *nd

Dr. Mark has also made provision for the Orphans of the Musical Profession possessing musical talent, who will find the shore institution a happy homo, and receive a most effective general and musical education, board, and clothing, free of all expense.

little Boys, from five to nine years of age, apprenticed for three, five, or seven yean by paying a moderate entrance fee to cover the expenses of instrument and books.

Twelvo appointments ready for Masters. For Prospectuses, apply direct to the Royal College of Music, Bridge-street, Manchester.

Dr. Mare Is also open to Engagements with his Littlo Men.

Dr. MARK begs to invito the Parents and Friends, and all those Interested in hi* Enterprise and in the Education of the Youths of this country to visit his establishment. Visiting hours:—From Nine to Eleven, a.m., and Two and Foot, p.m. Saturdays and Sundays excepted. .

LAURENT'S SECOND GRAND WINTER BALL, at St. James's Hall, Tuesday, January 31*t.— M. HENRI LAURENT has the

honour to anuounce, that in consequence of the distinguished success which attended his grand Christmas ball, he has, at the request of numerous persons of distinction, made arrangements to give a SECOND GRAND WINTER BALL, at St. James's Hall, Tuesday, January 31, on the same scale of magnificence which afforded so much satisfaction on the hist occasion. The hall will present the appearance of a beautiful winter garden, being decorated with flowers, plant*, and sculpture, arranged by Mr. Hurwitz. The orchestra will be complete iu every department, and will perform a variety of novelties composed for the occasion. Programme: Quadrille, Dinorah, Laurent; Valse, Reigning Beauty, D'Albert; Quadrille, SaUnella, Laurent; Polka. Marguerite, Laurent; Laucers, Original; Value, Sicilian Vespers,(firsttime)Laurent; Galop. Satan ella, Laurent; Quadrille, Christmas Waits, Laurent; Polka, Persian, D'Albert; Valse, Donna Julia, Laurent; Lancers, Second Set, Laurent; Galop, Four-in-hand, T. Browne; Quadrille, Martha, Laurent; Valse, Christy's, Laurent; Polka, Mistletoe, Laurent; Lancers, New, Tinncy ; Valse, Dinorah, Laurent; Quadrille, Serpentine. Burckhardt; Valse, Satauolla, Laurent; Quadrille, Keniiworth, Tinney; Valse, Undine, Coote; Galop, Avalanche, Coote; Polka, Soldiers, D'Albert; Lancers,

D'Albert; Valse Maud, Laurent; Galop, Argyle, Laurent. Conductor

—M. Laurent. The supper will be under the entire management of Mr. Donald, the celebrated restaurateur of St. James's Hall. Ball tickets for gentlemen, 10s. (id.; ladies, 7s.; supper tickets, 7s.; to be had of Mr. Austin, St. James's Hall, Piccadilly, and of the principal music-sellers.

MISS DOLBY begs to announce that her SECOND and LAST SOIREE MUSICALE will take place at her residence, 2. Hindestrect, Manchester-Square, Tuesday. 31st iust., to commence at half-past 8 precisely. Tho following artists will have the honour of appearing:—Messrs. Sainton, Bezeth, Schreurs, Paque, and G. A. Osborne; Vocalist, Miss Dolby; at tho pianoforte, Signor Randegger aud Mr. Fiancusco Berger. Tickets haif-a-guineaeaoh. to be had of Miss Dolby at her residence.

MYDDLETON HALL, ISLINGTON—NORTH LONDON MONDAY POPULAR CONCERTS. A series of Monday Evening Concerts under the direction of Mr. H. Davis, will be commenced iu the abovo Hall on Monday evening the 6th Feb.. 1880. A number of artist* mo engaged, Amongst whom are the following established favourites: Mad. Louisa Vinniug, Mdlle. Vaneri. Miss Fanny Reeves, Miss Messcnt, Mr. Allau Irving, J. G. Patey, and Elliot Galor, Viotti Collins. Medora Collins. J. D. Davies (harpist), R. Glenn Wesley. Conductor. Mr Frauk Mori. Admission one shi.ling aud two I'

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In presenting this prospectus, the projectors of this Association deem it worthy of remanc, that a great want is felt by a countless number of amateurs possessing i musical knowledge and capability of a society which would afford them ample ■ opportunity of .acquiring, at a moderate cost, a complete knowledge of the beauty andgntudeur uf tho choicest and recoguized orchestral compositions of this and •previous periods.

The object of this Association is to bring together tho amatenr instrumentalists of Loudon and its suburbs, for tht; practice and performance of oratorios, masses, cantatas, symphonies, operatic selections, and overtures, including compositions but little known lo the general public, with other chef-d'eeuvres of the great master*, suitable for bond and chorus conjointly or separately.

Fur the boutiftt of the amateur department, weekly rehearsals will bo held on o^ery . Saturday Evening, at Eight o'clock, at the Architectural Gallery, 0, Conduit-street, Regent-street, and during the season, concerts will bo given at one of the large theatres or concert-rooms, with the important i honorary professional members, and in conjunction with on as the necessary pSroficiency is attained.

Boosey and Sons, Holies-street.


stouul department there are. still vacancies for honorary members incuts;—Fowl- first violins, one second violin, and two

fee addressed to the Honorary Secretary of the London Conduit-street, Bcgent-atract, W.

H. J. BRAHAM, Hun, Sec.

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Judging from the number of pieces forwarded to our office for review, by the last mail, we are warranted in believing that our musical composers (amateurs especially) wish us to regard their contributions in the light of (as the French say) "e'trennes," or of (as the English say) "New Tear's gifts." As such, then, they must be welcomed with politeness, if not with warmth—with courtesy, if not with enthusiasm. It behoves, nevertheless, to turn them over in as little time as possible—a mere glance at their contents being all that we can spare (and, in most instances, all that is requisite).

First appears Mr. J. G. Callcott, with "Come in, and shut the door'' (Cramer, Beale and Chappell), a song to some lively verses by " J. P. H." The music—even livelier than the words —though simple as a hammer, is by no means ungenial. It contains, however, a progression, from the key of C major to that of E major, (Page 2, line 2); and another from the 6-4 on G natural to the common chord of A minor, by means of a harmony with G sharp in the bass, and F natural and G natural as melody; both of which might be advantageously reconsidered. At the same time let us thank Mr. Callcott for a really appropriate new year's gift.

Next comes the very prolific Mr. Balfe, with a couple of bran-new ballads (this gentleman's ballads are in number as the herrings), and neither of them in his least successful manner. "Tlie Hose on t/te Heath", indeed (Cramer, Beale and Chappell)— to a neat translation, by Mr. Alfred Baskerville, of a well known lyric of Goethe—is one of the prettiest and freshest that has recently dropped from the Balfic pen. As a no less tasteful, though perhaps less racy compound of materials, which, in Mr. Balfc's hands, would appear inexhaustible, "Farewell, dear home" (Cramer, Beale and Chappell)—a setting of some very well-turned lines by Mr. W. H. Bellamy, on a somewhat threadbare subject, will also find admirers.

Mr. H. T. Leftwich—" composer," as the foot of the titlepage assures us," of the favourite so^ng of ' The Fountain,'"— presents us with a river. "The River" (Clinton and Co.)— styled "canzonet"—an apostrophe to some inland water, name unmentioned, if not equal to that other and renowned apostrophe by Laureate Tennyson (who has four times successively immortalised himself in The Idylls of the King), is creditable to the poetic feeling of Mrs. Southey, the authoress. The music of Mr. Leftwich is attractive if not new, and singable if not always grammatical. The hidden octaves between bass and voice (page 2—last bar of line 2, and first bar of line 3), to single out an example, considerably damage the effect of a not ungraceful phrase of melody.

Mr. Bianchi Taylor—of whom the erewhile fashionable town of Bath is (and with reason) as proud now as at any foregone period—has made us a most acceptable offering, in the shape of a duet for treble voices, called "The Bird and the Blossom" (Cramer, Beale, and ChappeH), which has the double merit of being genuinely melodious and irreproachably scholar-like. The effect of this charming trifle, well sang, either in public or private, would be unquestionably gyod. But why suppress the name of a poet who makes the bird address the flower in such mellifluous epigram?

In "Aletheia "—nocturne pour le pianoforte (Clinton and Co.)—Mr. H. T. Leftwich—" Examiner," as the foot of the title page assures us, "to the College of Preceptors"—presents us with a veritable cadeau and a French inscription. We like his English token better. "Aletheia" (what a far-fetched

name for a near-fetched piece !) belongs to the ordinary—
very ordinary (earfra-ordinary V)—sort of florid, orna-
mental, sentimental, instrumental (detrimental—to taste '?)
drawing-room nocherne, in the drawing-room key of D flat
major, the type of which is absolutely worn to tatters, and
of which the patch now sewed on by Mr. Leftwich by no
means lessens the general seediness. "Aletheia" sounds
new; but " Aletheia" sounds old. Per Bacco!
The dear old nursery-rhyme sets out as follows :—

"First came the ladies, prim, prim, prim;
Then came the gentlemen, trim, trim, trim;
Then came the country-folks, &c."

But we have inadvertently reversed the order, and given precedence to the "gentlemen " (Messrs. Balfe and Co.) and "country-folks " (Messrs. Taylor and Co.). Soliciting " mille pardons" (which, we presume, means begging pardon 1000 times), we now acknowledge, with gratitude, Miss Virginia Gabriel's slightly tormented, a thought over-modulated, a trifle unfinished (see bare fowrth—page 1, line 3, bar 3), but otherwise graceful and expressive song, called "One passed by" (Hale and Son—Cheltenham),—which, but that the monosyllable, "One," is too frequently underlined—after the manner of the epistles attributed to ladies, generally, by the caustic and illustrious author of Pendennis—would be as creditable to the poet (Edward Maitland, Esq.) as to tho fairer minstrel who has married his lines to music. If Miss Gabriel would confer still less she would confer still more on her admirers. There is too much "fluster" in her method of harmonising. She should peruse the lines (we forget which) of (we forget what) Roman poet.

Dr. Doran's fragrant "Summer Flowers" set to music by Sarah Gilbert (Hale and Sons), would have been a more acceptable present had the compositress submitted her work to a pedagogue, able to detect, and willing to point out for reconsideration, such faults as occur in page 1, line 1, bar 2 (consecutive fifths); page 2, line 2, bars 2, 3 (bad harmony on the words," lilies wreath''); and elsewhere. At the same time, we regret to add, the song is in any case irredeemably common-place.

Mr. Balfe has transmitted us another New Year's gift, in the shape of " Songsfor the New Year; Album of Vocal Music" (Boosey and Sons). This Balfe-Annual is to be recommended in every way—recommended (with little reserve) for its music; recommended (except in one or two instances) for its poetry; recommended (unconditionally) for its engravings,—pictures, we mean; and recommended for the elegance of the designs, covers, and general gettingup. The front cover is curiously devised in Alhambraic fashion, the prevalent colours being scarlet, blue, and white on a gold ground. The Title and Presentation Pages are designed with infinite taste, white and gold alone being employed, with the exception of a delicate light pink, which is used to bestow a bloom on violets—whose hue, we have hitherto taken for granted, is generally deep blue. The Album contains fourteen pieces—songs duets, <Jic.,— the poets being Tennyson, Longfellow, Kingeley, John Oxenford, Jessica Rankin, Henry Neale and Uhland. In short, it may be commended as one of the most elegant musical offerings of the season.

And now, with an acknowledgement of yet two further presentations from the same source, we must conclude our chapter of thanks, until renewed strength, in our next number, allows us to resume it. These are, "Fortune and her Wheel"—poetry by Alfred Tennyson—music composed and dedicated to the Earl of Hillsborough by M. W. Balfe j and "The Song of Love and Death"—Poetry by Alfred Tennyson—music composed and dedicated to Lord Arthur Hill by M. W. Balfe. (Boosey and Sons.) system, the two systems being thus closely connected. It will be perceived that, if we take any primary basis on which to construct a diatonio scale, the whole of the sounds forming the scale are contained in the primary chords conneoted with that basis, and those of the two adjacent systems; these primary chords forming the most simple and natural harmonies of the scale. When these proceed from one system to the one adjacent, the harmonies flow in a natural and connected manner, but when they pass over the intermediate system the harmonies are unconnected—not one sound in the primary chords of one system being found in those of the other. Thus from C, the primary basis, the scale of C is formed from the primary chords of C, F, and G.

Mr. Balfe exhibits a more poetical feeling in some of his recent ballad compositions than even in his operatic works. This, no doubt, may be attributed to the higher class of poetry on which his muse has been employed. In Longfellow's lyrics, the composer of The Bohemian Girl first proved that he could divest himself of that leaning towards the modern sentimental school—himself the originator— which, however it may have tended to augment his popularity, has gained him but a questionable reputation with the thinking world. The vein, once discovered, has not been allowed to lie unexplored. In Tennyson's exquisite poem, "Come into the garden, Maud," and in others by the same illustrious poet, Mr. Balfe has achieved unwonted honours. These he has followed up with some characteristic ballads, to verses of striking beauty, by the Kev. Charles Kingsley—such as "The Sands of Dee," <fec. The two songs before us are from Tennyson's grand poem, The Idylls of the King—a work, though not yet thoroughly appreciated, destined to never-dying renown. That Mr. Balfe has succeeded in realising the ideas of Mr. Tennyson we will not assert; but that he has indicated a loftier aim in the compositions under notice than in his most favourite contributions to the stage or concert-room, cannot be denied. At all events, the songs from the Idylls of the King possess such merit as must raise Mr. Balfe in the estimation of all lovers of real melody.

Of the two songs, we prefer "Fortune and her Wheel." The air has caught with much felicity the self-reliant tone of the verses. The words it is impossible to refrain from quoting :—

"Turn, Fortune, turn thy wheel and lower the proud 5
Turn thy wild wheel thro* sunshine, storm, or cloud;
Thy wheel and thee we neither love nor hate.

"Turn, Fortune, turn thy wheel with smile or frown;
With that wild wheel we go not up nor down;
Our hoard is little, but our hearts are great.

"Smile and we smile, the lords of many lands;
Frown and we smile, the lords of our own hands j
For man is man, and master of his fate."

"The Song of Love and Deallt" is neither so simple nor so spontaneous, although the feeling is undeniable. Both songs are in 3-4 time, but the measured march of one, and the broken flow of the other, form an appropriate contrast. The poetry of the last is again so exquisite, that we must quote it, like its predecessor—

"Sweet is true love, tho' giv'n in rain;
And sweet is death, who puts an end to pain;

I know not which is sweeter; no, not I.
Love, art thou sweet? Then bitter death must be;
Love, thou art bitter; sweet is death to me.

0 Love, if death be sweeter, let me die!

"Sweet Love, that seems not made to fade away;
Sweet death, that seems to make us lifeless clay;

1 know not which is sweeter, no, not 11
I fain would follow love, if that could be;

I needs must follow death, who calls for me;
Call and I follow; let me die!"

Both of these songs are written—as one of Shakspere's commentators said of some of the Sonnets—in the " repetitive style," meaning thereby, we suppose, to point to the frequent reiteration of the same word. Mr. Tennyson seems, indeed, to have caught the very spirit which pervades that wondrous

series of heart-yearnings, in the songs of the Idylls of the King, and to have employed his pen on the same subjects— Love and Melancholy—"Fortune and her Wheel" constituting a solitary exception. The two lyrics under review form companions to the song "Trust me not at all, or all in all — another exquisite piece from the Idylls of the King, of which Mr. Balfe first made choice to exercise his art upon. The three should never be separated, for it is difficult to say which is most to be commended, each having its special excellence. "Fortune and her Wheel," and "The Song of Love and Death," do not differ more widely from each other than "Trust me all in all, or not at all," differs from both.

Thus Mr. Balfe's elrennes are in a style of munificence becoming his con spicuous station.

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In the attendant harmonies we proceed from system to system by single degrees unto A, the sixth of the scale, whioh is contained in F; the next sound, B, not being found in the adjacent system, C, but in that of G, the second from F. This disagreeable effect of the unconnected harmonies is avoided by passing through some of the derivative harmonies, in addition to the primary, connected with these systems, more generally by retaining the primary basis F iu combination with the primary major chord of the system G, thus forming the chord of the dominant 7th. It will now be perceived that this introduction of the primary basis F immediately leads the ear to the sounds and harmonies of that system, to which it is, as it were, the key; the resolution of the discord being upon any of the derivative chords belonging to that system, but usually upon one of the principal of these. The chord of the 7th thus becomes the fundamental principle of all modulations or transitions from system to system. When the 3rd of the primary chord is introduced in addition to the basis, it forms the chord of the 9th. If upon the unit-sound of the system as a bass, the chords of the 7th and 9th become the chords of the 11th and 13th, and like the chord of the 7th, the resolution of the discord is upon the derivative harmonies. I may here remark that sounds, although nominally the same, are not always the same in reality j but so long as any sound appears in adjacent systems it is exactly the same; when it re-enters after a disappearance, it is invariably changed. If the table were extended in both directions, it would be perceived that each aote enter* three different times; if we take the pitch of any sound when it enters as a primary, at unity, or then when it enters any ■yitem below the primary it is §£, and when any above it is f£, every sound, according to the order of the primaries, entering and disappearing under three distinct forms. Thus the sound G appears first in the system E, to which basis it is a minor 3rd, and has the form £which is continued in the adjacent system A; it disappears in;D, and re-enters Gut primary, having the form f$, or unity, which is continued in the systems C and F; it again disappears in B flat, and enters again in E flat as a major 3rd, having the form |f, which is continued in A flat, after which it finally disappears. It is remarkable that under whichever form the note appears in any chord, the forms of the other notes in that chord are varied accordingly, making the ratios of the minor 3rd, major 3rd, and 5th constant, a fact for the consideration of Mr. D. C. Hewitt, who will perceive that the sound F in the system G is not the same as the primary basis F, which is the true dominant 7th, and is always a major-tone (ratio f) below G; the other being a minor-tone (ratio y) below. Similar remarks apply to every dominant 7th, which sound and the 5th of the dominant chord never appear together in any system. I think Mr. Hewitt will now fully comprehend the true character of the chord of the 7th, and that the interval D F in this chord (his examples 3 and 7) is not a minor 3rd (ratio }), nor is it his minor 3rd (ratio although it is nearly so— the ratio of this interval being which, as compared with his ratio, is as 512 : 513. AMost unfortunate is it for him, and for his idea, that hit prime 19, in connection with his unit-basis, should be so near and jet not quite agree with the ratio even of this interval. It is evident from the preceding, that the true fundamental bass of this chord (his Kx, 3 and 7) is G, the F not being naturally connected with the concord D, G, B, but is the basis of another system added to the concord, leading the ear to the harmonies connected with that system, as has been previously shown. This will appear plainly to the eye by writing down the ratios,


1 W $ f

which, by eliminating the octave sounds, and giving all the same form of denominator, are—

i h i 4

The sounds which belong to the same system have the same denominator 3, which are the sounds of the concord; the numerator 3 of the unit-sound refers downwards a 6th, to G, the fundamental bass, which

is also the bass of the primary chord, or which is the same thing, the basis of the system; for the primary basis being a 5th below the unitsound has always the form £. The sound F also appears as a primary basis, but being in a modified form, the factor 9 in the denominator points upwards two-aths (or a major tone) to the fundamental bass of the chord with which it is connected; also, the numerator being unity, the complete denominator 27 points upwards three-5ths to D, the unit-sound. The same facts will appear on writing down the ratios of his equivocal chord (Ex. 9) :—


1 # «

eliminating the octave sounds, and giving all the s nator, they would 1

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the numerator 5 of the unit-sound B refers a major 3rd below to G, the fundamental bass; the factors 9 under F, and 16 under A flat point upwards respectively two-5ths and a major 3rd and 5th to G, as before; the complete denominators of the two last point upwards to B, the unit-sound. The equality of the numerators of F and A flat denotes them to be a minor chord; also, the numerators being unity, show that it is a primary, which will be evident on separating the denominators into their respective factors—

F A flat

T-4-t . , z-lr.x

and combining the same factors in each—

Whence the relation of F, A flat, and their connection with the other part of the chord is evideut; F being the primary, and A flat the minor 3rd of the primary ohord of the system F, added to the major chord of G, the discord resolving as before upon the derivative chords of F. The ratios of this chord admit of other forms being given to them, showing why it is an equivocal chord, but which it is unnecessary to enter upon, as they do not affect the fundamental bass of the chord in this form, which is one of transition.

Mr. Hewitt will perceive that in the preceding, and in my last letter (Musical World, December 24th), I have given the true basses of all the chords in his examples (November 19th) derived from the true ratios, by giving their true intrepretation, and therefore am perfectly just ified and correct in asserting that the ridiculous basses are the "genuinefruits" of his false theory, and derived from the ratios by a false interpretation. In saying this, I do not appear as the advocate of any particular theory, but as the upholder of truth, the foundation of every science. The discrepancy in bis minor 3rd he has not yet explained, nor can explain without stultifying himself, seeing that he has admitted the ratio of the major 3rd to be 5-4, in first asking for this explanation. I have now made it clear that I struck at the very root of his theory—error, "the nucleus to innumerable other similar errors." The other remarks in hie letter (M. W., Dec. 10th), are almost too puerile to deserve attention, being evidently written, not with a view of elicit ing tho truth, but for the purpose of drawing attention from the main points of the question, which are not in any way affected by his remarks. However, I will just notice them, that I may expose their puerility. The ratio fjfj'J -s, if expressed as a decimal fraction, is 1*20001 (truo to five places of decimals), J being 1'20000, which as they stand are in the ratio of 120001:120000, the remaining portion of the first would be loss than $ ; therefore if 1J nearly be substituted for one vibration or beat, all the rest is strictly correct, and would agree with his statement, that it is one vibration in 98304, which is the exact truth; the two sounds (E flat) would then give one beat in 5j minutes, when the C above gives 512 vibrations per second. Mr. Hewitt must excuse me correcting his corrections! but I advise him to try again, and not to confound the vibrations of E flat with those of the C above, but look at the figures as the representatives of certain facts, and not as merefigures. Even supposing his computations were correct, the difference in the two sounds would still bo "a minute quantity far beyond the power of the finest ear to detect," and the question would still remain, as before, which I now leave him to reply to. As regards the ratio tffft, it was never proposed by mo as a substitute for the truo ratio, g, but as an instance of the nearness to which that ratio could be approached by ratios "cast in his mould"—that is, the first term must be a prime number, and the second must be one of the series 1, 2, 4, 8, 16, Ac. There is no difficulty in finding ratios to agree with the form of the second term, they being, as I before stated, infinite in number; but, as there is no direct rulo for finding prime numbers, there is a little trouble in verifying the primes by those who do not possess extensive tables of them, as Sir. Hewitt will find if he attempt to give a few more nearer to f than the one just mentioned; and though he says that "prime numbers give original sensations," he has not yet

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