"THE WORTH OF ART APPEARS MOST EMINENT IN MUSIC, SINCE IT REQUIRES NO MATERIAL, NO SUBJECT-MATTER, WHOSE EFFECT MUST BE DEDUCTED. IT IS WHOLLY FORM AND POWER, AND IT RAISES AND ENNOBLES WHATEVER IT EXPRESSES."— Göthe. SUBSCRIPTION:-Stamped for Postage, 20s. per annum-Payable in advance, by Cash or Post Office Order, to BOOSEY & SONS, 28, Holles Street, Cavendish Square. VOL. 38.-No. 4. SATURDAY, JANUARY 28, 1860. R. UNDER THE MOST DISTINGUISHED PATRONAGE OF THEIR ROYAL HIGHNESSES THE PRINCESSES AND PRINCES OF THE The Most Worshipful the Grand Master of Ireland, And Several other Distinguished Freemasons; The LORD BISHOP OF MANCHESTER, The Right Worshipful the MAYOR OF MANCHESTER, His Worship the Mayor of Salford, W. HARVEY, Esq. SIR FREDERICK GORE OUSELEY, Bart., Director of Music at the University of Oxford. And many of the Nobility, Gentry, Clergy, and distinguished Families of the Empire. DR. MARK'S GREAT NATIONAL ENTERPRISE 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 the 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 CONSERVATOIRES OF MUSIC to be established throughout the United Kingdom, for LITTLE CHILDREN, the whole comprising an entirely new scheme of NATIONAL EDUCATION, by blending music with general instruction, so that the study of music shall become a branch of education in the humblest of schools of this country. To illustrate and to rouse an interest in 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 Efficient 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. &c., and sing Songs and Choruses in a most effective manner, and to whom Dr. Mark gives a gratuitous General and Musical Education. APPOINTMENTS OF MASTERS AND ARRANGEMENTS OF CLASSES IN THE ABOVE INSTITUTION. Violoncello, Double Bass, and Viola Flute, Piccolo, Oboe, and Clarionet Cornet and other Brass Instruments Concertina (German and English) Vocal Classes .. Dr. MARK has also made provision for the Orphans of the Musical Profession possessing musical talent, who will find the above institution a happy home, and receive a most effective general and musical education, board, and clothing, free of all expense. .. .. I Messrs. PowELL and ELDER. Little Boys, from five to nine years of age, apprenticed for three, five, or seven years by paying a moderate entrance fee to cover the expenses of instrument and books. Twelve appointments ready for Masters. For Prospectuses, apply direct to the Royal College of Music, Bridge-street, Manchester. Dr. MARK is also open to Engagements with his Little Men. Dr. MARK begs to invite the Parents and Friends, and all those interested in his 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 Four, p.m. Saturdays and Sundays excepted. LA PRICE 4d. STAMPED 5d. AURENT'S SECOND GRAND WINTER BALL, at St. James's Hall, Tuesday, January 31st.-M. HENRI LAURENT has the honour to announce, 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 last occasion. The hall will present the appearance of a beautiful winter garden, being decorated with flowers, plants, and sculpture, arranged by Mr. Hurwitz. The orchestra will be complete in every department, and will perform a variety of novelties composed for the occasion. Programme: Quadrille, Dinorah, Laurent; Valse, Reigning Beauty, D'Albert; Quadrille, Satanella, Laurent; Polka, Marguerite, Laurent; Lancers, Original; Valse, Sicilian Vespers, (first time) Laurent; Galop, Satanella, 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, Tinney; Valse, Dinorah, Laurent; Quadrille, Serpentine, Burckhardt; Valse, Satanella, Laurent; Quadrille, Kenilworth, 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. 6d.; 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, Hindestreet, Manchester-square, Tuesday, 31st inst., to commence at half-past 8 precisely. The following artists will have the honour of appearing:-Messrs. Sainton, Bezeth, Schreurs, Paque, and G. A. Osborne; Vocalist, Miss Dolby; at the pianoforte, Signor Randegger and Mr. Francesco Berger. Tickets half-a-guinea each, to be had of Miss Dolby at her residence. MYDDLETON HALL, ISLINGTON-NORTH LON DON MONDAY POPULAR CONCERTS. A series of Monday Evening Concerts under the direction of Mr. H. Davis, will be commenced in the above Hall on Monday evening the 6th Feb., 1860. A number of artists are engaged, amongst whom are the following established favourites: Mad. Louisa Vinning, Mdlle. Vaneri, Miss Fanny Reeves, Miss Messent, Mr. Allan Irving, J. G. Patey, and Elliot Guler, Viotti Collins, Medora Collins, J. D. Davies (harpist), R. Glenn Wesley. Conductor, Mr Frank Mori. Admission one shiding and two shillings. MONSIEUR ET MADAM RIEDER beg to announce that they have arrived in London, where they intend passing the season. Letters respecting lessons or engagements, may be addresse i to the care of Messrs. Chappell & Co., 50, Bond-street; or Messrs. Schott & Co., of 159, Regent-street. W ANTED, immediately, a Pupil in a Musical Establishment, where he will have an opportunity of acquiring a thorough knowledge of the profession in all its branches. Apply to Herr Winzer, Newcastle, Staffordshire. MEYERBEER'S DINORAH AND STERNDALE BENNETT'S MAY QUEEN, are sung nightly at the CANTERBURY HALL CONCERTS. Comic vocalists-Messrs. George Hodson (the Irish comedian and mimic), W. J. Critchfleid and E. W. Mackney. Several interesting pictures are added to the Fine Arts Gallery. The suite of Halls have been re-decorated and beautified, and constitute one of the most unique and brilliant sights of the metropolis. тол O THE MUSIC TRADE.-Wanted by a first-class Tuner a situation : undeniable references will be given. Address, K., Musical World Office. THE BAY OF DUBLIN QUADRILLES, on Irish THE Melodies by Wellington Guernsey, as performed by the bands of the Coldstream Guards, Royal Artillery, &c., has become one of the most popular of the day Price 3s. Beware of spurious imitations. London: Brewer and Co. TO VOLUNTEER RIFLE CORPS.-Boosey and Sons military band instruments, reed and brass, as well as bugles, drums and fifes, have been used and approved of by almost every regiment in the service, at home and abroad. Those regiments that contemplate the formation of a band. are invited to apply to the firm, who will be happy to recommend them competent bandmasters, and render any further assistance that may be required.—Boosey and Sons, Holles-street, London. In presenting this prospectus, the projectors of this Association deem it worthy of remark that a great want is felt by a countless number of amateurs possessing musical knowledge and capability of a society which would afford them ample 1. opportunity of acquiring, at a moderate cost, a complete knowledge of the beauty and graudeur of the choicest and recognized orchestral compositions of this and previous periods. The object of this Association is to bring together the amateur instrumentalists of London and its suburbs, for the practice and performance of oratorios, masses, cantatas, symphonies, operatic selections, and overtures, including compositions but little known to the general public, with other chef-d'oeuvres of the great masters, suitable for band and chorus conjointly or separately. For the benefit of the amateur department, weekly rehearsals will be held on every Saturday Evening, at Eight o'clock, at the Architectural Gallery, 9, Conduit-street, Regent-street, and during the season, concerts will be given at one of the large theatres, or concert-rooms, with the important of Make chorus to soon as the necessary proficiency is attained. junction with as W In the professional department there are. still vacancies for honorary members for the following instruments:-Four first violins, one second violin, and two All communications to be addressed to the Honorary Secretary of the London Orchestral Association, 9, Conduit-street, Regent-street, W. H. J. BRAHAM, Hon. Sec. THE HE COLOURED OPERA TROUPE-Wm. Albain, Proprietor. All the songs of this celebrated party (50 in number) can be had in a neat book, set to music, for thirteen stamps. Address to Wm. Albain, 21, Newington-crescent, London. S. MUSICAL DIRECTORY, REGISTER & ALMANAC FOR 1860.-Contents: Almanac with musical data; list of musical societies throughout the kingdom; musical transactions of the past year; names and addresses of professors, music-sellers and instrument makers; and list of music published between the 30th November, 1858, and 30th November, 1859. Price Is. 6d. ; per post, 1s. 8d. Publishers: Rudall, Rose, Carte and Co., 20, Charing Cross, S. W.; and Keith, Prowse and Co., 48, Cheapside, E. C. FERRARI'S WORK ON THE VOICE AND SINGING, price 8s., may be had at his residence, Devonshire-lobge, Portland-road, Portland-place, and at all the principal music-sellers. "Of all the treatises on the cultivation of the voice that have appeared for many years, it is the most sensible, concise, and useful."-Daily News. "There is more sense in this work than we find in nine out of ten publications of a similar kind."-Athenæum. "Here is a really sensible work."-Musical World. REVIEWS. 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) "étrennes," or of (as the English say) "New Year'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). name for a near-fetched piece!) belongs to the ordinary- Then came the gentlemen, trim, trim, trim; First appears Mr. J. G. Callcott, with "Come in, and shut But we have inadvertently reversed the order, and given the door" (Cramer, Beale and Chappell), a song to some lively precedence to the "gentlemen" (Messrs. Balfe and Co.) and verses by "J. P. H." The music-even livelier than the words" country-folks" (Messrs. Taylor and Co.). Soliciting "mille -though simple as a hammer, is by no means ungenial. It pardons" (which, we presume, means begging pardon 1000 contains, however, a progression, from the key of C major to times), we now acknowledge, with gratitude, Miss Virginia that of E major, (Page 2, line 2); and another from the 6-4 on Gabriel's slightly tormented, a thought over-modulated, a trifle G natural to the common chord of A minor, by means of a unfinished (see bare fourth-page 1, line 3, bar 3), but otherharmony with G sharp in the bass, and F natural and Gwise graceful and expressive song, called "ONE passed by" natural as melody; both of which might be advantageously (Hale and Son-Cheltenham),-which, but that the monoreconsidered. At the same time let us thank Mr. Callcott syllable, "One," is too frequently underlined-after the for a really appropriate new year's gift. 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 the 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. 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. "The Rose on the 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. Balfe'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. 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 Mr. H. T. Leftwich-" composer," as the foot of the titlepage assures us," of the favourite song of 'The Fountain,' presents us with a river. "The River" (Clinton and Co.)-common-place. 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 Chappell), which has the double merit of being genuinely melodious and irreproachably scholar-like. The effect of this charming trifle, well sung, either in public or private, would be unquestionably good. 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 Mr. Balfe has transmitted us another New Year's gift, in the shape of" Songs for 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, &c., the poets being Tennyson, Longfellow, Kingsley, 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. "Fortune and her Wheel"-poetry by Alfred Tennyson-music composed These are, and dedicated to the Earl of Hillsborough by M. W. Balfe; 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.) 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 Bokemian Girl first proved that he could divest himself of that leaning towards the modern sentimental school-himself the originatorwhich, 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 Rev. Charles Kingsley-such as "The Sands of Dee," &c. 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 : series of heart-yearnings, in the songs of the Idylls of the King, and to have employed his pen on the same subjectsLove 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 étrennes are in a style of munificence becoming his con-spicuous station. "Smile and we smile, the lords of many lands; "The Song of Love and Death" 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 vain ; And sweet is death, who puts an end to pain; Love, art thou sweet? Then bitter death must be ; "Sweet Love, that seems not made to fade away; I fain would follow love, if that could be; I needs must follow death, who calls for me; 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 system, the two systems being thus closely connected. It will be perceived that, if we take any primary basis on which to construct a diatonic scale, the whole of the sounds forming the scale are contained in the primary chords connected 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. In the attendant harmonies we proceed from system to system by single degrees unto A, the sixth of the scale, which 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 in 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 modu. lations 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; 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 note enters 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 system below the primary it is, and when any above it is, 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 G as a primary, having the form 8, 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, 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 g) below &; the other being a minor-tone (ratio) 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 18), although it is nearly sothe ratio of this interval being, which, as compared with his ratio, is as 512: 513. Most unfortunate is it for him, and for his idea, that his prime 19, in connection with his unit-basis, should be so near and yet 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 Ex. 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, D 1 F 34 B ៖ B 1 128 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-5ths (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): Ꭰ F A flat $4 eliminating the octave sounds, and giving all the same form of denomi⚫ nator, they would be— ៖ 3.3 3.15 the numerator 5 of the unit-sound B refers a major 3rd below to G, the fundamental bass; the factors 9 under F, and 15 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 factorsA flat 3.5.5 F 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 evident; F being the primary, and A flat the minor 3rd of the primary chord 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. 1966 "the 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 justified and correct in asserting that the ridiculous basses are the "genuine fruits" 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 his 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 54, in first asking for this explanation. I have now made it clear that I struck at the very root of his theory-error, nucleus to innumerable other similar errors." The other remarks in his letter (M. W., Dec. 10th), are almost too puerile to deserve attention, being evidently written, not with a view of eliciting the 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 may expose their puerility. The ratio 1899, if expressed as a decimal fraction, is 1.20001 (true to five places of decimals), being 1-20000, which as they stand are in the ratio of 120001: 120000, the remaining portion of the first would be less than ; therefore if 1 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 5 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 mere figures. Even supposing his computations were correct, the difference in the two sounds would still be "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 1899, it was never proposed by me as a substitute for the true ratio,, 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, which, by eliminating the octave sounds, and giving all the same form 2, 4, 8, 16, &c. There is no difficulty in finding ratios to agree with of denominator, are the form of the second term, they being, as I before stated, infinite in number; but, as there is no direct rule for finding prime numbers, there is a little trouble in verifying the primes by those who do not possess extensive tables of them, as Mr. Hewitt will find if he attempt to give a few more nearer to than the one just mentioned; and though he says that "prime numbers give original sensations," he has not yet |