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NEW ADDITIONS

TO

BOOSEY AND SONS CATALOGUE.

COMPLETE OPERA S.
IL TROVATORE, with English and Italian Words, in cloth
LA TRAVIATA, with English and Italian Words, in cloth

*** Forming the first Volumes of the New Series of the Standard Lyric Drama.

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CHOPIN'S MARURKAS complete .. ... ...
DUSSEK'S and WOELFFL'S PLUS ULTRA and NE PLUS ULTRA SONATAS ...

NEW GUITAR BOOK.
MADAME PRATTEN'S Popular Instruction Book for the Guitar (43 pp.) ...

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BOOSEY AND SONS. HOL LES STRE E T.

Published by Jonu Boosey, of Castlebar-hill, in the parish of Ealing, in the County of Middlesex, at 28, Holles-street. Printed by WILLIAM SPENCER JOHNSON, “Nassau Steam Pross." 60. St. Martin's-lane, in the Parish of St. Martin-in-the-Fields, in the County of Middlesex

Saturday, April 14, 1860.

“TIE WORTH OF ART APPEARS MOST EMINENT IN MUSIC, SINCE IT REQUIRES NO MATERIAL, NO SUBJECT MATTER, WHOSE EFPEOT JUST

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. 16.

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SATURDAY, APRIL 21, 1860.

ST. JAMES'S HALL, R.

REGENT-STREET AND PICCADILLY. MONDAY POPULAR CONCERTS.

THE NINETEENTH CONCERT OF THE SEASON, MONDAY EVENING, APRIL, 23rd, 1860,

MR. SIMS REEVES' BENEFIT.

The Programme will be selected from the works of

VARIOUS MASTERS.

.

. Mendelssohn.

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UNDER THE MOST DISTINGUISHED PATRONAGE OF
HER MOST GRACIOUS MAJESTY THE QUEEN

H.R.H. THE PRINCE CONSORT,
THEIR ROYAL HIGHNESSES THE PRINCESSES AND PRINCES OF TIIE

ROYAL FAMILY,
The Most Worshipful the Grand Master of Ireland,

His Grace the DUKE of LEINSTER,
And Several other Distinguished Freemasons;
His Excellency the Lord Lieutenant of Ireland, the

EARL of EGLINTON and WINTON,

The LORD BISHOP OF MANCHESTER,
The Right Worshipful the MAYOR OF MANCHESTER,

IVIE MACKIE, ESQ.
His Worship the Mayor of Salford, W. HARVEY, Esq.
BIR 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 those institutions, Dr. Mark travels with a number of his pupils occasionally through the country-giving lectures, and introducing bis highly approved and pleasing Musical Entertainment, entitled DR. MARK ANĎ 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.
Principal of the Royal College of Music ; Director, Composer, and

Conductor; Lecturer to both Private and Public, Theoretical Dr. MARK.

and Practical Instrumental and Vocal Classes .. Master of the General Educational Department: Writing, Reading, Arithmetic, Grammar, Dictation,

Mr. POWELL History, Geography, Practical Geometry, and Book. Assistant Teachers.

and Two keeping

Miss Arabella Goddard

..

.. Mozart.

PROGRAMME.

PART I.
POSTHUMOUS QUARTET, in F Major, No. 17 .. .. Beethoven.

M. Sainton, Herr Ries, Mr. Doyle, and Signor Piatti.
SONG, “Frühlingslied "
SONG, “Deeper and deeper still" ;

Handel.
Mr. Sims Reeves. "
SONG, “Night” .. ;

Mendelssohn. • Madame Saintön-Dolby. SONG, “Adelaido"

Beethoven, ido" "Mr. Sims Rooves SONATA, in F. Major diss Arabelle Goddard.

• PART II. SONATA, in E flat, Major, Pianoforto and Violin .. Dussek.

Miss Arabella Goddard and M. Sainton. SONG, “False friend, wilt thou smile or weep? (Cengi) J. W. Davison,

Madame Sainton-Dolby.
SONG, “ Dalla sua pace" .

Mozart.
Mr. Sims Reeves.
DUET, "Pray leave me but a moment'

Spohr.
Mrs. Sims Reeves and Madame S&
SONG, “The Stolen Kiss" **

. Beethoven. Mr. Sims Reeves. QUARTET, in E flat, No. 4.

Rossini.
M. Sainton, 'Herr Ries," Mr. Doyle, and signor Piatti.

CONDUCTOR-MR. BENEDICT.

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"PRACTICÄL ASSISTANT TEACHERS.

Stalls, 103, 6d. and 5s. ; Balcony, 39. ; Unreserved Seats, 18.-Tickets to be had of Mr. Austin, at the Hall. 28, Piccadilly; Messrs. Cramer and Co., Hammond, Addi. son, aud Co., Schott and Co., Ewer and Co., Simpson, Carter, and Oetzmann and Co., Regent-street; Brooks, 24, Old Cavendish-street; Bradberry's London Crystal Palace, Vxford-street: Duff and Co., 65, Oxford-street; Prowse, Hanway-street; Chidley, 195, High Holborn; Purday, 50, St. Paul's Church-yard; Keith, Prowse, and Co., 48, Cheapside: Turner, 19. Corphill: Cook and Co., 6, Finsbury-place, south; Humfress, 4, Old Church Street, Paddington-green; Mitchell, Leader and Co., Ollivier, Campbell, and Willis, Bond-street; and Chappell and Co., 50, New Bond-street.

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Organ .. ..

Mr. BAKER.
.

Herr SIEMERS.
Pianoforte .. .. .. .. ..

Mr. ELDER,

Mons. ROGUIER,
Violin .. .. .. .. .. .. .. Mr. BEARD.

Mons. VIEUXTEMPS.
Violoncello, Double Bass, and Viola

. Mr. T. DONOVAN. Flute, Piccolo, Oboe, and Clarionet

Sig. CORTESI. Cornet and other Brass Instruments

Mr. H. RUSSELL. Concertina (German and English)

Mr. ELDER.

Messrs. Powell and Vocal Classes .. .. .. ..

ELDER, 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.

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 bis 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,

ORCHESTRAL UNION.-MR. ALFRED MELLON

begs to announce that he will return to London about the middle of June, when he will be open to any engagements for the Band of the Orchestral Union, which he has reconstructed. Principal Artisteg-MM. Sainton, H. Hill, W. Watsov, E. Payton, Doyle, Trust, G. Collins, Aylward, Howell, senr, White, P. S. Pratten, Barret, Lazarus, T, Owen, Hausser, C. Harper, Standen, T. Harper, Stanton Jones, W. Winterbottom, Cioffi, Hughes, and F. C. Horton, Applications respecting engagements to be made to Mr. George Dolby, 2, Hinde-street, Manchester-square, W,

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THE MUSICAL SOCIETY OF LONDON. The Third

I CONCERT, on Wednesday Evening, April 25th, at St. Jamees: . Programme-First Part :-Overture, the Isles of Fingal, Mendelssohn Bartholdy : Air, Jours de mon enfance (Pré aux Clercs), Miss Augusta Thompson, Herold Symphony concertante, for two pianofortes and orchestha, Mr. Charles Salaman and Mr. Lindsay Sloper, Dussek; Scena, (MS.), Mr. Santley Benedict Overture, (Lurline), Wallace. Second Part :-Sinfonia Eroica, Beethoven, Nap_DI U città sei tu (L'Etoile du Nord), Miss Augusta Thompson aud Mr. beer; Overture (Gustave), Auber. Conductor, Mr. Alfred Melon

CHARLES SALAMAN, Hamn Sec.

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pRYSTAL PALACE—Friday, May 4th.—Tickets for MISS ELLEN LYON, Vocalist (Soprano). Letters

\J THE QUE AT FESTIVAL PERFORMANCE OF ELIJAH, on tlio occasion respoctinc all public and private euuiwomcats to bo addressed 26, Charles

of the Inauguration of the Bronze Memorial Statua of Mendelssohn, aro now on sale at the Crystal Palace; at No. 2, Exetor llall; or, by order, of the usual Agents.

Admission tickets, 5s. (if purchased beforo 1st M»y); Reserved stalls in blocks, as arrango 1 at tlio Handel Festival, In the area, 5s. extra; or in the corner I galleries, 10s. Od. extra. 1

The new Season Tickets will admit, subject to the usual regulations.

NOTICE — Immediate application is requisite for Central Blocks. Post Offlco I Ordors or Cheques to he payable to George Grove. 1

CRYSTAL PALAC K^June 25th, 26th, and 28th,
GREAT ORPHEONISTE MUSICAL FESTIVAL.
Vouchers for tickets for this great combination of tho French Choral Societies,
comprising deputations from nearly every Department of France, representing 170
distinct (JUoril Sociotaea, and numbering betweon Three and Four thousand
performers, who will visit England expressly to hold a Great Musical Festival at
tho Crystal Paloco on the above days, arc now on issue at the Crystal Palace; at
No. 2, Exeter Hall ; or by order of the usual agents.

Tho prices of admission will be as follows:—Tho sot of Transferable tickets (one admission to each of the S days) 12s. 6d. ; Reserved Beats (for tho S days) 12s. Od. extra; or iu tho corner galleries, 25s. extra.

Tho now Season Tickets will admit on the above occasion, subject to tho usual regulations.

HANOVER-SQUARE ROOMS.—MR. MELOHIOR WINTER (leuoie), and Mr. BENJAMIN WELLS (flautist), bag to announce thit their GRAND VOCAL AND INSTRUMENTAL CONCERT will tako place at tho nbovo rooms on tho 28th of May, (Whit Monday.) Full particulars will shortly be published.—17, St. Jamos's square, Nottiug-hill, W.

PHILHARMONIC S O 01 E T Y.—Tho Directors respectfully announce that the FIRST CONCERT will take place at the Hanover-square Rooms, ou Monday Eveniug next, tho 23rd of April. Programme: —Siufonia, Tho Seasons, Spotir; Concerto violin, Herr Becker, Mendelssohn; Overture, E^mout, Beethoven ; Sinfonia in C, Jupiter, Mozart; Overture, Zaira, Winter. Vocal performers: —Mdlle. IxmisoMicbalandSiguorBellettJ. Conductor, Professor Stcrndale Bennett, Mun. D. To begin at 8 o'clock. Subscription for the season, jt?3 3s.; single tickets, 15s. Subscriptions rcceivod and tickets issued by Messrs. Addison, Hollier, and Lucas, 210, Regent-street.

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respecting all public and private engagements to be addressed 26, Charles•treot, Borners-stroet, W.

TTISS SELENA PYKE (Pupil of Mr. Charles Salaman),

1t_l continues to give lessons on the PIANOFORTE. Miss P. attends schools and her pupils westward* twice a week. 52, Great Prcscott-strtct, E.

MBTJZZIAN (Violonist), has just arrived from the • Contineut, and is open for engagements; apply at Mr. Mapleson's, 12, II ay market.

R. LANGTON WILLIAMS begs to inform his friends

and the public that his Annual Concert will tako placo at St. Martin's Hall, on Wednesday evening, April 25th, when tho following distinguished artists will appear; Mdlle. Paropa, Madame Weiss, Mis* Poole, Miss B tab bach, Miss Letfler, Miss Julia Bleaden, Miss Clara Hamilton, and Miss La-sccllet; Mr. Weiss, Mr. Ramaden, Mr. R Seymour. Mr. J. W. Morgan, and Mr. Sims Reeves. Harp, MissChatturtnn; Concertina. Miss M. Collins; Violin, Mr. Viotti Collins; Pianoforte, Mr. L. Williams, Herr Wilhelm Ganz, and Mr. J. L. Hattou. Tickets Is., 2s. sofa stalls, 6s.

MISS ELEANOR ARMSTRONG begs to announce that her grand Evening Concert will take placo at the Queen's Concert Rooms, Hanover-square, ou Wednesday the 16th May, at 8 o'clock, when tho following eminent artist* will appear: Vocalists, Miss Elcauor Armstrong, Madame Laura Baxter, Mr. William Cummings, and Herr EibcnschUtz, of Pestb. Instrumentalists: Pianoforte, Mr. Charles Salaman, and Herr Adolphe Rics; Violin, Herr Louis Ries; Violoncello, Herr J. Lidel; Harp, Mr. Ellis Roberts, Harpist to II. H. R. tho Prince of Wales. Conductor, Mr. Frank Mori. Tickets 7s., Reserved scats 10s. 0d., to be had of Mi&s Eleanor Armstrong, at her residence, 36, Osnaburgh-st., Rceeut's-park, Messrs. Keith, Prowso and Co., City, aud of the principal musicso.fcrs.

MLLE. ELVIRA BEHREN'S EVENING CONCERT, under the immediate patronago of Her Excelloncy the Countess Bornstorff, Her Excollcncythe Countess d'Apponyi, & Her Excellency the Countess Platen, will tako placo at the Queen's Concert Rooms, Hanovur-square, on Wednesday, the 2nd May. Artistes, Madame Rioder, Mdlle. Elvira Behreus, Herr EibcnschUtz, Herr Ernst Pauer, Herr Wilhelm Ganz, Herr Becker, Herr C. OborthUr, Herr Datibert. Reserved Beats, 10s. 6d ; family tickets, admitting three, one guineA; unreserved scats, 5s.; to be had at Mdlle. Behren'a residence, 1*, Blenheim-road, St. John'swood; and of the principal west-end inusicsollors, and Messrs. Keith and Prowse, Cheapside, city.

MEYERBEER'S DINORAH AND STERNDALE BENNETTS MAY QUEEN, aro sung nightly at tho CANTERBURY HALL CONCERTd. Comic vocalists—Mossrs. George Hodson (the Irish comedian and mimic), W. J. Critchfie'id and E. W. Macknoy. Several interesting pictures are added to tho Fine Arts Gallery. The suite of Halls havo bsxm re-decorated and beautified, and constitute ono of tho most unique and brilliant sights of the metropolis.

MISS MARGARET Mc A L PIN E (Contralto), rcqucs's that letters respecting engagements for Oratorios, Concerts, and Pupils, be addressed to her resldenco, 63, Burton-crescent, New-road.

MADAME BORCHARDT having returned to Town from her Operatic Tour with Madlle. Piccolomiul, is at liberty to accept engagements for Concerts, toe, for tho season. Address to tho caro of Messrs. Duncan. Datisoa stud Go., 214, Regent-street) W,

MDLLE. PAREPA has removed to No. 17, Russell-place, Fitzroy-square, to which address she begs that all future communications respecting engagements may bo forwarded.—April 11,

TO MUSIC 'PUBLISHERS, CLERGYMEN, COMPOSERS, AND OTHERS.

PGRANT AND CO., Typographical Music and General
• Printers, Lithographers, and Engravers, Orange-street, and Rod Liou-
squarc, Holborn, respectfully inform tho above that they are prepared to undertake
works to any extent in Music Printing, upon the most reasonable terms, and
with the greatest accuracy and.dispatch.

MUSIC PRINTING FOR THE TRADE.
Estimates, and Specimens of Music Founts sent to any part of the United
Kingdom.

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ARTISTS' VOLUNTEER RIFLE CORPS.—

x~\. (38th Middlesex), Viscouut Bury, Captain Commandant. This corps, composed of Artists, Amateurs, and others interested iu any branch of Art, drills at the Argyll Reoms, on Monday, Wednesday, and Friday, at Five o'clock; Tuesday, Thursday, and Saturday evenings at Half-past Six; and at Burlington House on Wednesday mornings at Eight. Officers appointed to First Company: Captain, Viscount Bury; Lieutenant, H. W. Phillips; Ensign, J. E. Millais, A. R. A. Third and Fourth Companies are now forming; gentlemen wishing tojoiu the corps con be onrolted at the hours of drill, or on application to F. P. Cockerel!, Esq., Honorary Socretary, 8, Regent-street.

rPO VOLUNTEER RIFLE CORPS.—Boosey and Sons'

-1- military band instruments, rccd and brass, as well as bugles, drums and fifes, have been used and approved of by almost every regiment iu the service, at home and abroad. Tiiose regiments that contemplate the formation of a band, are invited to apply to the firui, who will be happy to recommend thorn competent bandmasters, and render any further assistance that may be required.—Boosey and Sons, Hollos-street, London.

EVANS'S ENGLISH HARMONIUMS.—Full particulars of these unrivalled instruments to be had of the manufacturers, Boosey and Sons, 24 and 23, Holies-street, London. Manufactories at Wells-street and Davies-streot.

pASE'S PATENT CONCERTINAS, as used by

8i«nor Rcgondi and Mr. George Case, are remarkable for their superior tone, and being less liablo to got out of tune than any other English Concertinas. Prices from four to twelve guineas each. Manufactured by Boosey and Sons, Holies-street.

Just Published, price 3s. Ci.

"T30MANZA," for the Violoncello aud Piano, composed

XV and dedicated to Frederick Charles Pawle, Esq., by Edward Thuraam. Robert Cocks and Co., New Burlington-street, London.

MEYERBEER'S NEW WORK—"ASPIRATION"— CANTIQUE. (Short Anthem.) Tho woids from tho original Latin of Thomas a Kcmpis, "Do imitatione Christi." Composed for SIX VOICES (three sopranos, two tenors, and bass), with Recitatives for a BASS SOLO, and Organ (or Harmonium) accompanimont ad libitum, by GIACOMO MEYER13EKR. Prico, in score. 4s. London: Duncan Duvison and Co., 244, Regent-street, whero Meyerbeer's setting of tho Lord's Pravor. for four voices, 3s , and the Serenade, for eight voices, "This house to love is holy," 4s., may bo obtained.

pHEAP EDITION OF MOZART'S TWELFTH

\J MASS aad ROSSINI'S STABAT MATER, arranged in tho most effective, raannor for tho Pianoforte, by Henry Smart, prico 3e. each, complete, or hand■omoly bound, is, each, Boosey aud Bona, Holles-stroot.

REVIEWS.

"' Thou art so near' ReicJtardt's celebrated song, arranged for the pianoforte"—by Brinley Richards (Boosey and Sons). An adaptation—or, as our "lively," "volatile," "pugnacious," "capricious," "mercurial," "spiritual," and thoroughly amiable neighbours say, "transcription"—of Herr Beicliardt's very popular melody, done with that neatness, elegance, and finish for which Mr. Brinley Richards is notorious, which imparts so genuine a charm to his smaller compositions for the drawing-room, and makes them invaluable as teaching pieces, both to master and pupil. A hajjpier example of his taste and facility in this direction has not been issued from the press.

."' Marche a Grand Orcltestre,' transcrite par Fauteur"— Frederick Scotson Clark (Augener and Co.). Mr. Frederick Scotso'n Clark, though an English- (Irish?—Scotch?— Welsh?—Manx?) -man, selects the French lingo for his title-page, and "transcribes"—" pour piano, liarmonium, ou grand orgue d'eglise." We have attempted his present "transcription" on the first-named instrument. Mendelssohn composed a certain Wedding March, which begins thus:—

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The theme itself is pretty, and the arpeggio variation beginning at page 4, a clever imitation of one ofM. Thalberg's most familiar expedients.

"' La Consolation,' revtrie," a son ami, R. Conolly, Esq.— H. F. Hcnniker (Avery). We protest against a French titlepage coming from an English Academy student. The late Earl of Westmoreland would not have sanctioned it; and we are ready to bet three "rivtries" to one that Mr. Henniker's "ami, R. Conelly, Esq." (why not Escuyer 1) would have preferred to have the work dedicated to him in plain English. The name of the "re've'rie," moreover, is ill chosen. There can be little consolation for any sorrow, disappointment, or misfortune in four or five pages of music skipping about after this fashion {style grenouille ?):—

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MATHEMATICAL THEORY OF THE MAJOR DIATONIC SCALE.

Sib,—I presume that as Mr. D. C. Hewitt offers no reply to my letters (Musical World, December 24th, nud January 28th), he is thoroughly couvinced of the unsoundness of the principles of his proposed theory of unit bosses, which is in reality a theory founded upon an unlimited scries of harmonica; and it could easily be made manifest that no theory, built upon such a complicated foundation, can give the true principles of harmony, that is, no theory derived from such a basis can show the true relations of musical sounds, whether as Bimple sounds or in combination as chords, or can explain the connection of these chords one with another, either when they proceed by simple progression or by modulation; on the other hand, all these relations, and many others, are with facility deduced from the simple, theory of limited harmonics, or systems of sounds, based upon the consonant intervals, the whole of which are formed by a principal sound as generator, and its first, second and fourth harmonics, represented by tho respective ratios, 1, 2, 3 and 5, to 1, and are those generally known us the common chord, which chord rnoy therefore, with propriety, be called tho very essence of harmony, and justly be designated the perfect concord.

In my last letter I pointed out, I believe for the first time, the mathematical relation existing between the chord of the dominant 7th and the chords of its resolution, hut as the limits of a letter written for the purpose of elucidating auother part of the subject, did not allow of more than a slight uotice of this, I may perhaps enlarge upon it at Bomo future period; for the same reason I assumed the sounds of the major diatonic scale to be those already acknowledged as such, but it is my principal object in the present to complete the link in the argumentative chain, by showing that these sounds of the scale can bo strictly deduced from the same scientific basis. In reference to the systems of sounds in the samo letter, I there noticed the fact that each sound (nominally the same), as, for instance, G, enters into these systems under three distinct forms, and when it enters as a primary it is continued through three system", in the other cases only through two. Now when it appears iu two systems only, as in E and A, it does not enter as a primary, hut only in a subordinate character: it is subject unto and governed by a primary sound, evidenced also by its accidental change, and though in combination with tho primaries, E and B, it establishes a connection between the two systems, yet it is of itself powerless, and has no influence over the sounds of these systems; the same mny be said cf the sound G in the systems E flat and A flit. But when it enters os a primary, as in G, then in the adjacent system C, it appears as the unit-sound, that is, the sound with which all the others in that system are consonant, and which it therefore governs; it is the ruling sound, in fact, the dominant sound, all the others being subject unto it, its influenco extending also into the adjacent systems, G and F, which thus become equally related to tho system C; also the sound G is the only one that is continued through tho three systems G, C, and F, which are in this manner brought into connection and form one mode of sound, of which G is the dominant. Moreover, the G as dominant, or unit-sound of a system, invariably leads to the 5th below, or C, as the primary basis (as shown in my letter, Musical World, December 24th), which thus becomes the basis or root of the sounds in this mode.

The mode may be either major or minor, accordingly as we take the sounds of the iniijor or minor primary chords. As the subject of our present consideration is the major diatonic scale, we must take tho sounds of the major primary chords, the individual sounds of which, orrdng d within the compass of on octavo in an ascending order, according t o the magnitude of their ratios, and commencing with the ascertained rcot, are—

CDEFGABC

In a 4 i a xa J

which arc oil tho sounds of the major primary chords, in the mode of which C is the root, and taken collectively are the sounds of the major diatonic scale of C only. All other major diatonic scules are formed in a similar way.

We have thus not only the sounds of the major diatonic scale, but also tho true reason why the 5th of the scale is tho dominant sound, and how it becomes so: tho whole of which are, I believe, now, for the first time, strictly deduced from a mathematical basis. It will be seen that the complete scale consists of eight sounds or seven intervals, which intervals, by a comparison of their ratios, are found to be of three degrees of magnitude, viz.: the major tone (ratio §), the minor tone (ratio y), and the diotonie semitone (ratio •{-§), which, if they be represented respectively by the letters T, fe S. then the following is the order in which they occur, and which serves as a simple illustration of the magnitude of the various intervals, any interval whatever may be easily measured and compared with another, by simply adding together the various magnitudes of which such intervals aro composed :—

CDEFGABC
T t S T t T S

Thus the interval of any of the minor 3rds, EG, A C, or B D contains the magnitudes T and g, whilst the interval D F contains only t and S, and is therefore less than a minor 3rd by the dtffereuco between T and t.

The equality between the magnitudes of the first three intervals, and the last three intervals of the scale, and the fact of the semitono occurring in tho samo situation, in each portion, has given rise to tho notion that the major diatonic scalo is in reality a compound sca'e, consisting of two scales of four sounds each, thus:—

CDEF GACB
T t S t T S

and it is thus tought in several theoretical works, but it is evident, on looking at the order of the intervals, that such notion is incorrect, the second portion, G A B C of the scalo of C, could never bocomo the first

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