from Notes and Queries, A Medium of Inter-Communication for Literary Men, Artists, Antiquaries, Genealogists, etc.
("When found, make a note of."--CAPTAIN CUTTLE.)

Organ Tuning.--Wanting to know something of the present practice, I looked into the large and excellent work of the organ by Hopkins and Rimbault,[*] but found nothing to my purpose. Can any of your readers answer the following Queries? Are organs now tuned by beats? If so, what rules or tables are used? Is Dr. Smith's account of the beats approved, that is, do his formulae answer their purpose? Are the rules or tables deduced from these formulae? If not, who else has written on the subject? A. DE MORGAN.
(Sept. 6, 1856)

* Hopkins, E. J. and Dr. Rimbault. The Organ: Its History and Construction. Robert Cocks & Co. London, 1857

...--PROFESSOR DE MORGAN'S questions not having been answered, I have much the pleasure in informing him that the late Col. Peyronnet Thompson wrote most ably, though I forget where, on the mathematical theory of the musical scale ; and it is upon his theory that organs, pianos, &c., are tuned by "equal temperament," as it is called. If a keyed instrument be tuned by perfect fifths, beginning say on c, its octave c will be in excess of truth twenty-two or twenty four beats, which error, resulting from an imperfection of the scale if distributed among the intervening semitones, will give a scale for adoption throughout the instrument, which will make all diatonic scales alike as to distance between each note of the scale and the tonic, and as litl short of absolute truth as possible. If the worthy PROFESSOR will try his "prentice hand" at tuning, and will make all his fifths two beats short of truth, he will succeed in doing all for his instrument which can be attained. I will only add that, independently of my wish to oblige that gentleman, this information may be of some service to country readers who, like myself, live without the pale of ready professional assistance. R. W. DIXON
(Dec. 6, 1856)

...--With reference to MR. DIXON'S observations on the above subject, I am most happy in stating , that it is an error to speak of the late Col. Perronet Thompson, for that gentleman is still living and now holds the rank of Major- General.
General Perronet Thompson has written several works relative to tuning ; among others, are Instructions to my Daughter for playing on the Enharmonic Guitar, folio, Goulding, 1830. Also, articles on the same subject in the Westminster Review, under the following titles, "Enharmonic of the Ancients," "Harmonics of the Violin," "Enharmonic Organ," "Woolhouse's Essay on Musical Intervals," &c., &c. The above were published in the Westminster Review between the years 1832 and 1835 ; but the whole of Major-Gen. Thompson's articles in that periodical, with other works by him, were republished in 1842, in 6 vols. small 8vo., by Effingham Wilson, Royal Exchange.
An enharmonic organ that had been constructed under Major-Gen. Thompson's superintendence was exhibitied among the musical instruments at the Great Exhibition in Hyde Park in 1851. R. H.
Kensington
(Dec. 27, 1856)

...PROFESSOR DE MORGAN inquires, 1st. If organs are tuned by beats? 2nd. If so, what tables are used? 3rd. Is Dr. Smith's account of the beats approved? 4th. Are the tables in use deduced from these formulae of Dr. Smith? 5th. If not, who else has written on the subject?
The PROFESSOR writes that he has looked into the work by Hopkins and Rimbault, but found nothing to his purpose. MR. R. W. DIXON replies that organs are tuned by equal temperament, on account of the imperfection of the scale of nature (!), and informs the PROFESSOR he must tune "all his fifths two beats short of the truth." MR. DIXON claims General Thompson in support of his thoery, but the General is an advocate for the true, in place of any set of artificial mean sounds of the gamut.
In reply to the PROFESSOR'S Queries, I answer: 1. The beat, by which I presume the PROFESSOR means the wave resulting from two sounds heard together, but not vibrating in any true ratio, is of the same service in tuning now as it was centuries ago, being the act of nature marking the disagreement of two sounds heard simultaneously. 2. No tables are used in practice, organ tuners and pianoforte tuners trusting to their eears and experience. 3. I believe the notions of the former Master of Trinity to be untrue, and his ratios of the scale contrary to nature, and therefore place no reliance on his deductions. I have never heard of any one adopting his formulae. 4. There are no tables in use that I am aware of. 5. Mr. Emerson gives a mode of calculating the beat differing from Dr. Smith; and Mr. John Farey, after giving Smith and Emerson, adds three other methods of his own invention. H.J. GAUNTLETT.
(Jan. 10, 1857.)

...it would seem PROFESSOR DE MORGAN'S Query respecting organ tuning, has raised a division in the musical world, to allay which a Musical Doctor, Oxon, assures his readers an equal division of the twelve semitones "will not do;" for the organ, because "Dame Nature settled that at least three generations ago," meaning, no doubt, that this was the opinion of his grandmother. And on Friday last, at Exeter Hall, I was informed in "an Analysis of the Oratorio of Israel in Egypt," that Handel was a dunce and a barbarian. H.J.GAUNTLETT.
Powys Place, March 23, 1857.
(April 4, 1857)

...Mr. Dyce in his letter to H.R.H. Prince Albert respecting the National Gallery, asks the question, "Is there a science in music? and replying to his own query, boldly decides: there is not. There may be a science of music falsely so called, the mere invention of man, and there may be a reality existing in nature, that is to say, a science of music yet to be discovered, or which may have been partially revealed to some and wholly so to others, I perceive freom the pages of "N. & Q." that PROFESSOR DE MORGAN has interested himself about the temperament of musical sounds; and as I have reduced the system of music to one of pure science by rejecting every invention, and holding only to discoveries obtained from experiments in nature, I beg to offer a few Queries, which I shall be too glad should the learned Professor be pleased to make a note of.
1. Can any key-note or sound generate of itself the sounds of its scale?
2. An interval being the distance from any given sound to another, bu what law is an interval considered either harmonic or otherwise?
3. If there be no inherent power in an interval -- as interval-- to prove itself harmonic or not, or what use is the calculation of intervals in determining the character of harmonics?
4. How many keys are there in nature?
5. If there are to be twelve semitones in an octave what are the mean proportionals?
6. Given the key of C, what right has D natural to be in the scale? or D flat ? or D sharp?
7. Is not the ratio of vibrations -- that is to say, numbers and arithmetic, the sole foundation of musical science?
8. Can the laws of nature be in opposition to our feelings or reason> Or can the dictates of the ear and the facts of science ever be at variance?
9. Is the scale in music a fact in nature, or a conventionality or artifice?
10. Is there a principle of unity in music, and if so, what is it?
11. Is the unit or number 1 to be considered the root of any or all numbers?
12. What is the basis of the major common chord and of htre minor common chord?
13. Given the canonic circle of Euclid, compare his ratios with those in nature.
14. Given the key of C, prove the ratio from E to G, and from C to E flat, and thus demonstrate the fact of a real minor third in the scale.
15. Given C, a sound vibrating 512 times in a second, and also two pipes, one sounding 1000 times in a second, and the other 1001 in the same time, demonstrate the time of the beat, and describe the beat and these two sounds in ordinary musical notation. D.C.HEWITT [*]
Park Street, Grosvenor Square
(June 27, 1857)

* ...--MR GREEENWOOD is informed there is no work of any real value which treats of harmony and acoustics, except that of Mr. D. C. Hewitt published in 1828. The articles in the Penny Cyclopaedia are perhaps the best of its kind, to which let me add the new edition of the little book by General Thompson. But all these sorts of treatises proceed on the principle that we may lengthen or shorten a string where we please, or cut off here and there, and call the remnant an harmonic. In nature, no string generates other than prime harmonics, or its octaves, thirgs, fifths, and sevenths; and chromas of these sounds. It is the height of absurdity to talk of seconds, fourths, and sixths, as generated from any key tone. The key sound, its fourth and its fifth, generate the scale; and it requires these three sounds to make the major and minor scales. H.J.GAUNTLETT. (June 6, 1857)

Organ-tuning by Beats. --MR.DIXON, in recommending a mode of obtaining an artificial scale of equal proportions by tuning the fifth two beats short of the truth proposes that which appears to me impracticable. Because every high ratio which approaches closely to any simple ratio renerates the fundamental or beat (for the beat is merely the root) anwering to that simple ratio, as well as the fundamental or beat answering to that high ratio. Furthermore the beats in many cases would come in so slowly that he would require some kind of calculating machine to record their appearance. HENRY JOHN GAUNTLETT.
(Sept. 19, 1857)

DR. BURNEY AND HANDEL'S TRUMPET
Dr. Burney,[*] in his account of the 1784 Commemoration of Handel, when recording his impressions upon The Messiah performance remarks,

"The favorite bass song, The Trumpet shall sound, was very well performed by Signor Tasca and Mr. Sarjant. Some passages however in the trumpet part have always a bad effect from the natural imperfection of the instrument, The fourth and sixth of a key on trumpets and French horns are naturally so much out of tune that no player can make them perfect. These sounds should never be used but in short passing notes, to which no bass is given that can discover their false intonation. Mr. Sarjant's tone is extremely sweet and clear, but every time he was obliged to dwell upon G, the fourth of D (the key sound) displeasure appeared in every countenance, for which I was extremely concerned, knowing how inevitable such an effect must be from such a cause. In the Halleluha Chorus G, the fourth of the key, is sustained during two entire bars. In the Dettingen Te Deum, and in many other places, this false concord or interval perpetually deforms the fair face of harmony, and indeed the face of almost any one that hears it, with an expression of pain."

* "Dr. Burney, in his 'Sketch of the Life of Handel,'...1785, says, 'The organ in the chapel of this [i.e.the Foundling] hospital was a present from Handel' But how are we to reconcile this statement with the following, [European Magazine, Feb. 1799] 'Handel did not give the organ to the Foundling Hospital. It was built at the expense of the charity, under the direction of Dr. Smith, the learned Master of Trinity College, Cambridge, who added demitones, &c., and some niceties not occurring on other organs.'" Edward F. Rimbault, April 17, 1852

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