BROADWOOD'S Temperament of the Musical Scale. For several years past, Mr James Broadwood, a piano forte maker in London, has been celebrated for the ex cellence of his instruments, as to perfection of work manship and tone ; and he has been supposed, also, to employ the best set of practical tuners, for attending to the tuning of the instruments of his customers at stated periods: in pursuance, therefore, of the notice we gave at the end of our article of our intention to present our readers with an account of all the most celebrated systems or methods of tuning keyed instru ments that are known, constituting the most curious and important part of the science of harmonics, we avail ourselves of a communication which Mr Broadwood lately made to the Monthly Magazine, (Vol. XXXII. p. 106 ; see also pages 238, 321, and 424,) to give what that gentleman calls his " practical method" of tuning, which we shall do in his own words ; inserting, in parentheses, the numbers of beats made in one second of time, by the several tempered fifths that are to be tuned, as they result from our calculation, which will be given at length below, along with some other matters, by way of explanation.
Mr Broadwoocl, after mentioning that most tuners begin their operations with the note C, says, " I prefer tuning from A, the second space in the treble cliff, as being less remote from the two finishing fifths, than any other point of departure : the A being tuned to the forte, (that for this particular temperament should make 403.0443 complete vibrations in one second of time,) tune A below an octave ; then E above that octave, a fifth (beating fat .9744 times in one second); then B above, a fifth (beating 1.4598) ; then B below, an octave; then F>g a fifth above (beating 1.0929) ; then its octave Fa( below ; then Ca: its filth above (beating .8183); then G* its fifth above (beating 1.2258) ; and then G>,k't its octave below.
We then take a fresh departure from A, tuning D its fifth below (heating fiat 1.3017) ; then G its fifth below (beating .8692) ; then G its octave above, then C its fifth below (beating 1.1618) ; then C its octave above, then F its fifth below (beating 1.5501) ; then 135 its fifth below (beating 1.0350) ; then BD its octave above, then Et) its fifth below (beating 1.3826). The five fifths tuned from notes below are to be tuned flatter than the perfect fifth, and the six fifths tuned from tones above must be made sharper than the perfect (i. e. the lower note is to be sharper than for a perfect fifth, thereby making the interval of the fifth flatter than the perfect as before), in a proportion I will endeavour to explain. If the whole he turned correctly, the with the 13)A (which is the same tone on the piano-forte as Eb) will be found to make the same concord, that is, possesses the same interval as the other fifths," but, we must observe, it is impossible that it should do this, since this bearing or resulting fifth will beat 1.3943 sharp, instead of .9175 fat, which it would beat if Et) were altered to the same interval as the other fifths (or rather if it were made Da(), or .9231 fiat, if Gaz were altered to such interval (or rather, made AO, but in either of these cases, it will be seen, that the former tuning would be undone and spilled ; but we must return to Mr Broadwood, who says, though not correctly, p. 107, "the old system of temperament (having a quint wolf, on douzeave instruments) is now deservedly aban doned, and the equal temperament generally adopted ;" —" suppose two strings B and C, in the middle octave of the piano-forte, to be, one a full semitone from the other," (we have here used the major semitone S, or–U, which is the interval B C in the natural or diatonic scale of all correct singers and violinists, and on the Rev. Henry Liston's patent organ, without any tem
perament in its harmony, now exhibiting at Flight and Robson's in London, being VW—VI" See the Philoso phical Magazine, Vol. X XXVI'. p. 273), " with your hammer," says Mr Broadwood, lower down, or flatten C by the smallest possible gradations, until it becomes unison with B ; with a tolerably steady hand, and a few trials, you will be enabled to enumerate lolly gradations of sound, which I call commas." Now, any one unac quainted with the subject, would think Irom this, that Mr Broadwood had discovered some hidden property of the full semitone, as he calls it, which disposed it to divide into just 40 smaller intervals, that the ear could appreciate so distinctly as to enable the tuner to make these commas all equal, than which nothing can be far ther from the fact. Although he continues, " alter hav ing, by a little practice, acquired a distinct and clear idea of the quantity meant to be represented by the term comma, nothing more will be required to make the proper fifth, (for the temperament as above), after hav ing tuned the fifth a perfect, or violin, or singing fifth, than to flatten the said perfect fifth, by lowering the string supposed to be tuning (the upper string), one of the afore-described commas ;" yet we may lurther add, without fear of being contradicted by the results of impartial trials, that without counting the beats which we have given above for that purpose, it is impossible for any tuner, however practised or expert he may be, to approach this system within tolerable limits: When we say within tolerable limits, we mean such as are essential to the discrimination of one system from another, and of exhibiting the peculiarities of each, which are sufficiently distinguishable, when the tuning is correctly done, by the beats, a monochord will not do it, as we shall she• in the article SONOMETER : Much less can the thing be effected by the ear, directing the " mere mechanical operation" of the tuning-hammer, (or winch used to tune the pegs on which the wires lap,) as Mr Broadwood maintains, in a subsequent num ber of the Monthly Magazine, above referred to : and where, with equal pertinacity, he insists, that an equal temperament is produced by these commas of his : It is true, as MrFarey has there observed, that Mr Broadwood has not expressly defined his "full semitone," to mean the major semitone ; but it is certain, that the car could not discriminate the semitone or interval (40I+33 m,) or its parts, of which one-fortieth (1.0006552Z) is the proper isotonic temperament, nor could it better ap preciate another interval, (48Z-I-4m, or or its parts, of which one-fortieth or 1.200786Z or answers to the system of 12 equally-tempered fifths, but one of them sharp, which just occurs to us, without hav ing been any where described,as far as we know, of which WC shall say more under EQUAL-TEMPERED FIFTHS ; and which it is not very probable that Mr Broadwood in tended, considering the degree of contempt with which he affects to treat the mathematical and only true or satisfactory method or treating this subject, which we are so anxious to see more generally understood by professors of music in general, and which would prevent them from being the dupes of every random or interested proposition respecting temperament, which is brought lorwards.