TEMPERAMENT AND TUNING. 



TEMl'EHAMKNT A NH T! 



ItO 



no attention is era- paid by thoce who understand such matters to 

 scientific secrets; and that until a full account U publiahed, and 

 authenticated oopiai of the tandard are made secure and accessible, 

 the acienee of the standard-makers will rank no higher than that of 

 the tailun who cut " on unerring geometrioal principles." 



Mr. Woolhoiue, who made experiment* on this subject (' Essay on 

 Musical Intervals,' p. 64), finds the "common pitch-note A" to make 

 uble vibrations iii a second, from whence he infers that c 1 gives 

 509 such vibrations ; but whence he got this pitch-note he does not 

 state, nor whether he was aware of the existence of a so-called Philhar- 

 monic standard. As matters stand, we should recommend every one 

 not to be led into the belief of the existence of a standard without 

 some better account of it than yet exists, and also in the mean time to 

 do what he can to ttep date* tmttrt-pitek, so as at least to prevent its 

 rising higher than it now generally is. 



There is another matter connected with the tuning-forks which 

 requires some attention. These forks (in England, not on the Conti- 

 nent) are differently manufactured : there are c forks and A forks 

 that is, forks which sound c 1 and A. In the orchestra, which must 

 follow the violins, the A fork U always used ; while in tuning a piano- 

 forte, harp, Ac., the c fork is used. It is much to be wished that only 

 one, the A fork, should be used. Even if the scale were perfect, it 

 would still be desirable not to run the risk of error arising from the 

 use of different forks ; add to which, that, without extreme care, 

 such care as never, is taken, it is impossible to avoid making the 

 temperament depend somewhat upon the note which is first tuned, 

 and which must be that sounded by the fork. We do not certainly 

 much believe in the temperament of an orchestra ; the characters of 

 the instruments are various, and the disposition of most of the wind 

 instruments to be a little out of tune, each in one or more particular 

 parta of the scale, gives them each something so like a temperament 

 (or dis temperament, if the reader please) of its own, that the united 

 body disobeys temperament to a degree which sets the slight differ- 

 ences between one system and another altogether aside. In the full 

 passages there is too much noise for the ear to be very nice on this 

 point, and in the solos the leading instrument marks its own tempera- 

 ment upon the whole orchestra. But when a few instrument* come 

 together, some of which are tuned from A and others from c, the dis- 

 advantage of different temperaments may be sensibly felt. But all 

 this must be said with much deference, for circumstances connected 

 with the scale or its adjustment may produce very different effects 

 on different ears. 



We leave the above as it stood in the ' Penny Cyclopaedia.' In 1859 

 the French ministry made the settlement of the musical pitch a govern- 

 ment business : the c 1 was settled at 522 vibrations per second, which, 

 so much had the pitch risen even in very recent time, was a consider- 

 able abatement Also in 1859, the Society of Arts took up the subject 

 in England, and a committee ascertained that c 1 had actually reached 

 546 vibrations per second. Looking at the love of singers and concerto- 

 pLtyers for brilliancy, which, we should explain to those unversed in 

 music, means t^uralcinea, there was much reason to fear that the rise 

 was not near its end. Since 1840 the pitch had risen a semitone. 

 For practical reasons, connected with the state of musical instruments 

 and the want of power to enforce, the society recommended that 528 

 should be the number of vibrations in c'. This proposal was generally 

 approved of, and tuning-forks (A and c, the interval being that of equal 

 temperament) were constructed accordingly. There is then some hope 

 that at least all further rise will be stopped ; and we cordially recom- 

 mend the proposal, not without a hope that in course of time a still 

 further fall may be found practicable. 



The leading note being settled, the tuner must learn to tune thai 

 note in perfect unison with his fork, and then to tune the octaves ol 

 that note both above and below. This seems to be the most plain and 

 straightforward part of the whole operation ; nevertheless, easily as 

 tuners take it, and readily as they refer to one of their octaves as being 

 as good an authority as the original note itself, we cannot help thinking 

 that more pains than is usually taken might be well bestowed. A note 

 and its octave, when the consonance is perfectly well tuned, should 

 sound like one note : now considering that in a grand piano there are six 

 strings to be tuned before an octave is ready, three unisons with the 

 lower note and three with the upper, it is not so very easy to present 

 that perfectly indivisible effect which a good artist ought to strive for. 

 There is a method (given in Jousse's work) of tuning the twelve semi 



ifths should be the same as seven octaves; and if we pass to the 

 octave below, as soon as we get out of the octave beginning with c, we 

 should have c, o, D, A, B, 4c., the last being c 1 . It will be found, how- 

 ever, that this is not true, but that the note obtained from 



its by fifths intermixed with six descents by octaves U sharper 

 c 1 . Again, if the perfect thirds be tuned from c, we should have 

 . ' ' ; but it will be found that c 1 obtained in thin way is too 

 fiat The octave derived from the fifths vibrates 223 times wl. 

 should vibrate 220 ; and that derived from the thirds vibrates 125 

 times where it should vibrate 128. The slight alterations which are 

 made in order that any one of the twelve notes of the octave may be 

 U to be used as a key-note, without any shock to the ear, constitute 

 the tcmptramrnt of a scale; the altered consonances are said to be 

 'emj>ertd. Some writers call the interval from the false octave obtained 

 i>y the fifths to the true one, by the name of the wo//; and using 

 the word in this sense, Lord Stanhope contends (and justly) for five 

 mint, one from the fifths, and one from each of the sets of thirds 

 beginning with c-, < :. i>, n- ; and three more might have been got i'i . m 

 the minor thirds. But by the term wolf other writers mean the bad 

 fifth which exists in the worst key, when the temperament is a ! 

 to favour some keys at the expense of others. Simple as this little 

 variation in the meaning of a term may be, it is worth while to t. 

 it A writer on tuning charges some of the pianoforte-makers of his 

 time with utter ignorance of the scale, in stipulating with the tuners 

 whom they employed that there should be no wolf. In all probability 

 they only meant that no key should be worse than another, or that the 

 temperament should be equal. This term wolf is said to be derived 

 from the jarring of a badly-tuned consonance, supposed to resemble the 

 distant howling of the animal : we rather suspect it was so called 

 because it was hunted from one part of the scale to another like a wild 

 beast, in hopes of getting rid of it 



Two systems of temperament suggest themselves : the first, 

 in which the necessary defects of the scale are distributed equally 

 throughout it ; the second, unequal, in which some mode is adopted 

 of distributing the imperfection so as to make some keys feel it leas 

 than others. The most common practice of our day is to endeavour at 

 equal temperament The two systems have their advocates, and the . 

 arguments for one and the other are as follows. In favour of equal 

 temperament it is urged that all the keys are made equally good, and 

 that in no one does the imperfection amount to a striking defect : also 

 that in the orchestra there is little chance of any uniform tempera- 

 ment among the various instruments, if it be not this one. Against 

 equal temperament it is urged that it takes away all distinctive 

 character from the different keys, and leaves no one single key perfect 

 All these arguments have force, both for and against : for ourselves, 

 we consider those against equal temperament much the stronger. We 

 have often felt that a pianoforte newly tuned has, with much correct- 

 ness, a certain insipidity, which wears off as the effect of the tuning 

 gradually disappears ; insomuch that the best phase of the instrument, 

 to our ears, is exhibited during the period which precedes its becoming 

 offensively * out of tune. At this time the progress towards the state 

 of being out of tune (for which there is no single word, mallunalion 

 would do very well) can only be called a change of the temperament ; 

 and the several keys begin to exhibit varieties of character which, until 

 maltonation arrives, render the instrument more and more agreeable. 

 But it must be remarked with respect to equal temperament, that it 

 cannot be obtained in the ordinary way of tuning. The only way, 

 unless beats be used, of obtaining a given temperament, equal or 

 unequal, with certainty, is to take a monochord, and having calculated 

 the proper lengths of the different strings, to form the successive notes 

 on the monochord, and to tune the several notes of the instrument in 

 unison with them. No tuner can get an equal temperament by trial : 

 so that the question lies between the having all sorts of approximations 

 to equal temperament, according to the propensities of different ears, 

 or as many sorts of approximations to some other systems. Had tin 

 English nation been as musical as it is mechanical, a portable mono- 

 chord, or system of monochords, would have been invented, on which 

 any given system of temperament could have been readily laid down 

 by rule, and thence transferred to the instrument. 



The mode of proceeding by approximation to equal temperament is 

 limply to tune the fifths a little too flat, aud the following order of 

 proceeding is the most usual, and has often been given. The first 

 letter represents the note already tuned, the second the one which is 



tones of one octave-interval first, without tuning the octave of any I to be tuned from it : a chord interposed in parentheses represents the 



' trial that should be made upon notes already in tune, in order to test 

 the success of the operation as far as it has gone. The first step is to 

 put c 1 ill tune by the tuning-fork : 



note, by proceeding upwards by fifths and downwards by fourths, 

 until the whole is completed, and this purposely to avoid depending 

 upon notes in the adjacent octave*. This mode, however, or any other, 

 must be matter of individual selection : it cannot be supposed that any 

 one method would be best suited to all ears. 



Those who are acquainted with the mathematical theory of the 

 scale know that all the concords cannot be made perfect : others may 

 learn it in the following way : Suppose twelve perfect fifths to be 

 tuned upwards from c, and give the results the names of the notes 

 which they would represent in the scale of twelve semitones, and in 

 the nomenclature of sharps, if the scale were perfect We should then 

 have 



c, (,, ii', A', K, B : , G-:, D 1 :, A:, E:, B:. ' 



C 1 ; C'C; CG; GO, j G,D; DA; AA, ; A,K; (CEC) ; lilt; (CKu, UGli) ; 

 BB, ;!,*:; (IIHU); WK.Sj r'.SCti (A,C3K i.<Hj ; C:'l'; 



(FAC')i FA,:; (AJtDF); A,;A: ; A: 1C; (IttUA: ; ICO,:; (<!.: 



We have written all the semitones as sharps, whether tuned from 

 above or from below. Of course, since the fifths are all to be a little. 



* A musical critic bat stated that we avowedly profcr an Instrument ml of 

 tu:ir. IIU mistake probably ariM* from bin confounding ryn.il temperament 

 with prrftit tune, average sin with perfect holinera : perhaps he did not know 



Now since B! is the same note M c', it appears that twelve perfect that any scale with twelve sounds cannot be in perfect tune in crery key. 



