MUSIC. 



new rules upon it on the wreck of their old ones 

 and again pronounced them final, and resisted 

 innovation, until they were again irresistibly swept 

 forward by another master-hand. Thus it happens 

 that the theory of music has generally remained 

 half a century behind its composition. 



The great principle underlying all theories of 

 harmony, so far as they embody themselves in 

 fixed rules for construction, should be, that what- 

 ever progression or chord sounds well, is right ; 

 whatever sounds ill, is wrong. Moreover, the 

 'well' and 'ill' are not absolute, but are to be 

 taken in connection with the poetic idea which 

 the composer wishes to express. A chord or a 

 phrase may not be beautiful ; it may be grotesque, 

 or it may be terrible ; but if the accompanying 

 emotion is intended to be the same, it must yet be 

 pronounced to sound 'well/ and to be perfectly 

 admissible rules or no rules. By modern writers 

 this is generally admitted ; the discussion we have 

 alluded to is not so much what should be allowed 

 and prohibited, as why it should be allowed and 

 prohibited. The one school of theorists maintains 

 that the cause lies in some connection, not always 

 very clearly defined, between the chords and the 

 natural series of partial tones we have already 

 explained ; the other school pronounces this to 

 be a mathematical fiction, without real basis in 

 musical experience. Intimately and necessarily 

 connected with this controversy is another, the 

 battle between perfect intonation and temperament, 

 and this we must endeavour to explain in as few 

 words as possible. We will use an illustration to 

 make our meaning clear. The note A on the 

 pianoforte is a major sixth, and the note G a fifth, 

 above the note C. We know, therefore, that each 

 one must vibrate at a certain fixed rate compared 

 with C, and therefore at a certain fixed rate com- 

 pared with each other ; and a simple calculation 

 shews us that this rate is V- This vibration 

 fraction determines the exact height of A above 

 G. But if we now take G as our tonic, and 

 start on a new scale, of which A is the second, 

 we find, from our list of vibration fractions, that 

 A should vibrate as fast as G, instead of 

 y. It follows, that to be able to play cor- 

 rectly both the major sixth in the scale of C 

 and the second in the scale of G, we should 

 require an instrument which could produce two 

 separate notes for A, instead of only one, as in the 

 piano. Many other similar duplications would also 

 be required in order to give correct intervals in all 

 the keys used in modern music, the total number 

 of notes necessary being stated by Mr Alexander J. 

 Ellis, F.R.S., who has investigated the subject most 

 minutely, to be 72 in the octave. An instrument 

 like the violin, which can (whether it does or not) 

 produce all these variations of sound, is said to 

 be capable of ' perfect intonation! Our ordinary 

 keyed instruments, such as the piano, have only 

 one-sixth as many intervals, and are therefore not 

 perfectly in tune. In order to make them as nearly 

 in tune as possible, the twelve intervals or semi- 

 tones into which the octave is divided are all made 

 precisely equal, and this is called the system of 

 * equal temperament! The believers in perfect inton- 

 ation do not assert that it can be practically applied 

 to keyed instruments, but simply maintain that the 

 ear can tell the difference between a true and a 

 tempered interval, and that it prefers the former 

 The upholders of temperament will not admit that 



the difference between A$ and Bb (for instance> 

 exists anywhere but on paper, and deny in toto that 

 it is ever made by performers. They main- 

 tain, in addition, that they alone speak for the 

 musicians, who, they say, write according to a 

 tempered scale ; and that the believers in perfect 

 intonation are mere theorists. Their arguments 

 are, however, more plausible than real, and expe- 

 rience leads us to believe that they are in error. A 

 good violinist or a good singer will naturally make 

 the true, untempered intervals, when not forced to 

 temper by the accompaniment of a keyed instru- 

 ment,* and the chords made by an unaccompanied 

 choir or string quartette of good performers will be 

 the true chords, and not the tempered ones. The 

 cause of this is, that the ear accepts the note or 

 chord in its true key relationship, and it is played 

 or sung accordingly. The performer neither 

 knows nor cares whether the note produced is Aft 

 or Bb, but he feels that it is a note which stands in 

 a certain key relationship to another in the one 

 case, perhaps the major seventh in the key of B ; 

 and in the other, the fourth in the key of F and 

 he produces the note which satisfies this relation- 

 ship to his ear. It will, therefore, be the true, 

 and not the tempered note If, however, there is 

 an accompaniment upon a pianoforte, he insen- 

 sibly modifies his voice to the tempered interval, 

 for the true intervals would cause a discord far 

 more intolerable than the mere tempering of the 

 note. Much of the confusion which unquestion- 

 ably has arisen on this subject is the consequence 

 of the ambiguity of an absolute notation, such as 

 that in common use. Perhaps the easiest way of 

 satisfying one's-self of the reality of the difference 

 between pure and tempered intervals is to go to 

 a concert at which a string quartette and a piano- 

 forte trio or quartette t are to be played. Even 

 if the one does not succeed the other immediately, 

 it is scarcely possible to help noticing the harder 

 and less satisfactory effect of the latter than of 

 the former. 



Chords. To return to the theories of harmony. 

 It does not appear to us that any satisfactory 

 or complete explanation of our comparative senst 

 of pleasure in different chords (or combinations 

 of notes) has yet been given. It is not even 

 possible to say whether it has a physical basis, 

 like our sense of the smoothness of certain 

 intervals, or is purely intellectual. It is certain, 

 however, that in penetrating to the real nature of 

 concord and discord, and of the quality of musical 

 sounds, physical science has done a very great 

 deal for musical art 



We shall only mention here a few technical points 

 in relation to harmony, without touching further 

 the theory which may be supposed to underlie them. 

 The combination of any note in a scale with the 

 third and the fifth above it in the same scale, is 

 called the chord, or common chord, of that note. The 

 whole effect and nature of such a chord depend 

 upon its relation to some particular scale or key, 

 and not upon its absolute pitch ; it therefore takes 

 the relative name of the note on which it is 

 founded. Thus (a), fig. 22, is the ' tonic chord 'of 

 the key of F, and (#) the ' dominant chord of the 

 same key. It is both shorter and better, however, 



Professor Hclmholtx determined, by careful experiment, that 

 Herr Joachim plays the true, and **t the tempered intervals upo 



t A trio or quartette for stringed instruments and a piano. 



