♦ KNO\VLEDGE 



DE GUSTIBUS— MUSICAL TEMPERAMENT. 



[18S3]— When tLe claesification wliich I put forward in letter 

 1742 is taken into account — namely of (I.) physical excitement, 

 (II.) intellectual satisfaction, and (III.) associations, ic— as three 

 elements in questions of taato, I think many quotations from critics 

 in painting might be made in justification. The early Florentine 

 and Roman schools will seem to have more of the spiritual, the 

 Venetian somewhat more of the sensual clement, and the Flemish 

 a great deal more of the sensual. But at present I have to offer 

 an illustration from another art, where, for want of observing the 

 above distinctions, a controversy remains open, in which mathe- 

 matically-exact philosophers appear arranged on the sensual side of 

 the question, as opponents to practical professors, who take the 

 intellectual side ; a curious position of things. 



My present subject is Musical Temperament ; which I propose to 

 take on the way — a roundabout way as it may seem — towards re- 

 suming the consideration of Symmetry. (I must still use the word 

 loosely for convenience, notwithstanding the objections of "Another 

 Old Draughtsman" — letter 1797 — which will deserve regard at 

 another time.) 



The subject may perhaps be new to some of your readers, and I 

 proceed to give an elementary statement. 



WwU J one 



Whdc Jone 



grea U r 



If the distances G X or A Y represent a second of time, and if 

 in that time a sounding body, associated with the line G X, make 

 800 audible vibrations, while at A Y are made 900, and at B Z 

 1,000 vibrations, the three effects are such as are known respec- 

 tively as the keynote of a musical scale, the so-called second, and 

 the so-called third of that scale.* 



In these cases, with low common measures, such as 8, 9, and 10, 

 the notes have readily-apprehended relative individualities ; and, 

 moreover, imaginary distances, as A G or B A, become readily con- 

 ceivable to the musical faculty, like distances extended between 

 the lines of an inscription or between stars in the sky. The 

 distances between the lines G X, AY, or A Y, B Z, are called in 

 musical language intervals of major seconds, or whole tones, by a 

 confusion of a word for a sound with one for an interval between 



The acoustic philosopher discriminates further, and distinguishes 

 the greater tone A G from the lesser tone B A. Perhaps he plumes 

 himself on superior accuracy, because the amount of the interval 

 is according to the ratio of numbers of vibrations, and 8 : 9 is 

 greater than 9 : 10. 



* The key of G has been chosen, because at the high pitch of 

 modern orchestras the note G above the treble stave would be very 

 close to 800 vibrations per second. If I had selected 80, 90, and 

 100 vibrations they would have constituted deep bass notes j 8, 9, 

 and 10 per second would not have been musical at all. 



The foregoing numbers illustrate " Just Intonation." Recourse 

 might be had to tuning A Y, so that it should consist of 895 vibrations 

 instead of 900. In that case as (barring fractions) 800 : 895 :: 

 865 : 1000 ; the two intervals G A, A B will be equal. This will 

 give an idea of what is termed Equal Temperament in opposition to 

 Just Intonation. 



In practice, however, something else must be done, for B Z 

 itself must be tempered ; and we must have B Z at 1008 vibrations, 

 snd A Y at 898 ; in which case 800 : 898: : 898 : 1008. With which 

 proportions musicians seem generally content in the present day, 

 in the case of keyed instruments. 



But sweetness of tone is associated with low, common measures 

 of the ratios of vibrations. The " 3rd " so called, of 800 and 1000 

 vibrations, in proportion 4 : 5, is especially sweet ; more so than 

 800 : 1008 ; whose lowest terms are as high as 50 : 03. 



How do these things concern the hearer ? The sweetness is of 

 sense, sensual. The individuality of 1008 vibrations in opposition 

 to 800, results in an interval, only by a trifle less intelligible to the 

 understanding than the very sweet interval. 



If the intellectual is to give way to the sensual, we want a 

 diatonic octave scale with these intervals, viz., keynote to 2nd, a 

 greater tone, with the ratio 8 : 9 vibrations ; 2nd to 3rd, a lesser 

 tone of 9 : 10 vibrations ; 3rd to 4th, a semitone of 15 : 16 vibra- 

 tions ; then a greater tone followed by a lesser, then a greater, and 

 then another semitone. These constitute a justly-intoned scale 

 (G g). But the system of music (not acoustics) implies liberty to 

 a composer to lead hearers, to draw intellectual analogies between 

 certain sets of notes called tetrachords.* A tetrachord consists of 

 two larger intervals (tones) followed by a smaller (semitone). 

 Upon the equal tem])erament system these analogies may bo 

 minutely true. Upon the system of just intonation they are loose 

 analogies. Thus, let the notes of one tetrachord justly intoned be 

 put on a level with another, dismounted from the upper part of the 

 same octave — G C on a level with D' g' — and let cross-lines be 

 drawn between the corresponding parts, G X D', A Y E', Ac. It 

 will then be seen that the line A Y E is crooked. The justly-intoned 

 tetrachords are not symmetrical. 



But if the tetrachords had been equally tempered, the line 

 AYE' would have been straight, and the "canonical" imitation 

 of a musical phrase in one group of notes G C by another group 

 D' g would have been a close one. Thus the intellectual under- 

 standing of music is served as well by equal as by just intonation, 

 however the unsophisticated outer sense of hearing in a few 

 persons of extraordinary delicate sensation may be offended by it. 



The third element, of association, may unite sometimes with 

 the intellectual branch, sometimes with the sensual. And if the 

 association be with the past sensations of childhood, or again be 

 a lingering relic of ancestral sensations, there seems less coarse- 

 ness than the word " sensual " generally implies. Time purifies it. 

 A. 0. D. 



IS THE GAME OF DRAUGHTS PLAYED OUT? 



[1884]— I was much amused by a sentence in letter 185G. " The 

 game of draughts is now played out." On referring to the Siicy- 

 clnp:un,i Brilaniur.i I find that the writer of the article 

 " Draughts " jn-actically says the same. He says that the game is 

 exhausted, and that the best reply to every possible move is known. 

 I wish to call your attention to a few facts which will show the 

 fal.?ity of this statement. There are in England and Scotland 

 about twenty newspapers which contain a Draught column. Week 

 by week these columns publish new play. There is also a weekly 

 magazine devoted entirely to draughts, and it contains weekly a 

 large amount of original play. Recently a pamphlet was pub- 

 lished containing sixteen pages of new and original play on an 

 hitherto unexplored opening. 



In April, 1884, an international match was played between 

 England and Scotland. Both countries were represented by the 

 finest players to be obtained. The result was — England, 7 won 

 games ; Scotland, 36 won games. Would this have been so if all 

 the best moves had been known ? Not one-hundredth part of the 

 possibilities of draughts are yet known. All the best players are 

 agreed that draughts is vet in its infancy. 



The writer of the article in the Ency. Br. cannot have had 

 any personal knowledge of the game. Ue is unknown to players 

 whose memory can carry tliem back twenty or thirty yeai-s. 



A. E. Hodgson. 



SMELL-CLOUDS. 



[1885]— We see the vapour of water travelling in well-defined 



masses, and sometimes are plunged into them. Heuce we do not 



dispute their consistency and locomotion. We do not see other 



