HAR 



HAR 



befs in harmonlcal proportion be either 

 multiplied or divided by some number, 

 the products, or the quotients, will still 

 be in harmonica! proportion. Thus, the 

 harmonicals 6^ 8, 12, multipled by 2, give 

 12, 16, 24, or divided by 2, give 3, 4, 6, 

 which are also harmonicals. 3. To find a 

 harmonical mean proportional between 

 two terms : divide double their product 

 by their sum. 4. To find a third term in 

 harmonical proportion to two given terms: 

 divide their product by the difference be- 

 tween double the first term and the se- 

 cond term. 5. To find a fourth term in 

 harmonical proportion to three terms giv- 

 en : divide the product of the first and 

 third by the difference between double 

 the first and the second term. Hence, of 

 the two terms a and b the harmonical 



mean is ^ ; the third harmonical pro- 

 portion is - ; also to a, b. c, the 



Z a o 



fourth harmonical i 



6. If there 



2 a b 



be taken an arithmetical mean and a har- 

 monical mean between any two terms, 

 the four terms will be in geometrical pro- 

 portion. Thus, between 2 and 6 the 

 arithmetical mean is 4, and the harmoni- 

 cal mean is 3 ; and hence 2 : 3 :: 4 : 6. Also, 

 between a and b the arithmetical mean 



a-\-b 

 is -~2~ and the harmonical mean is 



2 a b 2ab ab . 



HARMONICAX series, a series of many 

 numbers in continual harmonical propor- 

 tion. Thus, if there are four or more 

 numbers, of which every three immedi- 

 ate terms are harmonical, the whole will 

 make an harmonical series : such is 30 : 

 20 : 15 : 12 10. Or, if every four terms 

 immediately next each other are harmo- 

 nical, it is also a continual harmonical se- 

 ries, but of another species, as 3, 4, 6, 9, 

 18, 36, &c. 



HARMONICAL sounds, an appellation giv- 

 en to such sounds as always make a de- 

 terminate number of vibrations in the 

 time that one of the fundamentals, to 

 which they are referred, makes one vi- 

 bration. 



, Harmonical sounds are produced by 

 .the parts of chords, &c. which vibrate a 

 certain number of times, while the whole 

 chord vibrates once. 



The relations of sounds had only been 

 considered in the series of numbers, 1 : 

 2, 2 : 3, 3 : 4, 4 : 5, &c. which produced 

 th.e intervals called octave, fifth, fourth, 



third, 8cc. M. Sauveur first considered 

 them in the natural series, 1, 2, 3, 4, 5, 

 &c. and examined the relations of sounds 

 arising therefrom. The result is, that the 

 first interval, 1 : 2, is an octave ; the se- 

 cond, 1 : 3, a twelfth ; the third, 1 : 4, a 

 fifteenth or double octave ; the fourth, 

 1 : 5, a seventeenth ; the fifth, 1 : 6, a 

 nineteenth, &c. 



The new consideration of the relations 

 of sounds is more natural than the old 

 one: and is, in effect, all the music that 

 nature makes without the assistance of art. 



HARMONICS, that part of music which 

 considered the differences and propor- 

 tions of sounds, with respect to acute and 

 grave, in contradistinction to rhyme and 

 metre. 



HARMONY, in music, the agreeable re- 

 sult, or union, of several musical sounds, 

 heard at one and the same time ; or the 

 mixture of divers sounds, which toge- 

 ther have an effect agreeable to the ear. 

 As a continued succession of musical 

 sounds produces melody, so does a con- 

 tinued combination of these produce har- 

 mony. See Music. 



HARMONT of the spheres, or Celestial 

 Harmony, a sort of music much talked of 

 by many of the ancient philosophers and 

 fathers, supposed to be produced by the 

 sweetly-tuned motions of the stars and 

 planets. This harmony they attributed 

 to the various proportionate impressions 

 of the heavenly globes upon one another, 

 acting at proper intervals. It is impossi- 

 ble, according to them, that such prodi- 

 gious large bodies, moving with so much 

 rapidity, should be silent; on the con- 

 trary, the atmosphere, continually im- 

 pelled by them, must yield a set of 

 sounds proportionate to the impression it 

 receives ; consequently, as they do not 

 all run the same circuit, nor with one 

 and the same velocity, the different tones 

 arising from -the diversity of motions, di- 

 rected by the hand of the Almighty, 

 must form an admirable symphony, or 

 concert. They therefore supposed, that 

 the moon, as being the lowest of the pla- 

 nets, corresponded to mi/ Mercury tofaj 

 Venus to sol f the sun to la; Mars, to 

 si ; Jupiter, to ut ; Saturn to re ; and the 

 orb of the fixed stars, as being the high- 

 est of all, to mi, or the octave. 



HARP, a musical instrument of th 

 string kind, of a triangular figure, held 

 upright between the legs of the person 

 who plays upon it. See MUSICAL INSTRU- 

 MENTS. 



HARP, EoUan. See ACOUSTICS. 



HARPINGS, in a ship, properly dev 



