Page:Cyclopaedia, Chambers - Supplement, Volume 1.djvu/794

 'GEN

Gentiana nigra< ) a name given by fome botanical au- thors to the mountain daunts or black libanotis. Rump. Flor. Gen, 22t. See Daucus. GENTIANELLA, Little Gentian, a diminutive of the name gentiana, commonly applied to the (mailer (pedes of gentian. See Gentiana. GKNTILITIA /iOT, among the Romans. See Sacra. GENTIL1TIUS, an epithet ufed by fome authors, to exprefs difeafes propagated from father to (on, and running through whole families, fuch as are more ufually called hereditary diforders. Such is the gout very frequently, and often many others. See Disease. GENTLE Pit Ore, in mineralogy, a name given by our miners in Suffex to a kind of iron ore found in confiderable plenty in that county, and very readily running in the fire, though not over rich in metal. It is a ftrong fubftance, and lies in feveral parts of that county in form of a moderately thick ftratum. It is of a dufky brown colour, and in fome places much paler than in others. It has always a great number of glittering fpanoles in it, and very often contains foffile (hells, and other extraneous fubftances in it. JVoodw. Cat. Fof. Vol. I. p. 225. GENUS (Cycl.) — By the wor&genus, in natural hiftory, we un- derftand a certain analogy of a number of fpecies making them agree together in the number, figure, and fkuation of their parts in fuch a manner, that they are eafily diftinguifh- ed from the fpecies of any other genus, at lead: by fome one ar- ticle. This is the proper and determinate fenfe of the word genus. Some have extended it to the claffes under which thefe genera are formed, calling the clafs genus fummum, and this genus fubalternum.

A genus in ichthyology, for inftance, is a certain agreement be- tween feveral fpecies "founded on the fimilitude of their effen- tial external parts, generally regarding their fituat'1011, num- ber, figure, and proportion. On this foundation, if only one fifii fhould be found differing from all the known genera in fome effential point, the ichthyologift is not to force this into the ranks of fome former genus, but allow it one to itfelf, and it is extremely probable that fome other fifhes hereafter may be difcovered belonging to the fame genus with it, and no more than it reducible to any of the formerly eftablifhed ones. Artedi Ichthyolog. Genus, in the antient mufic, was a divifion of the diatejfa- ron, or fourth *, containing four founds, into three inter- vals b .— [■ Euclid. Introd. Harm. p. I. Ed. Meibom. b Phil. Tranf. N°. 481. p. 271. Gaudent. p. 5. Edit. Meibom.] The Greeks conftituted three fuch genera known by the names of enharmonic, chromatic, and diatonic. See En- harmonic, &c.

The enharmonic was not fubdivided, but the chromatic was divided into three fpecies, and the diatonic into two ; fo that the antients had fix fpecies, or different divifions of the fourth in ufe. The moderns know but four ', and one of thefe, the enharmonic, is fcarce ever met with. It does not appear that the antients themfelves could accurately define thefe feveral fpecies. Ariftoxenus left it to the ear and praaice, and did not pretend to affign any true propor- tions in numbers. However he has attempted to convey fome idea of thefe genera and fpecies, by fuppofing the fourth divided into thirty parts. That is (as Ptolemy underfrands him) he fuppofes'the difference of a chord and its fourth to be divided into 30 parts ; and then afligns a certain number of thefe parts to each interval, or divifion of the various fpecies. Hence the fourth d containing two tones and a half, the tones will each have twelve parts, and the femi-tone fix. — [' Philof. Tranf. N°. 481. p. 272. * Wallis Append, and Ptolem. Harm. p. 164.]

In the enharmonic, he makes the interval between the hy- pate and parypate, as alfo, between the parypate and the lichanus, to be a die/is quadrantalis, or -rt- ; and from the lichanus to the nete he makes a ditonus or fj. So that the enharmonic divifions will be 3 + 3 + 24 = 30. In the chromaticum molle *, he makes the interval between the hypate and parypate, as alfo from the parypate to the lichanus a triental diefis, or -i ; and from the lichanus to the nete ", that is, an undivided interval equal to a tone, a femitone, and a triental diefis. Hence the intervals of this fpecies will be reprcfented by the numbers, 4 + 4 -f 22 = 20 f . [" /*«*'""'■ ' Wallis Ibid.]

GEN

Ll the chromaticum hemiolium *, or fefquialterum k, he makes the interval from the hypate to the parypate, and from thence to the lichanus, a diefis fefquialtera, that is -J of the enharmonic diefis, or 4 | parts of his divifion of the 'fourth. The remaining undivided interval is of 2 r parts ; being equal to a tone, a hemitone, and quadrantal diefis. This fpecies will be reprefented by the numbers, 4 ', -f 4 I -|- 21 = 30. '. or to avoid fractions, 9 ~f- 9 + 42 — 60. — [ £ «>ioA l0 » h Phil. Tranf. N'. 481. pag. 272. ^Wallis ibid. J In the chromaticum tonicum or toniasum k, he makes the in- terval between the hypate to the parypate, and from thence to the lichanus, a hemitone or, 6 ,, and from thence to the nete, a tone and an half or ,'?. Hence the fpecies will beex- prefied by the numbers, 6 + 6 -\- 18 = 30 l. — [ k ronaw. 1 Wallis ibid.]

In the diatonicum molle ra, he makes the interval between the hypate and parypate a hemitone or T 6 ;> from hence to the li- chanus ,~, and from this to the nete ' \ ; fo that this fpecies will be reprefented by the numbers 6 -- 9 -j- 15 = 30 \ — [i* pxXctxw. * Wallh ibid.]

In the diatonicum intenfum or fyntonum °, the interval be- tween the hypate and parypate, is according to him a hernia tone ; and between the parypate and lichanus, as alfo between the lichanus and nete, is a tone. Hence the expreffion of this fpecies will be 6 + 12 + 12 — 30 '.— [° wnw. p Wallis ibid.]

The fame divifions are in Euclid % and Ptolemy r gives the like proportions from Ariftoxenus, only doubling the numbers to avoid fractions.— [1 Introd. Harm, p. 10, 11. Edit. Mei- bom. r Harmon. Lib. 1. c. 12.]

Ariftoxenus does not pretend that the divifions he propofes are accurate. He feems to doubt of the diatefiaron being- two tones and an half; and of its being at all meafurable by any fmall interval, as the hemitone or diefis. He queftions whether the enharmonic diefis be precifely the fourth part of a tone ; or if the chromatic diefis be its third part. All which doubts are very well grounded. And ir feems as if this famous mufician had only propofed his divifions of the tetra- chord, as approximations to convey fome idea of the different fpecies to the imagination ; and not as an accurate ftandard to guide the voice, and hand, in finging and playing. Wallis Append, and Ptofan. Harm. pag. 169.

1 'his is the doctrine of the antients concerning their fix fpe- cies of fourths. How to reconcile this to modern notions, and with the true principles of mufic, might be a work of fome difficulty. Dr. Pepufch has given us his opinion as to what thefe fix fpecies ought accurately to be. How far his opinion is deducible from the remains of the antient mu- ficians, has not yet been publicly fhewn. We have men- tioned his doctrine under the heads Chromatic, Diato- nic and Enharmonic, and fhall here give them in one fhortview. Phil. Tranf. N° 481. pag. 266. feq.

Intervals of the

Enharmonic, iv = s -\- d -• ur.

Cromaticum molle, iv — s -f- $ -f- (3 -J- d.) Chromaticum fefquialtemm, iv = S-f- j-j- 3. Chromaticum toniaeum, iv r= S -j- S -]- (*r\- $■} Diatonicum molle, iv = S -f- 1 s -\- (T~\- d.) Diatonicum intenfum, iv = £ -f- / -j- T.

To understand which, obferve, that d ftands for the diefis enharmonica, s for the femi-tone minor, S for the femi-tone major, t for the tone minor, 7Tor the tone major, 3 for the third minor, ill for the third major, iv for the fourth; and when two intervals are placed within a parenthefis, it &>*- nifies a fingle interval equal to the two joined by the fign of addition +. Thus (3 -f- d) is an interval equal to the third minor and diefis enharmonica ; (T-~ s) is equivalent to the tone major & femitone minor, commonly called a fuper- fluous tone; and laftly (?~4- d) fignifies a tone major and diefis enharmonica, which interval, no more than (3 -J- d) has no particular name. Phil. Tranf. N° 481. pag. 272. Dr. Wallis has given us a fynopfis of the genera and fpe- cies according to Ariftoxenus, we fhall here infert it, as it gives light to the doctrine of the antient tetrachords. Wallis. Append, ad Ptolm, Harm, pag. 164.

Gencrum