I N T
Tritonus, or falfe fourth — .
Semidiapente, or falfe fifth — i
Tritonus of the Greek Scale
Diminifhed fifth — — ■
Deficient fifth <
Fifth ■ i 1
Superfluous fifth ' — i
Sixth Minor _____ . —
Sixth Major ■■ _
Hexachord of the Greek Scale, or redun- dant fixth Major ■
Greater J diminifhed feventh — — . Greater J %> erlIu ° us Ex* ■
Greater } fcventh Mlnor
Seventh Major Diminfhed Octave Superfluous Seventh Oflave —
The Iimma, apotome, trihemitone, ditonus, femidiapente, and tritonus, mentioned in this Table, by the names of Iim- ma, apotome, SV. of the Greek fcale, are fuch as are either mentioned by the antients, or at leaft occur in their fcale, where fourths are divided into two tones and a limma, and where the oaavc confided of five tones and two limmas. The term redundant in the Table, is applied to fuch Inter- vals as exceed the truth by a comma; and fuch as fall fhort of the truth by a like quantity, are called deficient. Intervals that exceed true diatonic Intervals, by a femitone-minor, are laid to be fuperfluous ; and thofe which fall fhort by the fame quantity, are faid to be dimmjhed. Where an Interval exceeds a true diatonic Interval by the quantity of two femi-tones minor, we have called it an extreme fuperflueus Interval : And if it falls fhort by the fame quantity the aopellation of extreme diminijhed Interval is given it. Thus, if from A to D afcending be a true fourth, and from D to a a true fifth, then, if D be fuppofed raifed by a comma, from A to D will be a redundant fourth, and from D to a a deficient fifth. i rom A to D# will be a fuperfluous fourth, and from D+t to a will be a diminifhed fifth. In like manner, from A toT>, will be a diminifhed fourth ; and from I> to a, a fuperfluous fifth. From A to D## (D double (harp) will be an extreme fuperfluous fourth, and from A to Dt>b (D double flat) will be an extreme diminifhed fourth. In like manner, from Dftit to a will be an extreme diminifhed, and from D"> to a an extreme fuperfluous fifth. Such Intervals are not to be'met with in the praaice of mufic; but if the divifion of the oflave into ?i parts were once eflablifhed, as it ought for the perfection of mufic, fuch Intervals as thefe here men- tioned will neceflanly occur in the fcale. Vid. Phil Tranf N° 481. p. 273, 274. See the article Genus. This Table, among other ufes, will facilitate the examina- tion of any propofed fcale, or Interval. Suppofe, for infiance it were required to examine fome of Ptolemy's divifions of the fourth, as his Diatonicum molle, which he makes ! X V° X Is = t- Take the logarithm of * from the common tables, and divide it by the logarithm of ;.;, the quotient will be 10.75, which gives the meafure or number of com- mas, and its parts contained in an Interval expreffed by |. Look for the nearer! meafure of Intervals to I o. 75 in the table, it will be found to be jo.39058, which anfwers to the Interval of two femitones major, or of the diminifhed third as practitioners call it. But Ptolemy's exceeds this by . 0.36, or about ^ of a comma. The next Interval in Ptole- my s divifion is V°, which is a true tone-minor. The third is |j, which will be found to be 3.93 commas, that is 3 fc-
T N T
iv-j-i_v— s iv+s_v— ;
3T=V— S_IV + i'
6' VI
V-
S = 7 ..f
7° VII
VIII
V = IV + r
IV + T = III-i- 3.1,
V + r = 2.III
V + S= VIII — III
V + r_VIII_3»
VI = V + T=VIII- 6 b + S=2.IV— s=f- a'+S^y'-j
VI + s
vi+;=vin— 2 s vi + s = 2.iv=vra- vi-f-s-v-f^'^vni
VI-)-T = VIII_S
VII + d = VIII— t VII 4. j _• VIII — d VHI = V + IV
27.44423
28. 35340
28. 44423
2 9- 35340 31.63952
32. 63954
35-92564
37- 83481 41.12093 3 42- 12093 ■s 43.03010 44. 03010 44. 40705;
45-4°7°S -Tj46. 3162a
-'47-3!622 50. 60234
52-51151 53-88846
55- 79763
mi-tone minor and 0.64 of a comma, or a femi-tone minor redundant by near J of a comma. But this is much out of tune. In the common, and in Huygens's temperatures the femi-tone minor is mcreafed only by about i of a comma. Vid. Ptolcm. Harmon, p. 92. ap. Wallis Oper. Tom. 3.
Dhmni/hedlNTEKVAL, in mufic. See the article Diminished Interval.
Intervals, in hufbandry, a term ufed to exprefs the fpaces left between the feveral rows of plants fown or fet in a gar- den or field. The method of horfe-hoeing hufbandry7 fa fbrongly recommended by Mr. Tull, is objected to by many, on account of the largenefs of the Intervals which are to be . left between the rows of corn. Thefe are required to be about five foot wide ; and it is thought that fuch wide fpaces are fo much loft earth, and that the crop is to be fo much the lefs for it. But it is to be obferved, that the rows of com feparated by thefe Intervals need not be fmgle, they may be double, triple, or quadruple, at the pleafure of the farmer ; and four rows thus Handing as one will have the five foot Interval but one fourth of its bignefs as to the whole quantity, and it will be but as fifteen inch Intervals to plants in fmgle rows. Corn that is fown irregularly in the common way, feems indeed to cover the ground better than that in rows ; but this is a mere deceptic vifus, for the ftalks of corn are never fo thick as when they come out of one plant, or as when they ftand in a row, and a horfe-hoed plant of corn will have twenty or thirty ftalks in a piece of ground of the fame quantity, where an unhoed plant will have only two or three ftalks. If thefe ftalks of the hoed plant were feparated and planted over the Intervals the whole land would be better covered than it is in the common way ; and the truth is, that tho' thefe hoed fields feem to contain a much lefs crop than the common fown fields, yet they in reality do contain a much greater. It is only the different placing that makes the fown crop feem the larger,
and even this is only while both
crops are young, full's
Horfehoeing Hufbandry. The Intervals are not loft ground, as is ufually fuppofed, but when w-ell horfehoed they are all employed in the nourifh- ment of the crop, the roots of the plants in the adjoining rows fpreading themfelves thro' the whole Interval, and drawing fuch nourifhment from it, that they increafe accord- ingly. When the plants ftand in the fcattered way, as in com- mon fowing, they are too clofe to one another ; each robs its neighbours of part of their nourifhment, and confequently the earth is foon exhaufted, and all the plants half ftarved. The clofe Handing of them alfo prevents the benefit of after- tilling,
