MUSIC, 323 
In thefe natural harmonies, the 17th, that is, the third 
to the double oftave, is always fharp; and hence it has 
been affirmed, that minor mode, in Which the third of 
the key is flat, is entirely the work of art, not of nature. 
In whatever mode the above experiments m.^y be made, 
it is to be observed, that the additional founds are always 
generated above the key-note. But, if two different founds 
be made at the fame time, a perfon Handing between 
them will hear a third, which is lower than either of the 
notes that have been founded. This curious difcovery 
•was made by iignor Tartini, of which the reader may ac¬ 
cept the following compendious account. If two founds 
be produced at the fame time properly tuned and with due 
force, from their conjunction a third found is generated, 
fo much more dillinftly to be perceived by delicate ears 
as the relation between the generat.ng founds is more 
fimple; yet from this rule we mult except the unifon 
and oftave. From the fifth is produced a found in unifon 
with its loweft generator; from the fourth, one -which 
is an oftave lower than liigheft of its generators 5 from 
the third major, one which is an oftave lower than 
its loweft ; and from the lixth minor (whole highefl 
note forms an oftave with the loweft in the third for¬ 
merly mentioned) will be produced a found lower by 
a double oftave than the highefl of the minor lixth ; 
from the third minor, one which is double the diftance 
of a greater third from its loweft; but from the fixth 
major (whofe highefl note makes an oftave to the loweft 
in the third minor) will be produced a found only lower 
by double the quantity of a greater third than the highefl; 
from the fecond major, a found lower by a double oftave 
than the loweft; from a fecond minor, a found lower by 
triple the quantity of a third major than the liigheft; from 
the interval of a diatonic or greater femitone, a found 
lower by a triple oftave than the highefl; from that of a 
minor or chromatic femitone, a found lower by the quan¬ 
tity of a fifth four times multiplied than the loweft, &c. &c. 
In order that thefe mufical phenomena may be tried by 
experiments proper to afcertain them, two hautboys 
tuned with fcrupulous exaftnefs mull be procured, whilft 
the muficians are placed at the diftance of fome paces one 
from the other, and the hearers in the middle. The violin 
will likewife give the fame chords, but they will be lets 
diftinftly perceived, and the experiment more fallacious, 
becaufe the vibrations of other firings may be fuppofed 
to enter into it. If the Englifh reader ffiould be curious 
to examine thefe experiments, and the deductions made 
from them in the theory of mufic, he will find them 
clearly explained and illuftrated in Stillingfleet’s Princi¬ 
ples and Power of Harmony, printed at London in the 
year 177a. 
We now proceed to the divijion of the monochord.— 
When the open firing of a large bow'-inflrument, fuch 
as the trumpet-marine, the double-bafs, or the violon¬ 
cello, is afted upon with the bow, its whole length, be¬ 
tween the two bridges, vibrates in one undivided motion, 
and produces its fundamental or graveft found, called its 
ratio 1. A firing, whofe ratio 1 is C on the fecond leger 
line below in the bal's, when thus divided into aliquot 
parts, according to arithmetical progreffion, produces the 
follow ing fucceffion of founds, whole ratios (or the length 
of firing they require) are expreffed under each letter, viz. 
C C G C E G (Bb) C D E (F) G (A) (Bb) B C, &c. 
1 2 % i i e \ i ? t'o u 12 1? iz tz iV 
The founds expreffed by the letters in parenthefes, viz. 
Bb, F, and A, are thofe whofe exaft natural ratios have 
not been preferved in our modern fcale. Perfectly cor- 
refponding with the fcale that arifes from the vibrations 
of a firing, is that arifingfrom the vibrations of the air in 
a long tube that is open at both ends, fuch as a trumpet 
or a French horn. 
The fcale of Nature divides itfelf as follows : Firft, into 
a fundamental note and its repetition in the oftave, or 
the ratios 1, 2, being the compafs in which all the other 
notes are contained; fecondly, into the harmonic divilion 
of the oftave, or ratios 2, 3, 4, which is important in the 
explanation of modern mufic ; thirdly, into all the har¬ 
monics collected in an oftave, or ratios 4, 5, 6, 7, 8, being 
the only effential notes in modern harmony ; fourthly, 
into the faid harmonics and their diatonic means, or ratios 
9, 10, 11, 12, 13, 14, 15, 16; and fifthly, into the former 
and their chromatic means, or ratios 17, 18, 19, 20, &c, 
to 32. 
Of the Ancient Greek Modes. 
It appears, in general, as if the organ of the human 
voice had been calculated to give '■wo full intervals, and 
then half a one, as C, D, E, F. Three full intervals, as 
F, G, A, B, may therefore be confidered as unnatural; 
although they are brought in artificially with great effeft, 
and conllitute the upper part of the modern diapafon. 
Some modern writers have pretended, upon their inter¬ 
pretation of ancient documents, that the Greek melodifls 
conflantly played in the minor key, admitting only one 
full interval and half a one, as D, E F. But this notion 
appears unfounded ; and, we think, not probable 
The original tetrachord of the ancients was compofed, 
as it appears to us, of two full intervals and half a one, 
or three full tones and a femitone; and, in the relative 
pofition of the femitone with the three full tones, or the 
half with the two full intervals, we are perfuaded that the 
differenceof theirfamous modes confifted. The fucceffion 
of notes at Ex. 1. Plate III. will be eafily underltood. 
Farther than thefe three different politions of the femi¬ 
tone with relpeft to the full tones, or lemi-interval with 
regard to the full intervals in a tetrachord, we cannot 
conceive any other combination in the generation of 
founds. Therefore, and in all probability, thefe three 
tetrachords conftituted the three principal modes of the 
ancients. Let us obferve, however, that we ought not to 
confider the major and minor modulations or keys, as we 
have them, to have been the only inodes upon which the 
Greeks have pitched the various fyflems of their melody. 
We know that the major third is in general bolder than the 
minor, and that the intonation of the one has much more 
majelty than the other : but both have often interchanged 
their miniltration, and we have fpecimensof very impref- 
five compolitions in both thefe modes, although their 
particular charafteriftics be fo dillinft, that the major has 
been often Ityled the male, and the minor the female, mo¬ 
dulation. 
As to the notes in the foregoing example, the reader 
has already found, that the firlt tetrachord, according to 
our opinion, anfwers to the Doric mode, and is equiva¬ 
lent to C, D, E, F; the fecond, which we call Phrygian, is 
compofed of D, E, F, G: the Doric being the major, 
and the Phrygian the minor. The next, the Lydian, has 
not been adopted or preferved in modern mufic; fince we 
have no lemi-interval, or femitone, for a key-note. It is 
here the minor third inverted, E, F, G, A; but it is ufed 
in the plain chant for the intonation of pfalms, the finging 
of anthems, hymns, &c. the piece ending generally with 
a femitone. 
Such was, and fuch long remained, the fimple bafis of 
ancient mufic; but, in lapfe of time, a new tetrachord 
was invented, and obtained the name of Ionian. It is 
almoll impoffible to guefs how the intervals were placed 
in this combination, unlefs we l'uppofe two full intervals 
and two lemitones, or two femi-intervals and a full one. 
But this is mere matter of conjefture : the only point 
which appears indifputable is, that every one of thefe 
four modes or modulations, with its acceffaries, had a 
charafter, the features of which were fo dillinft, that to 
a Greek ear the difference was as perceptible as that be¬ 
tween major and minor is with relpeft to our auditory 
faculty. Lucian makes Harmonides fay to his mailer of 
mufic Timotheus, that he learnt from him how to keep 
the various charafters of the various modes: the nearly 
divine breathing, ilium quaji divinum afjjatam, of the 
Phrygian, our minor; the Bacchic raptures of the Lydian, 
Bacchicum furorem ; the folemn gravity, honejlam gravi- 
tutem, 
