1quioctave Tone for every nine Pulſations, one onely ſtrikes in Con
ſort with the other of the Graver Chord; all the reſt are Diſcords,
and received upon the Drum with regret, and are judged Diſſo
nances by the Ear.
ſort with the other of the Graver Chord; all the reſt are Diſcords,
and received upon the Drum with regret, and are judged Diſſo
nances by the Ear.
SALV. Suppoſe this line A B the Space, and dilating of a Vi
bration of the Grave Chord; and the line C D that of the Acute
Chord, which with the other giveth the Eighth: and let A B be
divided in the midſt in E. It is manifeſt, that the Chords begin
ing to move at the terms A and C, by that time the Acute Vibra
tion ſhall be come to the term D, the other
64[Figure 64]
ſhall be diſtended onely to the half E, which
not being the bound or term of the Motion,
it ſtrikes not: but yet a ſtroak is made in D.
The Vibrations afterwards returning from D
to C, the other paſſeth from E to B, where
upon the two Percuſſions of B and C ſtrike
both together upon the Drum: and ſo con
tinuing to reiterate the like ſubſequent Vi
brations; one ſhall ſee, that the union of the
Percuſſions of the Vibrations C D with thoſe of A B, happen al
ternately every other time: but the Pullations of the terms A B
are alwayes accompanied with one of C D, and that alwayes the
ſame: which is manifeſt, for ſuppoſing that A and C ſtrike to
gether; in the time that A is paſſing to B, C goeth to D, and
returneth back to C: ſo that the ſtroaks at B and C are alſo
together. But now let the two Vibrations A B and C D be thoſe
that produce the Diapente, the times of which are in proportion
Seſquialter, and divide A B of the Grave Chord, in three equal
parts in E and O; And ſuppoſe the Vibrations to begin at the
ſame moment from the terms A and C: It is manifeſt, that at the
ſtroke that ſhall be made in D, the Vibration of A B ſhall have
got no farther than O, the Drum therefore receiveth the Pulſa
tion D onely: again in the return from D to C, the other Vibra
tion paſſeth from O to B, and returneth to O, making the Pul
ſation in B, which likewiſe is ſolitary, and in Counter-time, (an
accident to be conſidered:) for we having ſuppoſed the firſt
Pulſations to be made at the ſame moment in the terms A and C,
the ſecond, which was onely by the term D, was made as long after
as the time of the tranſition C D, that is A O, imports; but
that which followeth, made in B, is diſtant from the other one
ly ſo much as is the time O B, which is the half: afterwards con
tinuing the Recurſion from O to A, whilſt the other goeth from
C to D, the two Pulſations come to be made both at once in A
and D. There afterwards follow other Periods like to theſe, that
bration of the Grave Chord; and the line C D that of the Acute
Chord, which with the other giveth the Eighth: and let A B be
divided in the midſt in E. It is manifeſt, that the Chords begin
ing to move at the terms A and C, by that time the Acute Vibra
tion ſhall be come to the term D, the other
64[Figure 64]ſhall be diſtended onely to the half E, which
not being the bound or term of the Motion,
it ſtrikes not: but yet a ſtroak is made in D.
The Vibrations afterwards returning from D
to C, the other paſſeth from E to B, where
upon the two Percuſſions of B and C ſtrike
both together upon the Drum: and ſo con
tinuing to reiterate the like ſubſequent Vi
brations; one ſhall ſee, that the union of the
Percuſſions of the Vibrations C D with thoſe of A B, happen al
ternately every other time: but the Pullations of the terms A B
are alwayes accompanied with one of C D, and that alwayes the
ſame: which is manifeſt, for ſuppoſing that A and C ſtrike to
gether; in the time that A is paſſing to B, C goeth to D, and
returneth back to C: ſo that the ſtroaks at B and C are alſo
together. But now let the two Vibrations A B and C D be thoſe
that produce the Diapente, the times of which are in proportion
Seſquialter, and divide A B of the Grave Chord, in three equal
parts in E and O; And ſuppoſe the Vibrations to begin at the
ſame moment from the terms A and C: It is manifeſt, that at the
ſtroke that ſhall be made in D, the Vibration of A B ſhall have
got no farther than O, the Drum therefore receiveth the Pulſa
tion D onely: again in the return from D to C, the other Vibra
tion paſſeth from O to B, and returneth to O, making the Pul
ſation in B, which likewiſe is ſolitary, and in Counter-time, (an
accident to be conſidered:) for we having ſuppoſed the firſt
Pulſations to be made at the ſame moment in the terms A and C,
the ſecond, which was onely by the term D, was made as long after
as the time of the tranſition C D, that is A O, imports; but
that which followeth, made in B, is diſtant from the other one
ly ſo much as is the time O B, which is the half: afterwards con
tinuing the Recurſion from O to A, whilſt the other goeth from
C to D, the two Pulſations come to be made both at once in A
and D. There afterwards follow other Periods like to theſe, that