1ſiſteth the Velocity, than the thickneſſe doth; contrary to what
others at the firſt would think: for indeed, in appearance, its more
reaſonable, that the Velocity ſhould be retarded by the Reſiſtance
of the Medium againſt Opening in a Moveable thick and light,
than in one grave and ſlender: and yet in this caſe it happeneth
quite contrary. But purſuing our firſt Intent, I ſay, That the
ncereſt and immediate reaſons of the Forms of Muſical Intervals,
is neither the length of the Chord, nor the Tention, nor the
thickneſſe, but the proportion of the numbers of the Vibrations,
and Percuſſions of the Undulations of the Air that beat upon the
Drum of our Ear, which it ſelf alſo doth tremulate under the
ſame meaſures of Time. Having eſtabliſhed this Point, we may,
perhaps, aſſign a very apt reaſon, whence it commeth, that of
thoſe Sounds that are different in Tone, ſome Couples are re
ceived with great delight by our Sence, others with leſs, and
others occaſion in us a very great diſturbance; which is to ſeek a
reaſon of the Conſonances more or leſſe perfect, and of Diſlo
nances. The moleſtation and harſhneſſe of theſe proceeds, as I
believe, from the diſcordant Pulſations of two different Tones,
which diſproportionally ſtrike the Drum of our Ear: and the
Diſſonances ſhall be extreme harſh, in caſe the Times of the Vi
brations were incommenſurable. For one of which take that,
when of two Chords ſet to an Uniſon, one is ſounded, and ſuch
a part of another, as is the Side of the Square of its Diameter;
a Diſſonance like to the ^{*} Tritone, or Semi-diapente. Conſonan
ces, and with pleaſure received, ſhall thoſe Couples of Sounds
be, that ſhall ſtrike in ſome order upon the Drum; which order
requireth, firſt, that the Pulſations made in the ſame Time be
commenſurable in number, to the end, the Cartillage of the Drum,
may not ſtand in the perpetual Torment of a double inflection of
allowing and obeying the ever diſagreeing Percuſſions. Therefore
the firſt and moſt grateful Conſonance ſhall be the Eighth, being,
that for every ſtroke, that the Grave-ſtring or Chord giveth upon
the Drum, the Acute giveth, two; ſo that both beat together
in every ſecond Vibration of the Acute Chord; and ſo of the
whole number of ſtrokes, the one half accord to ſtrike together,
but the ſtrokes of the Chords that are Uniſons, alwayes joyn
both together, and therefore they are, as if they were of the
ſame Chord, nor make they a Conſonance. The Fifth delighteth
likewiſe, in regard, that for every two ſtroaks of the Grave
Chord, the Acute giveth three: from whence it followeth, that
numbering the Vibrations of the Acute Chord, the third part of
that number will agree to beat together; that is, two Solitary ones
interpoſe between every couple of Conſonances; and in the Di
ateſſeron there interpoſe three. In the ſecond, that is in the Seſ-
others at the firſt would think: for indeed, in appearance, its more
reaſonable, that the Velocity ſhould be retarded by the Reſiſtance
of the Medium againſt Opening in a Moveable thick and light,
than in one grave and ſlender: and yet in this caſe it happeneth
quite contrary. But purſuing our firſt Intent, I ſay, That the
ncereſt and immediate reaſons of the Forms of Muſical Intervals,
is neither the length of the Chord, nor the Tention, nor the
thickneſſe, but the proportion of the numbers of the Vibrations,
and Percuſſions of the Undulations of the Air that beat upon the
Drum of our Ear, which it ſelf alſo doth tremulate under the
ſame meaſures of Time. Having eſtabliſhed this Point, we may,
perhaps, aſſign a very apt reaſon, whence it commeth, that of
thoſe Sounds that are different in Tone, ſome Couples are re
ceived with great delight by our Sence, others with leſs, and
others occaſion in us a very great diſturbance; which is to ſeek a
reaſon of the Conſonances more or leſſe perfect, and of Diſlo
nances. The moleſtation and harſhneſſe of theſe proceeds, as I
believe, from the diſcordant Pulſations of two different Tones,
which diſproportionally ſtrike the Drum of our Ear: and the
Diſſonances ſhall be extreme harſh, in caſe the Times of the Vi
brations were incommenſurable. For one of which take that,
when of two Chords ſet to an Uniſon, one is ſounded, and ſuch
a part of another, as is the Side of the Square of its Diameter;
a Diſſonance like to the ^{*} Tritone, or Semi-diapente. Conſonan
ces, and with pleaſure received, ſhall thoſe Couples of Sounds
be, that ſhall ſtrike in ſome order upon the Drum; which order
requireth, firſt, that the Pulſations made in the ſame Time be
commenſurable in number, to the end, the Cartillage of the Drum,
may not ſtand in the perpetual Torment of a double inflection of
allowing and obeying the ever diſagreeing Percuſſions. Therefore
the firſt and moſt grateful Conſonance ſhall be the Eighth, being,
that for every ſtroke, that the Grave-ſtring or Chord giveth upon
the Drum, the Acute giveth, two; ſo that both beat together
in every ſecond Vibration of the Acute Chord; and ſo of the
whole number of ſtrokes, the one half accord to ſtrike together,
but the ſtrokes of the Chords that are Uniſons, alwayes joyn
both together, and therefore they are, as if they were of the
ſame Chord, nor make they a Conſonance. The Fifth delighteth
likewiſe, in regard, that for every two ſtroaks of the Grave
Chord, the Acute giveth three: from whence it followeth, that
numbering the Vibrations of the Acute Chord, the third part of
that number will agree to beat together; that is, two Solitary ones
interpoſe between every couple of Conſonances; and in the Di
ateſſeron there interpoſe three. In the ſecond, that is in the Seſ-
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