Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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