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

Table of figures

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