Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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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.</
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* Or a falſe Fifth.</
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<
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>SIMP. </
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<
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>I could wiſh this Diſcourſe were a little explained.</
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<
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>SALV. </
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>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. </
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<
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>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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<
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>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. </
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<
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>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. </
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<
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>There afterwards follow other Periods like to theſe, that </
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