Alberti, Leone Battista, Architecture, 1755

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="003/01/273.jpg" pagenum="197"/>
              that the ſame Numbers, by means of which
                <lb/>
              the Agreement of Sounds affects our Ears with
                <lb/>
              Delight, are the very ſame which pleaſe our
                <lb/>
              Eyes and our Mind. </s>
              <s>We ſhall therefore bor­
                <lb/>
              row all our Rules for the finiſhing our Pro­
                <lb/>
              portions, from the Muſicians, who are the
                <lb/>
              greateſt Maſters of this Sort of Numbers, and
                <lb/>
              ſrom thoſe particular Things wherein Nature
                <lb/>
              ſhews herſelf moſt excellent and compleat:
                <lb/>
              Not that I ſhall look any further into theſe
                <lb/>
              Matters than is neceſſary for the Purpoſe of the
                <lb/>
              Architect. </s>
              <s>We ſhall not therefore pretend to
                <lb/>
              ſay any thing of Modulation, or the particular
                <lb/>
              Rules of any Inſtrument; but only ſpeak of
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              thoſe Points which are immediately to our Sub­
                <lb/>
              ject, which are theſe. </s>
              <s>We have already ob­
                <lb/>
              ſerved, that Harmony is an Agreement of ſeve­
                <lb/>
              ral Tones, delightful to the Ears. </s>
              <s>Of Tones,
                <lb/>
              ſome are deep, ſome more acute. </s>
              <s>The deeper
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              Tones proceed from a longer String; and the
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              more acute, from a ſhorter: And from the mu­
                <lb/>
              tual Connection of theſe Tones ariſes all the
                <lb/>
              Variety of Harmony. </s>
              <s>This Harmony the An­
                <lb/>
              cients gathered from interchangeable Concords
                <lb/>
              of the Tones, by means of certain determinate
                <lb/>
              Numbers; the Names of which Concords are
                <lb/>
              as follows:
                <emph type="italics"/>
              Diapente,
                <emph.end type="italics"/>
              or the Fifth, which is
                <lb/>
              alſo called
                <emph type="italics"/>
              Seſquialtera: Diateſſaron,
                <emph.end type="italics"/>
              or the
                <lb/>
              Fourth, called alſo,
                <emph type="italics"/>
              Seſquitertia: Diapaſon,
                <emph.end type="italics"/>
              or
                <lb/>
              the Eighth, alſo called the double Tone;
                <emph type="italics"/>
              Dia­
                <lb/>
              paſon Diapente,
                <emph.end type="italics"/>
              the twelfth or triple Tone, and
                <lb/>
                <emph type="italics"/>
              Diſdiapaſon,
                <emph.end type="italics"/>
              the fifteenth or
                <emph type="italics"/>
              Quadruple.
                <emph.end type="italics"/>
              </s>
              <s> To
                <lb/>
              theſe was added the Tonus, which was alſo
                <lb/>
              called the
                <emph type="italics"/>
              Seſquioctave.
                <emph.end type="italics"/>
              </s>
              <s> Theſe ſeveral Con­
                <lb/>
              cords, compared with the Strings themſelves,
                <lb/>
              bore the following Proportions. </s>
              <s>The
                <emph type="italics"/>
              Seſqui­
                <lb/>
              altera
                <emph.end type="italics"/>
              was ſo called, becauſe the String which
                <lb/>
              produced it bore the ſame Proportion to that
                <lb/>
              to which it is compared, as one and an half
                <lb/>
              does to one; which was the Meaning of the
                <lb/>
              Word
                <emph type="italics"/>
              Seſqui,
                <emph.end type="italics"/>
              among the Ancients. </s>
              <s>In the
                <emph type="italics"/>
              Seſ­
                <lb/>
              quialtera
                <emph.end type="italics"/>
              therefore the longer String muſt be
                <lb/>
              allowed three, and the ſhorter, two.
                <lb/>
                <arrow.to.target n="table2"/>
              </s>
            </p>
            <table>
              <table.target id="table2"/>
              <row>
                <cell>3 000</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                Seſquialtera.
                  <emph.end type="italics"/>
                </cell>
              </row>
              <row>
                <cell>2 00</cell>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s>THE
                <emph type="italics"/>
              Seſquitertia
                <emph.end type="italics"/>
              is where the longer String
                <lb/>
              contains the ſhorter one and one third more:
                <lb/>
              The longer therefore muſt be as four, and the
                <lb/>
              ſhorter as three.
                <lb/>
                <arrow.to.target n="table3"/>
              </s>
            </p>
            <table>
              <table.target id="table3"/>
              <row>
                <cell>4 0000</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                Seſquitertia
                  <emph.end type="italics"/>
                </cell>
              </row>
              <row>
                <cell>3 000</cell>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s>BUT in that Concord which was called
                <emph type="italics"/>
              Dia­
                <lb/>
              paſon,
                <emph.end type="italics"/>
              the Numbers anſwer to one another in
                <lb/>
              a double Proportion, as two to one, or the
                <lb/>
              Whole to the Halſ: And in the
                <emph type="italics"/>
              Triple,
                <emph.end type="italics"/>
              they
                <lb/>
              anſwer as three to one, or as the Whole to one
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              third of itſelf.
                <lb/>
                <arrow.to.target n="table4"/>
              </s>
            </p>
            <table>
              <table.target id="table4"/>
              <row>
                <cell>2 00</cell>
                <cell/>
                <cell>300</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                Diapaſon,
                  <emph.end type="italics"/>
                or double</cell>
                <cell/>
                <cell>
                  <emph type="italics"/>
                Triple
                  <emph.end type="italics"/>
                </cell>
              </row>
              <row>
                <cell>1 0</cell>
                <cell/>
                <cell>1 0</cell>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s>IN the
                <emph type="italics"/>
              Quadruple
                <emph.end type="italics"/>
              the Proportions are as
                <lb/>
              four to one, or as the Whole to its fourth Part.
                <lb/>
                <arrow.to.target n="table5"/>
              </s>
            </p>
            <table>
              <table.target id="table5"/>
              <row>
                <cell>4 0000</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                Quadruple
                  <emph.end type="italics"/>
                </cell>
              </row>
              <row>
                <cell>1 0</cell>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s>LASTLY, all theſe muſical Numbers are as
                <lb/>
              follows: One, two, three, four, and the Tone
                <lb/>
              before-mentioned, wherein the long String
                <lb/>
              compared to the ſhorter, exceeds it one eighth
                <lb/>
              Part of that ſhorter String.
                <lb/>
                <arrow.to.target n="table6"/>
              </s>
            </p>
            <table>
              <table.target id="table6"/>
              <row>
                <cell>1. 2. 3. 4.</cell>
                <cell>8 00000000</cell>
                <cell/>
              </row>
              <row>
                <cell/>
                <cell/>
                <cell>
                  <emph type="italics"/>
                Tone
                  <emph.end type="italics"/>
                </cell>
              </row>
              <row>
                <cell>Muſical Numbers</cell>
                <cell>9 00000000,0</cell>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s>OF all theſe Numbers the Architects made
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              very convenient Uſe, taking them ſometimes
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              two by two, as in planning out their Squares
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              and open Areas, wherein only two Proporti­
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              ons were to be conſidered, namely, Length
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              and Breadth; and ſometimes taking them three
                <lb/>
              by three, as in publick Halls, Council-cham­
                <lb/>
              bers, and the like; wherein as the Length was
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              to bear a Proportion to the Breadth, ſo they
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              made the Height in a certain harmonious Pro­
                <lb/>
              portion to them both.</s>
            </p>
            <p type="head">
              <s>CHAP. VI.</s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              Of the Proportions of Numbers in the Meaſuring of Areas, and the Rules for
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              ſome other Proportions drawn neither from natural Bodies, nor from Harmony.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Of theſe Proportions we are now to treat
                <lb/>
              more particularly, and firſt we ſhall ſay
                <lb/>
              ſomething of thoſe Areas where only two are
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              uſed. </s>
              <s>Of Areas, ſome are ſhort, ſome long,
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              and ſome between both. </s>
              <s>The ſhorteſt of all
                <lb/>
              is the perfect Square, every Side whereof is of </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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