Chladni, Ernst Florens Friedrich: Die Akustik. Leipzig, 1802.
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<TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <pb facs="#f0061" n="27"/> <table> <row> <cell/> <cell cols="2">Verhaͤltniſſe<lb/> der Schwingungen.</cell> <cell cols="2">Verhaͤltniſſe<lb/> der Saitenlaͤngen.</cell> </row><lb/> <row> <cell>1) der Einklang <hi rendition="#aq">c:c</hi></cell> <cell>1</cell> <cell>1,</cell> <cell>1</cell> <cell>1,</cell> </row><lb/> <row> <cell>2) der kleine halbe Ton <hi rendition="#aq">c:cis,</hi> wird bisweilen<lb/> auch die uͤbermaͤßige Prime genennt</cell> <cell> <formula notation="TeX">\frac{23}{24}</formula> </cell> <cell>1,0416⅔</cell> <cell> <formula notation="TeX">\frac{24}{25}</formula> </cell> <cell>0,96</cell> </row><lb/> <row> <cell>3) die kleine Secunde <hi rendition="#aq">c:des</hi></cell> <cell> <formula notation="TeX">\frac{16}{15}</formula> </cell> <cell>1,0666⅔</cell> <cell> <formula notation="TeX">\frac{15}{16}</formula> </cell> <cell>0,9375</cell> </row><lb/> <row> <cell>4) die große Secunde <hi rendition="#aq">c:d</hi></cell> <cell> <formula notation="TeX">\frac{10}{9}</formula> </cell> <cell>1,1111⅑</cell> <cell> <formula notation="TeX">\frac{9}{10}</formula> </cell> <cell>0,9</cell> </row><lb/> <row> <cell>oder</cell> <cell> <formula notation="TeX">\frac{9}{8}</formula> </cell> <cell>1,125</cell> <cell> <formula notation="TeX">\frac{8}{9}</formula> </cell> <cell>0,8888⅑</cell> </row><lb/> <row> <cell>5) die verminderte Terz <hi rendition="#aq">c:eſ♭</hi> wuͤrde viel-<lb/> mehr als <hi rendition="#aq">cis:es</hi> gebraucht werden</cell> <cell> <formula notation="TeX">\frac{144}{125}</formula> </cell> <cell>1,152</cell> <cell> <formula notation="TeX">\frac{125}{144}</formula> </cell> <cell>0,8680<formula notation="TeX">\frac{5}{9}</formula></cell> </row><lb/> <row> <cell>6) die uͤbermaͤßige Secunde <hi rendition="#aq">c:dis</hi></cell> <cell> <formula notation="TeX">\frac{125}{108}</formula> </cell> <cell>1,1574<formula notation="TeX">\frac{2}{27}</formula></cell> <cell> <formula notation="TeX">\frac{108}{125}</formula> </cell> <cell>0,864</cell> </row><lb/> <row> <cell>oder</cell> <cell> <formula notation="TeX">\frac{75}{64}</formula> </cell> <cell>1,1718¾</cell> <cell> <formula notation="TeX">\frac{64}{75}</formula> </cell> <cell>0,8533<formula notation="TeX">\frac{5}{3}</formula></cell> </row><lb/> <row> <cell>7) die kleine Terz <hi rendition="#aq">c:es</hi></cell> <cell> <formula notation="TeX">\frac{6}{5}</formula> </cell> <cell>1,2</cell> <cell>⅚</cell> <cell>0,8333<formula notation="TeX">\frac{5}{3}</formula></cell> </row><lb/> <row> <cell>8) die große Terz <hi rendition="#aq">c:e</hi></cell> <cell> <formula notation="TeX">\frac{5}{4}</formula> </cell> <cell>1,25</cell> <cell>⅘</cell> <cell>0,8</cell> </row><lb/> <row> <cell>9) die verminderte Quarte <hi rendition="#aq">c:fes</hi></cell> <cell> <formula notation="TeX">\frac{32}{25}</formula> </cell> <cell>1,28</cell> <cell> <formula notation="TeX">\frac{25}{32}</formula> </cell> <cell>0,7812½</cell> </row><lb/> <row> <cell>10) die vollkommene Quarte <hi rendition="#aq">c:f</hi></cell> <cell> <formula notation="TeX">\frac{4}{3}</formula> </cell> <cell>1,3333⅓</cell> <cell>¾</cell> <cell>0,75</cell> </row><lb/> <row> <cell>11) die uͤbermaͤßige Quarte <hi rendition="#aq">c:fis</hi></cell> <cell> <formula notation="TeX">\frac{25}{18}</formula> </cell> <cell>1,3888<formula notation="TeX">\frac{8}{9}</formula></cell> <cell> <formula notation="TeX">\frac{18}{25}</formula> </cell> <cell>0,72</cell> </row><lb/> <row> <cell>12) die verminderte Quinte <hi rendition="#aq">c:ges</hi></cell> <cell> <formula notation="TeX">\frac{36}{25}</formula> </cell> <cell>1,44</cell> <cell> <formula notation="TeX">\frac{25}{36}</formula> </cell> <cell>0,6944<formula notation="TeX">\frac{4}{9}</formula></cell> </row><lb/> <row> <cell>13) die vollkommene Quinte <hi rendition="#aq">c:g</hi></cell> <cell> <formula notation="TeX">\frac{3}{2}</formula> </cell> <cell>1,5</cell> <cell>⅔</cell> <cell>0,6666⅔</cell> </row><lb/> <row> <cell>14) die uͤbermaͤßige Quinte <hi rendition="#aq">c:gis</hi></cell> <cell> <formula notation="TeX">\frac{25}{16}</formula> </cell> <cell>1,5625</cell> <cell> <formula notation="TeX">\frac{16}{25}</formula> </cell> <cell>0,64</cell> </row><lb/> <row> <cell>15) die kleine Serte <hi rendition="#aq">c:as</hi></cell> <cell> <formula notation="TeX">\frac{8}{5}</formula> </cell> <cell>1,6</cell> <cell>⅝</cell> <cell>0,625</cell> </row><lb/> <row> <cell>16) die große Sexte <hi rendition="#aq">c:a</hi></cell> <cell> <formula notation="TeX">\frac{5}{3}</formula> </cell> <cell>1,6666⅔</cell> <cell>⅗</cell> <cell>0,6</cell> </row><lb/> <row> <cell>17) die verminderte Septime <hi rendition="#aq">c:bb</hi> wird<lb/> mehr als <hi rendition="#aq">cis:b</hi> gebraucht</cell> <cell> <formula notation="TeX">\frac{128}{75}</formula> </cell> <cell>1,7066⅔</cell> <cell> <formula notation="TeX">\frac{75}{128}</formula> </cell> <cell>0,5859⅜</cell> </row><lb/> <row> <cell>oder auch</cell> <cell> <formula notation="TeX">\frac{216}{125}</formula> </cell> <cell>1,728</cell> <cell> <formula notation="TeX">\frac{125}{216}</formula> </cell> <cell>0,5787<formula notation="TeX">\frac{1}{27}</formula></cell> </row><lb/> <row> <cell>18) die uͤbermaͤßige Sexte <hi rendition="#aq">c:ais</hi></cell> <cell> <formula notation="TeX">\frac{125}{72}</formula> </cell> <cell>1,7361⅑</cell> <cell> <formula notation="TeX">\frac{72}{125}</formula> </cell> <cell>0,576</cell> </row><lb/> <row> <cell>19) die kleine Septime <hi rendition="#aq">c:b</hi></cell> <cell> <formula notation="TeX">\frac{16}{9}</formula> </cell> <cell>1,7777<formula notation="TeX">\frac{7}{9}</formula></cell> <cell> <formula notation="TeX">\frac{9}{16}</formula> </cell> <cell>0,5625</cell> </row><lb/> <row> <cell>oder</cell> <cell> <formula notation="TeX">\frac{9}{5}</formula> </cell> <cell>1,8</cell> <cell> <formula notation="TeX">\frac{5}{9}</formula> </cell> <cell>0,5555<formula notation="TeX">\frac{5}{9}</formula></cell> </row><lb/> <row> <cell>20) die große Septime <hi rendition="#aq">c:h</hi></cell> <cell> <formula notation="TeX">\frac{15}{8}</formula> </cell> <cell>1,875</cell> <cell> <formula notation="TeX">\frac{8}{15}</formula> </cell> <cell>0,5333⅓</cell> </row><lb/> <row> <cell>21) die verminderte Ocrave <hi rendition="#aq">c:ces</hi></cell> <cell> <formula notation="TeX">\frac{48}{25}</formula> </cell> <cell>1,92</cell> <cell> <formula notation="TeX">\frac{25}{48}</formula> </cell> <cell>0,5208⅓</cell> </row><lb/> <row> <cell>22) die vollkommene Octave <hi rendition="#aq">c:c</hi></cell> <cell>2</cell> <cell>2,</cell> <cell>½</cell> <cell>0,5.</cell> </row><lb/> </table> </div> <fw place="bottom" type="sig">D 2</fw><lb/> </div> </div> </body> </text> </TEI> [27/0061]
Verhaͤltniſſe
der Schwingungen. Verhaͤltniſſe
der Saitenlaͤngen.
1) der Einklang c:c 1 1, 1 1,
2) der kleine halbe Ton c:cis, wird bisweilen
auch die uͤbermaͤßige Prime genennt [FORMEL] 1,0416⅔ [FORMEL] 0,96
3) die kleine Secunde c:des [FORMEL] 1,0666⅔ [FORMEL] 0,9375
4) die große Secunde c:d [FORMEL] 1,1111⅑ [FORMEL] 0,9
oder [FORMEL] 1,125 [FORMEL] 0,8888⅑
5) die verminderte Terz c:eſ♭ wuͤrde viel-
mehr als cis:es gebraucht werden [FORMEL] 1,152 [FORMEL] 0,8680[FORMEL]
6) die uͤbermaͤßige Secunde c:dis [FORMEL] 1,1574[FORMEL] [FORMEL] 0,864
oder [FORMEL] 1,1718¾ [FORMEL] 0,8533[FORMEL]
7) die kleine Terz c:es [FORMEL] 1,2 ⅚ 0,8333[FORMEL]
8) die große Terz c:e [FORMEL] 1,25 ⅘ 0,8
9) die verminderte Quarte c:fes [FORMEL] 1,28 [FORMEL] 0,7812½
10) die vollkommene Quarte c:f [FORMEL] 1,3333⅓ ¾ 0,75
11) die uͤbermaͤßige Quarte c:fis [FORMEL] 1,3888[FORMEL] [FORMEL] 0,72
12) die verminderte Quinte c:ges [FORMEL] 1,44 [FORMEL] 0,6944[FORMEL]
13) die vollkommene Quinte c:g [FORMEL] 1,5 ⅔ 0,6666⅔
14) die uͤbermaͤßige Quinte c:gis [FORMEL] 1,5625 [FORMEL] 0,64
15) die kleine Serte c:as [FORMEL] 1,6 ⅝ 0,625
16) die große Sexte c:a [FORMEL] 1,6666⅔ ⅗ 0,6
17) die verminderte Septime c:bb wird
mehr als cis:b gebraucht [FORMEL] 1,7066⅔ [FORMEL] 0,5859⅜
oder auch [FORMEL] 1,728 [FORMEL] 0,5787[FORMEL]
18) die uͤbermaͤßige Sexte c:ais [FORMEL] 1,7361⅑ [FORMEL] 0,576
19) die kleine Septime c:b [FORMEL] 1,7777[FORMEL] [FORMEL] 0,5625
oder [FORMEL] 1,8 [FORMEL] 0,5555[FORMEL]
20) die große Septime c:h [FORMEL] 1,875 [FORMEL] 0,5333⅓
21) die verminderte Ocrave c:ces [FORMEL] 1,92 [FORMEL] 0,5208⅓
22) die vollkommene Octave c:c 2 2, ½ 0,5.
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Zitationshilfe: | Chladni, Ernst Florens Friedrich: Die Akustik. Leipzig, 1802, S. 27. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/chladni_akustik_1802/61>, abgerufen am 15.08.2024. |