TABLE OF OCTAVES AND OF QUINTS. 



The length of a wire which would yield the same sound as the lowest C, (or fourth bass C,) 

 in the first and second instruments, is represented, in this Table, by the number 960. 



<2 3 



-8* 



-2~ 4, 



S3 



Ascending PERFECT OCTAVES 



IN THE FIRST INSTRUMENT. 



(Read them from the bottom upwards.) 



7th octave, or 3d treble C. 



6th octave, or 2d treble C. 



5th octave, or 1st treble C. 



4th octave, or middle C. 



3d octave, or 1st bass C. 



2d octave, or 2d bass C. 



1st octave, or 3d bass C. 



Lowest C, or 4th bass C. 



Ascending PERFECT QUINTS 



IN THE SECOND INSTRUMENT. 



(Read them from the bottom upwards.) 



12th quint, or 3d treble C. 



11th quint, or 2d treble F. 



10th quint, or 1st treble B flat. 



9th quint, or 1st treble E flat. 



Sth quint, or middle A flat. 



7th quint, or middle D flat. 



6th quiut, or 1st bass G flat. 



5th quint, or 2d bass B. 



4th quint, or 2d bass E. 



3d quint, or 3d bass A. 



2d quint, or 3d bass D. 



1st quint, or 4th bass G. 



Lowest C, or 4th bass G. 



Descending PERFECT OCTAVES 



IN THE THIRD INSTRUMENT, 



derived from the twelfth quint in the second 

 *■ instrument. 

 (Read them downwards.) 



Upper C, or 3d treble C. 

 1st octave, or 2d treble C. 

 2d octave, or 1st treble C. 

 3d octave, or middle C. 

 4th octave, or 1st bass C. 

 5th octave, or 2d bass C. 

 6th octave, or 3d bass C. 

 7th octave, or 4th bass C. 



The difference of pitch, between the C 

 derived from the quints and the corre- 

 sponding C derived from the octaves, is 

 THE QUINT WOLF. 



The length of the wire, for example, ^ 

 which would yield the sound of the first ? 

 bass C derived from the octaves, is 3 



The length of the wire, which would ^ 

 vield the sound of the corresponding first > 

 bass C derived from the quints, is 3 



Consequently, the difference between those ~f 

 two lengths shews the value of the corre- > 

 sponding QUINT WOLF. 3 



Quarters 

 of an 

 inch. 



7 



15 



30 



60 



120 



240 



480 



960 



7 



11 



16 



24 



37 



56 



84 



126 



189 



284 



426 



640 



960 



14 

 29 

 59 

 118 

 236 

 473 

 947 



120 

 118 



1 



Hundredths of one quarter of an inch, 

 and decimal parts of one hundredth 

 of one quarter of an inch. 



50, 



39, 



09, 

 64, 



97, 

 45, 

 18, 

 27, 

 41, 



6% 



44, 



66, 



905.276, 

 857.914, 

 786.871. 

 180.307. 

 770.461. 

 655.692. 

 983.539, 

 975.308. 

 962.962. 

 444.444. 

 666.666, 



,408.858.179.929, 

 ,613.287.269.894 

 919.930.904.841. 

 879.896.357.262. 

 819.844.535.893. 

 729.766.803.840. 

 094.650.205.761, 

 641.975.308.641, 

 , ad infinitum, 

 ad infinitum. 

 . ad infinitum. 



,662.935 + 

 ,494.402 + 

 741.604 + 

 612.406 + 

 918.609 + 

 877.914 + 

 ,316.872 + 

 , ad infin. 



39, 905. 

 79, 310. 

 59, 621. 

 19, 242. 

 38, 484. 

 76, 968, 

 53, 937 

 07, .875 



276.408.858, 

 552.817.716, 

 105.635.432, 

 211.270.865 

 422.541.730, 

 845.083.461 

 690.166.923 

 280.333.847 



179.929.662. 

 359.859.325. 

 719.718.651. 

 439.437.303, 

 878.874.606. 

 757.749.213. 

 515.498.427, 

 .030.996.855, 



935 + 

 870 4- 

 741 + 

 482 + 

 964 4- 

 929 + 

 859 4- 

 718 + 



38, 484.422.541.730.878.874.606.964 4- 

 6l , 515.577.458.269.121.125.393.035 + 



( 6 ) 



