. The
first two columns cover the tones of the two octaves used in setting
the temperament by our system.

TABLE OF VIBRATIONS PER SECOND.

C |128. |256. |512. |1024. |
C[#] |135.61 |271.22 |542.44 |1084.89 |
D |143.68 |287.35 |574.70 |1149.40 |
D[#] |152.22 |304.44 |608.87 |1217.75 |
E |161.27 |322.54 |645.08 |1290.16 |
F |170.86 |341.72 |683.44 |1366.87 |
F[#] |181.02 |362.04 |724.08 |1448.15 |
G |191.78 |383.57 |767.13 |1534.27 |
G[#] |203.19 |406.37 |812.75 |1625.50 |
A |215.27 |430.54 |861.08 |1722.16 |
A[#] |228.07 |456.14 |912.28 |1824.56 |
B |241.63 |483.26 |966.53 |1933.06 |
C |256. |512. |1024. |2048. |

Much interesting and valuable exercise may be derived from the
investigation of this table by figuring out what certain intervals
would be if exact, and then comparing them with the figures shown in
this tempered scale. To do this, select two notes and ascertain what
interval the higher forms to the lower; then, by the fraction in the
table below corresponding to that interval, multiply the vibration
number of the lower note.

EXAMPLE.--Say we select the first C, 128, and the G in the
same column. We know this to be an interval of a perfect fifth.
Referring to the table below, we find that the vibration of the fifth
is 3/2 of, or 3/2 times, that of its fundamental; so we simply
multiply this fraction by the vibration number of C, which is 128, and
this gives 192 as the exact fifth. Now, on referring to the above
table of equal temperament, we find this G quoted a little less
(flatter), viz., 191.78. To find a fourth from any note, multiply its
number by 4/3, a major third, by 5/4, and so on as per table below.

TABLE SHOWING RELATIVE VIBRATION OF INTERVALS BY IMPROPER FRACTIONS.

The relation of the Octave to a Fundamental is expressed by 2/1
" " " Fifth to a " " 3/2
" " " Fourth to a " " 4/3
" " " Major Third to a " " 5/4
" " " Minor Third to a " " 6/5
" " " Major Second to a " " 9/8
" " " Major Sixth to a " " 5/3
" " " Minor Sixth to a " " 8/5
" " " Major Seventh to a " " 15/8
" "