The following table, comparing vibration numbers of the diatonic scale
with those of the tempered, shows the difference in the two scales,
existing between the thirds, fifths and other intervals.

Notice that the difference is but slight in the lowest octave used
which is shown on the left; but taking the scale four octaves higher,
shown on the right, the difference becomes more striking.

|DIATONIC.|TEMPERED.| |DIATONIC.|TEMPERED.|
C|32. |32. |C|512. |512. |
D|36. |35.92 |D|576. |574.70 |
E|40. |40.32 |E|640. |645.08 |
F|42.66 |42.71 |F|682.66 |683.44 |
G|48. |47.95 |G|768. |767.13 |
A|53.33 |53.82 |A|853.33 |861.08 |
B|60. |60.41 |B|960. |966.53 |
C|64. |64. |C|1024. |1024. |

Following this paragraph we give a reference table in which the
numbers are given for four consecutive octaves, calculated for the
system of equal temperament. Each column represents an octave. 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 |