is
. The same letters are in both intervals, but the first interval is a third and the inverted interval is a sixth.
Rule 8. The Sum of an Interval and Its Inversion is Nine.
The above rule, therefore, gives the following inversions:—
| a prime | inverts | to | an octave | (1 + 8 = 9) |
| a second | " | " | a seventh | (2 + 7 = 9) |
| a third | " | " | a sixth | (3 + 6 = 9) |
| a fourth | " | " | a fifth | (4 + 5 = 9) |
| a fifth | " | " | a fourth | (5 + 4 = 9) |
| a sixth | " | " | a third | (6 + 3 = 9) |
| a seventh | " | " | a second | (7 + 2 =9) |
| an octave | " | " | a prime | (8 + 1 = 9) |
To find to what intervals ninths, tenths, elevenths, twelfths, etc., invert, consider them respectively as seconds, thirds, fourths, fifths, etc., and consider the lower note placed two octaves higher instead of one octave.
Qualifications invert in the following manner:—