A diminished interval is one half step smaller than a minor or a perfect interval. By lowering the upper tone of any minor or any perfect interval one half step, or by raising the lower tone of any minor or any perfect interval one half step (not altering the letter name in either case) a diminished interval is formed, thus:—
The tones of the diminished second are the same pitch, but must be called a second because two letters are comprised. The diminished prime is possible melodically, but harmonically, only in theory. It is
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An augmented interval is one half step larger than a major or a perfect interval. By raising the upper tone of any major or perfect interval one half step, or by lowering the lower tone of any major or perfect interval one half step (not altering the letter name in either case) an augmented interval is formed, thus:—
Notice that the tones of the augmented seventh are the same pitch, but must be called a seventh as seven letters are comprised.
The following intervals are the same in sound, but not in name:—
| perfect prime | sounds | the | same | as | diminished 2nd |
| augmented prime | " | " | " | " | minor 2nd |
| diminished prime | " | " | " | " | minor 2nd |
| major 2nd | " | " | " | " | diminished 3rd |
| minor 3rd | " | " | " | " | augmented 2nd |
| major 3rd | " | " | " | " | diminished 4th |
| perfect 4th | " | " | " | " | augmented 3rd |
| augmented 4th | " | " | " | " | diminished 5th |
| perfect 5th | " | " | " | " | diminished 6th |
| minor 6th | " | " | " | " | augmented 5th |
| major 6th | " | " | " | " | diminished 7th |
| minor 7th | " | " | " | " | augmented 6th |
| major 7th | " | " | " | " | diminished 8th |
| perfect octave | " | " | " | " | augmented 7th |