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In chapter Interval quality, the table of intervals was given. Although the table looks exhaustive, it is possible to find intervals that are not listed in the table. There exist some intervals that occur rarely and are often not mentioned in music theory. They were not listed in the table of intervals for the purpose of simplicity but they will be briefly described here. As an example, we can examine the intervals in the next figure. They all span the same number of staff positions but each next one spans a less number of pitches than the previous one.
Figure: A perfect, diminished, doubly diminished and triply diminished fifth
The first interval B – F# is a perfect fifth. The second one B – F is a diminished fifth. We already know these two intervals. What about the third B – Fb and the fourth interval B# - Fb? Analogous to the diminished fifth, they are called the doubly diminished fifth and the triply diminished fifth.
The next figure shows a similar case with augmented intervals. In fact, the intervals in this figure are the inversions of the intervals from the previous figure.
Figure: A perfect, augmented, doubly augmented and triply augmented fourth
The first interval #F – B is a perfect fourth. The second one F – B is an augmented fourth. The third interval Fb – B is a doubly augmented fourth while the fourth Fb – B# is a triply augmented fourth.
By using double sharps or double flats, it is possible to generate even higher multiplicities of augmented and diminished intervals.
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