Flipping Intervals


When an interval is “flipped”, it forms the “compliment of an interval”;  the number of the two intervals always adds up to nine.
For example, when a 5th is flipped, it becomes a 4th. When a 7th is flipped, it becomes a 2nd. And so on…
Note for those who are more advanced: The illustration only shows white keys, but sharps and flats do not change the number of the interval, and we are not yet concerned about the “quality” of the interval, expressed with these words: Perfect, Major, minor, augmented, diminished. It is my habit to capitalize “Perfect” and “Major”. These words may always be written lower-case.



All other intervals have at least two names, based on enharmonic spellings. But the “tritone” is unique. There is only one interval “between” the perfect 4th and the perfect 5th. No matter what harmonic spelling is used, the name for this interval remains the same: tritone.
Note to more advanced students: the tritone is also labeled according to spelling, so there are at least two common terms that are used to describe the way it is notated—augmented 4th and diminished 5th. However, both of these are tritones, so these extra terms are not needed to describe what we hear. In addition, we can only say that an augmented 4th and diminished 5th are exactly the same when referring to equal-temperament, which is the tuning system used for all modern pianos and the default tuning used for digital keyboards.

Mirror Intervals


The following is the explanation I use in lessons to teach the concept of “mirror intervals” to my students:
“At the piano, put both thumbs on middle C. Play D with the right hand, while holding the thumb down. Play B with the left hand, while holding the other thumb down. Both Cs will be pressed, but also D (right hand) and B (left hand). Compare the distance going up from C and down from C.
You are now playing 2nds.
Then, with thumbs still on middle C, now play E with the RH and A with the LH.
You are now playing 3rds.
Continue this pattern until you are playing octaves with both hands, thumbs still on middle C.”
Summing up:
  1. Compare the distance going up from C and down from C. Count the keys any way that makes sense, but be sure to always count the black keys.
  2. If the number of keys between the keys you are pressing is different (be sure to count the black keys), the interval is major or minor. Minor is always “smaller”. Major is always “bigger”.
  3. If the number of keys between the keys you are pressing is the same (be sure to count the black keys), the interval is perfect.
Conclusion: 2nds, 3rds, 6ths and 7ths may be either major or minor, while unisons, 4ths, 5ths and octaves (8ths) are always perfect.
Note: At this time I will not cover augmented or diminished intervals, which has to do with notation and not with sound. For the same reason, I am not yet addressing the subject of “tritones”. I will leave these advanced and difficult concepts for later.