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An easy way to find an interval below a given note would be to invert it.

To invert, first subtract the # of the interval from the number 9.

For example: Find the inversion of a 6th. 9-6=3. Which will translate to a 3rd above the given note.

Quick tips=

Subtractions:

7th<=>2nd (visa versa)

6th<=>3rd

5th<=>4th

The Quality gets reversed too:

Major<=>minor (visa versa)

Perfect=Perfect

Diminished<=>Augmented

M=Major

m=minor

P=Perfect

D=diminished

A=Augmented

Example: Find the inversion of a M3.

9-3=6

A Major gets reversed to a minor.

So the inversion of a M3 would be a m6.

Example: Find a P4 below B.

Step 1) a P4 inverts to a P5. 9-4=5. A perfect doesn't get reversed.

Step 2) think of the P5 above the B (Which would be a F#. We know it's an "F#" because a P5 has 7 half steps in it.)

Step 3) Drop the F# down an octave (below the B). And there you have the complete interval. F# and B is the P4.

Your next question is how did I know how many half steps for each interval.

Take a look at this chart:

P1=0 (unison)

m2=1 half step

M2=2

A2=3

m3=3

M3=4

P4=5

A4=6

D5=6

P5=7

m6=8

M6=9

A6=10

m7=10

M7=11

P8=12

Quick Reminder:

2nd, 3rd, 6th, 7th intervals can be Augmented, Majored, minored, and Diminished.

But the PERFECT 4ths, 5ths, and 8ths, can't be considered minored or majored. They can only be Augmented, or Diminished.

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Q: How do I find a perfect or major interval below a given note?
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