[Basic harmonics] Course 2 Interval #2 / How to find intervals easily

Intervals wider than the ninth degree 

Intervals wider than the ninth degree can be easily understood by inversions within an octave. 

How to calculate an interval easily 

Major, minor and perfect intervals that we have learned so far are determined by the number of half tones and whole tones within each interval. It would be better for you to memorize each interval with the accurate number of whole tones and half tones but if you are not familiar with them, you may have difficulty in identify which one is the major one or the minor one. First, you need to correctly understand the relationship between a whole tone and a half tone within the C major scale. 

As shown in the above figure, the C major scale has two half tones between E and F and between B and C and whole tones with the rest of the notes. 

If you see this on piano, 

all the intervals up from the lower C are either major or perfect ones in the C major scale. 

You can see that there is one half tone (E-F) from the second degree (D) to the seventh degree (A). 

You can also see that there are two half tones (E-F and B-C) up to an octave.

But on the other hand, all the intervals down from the higher C are either minor or perfect ones. 

You can see that sixth and seventh degrees have two half tones (E-F and B-C) while second, third, fourth and fifth degrees have one half tone (E-F) respectively. 

So you will find two half tones (E-F and B-C) up to an octave. 

Now keep this in your mind and let’s calculate the interval of the following: 

1. Find out the degree. 

You can see it is the sixth degree from D to B. 

2. Find out half tones. 

There is only one half tone in between. 

3. Draw the C major scale. 

If you figure out how many half tones are up to the sixth degree, you can see that there is only one half tone of E-F. Such calculation lets you understand that the above interval is the major sixth. 

Let’s try another one with an accidental mark. 

1. Find out the degree. 

Please focus on finding the degree without thinking of the flat to B. 

You can see it is the sixth degree from D to B. 

2. Find out half tones. 

There is only one half tone of E-F in between. 

Please do not care for the flat to B for now. 

3. Draw the C major scale. 

If you figure out how many half tones are up to the sixth degree, you can see that there is only one half tone of E-F. Until now, you can see it is the major sixth. 

4. Consider the accidental mark. 

The flat was attached to the higher B thus reducing the interval by a half tone. 

5. Refer to the interval table. 

As it got narrower by a half tone from the major sixth, it is the minor sixth. 

Intervals wider than an octave can be calculated by inversions within the octave based on the same method. 

We have learned about the intervals so far. 

As such intervals are the basis of the chords or harmonics that we will learn from now on, please try to understand them completely.