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  • Candice Alderfer

Major and Minor Thirds

Updated: May 1, 2019

Okay, what the hell. I thought this was music, not algebra. Music is not algebra, but let’s just say that music and math are basically like Ryan Gosling and Rachel McAdams from the movie, The Notebook. For those that haven’t seen that movie, those two are madly in love and are basically soulmates. Math and music are just that. You don’t have to be a mathematician to understand music (although it sure would help me), but you do need to count steps and distinguish distances between notes. knowing how to distinguish intervals will also help you to understand why certain notes work together in harmonies, and why others clash together and may not sound too comforting to the ear. Intervals also make up chords, which basically are apart of almost all the music we hear.


Remember that equation to a major scale? That “whole, whole, half, whole, whole, whole, half”, thing? If you have taken my advice and gotten yourself comfortable with memorizing major scales, then congratulations, understanding intervals has just gotten a little easier to you.


What is an interval?

An interval is the difference in pitch between two sounds. In music, you distinguish intervals based on their type and quality. The interval type refers to the number of the interval.


Interval types


Unison = 1

Second = 2nd

Third = 3rd

Fourth = 4th

Fifth = 5th

Sixth= 6th

Seventh = 7th

Octave = 8th

Ninth = 9th

Tenth = 10th

Eleventh = 11th

Twelfth = 12th

Thirteenth = 13th

Interval Quality

The quality of an interval refers to whether it's a major (M), minor (m), perfect (P), augmented (A) or diminished (d) interval.


An important note to remember

You can never have a major or minor fourth, fifth or octave (eighth) interval. Those interval types can only be perfect, diminished or augmented.


For example: Let's use C natural. If we are looking to find the interval type between C and E, it will be 3.


It is also EXTREMELY important to note that the interval between C and E is completely different from E to C.


If we were considering the interval type from E to C, it would then be 6. You may also notice that I did not include any sharps or flats when writing out the E scale.. The accidentals don't affect the interval when it comes to figuring out it's type. Here's a quick example:




YES, this definitely looks like algebra now. Remember what I said earlier about math and music essentially embodying Ryan Gosling and Rachel McAdams? The presence of accidentals will have you solving algebraic equations in no time. These accidentals will determine the quality of an interval.


Here are some important basic rules to note when it comes to interval quality



This chart below lists all the notes that exist in chromatic order starting from C natural on the first position, P1. This displays all the interval relationships between C natural and all other existing notes.



If you'd like to do the same for any other, replace P1 with the note of choice and list all the following notes chromatically after in the corresponding positions. Here is another example using G natural.



1. Augmented intervals have one more half step than a perfect interval. To augment an interval, you raise the interval by adding a half step.


2. Diminished intervals have one less half step than a perfect interval. Minor intervals can become diminished by lowering a half step.



If you know all of your major scales by heart, figuring out intervals will be much easier for you. You'll automatically know that the interval between D to F is a minor third because in a D major scale, you will automatically know that F is sharp. F is a half step lower in this interval than F# in the D major scale, and if we refer to the important rules of intervals stated above, we know that a minor 3rd is 3 half steps, one less than a Major 3rd.

Another example is between C and G. That interval is a perfect fifth. But if we raise G a half step and make it G#, the interval becomes an augmented 5th. If we lower G a half step and make it Gb, the interval becomes a diminished 5th.




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