The Music Theory Advantage TM
Rapid Skill Development with the Cycle of Thirds

Created by
Max Maxwell
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Cycle of Thirds as a
Musical Interval Calculator
Read Introduction

This method for spelling intervals was created over the course of six years of the research and development of music and mathematics curriculum that have been used in schools all over the U.S. and internationally. It is the fastest and easiest method to learn AND remember how to spell all the musical intervals. This, and other methods released on this site are part of our mission to give education improvements to the public for free. See our Mission Statement.

Let's Get Started!

There are three steps to install this new music calculator into your mind. The use of the Cycle of Thirds as a musical interval calculator is the foundation of this course and is very important, so be sure to thoroughly master these three steps. In order to make the most of this course, it is essential that you master each step as you proceed.

Step One: Memorize The Cycle of Thirds

The cycle of thirds, (A C E G B D F A), is the interval structure I used to create a mental musical interval calculator. The first step is to be able to recite this interval structure forward and backward. It is a Cycle of Thirds because each note in this interval structure is either a minor or Major third from its adjacent notes. Below, you see the Cycle of Thirds. In this structure, C is a third above A, E is a third above C, G is a third above E, etc. Moving to the right in the cycle will be referred to as "Up." Moving to the left in the cycle will be referred to as "Down." Moving up in the cycle moves toward higher pitches. Moving Down in the cycle moves toward lower pitches.

The Cycle of Thirds
Higher pitch =>>
<<= Lower Pitch

Before moving on to step two, you must be able to:

  • Recite the Cycle of Thirds forward from memory starting with A and ending with A. From memory say, "A, C, E, G, B, D, F, A."

  • Recite the Cycle of Thirds backward from memory from A to A. From memory say, "A, F, D, B, G, E, C, A"

  • Recite the Cycle of Thirds forward from memory starting from any note. If you start with D then say, "D, F, A, C, E, G, B, D". If you start with E then say, "E, G, B, D, F, A, C, E". Remember, when starting on a different note than "A", do not repeat the A twice just because it is listed that way above. It is listed twice just to let you know it comes before C and after F. Always end with the same note that you begin.

  • Recite from memory the Cycle of Thirds backward starting from any note. If you start on B then say, "B, G, E, C, A, F, D, B." If you start on C then say, "C, A, F, D, B, G, E, C."

  • Recite four notes in the Cycle of Thirds starting from any note. If you start with A then say, "A, C, E, G." If you start with F then say, "F, A, C, E." This additional practice is not just redundant. When you start using the cycle to spell chords you will only pull three (triad chords) and four (seventh chords) notes at a time. This will help you get into the rhythm of that. Practice this by randomly choosing a starting note.

After you memorize the Cycle of Thirds, you should continue to practice reciting it daily (forward and backward) for at least several months after taking the course. It will not take nearly that long to get lightning fast with it. Some people will be able to do it well in just 15 minutes of practice. However, the goal of extended daily practice is to encode this skill for the long term. The good news is that you only have to do this for a minute or two each day. By all means, do more practice if you want to or feel the need. The reason for this is that you want to encode the memorization for long term storage. This calculator will do you no good if you forget it after just a few months of not using it.

Since all the practice required for this entire course can be done in your mind, you can do it anywhere. Practice on a bus, in the shower, waiting at the doctor's office or anywhere (but not while driving, working or crossing the street!). A big advantage of this course is that it is easy to get in your daily practice!


Beware of “False Success Syndrome!”

False Success Syndrome results from the fact that the Cycle of Thirds is so easy to learn that some people will “feel” like they have mastered it in just minutes. Although it is true that some can learn to recite the Cycle of Thirds without much practice, it is strongly recommended that you follow through with daily practice until you reach true mastery. Just “feeling” like you can do it easily is not good enough. The criterion for evaluating if you know the Cycle of Thirds well enough is that you have to be able to quickly and immediately, without pause for thought, recite the Cycle of Thirds forward and backward from any starting note. If you have to pause before or during reciting the Cycle of Thirds then you have not practiced enough. This should become second nature. Even if you take a break from practice for weeks or months, you should still be able to recite the Cycle of Thirds quickly and without pausing. This should become like counting. You do not have to practice counting from one to ten in order to do it quickly without pause. Counting is burned into your brain. You must burn the Cycle of Thirds into your brain just like counting. If, when starting to recite the cycle you have to stop and think even for a second, you do not know it well enough. Just reciting from A to A is not enough. Be sure to practice reciting the Cycle starting from any note both forward and backward. Musical intervals are the numbers of music. Thus, you should be able to handle intervals as easily as you can count. This mental musical calculator will let you do that.

<<=PREV  Step Two: Memorize the intervals between adjacent  NEXT=>>
pairs of notes in the Cycle of Third

Copyright © 2008-2011 Kenneth J. Maxwell Jr.