Rapid Skill Development with the Cycle of Thirds

Created by
Max Maxwell

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After you learn how to spell all the intervals, you will know how to spell any chord for any root just by knowing its standard interval notation. For example, a C Major Seventh is 1357. It is important to first learn how to spell triad and seventh chords based on their interval structure as a stack of thirds in order to practice using the Cycle of Thirds to find Major and minor 3rds. This increases your skill in using the cycle in preparation for interval spelling. Chord spelling in this manner is fast and easy.

Being able to recite the Cycle of Thirds in ascending order (ACEGBDFA) is a fast and powerful way to learn chord spelling. You may not realize it but you already know how to spell some triad chords.  What is a chord?  Any time three or more notes play together you have a chord.  If a chord has only three notes it is called a triad chord. If you were sitting at a piano keyboard and played the notes C, E and G at the same time, you have played a chord.  Notice that C, E and G are in the order of the Cycle of Thirds.  This is because triad chords are built with 3rds

1st        3rd       5th

The lowest note in the chord is the 1st, or the root note.  The next note is called the 3rd because it is the third letter named note above the 1st, it is also an interval of a 3rd above the 1st or root note.  The last note in a triad chord is called a 5th because it is the 5th letter named note above the root (counting the root as the 1st).  It is also an interval of a 5th above the 1st or root note. You will learn about 5ths later.

When chords are named they have two parts to their name.  The first part is the letter name which is taken from the root note of the chord.  In the triad chord illustrated above (C Major) the root is C. This is why C is also in the name of the chord.  The second part of the name is based on the interval structure of the chord.  For the A Minor triad chord, “A” is the root note and Minor refers to the specific interval structure of the chord.  What is an interval structure?  An interval structure is any sequence of intervals that work together for a particular purpose. For a chord, this is the set of intervals that make up the chord.  Triad chords have two intervals of a 3rd. The first interval is between the root and the 3rd, and the second interval is between the 3rd and the 5th.

Some chords fall directly onto the Cycle of Thirds. For example, you already know how to spell the A Minor triad chord.  Just start with A and recite the next two letters in the Cycle of Thirds.  A, C and E is the correct spelling of the A Minor triad chord. Look at the A Minor triad chord below. Notice the chord notes are in the order of the Cycle of Thirds.

minor 3rd   C  Major 3rd   E

1st                      3rd                      5th

For a minor triad chord, the interval structure of two 3rds is “minor 3rd - Major 3rd.” This means that from A, you move a minor 3rd above to the next note C (the 3rd) and then move from C a Major 3rd above to the last note E (the 5th).  This works for any root note.  There is more common way of notating interval structures for chords described in the section on "Spelling Chords with Standard Interval Structures," which presupposes you know how to spell all the intervals. For now, focus on the interval structure of 3rds in a chord, because this is how you will learn to easily spell them while developing your skills using the Cycle of Thirds. After you learn how to spell the intervals, you can see the later section for more information on chord spelling.

If your root note was E instead of A, you could spell a minor triad chord by adding the next two notes in the Cycle of Thirds.  E, G and B spell a minor triad chord because E to G is a minor 3rd and G to B is a Major 3rd
(E  minor 3rd  G   Major 3rd  B).

Focal Point Four Introduction Questions:

To illustrate the natural relationship between the Cycle of Thirds and triad chords, I will ask you to spell a chord in each of the questions below.  Just recite three notes in the cycle of 3rds starting with the given note in the chord name. Do not worry that you may not know the chord names and focus on the note name in the chord.  For example, the note name in the chord “A Minor” is “A.”  The note in the chord name is the root of the chord.  So you would start to spell the chord with the root note A.  Then add the next two notes in the Cycle of Thirds.  The answer for A Minor would be just three adjacent notes in the Cycle of Thirds, A, C, E.

1. B Diminished Triad Chord        ____   ____   ____

2. G Major Triad Chord                ____   ____   ____

3. F Major Triad Chord                ____   ____   ____

4. D Minor Triad Chord                ____   ____   ____

5. C Major Triad Chord                ____   ____   ____

If you use the given root and correctly state the next to steps in the cycle of thirds, your answer will be correct. You may use the Chord Answer Chart to check your answers if you wish.

Just by knowing the Cycle of Thirds you can already easily spell some chords that naturally fall on the Cycle of Thirds. What about the rest of the triad chords?  How can you know how to spell chords that require a sharp or flat in its spelling?  The D Major triad chord, for example is spelled D  F#  A.  You will learn how to spell all triad chords in Focal Point Five.  By the time you are done practicing Focal Point Five you will be able to spell all triad chords without the need to refer to any external references.  We are moving to chord spelling now because this will keep you developing your skills using the Cycle of Thirds.

Triad Chord Types and Their Interval Structures

Spend a few moments right now memorizing the four triad chord types above. Each type of triad chord has an interval structure.  An interval structure exists when two or more intervals work together to construct something like a chord, a scale or a melody.  As you learned in the introduction to this Focal Point, triad chords have two intervals of a third and each triad chord has three notes.  The interval structures in the chart below list two intervals of a 3rd.  This means that, Major triads, for example, have a Major-minor interval structure which is a distance of a Major 3rd between the root and the 3rd and a distance of a minor 3rd between the 3rd and the 5th. The C Major triad, for example, is:

C Major 3rd E minor 3rd G

1st                    3rd                   5th

It is four half-steps from C to E and that is a distance of a Major 3rd. It is three half-steps from E to G and that is a distance of a minor 3rd. That creates an interval structure of Major-minor.

In the chart, you see the interval structures for all four types of triad chords. Triad chords of the same type will have the same interval structure regardless of the root.

In Part I and IV, when used in chord interval structures, the words Major and minor always refer to distances of 3rds (Major 3rd, minor 3rd).

You MUST memorize the four types of triad chords and their interval structures.

I will show you how.

Just pretend that the triad chords are named after their 3rd based interval structures.  The major and minor triad chords have one of each type of 3rd in their interval structure.  Just think of the name major triad and minor triad as being determined by which type of third is first in their respective interval structures.

1. Major Triad Chord (Major – minor): Think of this triad chord as being named “Major” because its interval structure starts with a Major 3rd and ends with a minor 3rd.

2. Minor Triad Chord (minor – Major):  Think of this triad chord as being named “Minor” because its interval structure starts with a minor 3rd and ends with a Major 3rd.

3. Diminished Triad Chord (minor – minor):  To diminish something means to make it smaller. Think of this triad chord as being named “Diminished” because it is the smallest triad chord.  It is the smallest triad chord because its interval structure is made of two minor 3rds.  Minor 3rds (three half-steps) are smaller than Major 3rds (four half-steps), therefore two minor 3rds make up the smallest triad chord, which is a diminished triad chord.

4. Augmented Triad Chord (Major – Major):  To augment something is to make it larger. Think of this triad chord as being named “Augmented” because it is the largest triad chord.  It is the largest triad chord because its interval structure is made of two Major 3rds. Major 3rds are larger than minor 3rds. Therefore two Major 3rds make up the largest possible triad chord, which is an Augmented triad chord.

Recite and memorize the information in the chart below:

 Triad Type Mnemonic for Name Interval Structure 1. Major Triad Chord starts with a Major 3rd Major-minor 2. Minor Triad Chord starts with a minor 3rd minor-major 3. Diminished Triad Chord the smallest triad chord minor-minor 4. Augmented Triad Chord the largest triad chord Major-Major

For each triad chord type above, recite the triad type, the reason it is named and then recite the interval structure.

Exercise:

Memorize the above information in the chart until you can think of a triad type and quickly give its interval structure.  You should also be able to think of one of the four interval structures and give its triad type. Practice until you do not need the book to recite all four triad types and their interval structures. For example, for #1 in the chart above say “Major Triad, Major-minor” There is no need for any additional exercises for Focal Point #3 other than drilling with the above chart until you have mastered the information. Do not proceed further in the course until you are quick at naming triad types and their interval structures. Use the chart to verify your accuracy.

The following four examples will show the steps you need to follow to spell triad chords. If you are having trouble quickly finding the correct Major and minor 3rds above notes, then practice finding 3rds before spelling chords.

Spell the A Major triad Chord:

1. Start with the root note, which is in the name of the chord.
Example: For the A Major triad - A is the root or 1st note.

2. Recall the interval structure of the type of triad you want to spell.
Example: For A Major, the interval structure of a major triad is Major-minor.

3. Spell the first interval (Major 3rd). The first interval starts with A and ends a Major 3rd above A. The next note forward in the cycle from A is C. C is a minor 3rd, with three half steps, above A. Therefore C# (one half step higher) is a Major 3rd, with four half steps, above A. A to C# is the first interval.

4. Spell the second interval (minor 3rd). The second interval starts with C#. The next note forward in the cycle is E# (remember to always add a sharp or flat to match the signs). E# is a major 3rd, with four half steps, above C#. Therefore, flatten E# to E. C# to E is a minor 3rd with three half steps.

Put the intervals together. The A Major Triad is spelled A C# E.

A Major Triad - A  C#  E

Spell the F Minor Triad Chord:

1. Start with the root note, which is in the name of the chord, (F)

2. Recall the interval structure for a minor triad (minor-Major).

3. Spell the first interval (minor 3rd). The first interval starts with F and ends a minor 3rd above F.  The next note forward in the cycle is A. F to A is a Major 3rd with four half steps. Lower A by one half step to Ab to make a minor 3rd with three half steps. The first interval, F to Ab, is a minor 3rd.

4. Spell the second interval (Major 3rd). The second interval starts with Ab and ends a Major 3rd above Ab. The next note forward in the cycle is Cb. Ab to Cb is a minor 3rd with three half steps.  Raise Cb by one half step to C. The second interval, Ab to C, is a Major 3rd with four half steps.

Put the intervals together. The F Minor triad chord is spelled  F  Ab  C.

Spell the D# Diminished Triad Chord:

1. Start with the root note, which is in the name of the chord. (D#)

2. Recall the interval structure for a diminished triad (minor-minor).

3. Spell the first interval (minor 3rd). The first interval starts with D# and ends a minor 3rd, with three half steps above D#. The next note forward in the cycle from D# is F#. The first interval, D# to F#, is a minor 3rd with three half steps.

4. Spell the second interval (minor 3rd). The second interval starts with F# and ends a minor 3rd above F#. The next note forward in the cycle from F# is A#. F# to A# is a Major 3rd with four half steps. Lower A by one half step to get a minor 3rd. The second interval, F# to A, is a minor 3rd with three half steps.

Put the intervals together. The D# Diminished triad chord is spelled  D#  F#  A.

Spell the B Augmented Triad Chord:

1. Start with the root note, which is in the name of the chord. (B)

2. Recall the interval structure for an augmented triad (Major-Major).

3. Spell the first interval (Major 3rd). The first interval starts with B and ends a Major 3rd above B. The next note forward in the cycle is D. B to D is a minor 3rd with three half steps. Raise D by one half step to get a Major 3rd. The first interval, B to D#, is a Major 3rd with four half steps.

4. Spell the second interval (Major 3rd).  The second interval starts with D# and ends a Major 3rd above D#. The next note forward in the cycle is F#. D# to F# is a minor 3rd with three half steps. Raise F# by one half step to get a Major 3rd. The second interval, D# to F##, is a Major 3rd with four half steps.

Put the two intervals together. The B Augmented triad chord is spelled B  D#  F##.

Exercise :

Spell the following triad chords. Write the Chord names and spellings as you go on a piece of paper, then check the answers with the Triad Chord Spelling Chart on the Answer Chart page.

Root     3rd     5th
1. A Minor _____ _____ _____
2. B Minor _____ _____ _____
3. C Minor _____ _____ _____
4. D Minor _____ _____ _____
5. E Minor _____ _____ _____
6. F Minor _____ _____ _____
7. G Minor _____ _____ _____
8. A Dim _____ _____ _____
9. B Dim _____ _____ _____
10. C Dim _____ _____ _____
11. D Dim _____ _____ _____
12. E Dim _____ _____ _____
13. F Dim _____ _____ _____
14. G Dim _____ _____ _____

15. A Major _____ _____ _____
16. B Major _____ _____ _____
17. C Major _____ _____ _____
18. D Major _____ _____ _____
19. E Major _____ _____ _____
20. F Major _____ _____ _____
21. G Major _____ _____ _____
22. A Aug _____ _____ _____
23. B Aug _____ _____ _____
24. C Aug _____ _____ _____
25. D Aug _____ _____ _____
26. E Aug _____ _____ _____
27. F Aug _____ _____ _____
28. G Aug _____ _____ _____

Exercise P1-5B:

Spell the following triad chords. Use double sharps or flats as needed. Write the Chord names and spellings as you go on a piece of paper, then check the answers with the Triad Chord Spelling Chart on the Answer Chart page.

Root    3rd     5th
1. A# Minor _____ _____ _____
2. Bb Minor _____ _____ _____
3. C# Minor _____ _____ _____
4. Db Minor _____ _____ _____
5. E# Minor _____ _____ _____
6. Fb Minor _____ _____ _____
7. G# Minor _____ _____ _____
8. Ab Dim _____ _____ _____
9. B# Dim _____ _____ _____
10. Cb Dim _____ _____ _____
11. D# Dim _____ _____ _____
12. Eb Dim _____ _____ _____
13. F# Dim _____ _____ _____
14. Gb Dim _____ _____ _____
15. Ab Major _____ _____ _____
16. B# Major _____ _____ _____
17. Cb Major _____ _____ _____
18. D# Major _____ _____ _____
19. Eb Major _____ _____ _____
20. F# Major _____ _____ _____
21. Gb Major _____ _____ _____
22. A# Aug _____ _____ _____
23. Bb Aug _____ _____ _____
24. C# Aug _____ _____ _____
25. Db Aug _____ _____ _____
26. E# Aug _____ _____ _____
27. Fb Aug _____ _____    _____
28. G# Aug _____ _____ _____

WolframAlpha Practice Widget

I made this practice widget using the computational knowledge engine at WolframAlpha. To use it, just think of a triad chord to spell. Enter the root, third and fifth into the appropriate boxes. If you are correct, the answer will come back with the chord you thought you were spelling. You must enter all notes as capitals or it will not work.

Daily and Weekly Practice

If you continue to recite the cycle of thirds daily for one minute and practice spelling triad chords at least once a week (five minutes), you will be able to spell all possible triad chords fast and easy! After you do your initial practice to master this Focal Point, practice chord spelling once a week for several months after the course is complete. Spell one of each triad chord types with random roots as a minimum weekly practice. Use the triad chord spelling chart in the appendix to check your answers. Even though it may seem easy for you, keep up with daily and weekly practice. The goal is to burn this all into your long term memory so you can use the calculator anytime, even when you have not used it in a long time.