Rapid Skill Development with the Cycle of Thirds

Created by
Max Maxwell

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You have learned how to work with intervals from the Perfect Prime to the Perfect 8th. So far, you have learned three types of intervals. The three types are the Major, minor and Perfect intervals. Each of the intervals you have learned so far has a unique number of half steps. There are two other interval types that can be applied to numerical intervals of a 2nd and higher. They are called Augmented and diminished intervals. These intervals do not actually exist as a truly separate entity with their own unique half step count. For example, A Major 2nd has two half steps and so does a diminished 3rd. Augmented and diminished intervals are merely different names for numbers of half steps that already have a Major, minor or Perfect modifier in its name. Why have a separate name? The reason is so a specific number of half steps can associated with a wider range of scale and chord positions. A similar function is achieved by the naming of notes. Take a look at the A Major triad chord below.

A  C#  E

The 3rd in the chord is C#. You know that sharps and flats do not really have their own name. The pitches represented by the black keys on the piano are named after the note names of the white keys. The 3rd in the A Major Triad could be called C# or Db. It all depends on what note, scale position, or chord position you want to reference. In the chord above, C is a 3rd above A. Therefore the pitch class will be named after C so its name references the function of a 3rd in this chord. The reason for having interval types of augmented and diminished is similar. C# is a unique pitch class with two names (C# and Db). In a similar way an augmented or diminished interval is an extra name for a unique number of half steps. To see how this works we will learn how augmented and diminished intervals are constructed.

A Major interval is one half step more than a minor interval of the same numerical name. A minor interval is one half step less than a Major interval of the same numerical name. You first learned this with Major 3rds (4 half steps) and minor 3rds (3 half steps).

Decrease one half step             Increase one half step
minor               Major

Half Step Counts for Intervals of the Same Numerical Name

 minor 2nd 1 Half Step Major 2nd 2 half Steps minor 3rd 3 Half Steps Major 3rd 4 half Steps minor 6th 8 Half Steps Major 6th 9 half Steps minor 7th 10 Half Steps Major 7th 11 Half Steps

A diminished interval is always one half step less than a minor interval of the same numerical name. An augmented interval is always one half step more than a Major interval of the same numerical name. In the illustration below, the different interval types increase by one half step when you move to the right. They decrease by one half step when you move to the left.

diminished - minor - Major - Augmented

You must memorize the order of interval types (diminished, minor, Major, Augmented), which moves from the least number of half steps to the greatest number of half steps. Then you will know the number of half steps to add or subtract for each type of interval to change it into a diminished or augmented interval. Remember, these relationships are valid only for intervals of the same numerical type. For example, a minor 3rd becomes a diminished 3rd by dropping one half step.

A Perfect Interval always adds or subtracts one half step to get an Augmented or diminished interval of the same numerical type. For example, a Perfect 5th becomes an Augmented 5th by adding one half step.

diminished - Perfect - Augmented

The chart below summarizes the numbers of half steps from each interval type to get an Augmented or diminished intervals.

Interval Type      To get a diminished        To Get an Augmented

 minor Subtract One Half Step Add Two Half Steps Major Subtract Two Half Steps Add One Half Step Perfect Subtract One Half Step Add One Half Step

EXAMPLES:

If you decrease the number of half steps in a minor 3rd (three half steps) by one half step, you get a diminished 3rd (3-1=2). If you want to change a Major 3rd (four half steps) to a diminished 3rd (two half steps) you must take away two half steps (4-2=2). A diminished 3rd has two half steps, which is the same number of half steps as a Major 2nd.  A diminished 3rd and a Major 2nd are two names for one interval with the same number of half steps (two). If your interval is a Major 2nd, but you want to refer to the function of a 3rd, you can just call it a diminished 3rd. It is the same number of half steps, but has two different names so that you can reference more scale and chord positions.

If you decrease the number of half steps in a minor 7th (ten half steps) by one half step, you get a diminished 7th (nine half steps, 10-1=9). A diminished 7th has nine half steps, which is the same number of half steps as a Major 6th. A diminished 7th and a Major 6th are two names for the same number of half steps (nine). They are the same interval with two different names.

If you increase the number of half steps in a Perfect 5th (seven half steps) by one half step, you get an Augmented 5th (eight half steps). This is the same number of half steps as a minor 6th. It is one interval with two different names. If you are working with an interval that has eight half steps, but still want to refer to the function of a 5th, you can call it an Augmented 5th instead of a minor 6th.

When you change an interval to its diminished or augmented form, remember to keep the number part of the name (a 3rd stays a 3rd, a 6th stays a 6th, and so on). You already know that an interval name can be abbreviated. A Major 3rd can be shown as M3. A minor 3rd can be shown as m3. A Perfect 3rd can be shown as P3. You can also abbreviate diminished and Augmented intervals. A diminished 3rd can be abbreviated as d3. An Augmented 3rd can be abbreviated as A3. There are other forms of abbreviation, but we will stick with the above in this book.

Exercise:

Change the second note in each interval to make it to an Augmented interval. Remember to keep the same letter name. The name of the given interval is in parentheses. The second note in each interval is above the first note. Use the Interval Answer Charts to check your answers.

 1. (m3) C to Eb ______ 2. (m3) G# to B ______ 3. (M3) D to F# ______ 4. (M2) A to B ______ 5. (P5) E to B ______ 6. (m6) Bb to Gb ______ 7. (m3) F# to A ______ 8. (P4) C# to F# ______ 9. (m3) G to Bb ______ 10. (m7) D to C ______ 11. (M6) Ab to F ______ 12. (M7) Eb to D ______ 13. (P5) B to F# ______ 14. (m2) F to Gb ______

Exercise:

Change the second note in each interval to make it to a diminished interval. Use the Interval Answer Charts to check your answers.

Remember to keep the same letter name. The second note in each interval is above the first note.

 1. (m3) C to Eb ______ 2. (m3) G# to B ______ 3. (M3) D to F# ______ 4. (M2) A to B ______ 5. (P5) E to B ______ 6. (m6) Bb to Gb ______ 7. (m3) F# to A ______ 8. (P4) C# to F# ______ 9. (m3) G to Bb ______ 10. (m7) D to C ______ 11. (M6) Ab to F ______ 12. (M7) Eb to D ______ 13. (P5) B to F# ______ 14. (m2) F to Gb ______

Daily and Weekly Practice

Continue to recite the Cycle of Thirds forward and backward daily. Weekly, practice spelling triad and seventh chords for five minutes and practice constructing intervals for five minutes. Now that you have completed the section on intervals, you can go to the appendix and learn how to spell all other types of chords based on knowing their interval structure. Be sure to practice each type of interval at least a couple of times. In your interval practice, also add augmented and diminished intervals by first finding a Major, minor or Perfect interval, then converted to a diminished or augmented interval.

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