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

Created by
Max Maxwell
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Advanced Course Description

The greatest value offered in this course is not the method provided below. The greatest value is the insight that this method affirms. The insight is that any student of music who is able to spell any interval above or below any note as easily as they can name an adjacent number will have a significant advantage in the study of music theory pertaining to the handling of pitch differences in the creation and interpretation of music. Naming a Major 6th above Eb, for example, should be as easy as naming the number that comes after five. With the method below, developing such skill in the spelling of musical intervals is the normative expectation. If you practice the method below, you will master the spelling of intervals. Learning to spell musical intervals is a lot easier than you might think. The Music Theory AdvantageTm is the fastest and most effective method to gain significant skill in spelling intervals (and chords).

If you know your music theory, the following description of how to use the mental musical interval calculator, which is based on the Cycle of Thirds, is all you need to learn how to quickly and easily spell musical intervals above or below any note. If you do not understand this description, click on the "Introduction" link at the top of the page to read the intro and take the full course with the link at the bottom of that page. The full course has much more detailed descriptions, illustrations and practice exercises.

Installing the Musical Interval Calculator Into Your Mind

The Cycle of Thirds
A C E G B D F A
<<= Lower Pitch (Below)    Higher pitch (above) =>>


1. Memorize the Cycle of Thirds (A  C  E  G  B  D  F  A) and be able to recite it very quickly forward and backward from any starting note (for example,  B  D  F  A C  E  G  B) . It is absolutely critical that you practice until you can do this as easily as you can count from one to ten.

2. Memorize what type of 3rd represents the distance in pitch between any two adjacent notes in the Cycle of Thirds.

A to C = minor 3rd,  C to E = Major 3rd,  E to G = minor 3rd,
G to B = Major 3rd, B to D = minor 3rd, D to F = minor 3rd, F to A = Major 3rd.

You should instantly be able to say what type of 3rd is the distance between any two adjacent notes in the cycle. If you think B to D, you should immediately be able to say, "minor 3rd."

3. Be sure you can apply this knowledge to determine what type of 3rd is above or below any note. For example, if you want to know what note name (pitch class) is a Major 3rd above A, you must first find the naturally occurring 3rd above A in the cycle. Just go to the next step "above" (or to the right if the cycle is written out as shown above) in the cycle. C is the next note in the cycle to the right of A. C is a minor 3rd above A. Since Major 3rds are four half steps and minor 3rds are three half steps, you must raise C by one half step to get a major 3rd. C# is a major 3rd above A. The reverse of this principle works to convert Major 3rds (G to B) to minor 3rds (G to Bb). If you want to find a Major or minor 3rd down from a note, move to the next note to the left (as written out above) in the cycle. If You started on C, then the next step in the cycle to the left (below C) would be A. C to A is a minor 3rd. Drop A one half step to Ab and you get C to Ab (Major 3rd). It is absolutely critical that you make yourself able to INSTANTLY name what type of 3rd is above or below any note in the cycle. This extends from any note in the cycle to any note because if C is a minor 3rd above A, then C# is also a minor 3rd above A# and Cb is a minor 3rd above Ab. C## is also a minor 3rd above A##, etc. Just apply the sign of your starting note to the result in the cycle. For example, if you want a Major 3rd above G#, you know that B is a Major 3rd above G. Just apply the sharp of your starting note (G#) to B and you get B#. B# is a Major 3rd above G#. If you have any problems finding 3rds above or below any note, I recommend following the link at the bottom of the page to take the full course.

The above three steps make up the foundation for you to be able to spell intervals very quickly and easily. It is critical that you practice it well. When you can quickly and easily name the note that is a Major or minor 3rd above or below any given note, you can proceed to learn the rest of the intervals. If you practice the preceding three steps well, you will be very, very pleased with the results.

Learning to Spell Musical Intervals

You will only have to use the Cycle of Thirds to find 3rds and 5ths. The rest of the intervals can be quickly determined through the use of the principle of interval inversion (4ths, 6ths, 7ths) or because the note names are easy to determine without any extra help (Perfect Primes, 2nds, 8ths).

Perfect Primes, 2nds, and 8ths

A Perfect Prime is always the same pitch as the given note, thus it has the same note name. A perfect 8th is always an octave above or below the given note and it also will have the same note name, but not be the same pitch. A P1 of C is C (same pitch). An P8 above C is C (one octave higher).

Seconds are small and easy to count half steps. A minor 2nd is just one half step above or below the given note. A Major 2nd is just two half steps above or below the given note. You must have memorized the chromatic order of notes in order to count out 2nds above or below a note. Be sure to practice counting out seconds well, because (through the principle of inversion) you will use the same method to count out 7ths.

Perfect 5ths

In order to find a P5 above a note, move two steps in the cycle to the right (above). Thus a P5 over C is G (A  C  E  G  B  D  F  A). And a P5 below G is two steps in the cycle to the left (below). This is one reason why it is so important to be an expert at reciting the cycle. If you are fast and accurate, it is very easy to count two steps to the right (above) or left (below).

There is one exception to memorize. This method gives the correct P5 for all notes in the cycle except when moving between B and F. The distance in pitch between B and F is one half step less. Thus B to F or F to B is a diminished 5th / Augmented 4th. You must add or subtract one half step depending on which direction you are moving. If your given note is B and you want to find a 5th above B, move two steps to the right to get F then ADD a half step. F# is a P5 over B. If your given note is F and you want a P5 below F, move two steps to the left in the cycle and subtract one half step. Bb is a P5 below F. Apply the same concept when starting on any form of B or F (Bb, B, B#, Fb, F, F#). For example, B is a P5 below F#. Once you memorize this and practice a little, it becomes second hand and as easy as any of the other notes for finding a Perfect 5th.

An easy way to remember this is to imagine that B represents a bunny and F represents a fly. The bunny is looking up at the fly in the air (raises one half step). The fly always looks down at the bunny (lowers B one half step). The bunny looks up so raise F a half step. The fly looks down so lower B a half step.

Perfect 4ths

Perfect 4ths are found via the principle of inversion. Since 5ths invert to 4ths, just move in the opposite direction to find a P4 above or below any note. If a P5 above is two steps to the right in the cycle, then a P4 above will be two steps to the left. For G, a P5 above is D and a P4 above is C (A  C  E  G  B  D  F  A). For E, a P5 below is A and a P4 below (move in the opposite direction) is B (A  C  E  G  B  D  F  A). The key is to first master finding Perfect 5ths. Then it will be easy to move in the opposite direction two steps to find Perfect 4ths. Remember that the exception of moving between B and F still applies when jumping two steps to find 4ths. If starting on B, raise F one half step. If starting on F lower B one half step. For example, A P4 below B is not F. You must raise F one half step to F#. F# is a P4 below B. The reverse is also true. B# is not a P4 above F. You must lower it to B.

Major and minor 6ths

6ths invert to 3rds. Since you already know how to easily find 3rds, you also can easily find 6ths. When seeking the note that is a Major or minor Sixth above or below a note just find the inverted 3rd. Major and minor intervals invert differently than Perfect intervals. A P5 inverts to a P4 and visa versa. However, a Major 6th does not invert to a Major 3rd , but inverts to a minor. Likewise, a minor 6th inverts to a Major 3rd. The note name that is your inverted 3rd will be the same note name you want for your 6th.

You must memorize the following inversion pattern:

To name the note that is a Major 6th above C, use the cycle to find the minor 3rd below C.
To name the note that is a minor 6th above C, use the cycle to find the Major 3rd below C.

To name the note that is a Major 6th below E, use the cycle to find the minor 3rd above E.
To name the note that is a minor 6th below E, use the cycle to find the Major 3rd above E.

Major and minor 7ths

7ths invert to seconds. Since you can count out 2nds, you can also count out 7ths.

You must memorize the following inversion pattern:

To name the note that is a Major 7th above B, count out the minor 2nd below B.
To name the note that is a minor 7th above B, count out the Major 2nd below B.

To name the note that is a Major 7th below G, count out the minor 2nd above G.
To name the note that is a minor 7th below G, count out the Major 2nd above G.

Converting to Augmented and diminished intervals

To find intervals above or below a note that are augmented or diminished, just convert from the types you already know. If you want an Augmented 5th, you already know Perfect 5ths. Just find the Perfect, then add one half step to get an Augmented interval (For P5, C to G becomes the Augmented 5th C to G#) or subtract one half step to get a diminished interval (for P5, C to G becomes the diminished 5th C to Gb). If your interval is Major or minor (2nds, 3rds, 6ths, 7ths), to get to Augmented add one (from Major) or two (from minor) half steps. To convert a Major or minor to a diminished interval, subtract two (from Major) or one (from minor) half steps. With a little practice, you will be able to easily and quickly convert any Major, minor, or Perfect interval to their Augmented or diminished form.

Compound Intervals

The quality of compound intervals is determined by the quality of the interval it is based on. For example, a Perfect 11th is an octave above the P4. A P11 over a given note (e.g. C) will have the same note name as a P4 over the same given note (e.g. C). When you know what interval a compound is based on, you can quickly and easily spell it for any root note with what you learned on this page.

Using The Cycle of Thirds to Spell Chords

Once you can use the Cycle of Thirds to spell intervals, you can use it to spell chords in two different ways. First, once you learn the interval structure of a chord it is easy to spell the chord if you can spell intervals. A C Major Seventh in interval notation is 1357. Start with C, find the Major 3rd (E), find the Perfect 5th (G), find the Major 7th (B) and you have spelled a C Major Seventh Chord (CEGB). The quicker and easier you can spell intervals, the quicker and easier you can spell chords for any root using their interval notation.

Spelling Chords as a Stack of Thirds

There is another method to spell chords. Triad and seventh chords are constructed in stacks of 3rds. The Cycle of Thirds is also a series of 3rds. If you memorize the interval structure of Chords as a stack of 3rds, then spelling them is very fast with the Cycle. In this method, spelling chords is a matter of finding Major and minor 3rds.

Spelling Triads as a Stack of Thirds

Memorize the Triad interval structures. 

1. Major Triad is Major-minor (Major means Major 3rd. Minor means minor 3rd.)

2. minor Triad is minor-Major

3. diminished Triad is minor-minor

4. Augmented Triad is Major-Major

Application Example:
To spell a C Major Triad, first recall the interval structure. The Major Triad has the interval structure Major-minor. The C Major triad is spelled starting with the root C. Next, find the Major 3rd above C, which is E. Next, find the minor 3rd above E, which is G. The C Major Triad is spelled C E G.

Spelling Seventh Chords as a Stack of Thirds

Memorize the interval structure for five common seventh Chords:

1. Major Seventh = Major-minor-Major

2. Minor Seventh = minor-Major-minor

3. Major / Minor Seventh (Dominant) = Major-minor-minor

4. Half Diminished Seventh = minor-minor-Major

5. Diminished Seventh = minor-minor-minor

Application Example:
To spell a C Major Seventh Chord, first recall the interval structure. The Major Seventh Triad has the interval structure Major-minor-Major. The C Major Seventh chord is spelled starting with the root C. Next, find the Major 3rd above C, which is E. Next, find the minor 3rd above E, which is G. Next, find the Major 3rd above G, which is B.  The C Major Seventh Chord is spelled, C E G B.

SPELLING SCALES

This section of the course cannot be fully described in a textual summary as it uses images. Here is a limited summary of the principles used.

1. A series of seven images are memorized so that they can be named forward and backwards. The images are visually linked so this is very easy. The first letter of the image names represent keys and notes. Thus, the series of images is a series of notes (F, C, G, D, A, E, B). This series of notes is the same order of notes as the order of sharps (reciting forward) and the order of flats (reciting backward) in keys signatures. It is also a series of fifths. This is the series of images that let you name the notes that are sharp or flat in every key.

2. Each of these images are connected to two other images that are easy to remember. These images tell you how many sharps or flats are in the keys represented by the first image.

3. Once you know how many sharps or flats are in a key, you use the original image sequence to name what notes are sharp or flat. They always follow the same order. Just recite the sequence (F, C, G, D, A, E, B) forward for sharps and backward for flats. Thus, a major key with two sharps, those sharps are F and C. A key with two flats, those flats are B and E.

It is that simple and just looking over the full scales course is fast and easy so....Take a look.

 

The full Music Theory AdvantageTM course offers much more detailed explanations, illustrations and practice exercises.

Check Out The Full Course
The full course will take you by the hand and lead you, step by step, to interval and chord spelling success!

 

Copyright 2008-2011 Kenneth J. Maxwell Jr.