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The following is a general list of some of the commonly used chords and their formulas. All of the examples are in root position for convenience, but the notes could conceivably be arranged in any order.
C (C major)—1, 3, 5. The letter name with nothing after it automatically implies 1, 3 and 5 (except on sus chords). Notice how in the following examples we are “stacking” 3rds onto the basic 1, 3, and 5 of the triad.
Cmaj7—1, 3, 5, 7
Cmaj9—1, 3, 5, 7, 9
Cmaj11—1, 3, 5, 7, 9, 11. This is not generally considered a functional chord because of its dissonant sound. I have included it to show how the addition of successive thirds keeps building larger chord forms. The conflict is the minor 9th interval between E and F, as well as the augmented 4th interval of B and F. It’s not unusual to substitute the #11 for the 11th, especially in a jazzier context. This alteration gets rid of the offending intervals. Of course, the chord is no longer diatonic to C, but still works in many of the instances where C major type chords are used.
Cmaj9#11—1, 3, 5, 7, 9, #11
Cmaj13—1, 3, 5, 7, 9, 11, 13. Again, not very pretty with the 11th; but, in this case, Cmaj13 is taken to mean without the 11th. Sometimes it is written Cmaj13(omit 11). Notice that each successive chord above the triad also includes the notes from the previous chord. Cmaj13#11 is also possible.
Sus chords (short for suspended), are substituting the 4th or 2nd for the third.
Csus4—1, 4, 5
Csus2—1, 2, 5
Add chords are used to designate the addition of a specific pitch to a chord. Sometimes the / symbol is used instead of the word “add.”
Cadd9 (C/9)—1, 3, 5, 9. This is a C triad, with an added 9th, without the 7th, as opposed to Cmaj 9 which includes the 7th.
C6 (Cadd6)—1, 3, 5, 6. In the case of the 6th or 6/9 chord, the word “add” is rarely used.
C6/9 (C6add9)—1, 3, 5, 6, 9
Cadd4—1, 3, 4, 5
Cadd9sus4—1, 4, 5, 9
Dominant 7th Family
The dominant 7th family is major with a flattened 7th. The scale for diatonic dominant chords is the Mixolydian scale. The word major is never used in the spelling of dominant chords. When you see a 7th, 9th, 11th or 13th without “major” preceding it, assume b7.
C7—1, 3, 5, b7
C9—1, 3, 5,b7, 9
C11—1, 5, b7 , 9, 11. To avoid the minor 9th clash between E and F, the third (E) has been eliminated.
C13—1, 3, 5, b7 , 9, 13. To avoid the minor 9th clash between E and F, the 11th (F) has been eliminated.
C7sus4—1, 4, 5,b7
C9sus4—1, 4, 5, b7, 9
Lydian dominant chords contain the # 4. The scale is similar to the Mixolydian except the 4th/11th degree is raised. The #11 eliminates the minor 9th clash between E and F.
C7#11—1, 3, 5, b7, #11
C9#11—1, 3, 5, b7, 9, #11
C13#11—1, 3, 5, b7, 9, #11, 13
Other possibilities in the dominant family include what are known as the altered tones. These refer specifically to the tones above the 7th: b9, # 9, #11 and b13/#5. In spelling these altered chords, think: 1) triad, 2) b7 , and 3) the alterations in the chord symbol. Eliminate the 5th in any of the chords with a b13.
C7b9#9#11—1, 3, 5, b9, #9, #11
C7b9, C7#9, C7b13, C7b9#9, C7b9#11, C7#9#11, C7b9b13, C7#9b13, C7#11b13, C7b9#9b13, C7b9#11b13, C7b9#9#11, C7#9#11b13, C7b9#9#11b13, C7#5b9, C7#5#9, C7#5#11, C7#5b9#9#11 and are examples of altered C dominant chords.
The b3 must be in the chord for it to be minor. Cm--Cm-11 can be thought of being harmonized from the Dorian or natural (Aeolian) minor scale. Anything with a 13th or 6th is from the Dorian or melodic minor scale.
Cmi—1, b3, 5
Cmi7—1, b3, 5, b7
Cmi9—1, b3, 5, b7, 9
Cmi11—1, b3, 5, b7, 9, 11
Cmi13—1, b3, 5, b7, 9, 11, 13
The “add” chords in minor work the same way as in major.
Cmi6 (C minor add 6)—1, b3, 5, 6
Cmi6/9 (Cm6add9)—1, b3, 5, 6, 9
Cmi add9—1, b3, 5, 9
Cmi add11—1, b3, 5, 11
Cmi7add11—1, b3, 5, b7, 11
The major 7th can be included in a minor chord. Remember, the use of the word “major” indicates the major 7th. The scale for m/maj7 chords is either the melodic or harmonic minor.
Cmi/maj7—1, b3, 5, 7
Cmi/maj9—1, b3, 5, 7, 9
The b5 is a very common alteration. The scale commonly used is either Locrian, if the 9th is flat, or the 6th mode of the melodic minor scale, if the 9th is natural.
Cmi7b5—1,b3, b5, b7
Cm9b5—1, b3, b5, b7, 9
Cm11b5—1, b3, b5, b7, 9, 11
Cdim—1, b3, b5
Diminished 7th is a diminished triad with an added double flatted 7th (which is really a natural 6th).
Cdim7th (Cdim7or Co7)—1, b3, b5, bb7
Caug—1, 3, #5
Augmented 7th is an augmented triad with a b7
Caug7 (C+7)—1, 3, #5, b7
Inversions. If another note besides the root (usually 3rd, 5th or 7th) is used as the bass, then the chord is called an inversion and is written: name of chord/bass note. The C major chord with an E in the bass is written C/E. The upper tones can be in any order.
Main points to remember:
The majority of chords are built up from triads, and contain some version of a 1, 3 and 5.
- Major = 1 3 5
- Minor = 1 b3 5
- Diminished = 1 b3 b5
- Augmented = 1 3 #5
The 3rd determines whether a chord is major or minor.
If the 7th is natural, then the word “major” will appear in the chord symbol (e.g., Cmaj7, Cmaj9, except for maj6, which is 1,3, 5 and 6).
If the 7th is flat, then the word “major” is not used (e.g., C7, C9, Cmi7 means the 7th is flat).`
The notes in a chord can appear in different orders than the ones shown.
The higher extensions imply the inclusion of some or all of the lower ones (e.g., 9th implies the inclusion of the 7th).
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