final notes for second theory test on Oct. 30

TRIADS AND SEVENTH CHORDS

1. Triads (3-Note chord structures)

a.       Major Triad-contains the 1^st, 3^rd, and 5^th steps of a Major Scale. For example a C Major Triad (CM) would have the following notes (C, E, G) since the C Major Scale is : C D E F G AB C.

b.       Minor Triad- contains the 1^st, flatted 3^rd, and 5^th steps of a Major Scale. For example a C Minor Triad (Cm) would have the following notes (C, Eb, G).

c.       Diminished Triad - contains the 1^st, flatted 3^rd, and flatted 5^th steps of a Major Scale. For example a C Diminished Triad (Co)would have the following notes (C, Eb, Gb).

2. Seventh Chords (4-note chord structures)

a.       Major 7^th chord- contains the 1^st, 3^rd, 5^th, and 7^th  steps of a Major Scale. For example a C Major 7^th (CM7) chord would have the following notes (C, E, G, B) since the C Major Scale is : C D E F G AB C.

b.       Minor 7^th chord- contains the 1^st, flatted 3^rd, 5^th, and flatted 7^th  steps of a Major Scale. For example a C Minor 7^th (Cm7) chord would have the following notes (C, Eb, G, Bb).

c.       Dominant 7^th chord- contains the 1^st, 3^rd, 5^th, and flatted 7^th  steps of a Major Scale. For example a C dominant 7^th (C7) chord would have the following notes (C, E, G, Bb.

d.       Half Diminished 7^th chord (also called a “minor seven flat five chord”)- contains the 1^st, flatted 3^rd, flatted 5^th, and flatted  7^th  steps of a Major Scale. For example a C half diminished  7^th (C^ø7 or Cm7(♭5) ) chord would have the following notes (C, Eb, Gb, Bb).

e.       Diminished 7^th chord - contains the 1^st, flatted 3^rd, flatted 5^th, and double flatted  7^th  steps of a Major Scale. For example a C diminished  7^th (C dim. 7th ) chord would have the following notes (C, Eb, Gb, Bbb).

1. Extensions- These are the 9^th, 11^th and 13^ths that are added on to 7^th chords.
2. A  9^th would be the equivalent of the 2^nd degree of a scale. A C Major  9^th (CM9) contains the 1^st, 3^rd, 5^th, 7^th, and 9^th of a major scale and would be constructed using the following notes (C, E, G, B, D) as per the major scale below:

C             D             E              F              G             A             B             C             D

1              2              3              4              5              6              7              8              9

               

The 11^th would be the equivalent of the 4^th , and the 13^th would be the equivalent of the 6^th.  Remember that when playing dominant or major chords that extend above a 9^th (CM11, CM13, C11 or C13), we automatically raise the 11^th scale degree by ½ step to avoid the clash between the 3^rd and the 11^th of the chord.

The CM11 chord would therefore have the following notes: C, E, G, B, D, F#. If we didn’t raise the F we would have the not so good sounding interval between the E (3^rd of the chord) and the F (11^th of the chord).

The 11^th is not raised on a minor 11^th or minor 13^th chord as there is no clash that occurs here between the 3^rd and the 11^th. The notes in a C minor 13^th chord would include C, Eb, G, Bb, D, F, and A.

Altered Notes on a Dominant 7 chord:

For the purposes of our study, we will deal with altered notes that only appear with relation to a dominant chord. The one exception to this is the chord that we have already talked about which is the minor 7 (b5) or half-diminished chord.

With respect to a C13 (C, E, G, Bb, D, F#, A) chord we have the several  possibilities for alterations. Remember that we automatically raise the 11^th of any chord that has a regular or major third. In this case the major 3^rd is the “E”. Therefore the “F” must be raised to an F# to avoid the horrible clash that would otherwise occur between the “E” and the “F”. The full list of alterations is as follows:

A (the 13^th) could be lowered one half step to Ab making it a b13.

As stated above the F (the 11^th) must be raised by one half step to F# making it a #11.

The D (the 9^th) can be raised by one half step to D# making it a #9.

The D (the 9^th) can be lowered by one half step to Db making it a b9.

The b13 and the #11 can also be written as altered 5ths. In other words the Ab could be written as G# (#5) and the F# could be written as Gb (b5).

Based on the above discussion, there are 4 basic alterations for a dominant  chord. They are:

1. b13 or its enharmonic  alteration of a #5.
2. #11 or its enharmonic  alteration of b5.
3. #9
4. b9

 1. Diminished Scale (starting with ½ step) is a scale that alternates by using a half-step followed by a whole step over and over.

C             Db          Eb           E              F#           G             A             Bb           C

                                                Or

Db          D             E              F              G             Ab          Bb           B             Db

                                                Or

D             Eb           F              Gb          Ab          A             B             C             D

The next octotonic scale starts on Eb and it uses the exact same pitch collection as the C octoto3nic scale.

2. Whole-Tone Scale consists entirely of whole steps. A whole step is equal to 2 half steps.

C             D             E              F#           G#          Bb           C

                                                Or

Db          Eb           F              G             A             B             Db

Diminished Whole-Tone Scale: This is a combination of the Diminished and Whole-Tone Scales. The bottom half is derived from the Diminished Scale and the top half from the Whole-Tone Scale.

An example of this would be: C, Db, Eb, E, F#, G#, Bb, C. .   Notice in the key of C , we have a b9(Db), a #9 (Eb),  a b5  or #11 (F#), and a #5 or b13 (G#) as altered pitches. This scale would be applied against a dominant 7 chord—in this case a C7 chord.

I.                     Minor Scales (3 forms):

a.       Natural Minor – This is derived from starting on the 6^th step of a major scale and using the major scale pitch collection with no alterations, consequently  the name “natural”.

If you have an A Major scale: A, B, C#, D, E, F#, G#, A   you would derive the natural minor scale by starting on the 6^th scale degree which in this case is F#. Your F# natural minor scale would then be  F#, G#, A,  B, C#, D, E, F#.

b.       Harmonic  Minor – This is the natural minor scale with the 7^th step raised by one half step.  The F# harmonic minor scale would be : F#, G#, A,  B, C#, D, E#, F#. The seventh step (E) has been raised one half step to E#.

c.       Melodic Minor – This is the natural minor scale with the 6^th and 7^th steps raised while ascending and lowered back to their natural form while descending. The F# melodic minor scale is: (ascending) F#, G#, A,  B, C#, D#, E#, F#. When descending it would be: F#, E, D, C#, B, A, G#, F#.

II.                   Relative Minor

A minor and major scale are relative to each other  if they share the same key signature. Relative is not a type of key signature. It is only a condition that exists when two scales (one minor and one major) share the same key signature. A Major and F# minor are relative to each other because they share the same key signature of 3 sharps (F#, C#, and G#). 

Every Major Scale has a Minor Scale that is relative to it. Relative is only a condition that exists between two scales when they share the same key signature. If a major and minor scale have the same key signature, then by definition, they are relative to each other. Relative is NOT a type of minor scale.

The 6^th step of the major scale is where the relative minor scale starts. If we consider the same pitch collection with no altered notes then we have the Natural Minor. An example of this is:

C Major = C, D, E, F, G, A, B, C. The 6^th step (in red) is A. If we use the same pitch collection starting on A we have:  A, B, C, D, E, F, G, A. This is the A Natural Minor scale and it is relative to C Major because they both have the same key signature of no sharps or flats.